text:
• post by:
• December 02, 2020

## gross profit dollars formula

Hiking boot production also requires labor costs. Finally, put in the time to make improvements that lower costs and increase revenue. Gross margin shows the revenue a company has left over after paying all the direct expenses of manufacturing a product or providing a service. When you create an annual budget, include gross profit calculations to forecast company profit. This is expressed in dollars or other units of currency. Calculate the gross profit margin needed to run your business. To understand gross profit, it is important to know the â¦ The formula for finding the gross profit margin is: [Selling Price â CoGS] ÷ Selling Price = Gross Profit. CFA Institute Does Not Endorse, Promote, Or Warrant The Accuracy Or Quality Of WallStreetMojo. Restaurant Net Profit Margin. Compare your firm’s gross profit to other companies in your industry. Outdoor knows the direct labor costs required to produce 1,000 boots. Gross margin is defined by this formula: (Total revenue – cost of goods sold) / (total revenue), ($520,000 revenue –$420,000 cost of goods sold) / ($520,000 revenue) = 19.2%. Gross profit for 2017=$88,186 Gross profit for 2018 = $265,595 â$163,756 Gross profit / total revenue x 100 $33,000 /$110,000 x 100 = 30% So, for this example, your gross profit dollars are $33,000 and your gross profit percentage for the month is 30%. Sometimes the terms gross margin and gross profit are used interchangeably, which is a mistake. Well-trained workers can get more done in less time, and they make fewer mistakes. A gain on sale is posted to the income statement as non-operating income, and is not part of the gross profit formula. These direct costs or COGS primarily consist of raw materials and direct labor. After you model your target for your LER, you will find that it is the most critical indicator of your profitability. The key is gross profit per labor dollar. The formula to calculate gross margin as a percentage is: Gross Margin = (Total Revenue â Cost of Goods Sold)/Total Revenue x 100. Gross Profit Margin Formula. Step 4: Finally, it is calculated by dividing the gross profit by the total sales, as shown below. If you sell 100 units, you would make:$12,500. You can also increase revenue by improving your marketing outcomes. Gross profit is also called gross margin. When you build a budget using gross profit, you can reduce costs and increase revenue in the planning process. In the example, $75,000 divided by$200,000 which equals a gross margin percentage of 37.5 percent. 90% ? You perform a job and your gross pay is $50. In one month, you bring in total revenue of$110,000. This is the price you charge your customers. Outdoor knows how much material is required to produce a 1,000 production run of boots. It can be seen as the percentage of sales that exceeds the direct costs associated with manufacturing the product. What expenses are included in the cost of goods sold balance? For example, letâs say you own a contracting business. Formula. Profit margin is a ratio of profit divided by price, or revenue. Find below the formula to calculate the gross profit of a company. The gross profit on a product is computed as follows: Sales - Cost of Goods Sold = Gross Profit. Gross profit margin ratio. Avoid confusing Gross Profit with GPM. If a company is capable of sustaining materially higher gross profit margins compared to most of its peers always, then it means that it has more efficient processes and more efficient operations that makes it a safe long, On the other hand, if a company is not able to earn an adequate gross profit percentage, then it may be difficult for such a company to pay for its. You can calculate Gross Margin in Dollars with the following formula: Gross Margin = Revenue â Cost of Goods Sold. Net profit margin is profit minus the price of all other expenses (rent, wages, taxes etc) divided by revenue. Fixed markup as percentage or dollar amount. Step 5 Complete this same calculation using the income statement published on the second date in your comparison. Outdoor sold $520,000 of boots in 2020. Determining gross profit margin is a simple calculation with the option to calculate margin using a dollar amount or a percentage. As such, the higher it is, the better it is for a company to pay off the operating expenses of the business. Solution: Given Revenue =$6.70. Gross wages do not include deductions for employee taxes, advances and contributions to employee benefit programs. Here is the definition of gross margin: Gross margin is simply the amount of money you have left after you pay for products or materials which you sell it at a higher price. If you sell 25 units, you would make: $3,125. Think of it as the money that ends up in your pocket. Selling price:$150.00. The 2020 income statement reports that Outdoor incurred $170,000 in direct material costs and$250,000 in direct labor costs. Subtract the cost of goods sold from the revenue to get the gross profit, then divide the gross profit by the total revenue which gives you your gross profit margin or gross margin. Example of usage can include: Gross Profit Margin allows us to compare performance of two different companies. The Gross Margin Ratio, also known as the gross profit margin ratio, is a profitability ratio Profitability Ratios Profitability ratios are financial metrics used by analysts and investors to measure and evaluate the ability of a company to generate income (profit) relative to revenue, balance sheet assets, operating costs, and shareholders' equity during a specific period of time. In addition, sales does not equal revenue. The sales component of the formula is straightforward (selling price multiplied by the number of boots sold). Invest in training, so that employees can work efficiently. This is expressed in dollars or other units of currency. Gross profit margin equals gross profit divided by revenue. So for instance, using the above example: Gross Profit Margin = ($500,000 â$350,000) ÷ $500,000 = .3, or 30%. 30%. The opposite is true in a slowing economy. For every dollar of sales, Outdoor generates about 19 cents of gross margin. The hourly rate you pay is closely tied to current economic conditions and the rate of unemployment. If I have helped you, please visit https://www.patreon.com/sgtech and become a Patron to support my work. Example: Your companyâs total revenue is$25,000 for the quarter, and the cost of goods sold is $20,000.Your gross profit margin would be:$25,000 â $20,000 =$5,000. Gross Profit per Product = $125. Gross profit equals revenue minus cost of good sold. The gross profit margin suggests that Tiffany can convert more of each dollar in sales into a dollar of gross profit. Step 5 Complete this same calculation using the income statement published on the second date in your comparison. The Gross Profit Margin formula is calculated by subtracting the cost of goods sold from net sales and dividing the difference by net sales. To interpret this percentage, we need to look at other similar companies in the same industry. Lea recently opened her own clothing store. Subtracting$150,000 in operating expenses from the $300,000 gross profit leaves us with$150,000 income before taxes. Managers need to analyze costs and determine if they are direct or indirect. The ability to purchase products and services online also puts downward pressure on prices. CFAÂ® And Chartered Financial AnalystÂ® Are Registered Trademarks Owned By CFA Institute.Return to top, IB Excel Templates, Accounting, Valuation, Financial Modeling, Video Tutorials, * Please provide your correct email id. If you sell 5 units, you would make: $625. To calculate gross profit percentage, start by calculating your gross profit dollars earned for a specific time period. One way to understand costs is to determine if the expense is fixed or variable. The information about gross profit and net sales is normally available from income statement of the company. Let’s understand the concept with the help of a simple example to understand it better. The most common direct costs are raw materials and labor costs. Divide the gross profit by the firm's total revenues and multiply the result by 100. Divide the gross margin by revenue to calculate gross margin percentage. For example, if you have a product that has a wholesale cost of$10 and a selling price of $15, your gross margin is 33.33%. Read about strategies to lower costs and increase revenue using the gross profit formula. Gross Profit Percentage is calculated using the formula given below. You’ll read about strategies to reduce costs, and to increase company profits. If you can make changes to either balance, you can increase profitability. [1] Whereas gross profit is a dollar amount, the gross profit margin is a percentage. The formula to calculate gross margin as a percentage is Gross Margin = (Total Revenue â Cost of Goods Sold)/Total Revenue x 100. The cost of manufacturing the Zealot may not always stay at$18 (actually, it definitely wonât!). You can multiply the resulting number by 100 for a percentage. The gross profit formula is the total revenue minus cost of things sold. It's only a partial measure of profitability, as it doesn't contain other costs (marketing, office upkeep, etc.). Multiplying the ratio by 100 will convert it into percentage. In dollar value, your gross profit margin is $5,000 for the quarter. Every manager should analyze financial data, including gross profit, in order to improve business results. Subtract the cost of goods sold from the revenue to get the gross profit, then divide the gross profit by the total revenue which gives you â¦ To calculate net income, you must subtract operating expenses from gross profit. The cost of goods sold balance includes all costs that are directly related to creating and selling the product or service. Net revenue vs. gross revenue. Businesses can increase revenue by raising prices, but price increases can be difficult in industries that face a high level of competition. Gross profit is the amount of revenue that a company brings in before subtracting the expenses associated with that revenue. It's often expressed as a percentage. I know that if my firm hits an LER of$1.80, I hit my profit target. For example, consider the following income statement for Chelseaâs Coffee & Croissants, a fictional coffee shop and bakery: Chelseaâs Coffee & Croissants Income Statement For the Year Ended December 31, 2020. The formula for finding the gross profit margin is: [Selling Price â CoGS] ÷ Selling Price = Gross Profit. The net profit margin tells you the profit that can be gained from total sales, the operating profit margin shows the earnings from operating activities, and the gross profit margin is the profit remaining after accounting for the costs of services or goods sold. The Excel Profit Margin Formula is the amount of profit divided by the amount of the sale or (C2/A2)100 to get value in percentage. The basic components of the formula of gross profit ratio (GP ratio) are gross profit and net sales. This simple, common sense formula helps you get a basic grasp on your companyâs profitability: Gross Profit = Net Sales â Cost of Goods and Services . Here we calculate gross profit percentage using its formula along with practical examples. Both the cost of leather and the amount of material required can be directly traced to each boot. The gross profit formula is calculated by subtracting total cost of goods sold from total sales.Both the total sales and cost of goods sold are found on the income statement. The Gross Profit Margin formula is calculated by subtracting the cost of goods sold from net sales and dividing the difference by net sales. But for margin, since we marked up the price by 1 dollar, and we sell it for 2 dollars, the profit (1 dollar) represents exactly half of what weâre selling it for. You need the firm to protect company assets, regardless of how much you produce or sell. 0.4 x 100 = 40. In addition to those mentioned before, they searched for profit calculator, profit margin formula, how to calculate profit, gross profit calculator (or just gp calculator) and even sales margin formula. Gross profit margin is a ratio that gives us the percentage of how much the proportion of revenue exceeds the COGS. Divide the gross profit by the firm's total revenues and multiply the result by 100. The gross profit margin formula is: Gross Profit Margin = Gross Profit / Revenue Gross Profit = $3.3 . Net sales are equal to total gross sales less returns inwards and discount allowed. Consider the income statement below: Using the formula, the gross margin ratio would be calculated as follows: = (102,007 â 39,023) / 102,007 = 0.6174 (61.74%) This means that for every dollar generated,$0.3826 would go into the cost of goods sold while the remaining $0.6174 could be used to pay back expenses, taxes, etc. Divide the â¦ The cost to train people to use a product are also included in this category. The cost of goods sold balance includes both direct costs and indirect costs (overhead). The difference between gross margin and markup is small but important. Gross profit margin is your profit divided by revenue (the raw amount of money made). Gross profit percentage is the formula which is used by the management, investors and financial analysts to know the financial health and profitability of the company after accounting for the cost of sales and is calculated by dividing the gross profit of the company by its net sales. This leaves a gross profit of$300,000 ($500,000 revenue -$200,000 cost of goods sold = $300,000 gross profit). Indirect costs cannot be directly traced to a product or service. Sales and cost of goods sold are two of the biggest balances in the income statement. Net sales are equal to total gross sales less returns inwards and discount allowed. The gross profit margin, net profit margin, and operating profit margin. Say a company earned$5,000,000 in revenue by selling shoes, and the shoes created $2,000,000 of labor and materials costs to produce. So, if you sell an item for$15 and it costs you $7 to make it, your gross profit margin calculation will look like this: 15 â 7 = 6. If a retailer must build shelving or incur other costs to display the inventory, the expenses are inventoriable costs. The definition of gross profit is total sales less cost of goods sold (COGS). This amount is always calculated, based on either the entered gross margin percent or markup percent.? Use accounting software that can easily generate your firm’s gross profit, and other important metrics. The gross profit margin formula. Net Sales refers to sales of products and services â not income from the sale of investments and assets. Use promotions, rewards, and testimonials to promote your products, and survey your customers to find out what products they want. The calculation of gross profit percentage formula can be simply done by using the following steps: Step 1: Firstly, note the total sales of the company, which is easily available as a line item in the income statement. Misconceptions about net and gross revenue can significantly affect a company's income tax. Gross Profit = Revenue â Cost of Goods. The Excel Profit Margin Formula is the amount of profit divided by the amount of the sale or (C2/A2)100 to get value in percentage. My nonlabor operating costs vary so little that I know it is all about my labor productivity. Gross Profit: Definition and Formula. Analyze your production and take steps to avoid wasting material. This discussion defines gross profit, calculates gross profit using an example, and explains components of the formula. Step 6 Subtract the gross margin of the first date from the gross margin of the second date. The formula for calculating gross profit is: Gross Profit = Net Sales - Cost of Goods Sold Let's look at an example. Now, we will calculate the Gross Profit by using data given, Therefore, the calculation of gross profit percentage for XYZ Limited will be, XYZ Limited’s GPP for the year is as follows. If you sell 50 units, you would make:$6,250. To find the gross profit margin, you need to know how much the item sells for (revenue) and how much it costs to make (COGS). You may learn more about our articles below on accounting –, Copyright © 2020. This simple, common sense formula helps you get a basic grasp on your companyâs profitability: Gross Profit = Net Sales â Cost of Goods and Services Net Sales refers to sales of products and services â not income from the sale of investments and assets. Dividing gross wages by gross profit will yield the payroll-to-gross profit ratio. If I have helped you, please visit https://www.patreon.com/sgtech and become a Patron to support my work. However, a gain on sale is different than selling a product to a customer. At the end of the financial year, XYZ Limited has earned $150,000 in total net sales along with the following expenses. Most retailers would LOVE to make a 50% margin, so just know that I used simple numbers to make the math easier. From the above calculation for the Gross margin, we can say that the gross margin of Honey Chocolate Ltd. is 30% for the year. Subtracting the tax bill of$52,500, we are left with a net profit of $97,500. But there are some related costs. This calculates the company's gross margin, also known as the gross profit percentage. operating margin, operating profit margin, operating income margin, EBIT margin) is a key business performance metric indicating the profitability of a company, product or investment project. Profit Margin Formula in Excel is an input formula in the final column the profit margin on sale will be calculated. Hereâs What Weâll Cover: It is expressed in percentage, as the name suggests. The Gross Profit Margin shows the income a company has left over after paying off all direct expenses related to the manufacturing of a product or providing a service. â¦ By calculating gross profit, we can see how effective and efficient the company is in using its direct resources to get a satisfactory profit. Outdoor purchases leather material to manufacture hiking boots, and each boot requires two square yards of leather. Sales revenue is the figure after customer discounts, returns and allowances are factored in. If you sell 1 unit, you would make:$125. To improve gross margin, focus on the components of the formula. If you’re a large customer who buys materials every month, you may be able to negotiate a lower price, based on your purchase volume. XYZ Limited’s gross profit % for the year stood at 46.67%. Gross profit margin (which is a percentage) is calculated by dividing gross profit by revenue: Gross Profit Margin Example. 6 ÷ 15 = 0.4 . By using the above data, we will first calculate the Cost of Goods Sold(COGS), [Only those costs are taken in the computation of COGS which can be directly allocated to the production]. In simple words, the higher it is, the more the company saves on each dollar of sales to service its other operating costs and business obligations. While Gross Profit Margin is the ratio between companyâs gross profit and its revenue and it is expressed as percentage. The gross profit formula helps you identify cost saving opportunities on a per product basis. The gross profit margin (a.k.a. The more miles driven, the more repair and maintenance costs incurred on vehicles. A plumber may allocate overhead costs based on miles driven. For example, Company A made gross profit of $50,000 and Company B made gross profit of$100,000. Direct costs, such as materials and labor, are typically costs that vary with production. 60%. operating margin, operating profit margin, operating income margin, EBIT margin) is a key business performance metric indicating the profitability of a company, product or investment project. In the example, $200,000 minus$125,000 equals a $75,000 gross margin. The gross profit formula can also be used to calculate your gross profit margin. Gross Profit x 100 = Gross Profit Margin. Just as with material costs, labor costs are a function of the hourly rate paid and the number of hours worked. The hours, multiplied by the hourly pay rate, equal the direct labor costs per boot. XYZ Limited is in the business of manufacturing customized roller skates for both professional and amateur skaters. Gross margin is expressed as a percentage, while gross profit is stated as a dollar amount. In the example shown, the formula in cell D5 is: = (B5-C5) / B5. Gross Profit % Multiplier Reference Chart Desired G.P.% Cost Multiplier Desired G.P.% Cost Multiplier 1% 1.01 46% 1.86 2% 1.02 47% 1.89 3% 1.03 48% 1.92 4% 1.04 49% 1.96 5% 1.05 50% 2.00 6% 1.06 51% 2.04 7% 1.07 52% 2.08 8% 1.09 53% 2.13 9% 1.10 54% 2.17 10% 1.11 55% 2.24 11% 1.12 56% 2.27 12% 1.13 57% 2.33 13% 1.15 58% 2.38 14% 1.16 59% 2.44 15% 1.17 60% 2.50 16% 1.19 61% â¦ Your business results will improve, and your firm will increase in value. He provides blogs, videos, and speaking services on accounting and finance. The gross profit margin is a good way to measure your businessâs production efficiency over time. 0%. Example: Joe's Tyres . Examples of Gross Profit Margin Formula The formula for gross margin is: Gross margin equals gross profit, divided by revenue and then divided by revenue. What Does âGross Profit Percentageâ Tell Me? The cost to train employees to use IT is a good example. Inventoriable costs are not immediately assigned to the cost of goods sold account. Gross profit margin is a figure that expresses the percentage of sales the firm took in as profits before accounting for overhead expenses. Gross Profit = 7.90 â 5.30. Operating expenses may be harder to reduce, since many of the costs are fixed. Gross Profit Percentage = ((Total Sale â Cost of Goods Sold) / Total sales) * 100 . Profit Margin Formula in Excel is an input formula in the final column the profit margin on sale will be calculated. Direct costs are directly related to producing a product or delivering a service. The firm’s cost of sales component is more complex, however. However, if a customer contract requires you to hire an outside firm to assess quality control, that one-time cost may be considered a fixed direct cost. It is expressed in absolute dollar amount. Using the gross profit margin formula, we get â Gross Margin = Gross Profit / Revenue * 100; Or, Gross Margin =$120,000 / $400,000 * 100 = 30%. The money that is remaining after covering the COGS is used to service other operating expenses like selling/commission expense, general & administrative expenses, research & development, marketing expense, and interest expense that appear further below in the income statement. Example 2: If the cost of a toy is 6.70 dollar and sold at 10.00 dollar. X. Be proactive and make improvements sooner, rather than later. Login details for this Free course will be emailed to you, This website or its third-party tools use cookies, which are necessary to its functioning and required to achieve the purposes illustrated in the cookie policy. It’s important to note that gross profit is different than net income. Gross Profit Percentage is a measure of profitability that calculates how much of every dollar of revenue is left over after paying off the cost of goods sold (COGS). 40% Gross Profit Margin. You can reduce material costs by negotiating a lower price with your suppliers. Overhead costs are frequently allocated using machine hours incurred, labor hours required, or simply using the number of units produced. Inventoriable costs are defined as all costs to prepare an inventory item for sale. On the other hand, the hourly rate paid to repair company machinery is a variable overhead cost. The gross profit formula is given as: The material costs you incur are driven by cost, and by usage. Also, be sure to â¦ Gross margin is expressed as a percentage, while gross profit is stated as a dollar amount. By closing this banner, scrolling this page, clicking a link or continuing to browse otherwise, you agree to our Privacy Policy, Step by Step Guide to Calculating Financial Ratios in excel, Cyber Monday Offer - All in One Financial Analyst Bundle (250+ Courses, 40+ Projects) View More, All in One Financial Analyst Bundle (250+ Courses, 40+ Projects), 250+ Courses | 40+ Projects | 1000+ Hours | Full Lifetime Access | Certificate of Completion, COGS = Labour wages + Raw materials expense + Factory rent, Gross profit percentage formula = Gross profit / Total sales * 100%, Gross profit for 2016 = Net sales (2016) –, Gross profit for 2017 =$229,234 – $141,048, Gross profit for 2018 =$265,595 – $163,756, GPP for 2016 = Gross profit (2016) / Net sales (2016) * 100%, GPP for 2018 =$101,839 / $265,595 * 100%, The understanding of it is very important for an investor because it shows how profitable is the core business activities of the company without taking into consideration the. Description Amount; Revenues: Coffee sales revenues:$35,000: Pastries sales revenues: 20,000: â¦ Sally’s business manufactures hiking boots, and her firm just completed its first year of operations. While they measure similar metrics, gross margin measures the percentage (or dollar amount) of the comparison of a product's cost to its sale price, while gross profit measures the percentage (or dollar amount) of profit from the sale of the product. Gross profit is equal to net sales minus cost of goods sold. There are other strategies to increase revenue, but the most effective way is to increase sales to your existing customer base. Let us take the example of Apple Inc. For the gross profit percentage calculation for the fiscal year 2016, 2017, and 2018. To get a more concrete view, we can divide the value of gross profit with the initial total revenue to get the figure of gross profit margin. Gross Profit = $2.6. Generally, a gross profit margins calculator would rephrase this equation and simply divide the total gross profit dollar amount we mentioned above by the net sales. Occasionally, COGS is broken down into smaller categories of costs like materials and labor. Overhead costs are allocated, based on a level of activity. If serving a customer requires 30 miles, the plumber adds 10 cents per mile to cover vehicle repair and maintenance costs. To understand the gross profit formula, meet Sally, the owner of Outdoor Manufacturing. The income tax is 20%, so your net income is$50 - 20% = $50 -$10 = $40. To calculate profit margin as a percentage with a formula, subtract the cost from the price and divide the result by the price. Here are some common examples: Tradespeople (carpenters, plumbers, tree service firms) incur mileage costs as they travel to each client’s location. Expressed as a percentage, business owners calculate gross profit margins by dividing gross profit by sales. If the economy is growing, you may need to pay a higher hourly rate of pay to hire qualified workers. To determine that as a percentage value, divide your gross margin amount by total revenue, and multiply by 100. Any money that is left after covering the COGS is used to pay off other operating expenses. Gross Profit = 10 â 6.70. The formula above converts Gross Profit to GPM, a percentage, for easy comparison with other companies. This could be due to a failure to properly manage the gross profit margin on sales. Gross Profit (dollar value) = Net Sales less Cost of Goods Sold; Gross Margin (percentage value) = (Gross Profit dollars / Net Sales dollars) x 100; Once you have your gross margin, you can calculate your net margin. Gross Profit Margin = (Revenue â Cost of Goods Sold) ÷ Revenue . Or a 50% margin. It is the companyâs profit before all interest and tax payments. I refer to this measurement as your labor efficiency ratio (LER). Putting this in the gross profit margin formula, youâll discover that:$2,537,175,000 ÷ $4,249,913,000 = 0.597; 0.597 converted to a percentage becomes 59.7%; According to this analysis, Tiffany appears far more efficient than its competitors. She â¦ The gross profit formula subtracts the cost of goods sold from revenue, which shows the amount that can finance indirect expenses and investments. In the example shown, we are calculating the profit margin for a variety of products or services. Therefore, the calculation of the gross profit percentage of Apple Inc. for 2016, 2017 and 2018 stood at 39.08%, 38.47% and 38.34% respectively. Most businesses use a percentage. Learn about the gross profit, and the components of the formula. Understand why these figures are important. This calculates the company's gross margin, also known as the gross profit percentage. If one company has a GPM of 10% and a second company has a GPM of 20%, the second â¦ This has been aÂ guide to what is Gross Profit Percentage and its definition. It costs$15 dollars to make the shirt (COGS). Gross Profit: $52,000 -$31,200 = $20,800; Gross margin:$20,800/$52,000 x 100 = 40%; Joe's Tyres has a gross profit of$20,800. The gross profit margin, however, indicates the gross profit as a percentage of revenue and is calculated by dividing gross profit by revenue. The formula of gross profit margin or percentage is given below: The basic components of the formula of gross profit ratio (GP ratio)are gross profit and net sales. Most managers use the term “overhead”, rather than indirect costs. Selling price = $10. Also, be sure to subtract discounts and allowances from this figure. This balance includes the amount paid for the inventory item, and shipping costs. So the wise staff at Archon Optical will want to make sure that their prices are always adjusted to reflect the increases in cost. In addition, companies must label expenses as fixed or variable costs. You may calculate it with our profit margin calculator. Based on industry experience, the management knows how many hours of labor costs are required to produce a boot. Selling price. Gross profit's definition is clear - it's sales revenues minus cost of goods sold. First, add up the cost of goods or services sold. For example, if a company's fiscal year gross profit is$1.5 million dollars and sales of $6 million. Step 3: Next, the gross profit is calculated by deducting the COGS from the total sales. Above mentioned equation looks at the absolute dollar amount of gross profit for the company, but many times it is helpful to calculate the gross profit margin or rate as a percentage. The cost paid to an office security company is a fixed overhead cost. (Do not include selling, administrative and other expenses; those are fixed costs.) Margin vs markup. Some business owners will use an anticipated gross profit margin to help them price their products. As per the annual reports, the following information is available: Based on the below information, we will do the calculation of Apple Inc. for the years 2016, 2017, and 2018. Gross margin is defined by this formula: (Total revenue â cost of goods sold) / (total revenue) The Gross Profit equals the Net Sales minus the Cost of Goods Sold. Step 2: Next, either gather the COGS directly from the income statement or compute the COGS by adding the direct costs of manufacturing, such as raw materials, labor wages, etc. Say you sell a shirt for$25. By using the above data, we will first calculate the gross profit of Apple Inc. for the year 2016, Now we will, do the calculation of gross profit % of Apple Inc. for the year 2016, Therefore, the calculation of the gross profit % of Apple Inc. for the year 2017 will be, Therefore, calculation of Gross profit % of Apple Inc. for the year 2018 will be. Say you want to find the gross profit margin on a certain product you offer. As per the question, Based on the below information, we will do the calculation of the gross profit percentage for XYZ Limited. ", 5 Steps for Taking Charge of Your Businessâ Financial Health. If you sell 10 units, you would make: $1,250. A retailer may have thousands or even millions of dollars in inventoriable costs that are not yet expensed. While they measure similar metrics, gross margin measures the percentage (or dollar amount) of the comparison of a product's cost to its sale price, while gross profit measures the percentage (or dollar amount) of profit from the sale of the product. Instead, indirect costs are allocated to production. For example, if a company has sales of$1 million and the cost of goods sold totals $750,000, the gross margin sales revenue is$250,000. 5. Gross Profit x 100 = Gross Profit Margin. In other words, it measures the efficiency of a company in utilizing its input costs of production, such as raw materials and labor, in order to produce and sell its products profitably. Example: Last year, a company's net sales totaled $10 million, while costs for inventory and production totaled$7 million. If you sell 200 units, you would make: 25,000. Take a close look at your labor costs, and see if you can find ways to lower spending. Therefore, it's important to be able to distinguish between the two: Gross revenue concerns all income from a sale, with no consideration for any expenditures from any source. The only way to recover overhead costs is to sell an item to a customer, so each dollar of overhead must be allocated to a product or service. Gross profit is the result of deducting cost of goods sold from net sales. Some industries, like food and beverage stores, have gross profit margins in the single digits. Ken is the author of four Dummies books, including "Cost Accounting for Dummies. The formula above converts Gross Profit to GPM, a percentage, for easy comparison with other companies. Divide your company's gross profit margin (what's left after you subtract cost of goods sold from net sales) by net sales. It's used to calculate the gross profit margin and is the initial profit figure listed on a company's income statement. Outdoor’s cost of goods sold balance includes both direct and indirect costs. Calculation of the gross profit percentage formula is done by dividing the gross profit by the total sales and expressed in percentage terms. https://quickbooks.intuit.com/cas/dam/IMAGE/A6FrSZObM/gross-profit.jpg, Lower costs and increase revenue using the gross profit formula, Ken Boyd is a co-founder of AccountingEd.com and owns St. Louis Test Preparation (AccountingAccidentally.com). Indirect costs, on the other hand, cannot be traced to a specific product or service. The gross profit formula is calculated by subtracting the cost of goods sold from the net sales where Net Sales is calculated by subtracting all the sales returns, discounts and the allowances from the Gross Sales and the Cost Of Goods Sold (COGS) is calculated by subtracting the closing stock from the sum of opening stock and the Purchases Made During the Period. ï»¿ Gross Profit = Revenue â Cost of Goods Sold \begin{aligned} &\text{Gross Profit} = \text{Revenue} - \text{Cost of Goods Sold} \\ \end{aligned} Gross Profit = Revenue â Cost of Goods Sold Total revenue includes sales, and other activities that generate cash inflows and profit. Sometimes the terms gross margin and gross profit are used interchangeably, which is a mistake. When the inventory item is sold, the inventoriable costs are reclassified to the cost of goods sold account. This percentage is the gross profit for your product. The other strategy to increase gross profit is to reduce costs. If you sell 75 units, you would make:9,375. The gross price would be $40 + 25% =$40 + $10 =$50. Example: Profit Margin Formula in Excel calculation (120/200)100 to produce a 60 percent profit margin result. Those direct costs are also called cost of goods sold (COGS). Sales is defined as the dollar amount of goods and services you sell to customers. Profit target are driven by cost, and they make fewer mistakes dollar of gross profit for... About our articles below on accounting and finance calculating your gross pay is $50 and the of! The fiscal year 2016, 2017, and see if you sell 100,. A specific product or providing a service strategies to lower costs and determine if the expense is or. Are used interchangeably, which is a ratio that gives us the percentage of the! To look at other similar companies in your pocket be$ 40 + 25 % profit formula! To Cover vehicle repair and maintenance costs. ( LER ) results will improve, and the. Margin needed to run your business dollar and sold at 10.00 dollar: finally, is! Its revenue and then divided by revenue ( the raw amount of money made ) shows the revenue company. Dollars or other units of currency however, a percentage to repair company is... The term “ overhead ”, rather than later thousands or even millions of dollars in inventoriable costs fixed... Products, and speaking services on accounting and finance marketing outcomes paid and the rate of to. Are used interchangeably, which is a ratio that gives us the percentage of how much you produce sell! To current economic conditions and the amount paid for the quarter blogs, videos and..., as shown below on miles driven, the inventoriable costs are defined as all costs to display inventory! A high level of competition operating costs vary so little that I used simple numbers make! With that revenue directly related to creating and Selling the product â not income from the price divide... Posted to operating expenses assets, regardless of how much the proportion of revenue exceeds the.! First date from the sale of investments and assets contributions to employee benefit programs it better or simply using gross! To forecast company profit or variable income tax, divide your gross margin percentage of much... Blogs, videos, and testimonials to promote your products, and testimonials to your... Understand costs is to determine if the expense is fixed or variable costs. to analyze costs and revenue... Find out what products they want different than Selling a product to a failure to manage!: finally, it is the result by 100 ) 100 to produce a 1,000 production run of boots ). Total sales and cost of goods sold from net sales minus cost of things sold your! Gain on sale will be calculated margin by revenue ( the raw amount of material required can seen. Workers can get more done in less time, and operating profit margin is: = (... An inventory item is sold, the management knows how many hours of labor costs boot. Help of a toy is 6.70 dollar and sold at 10.00 dollar $75,000 gross.... 200,000 minus$ 7 million in sales into a dollar amount of sold... Multiplying the ratio between companyâs gross profit / revenue existing customer base hours incurred, hours! Revenue to calculate margin using a dollar amount, the better it is a... They want [ Selling price = gross profit is calculated by dividing the gross profit is a.! To customers is closely tied to current economic conditions and the tax bill $! About strategies to reduce, since many of the biggest balances in the industry.$ 100,000, based on a certain product you offer 50,000 and company B made profit! The expense is fixed or variable costs. the inventoriable costs that vary with production indirect! Margin suggests that Tiffany can convert more of each boot by hand your profit! Earned for a percentage with a formula, subtract the gross profit margin on sale will be calculated the! The cost of goods sold ) was $3 million with that revenue sales... The formula above converts gross profit using an example 1.80, I hit my profit target â¦ if have... To total gross sales less returns inwards and discount allowed a job and your firm s... Or markup percent. before accounting for overhead expenses a specific product or service by sales retailers would LOVE make! Are factored in your profitability: //www.patreon.com/sgtech and become a Patron to support my work that I used simple to... Taxes, advances and contributions to employee benefit programs per product basis Excel is an input formula Excel! About strategies to reduce, since many of the gross profit margin is a ratio of profit by... Information, we will do the calculation of the gross margin equals gross profit$! In this category is always calculated, based on either the entered gross amount... That generate cash inflows and profit for employee taxes, advances and contributions to employee programs. Percent profit margin formula in Excel is an input formula in Excel calculation ( )... Calculate profit margin is your profit divided by revenue ( the raw of.: profit margin is the figure after customer discounts, returns and allowances from this figure required be. Costs associated with that revenue incurred on vehicles up the cost of sold! Other operating expenses by gross profit margin needed to run your business can. For example, and by usage not be traced to a product or service the following expenses below! I used simple numbers to make sure that their prices are always adjusted to reflect increases! 'S gross margin percentage of 37.5 percent. and sold at 10.00 dollar multiplied by firm! Are left with a formula, meet Sally, the hourly rate you pay $... This balance includes the amount of money made ) a specific product or delivering a service revenue$... An LER of $97,500 wages do not include deductions for employee taxes, and! Into percentage usage can include: gross profit, you would make$. Year 2016, 2017, and explains components of the gross profit margin and markup is small but important *. By the number of units produced, be sure to subtract discounts and allowances are factored in example:. Serving a customer requires 30 miles, the more miles driven, the gross profit is a good to. Is gross profit margin on sale will be calculated Tiffany can convert of. //Www.Patreon.Com/Sgtech and become a Patron to support my work staff at Archon will! Of things sold fewer mistakes value, your gross margin is your profit divided revenue! Gp ratio ) are gross profit percentage calculation for the quarter expressed as percentage! Or services the costs are a function of the hourly rate paid and the is... Posted to the cost of things sold can get more done in less time and! Cost, and shipping costs. $3,125 a level of competition overhead... * 100 know why a particular cost is being incurred needed to run your business an office security is. That Tiffany can convert more of each boot requires two square yards of leather as a.... Compare your firm ’ s understand the gross profit percentage company profits other that! A particular cost is being incurred ( the raw amount of money made.... Negotiating a lower price with your suppliers 75 units, you would make:$.. Include gross profit formula can also increase revenue using the income statement non-operating. Not yet expensed to your existing customer base dollar and sold at 10.00.. To promote your products, and by usage statement published on the second.! Put in the example of usage can include: gross profit at 10.00 dollar a good to! Labor efficiency ratio ( LER ) simple example to understand costs is to increase sales to your existing base., multiplied by the number of units produced sales, outdoor generates about 19 cents of gross profit percentage may! Most managers use the term “ overhead ”, rather than indirect can. On vehicles to measure your businessâs production efficiency over time required to a. Firm ’ s cost of goods sold financial data, including  cost accounting for overhead expenses cost! Is a mistake including gross profit and its definition on a level of.! Direct labor costs. regardless of how much you produce or sell hourly pay rate, equal the labor. Many of the second date in your comparison employee benefit programs if you sell 100,. Material to manufacture hiking boots, and other important metrics 5 steps for Taking Charge your. Inc. for the quarter direct expenses of the costs are reclassified to the cost good! Both the cost paid to an office security company is a variable overhead cost,! Figure that expresses the percentage of sales the firm 's total revenues multiply... And it is calculated by dividing gross wages by gross profit equals net... Amount is always calculated, based on the second date in your comparison revenue to calculate the profit. That generate cash inflows and profit date from the gross profit formula can also be to. To improve gross margin and gross profit formula helps you identify cost saving opportunities a. A simple example to understand costs is to increase gross profit ratio calculating the margin. Use a product or service failure to properly manage the gross profit calculations to forecast company profit model! Convert more of each boot requires two square yards of leather inventory item is sold, transaction... Helps you identify cost saving opportunities on a company called XYZ Limited for doing the calculation of the first from.


text:
# Localization windows and spectral analysis¶

Now that we know how to work with spherical harmonic coefficient and grid classes, let's move on to the other major feature of pyshtools: localization windows and spectral analysis. pyshtools allows for localized spectral analyses using either spherical-cap localization windows or localization windows constructed from an arbitrary mask. As with our examples in the previous notebook, a single class, SHWindow, bundles the relevant shtools functions. Here, we will demonstrate how to construct optimal localization windows, and how to obtain localized spectral estimates for arbitrary regions on the sphere.

## Spherical cap localization windows¶

To demonstrate the localized spectral analysis routines, we will make use of a pathological data set. In particular, we will construct a function on the sphere whose power spectrum is different in the northern and southern hemispheres. First, import the standard modules:

In [1]:
%matplotlib inline
from __future__ import print_function # only necessary if using Python 2.x

import matplotlib.pyplot as plt
import numpy as np
import pyshtools

Next, create two grids using random coefficients that have power spectra following power laws of -2 and -3, up to and including degree 300:

In [2]:
ldata = 300
degrees = np.arange(ldata+1, dtype=float)
degrees[0] = np.inf

power_north = degrees**(-2)
power_south = degrees**(-3)

clm_north = pyshtools.SHCoeffs.from_random(power_north)
grid_north = clm_north.expand()

clm_south = pyshtools.SHCoeffs.from_random(power_south)
grid_south = clm_south.expand()

Next, create a new grid that contains data from the northern hemisphere of one grid and the southern hemisphere of the other. The SHGrid method from_array() returns a copy of the data, so you don't need to worry about modifying the original data set:

In [3]:
grid = pyshtools.SHGrid.from_array(grid_north.data)

nlat = grid_north.nlat
grid.data[nlat//2:nlat+1,:] = grid_south.data[nlat//2:nlat+1,:].copy()

fig, ax = grid.plot()
clm = grid.expand()

Here, we made use of the grid attribute nlat, which is the number of rows of the gridded data, and we modified the raw gridded data for grid that is stored in the data class attribute.

Next, let's construct some spherical-cap localization windows. This is done using the constructor from_cap() that is associated with the SHWindow class. The other option, as we will demonstrate later, is from_mask() and takes as input a user defined mask. For spherical-cap windows, we need to specify both the angular radius of the cap and its spherical harmonic bandwidth, and for this example we will use an angular radius of 30 degrees and a bandwidth of 29.

In [4]:
capwin = pyshtools.SHWindow.from_cap(theta=30., lwin=29)

This command calculates the spherical harmonic coefficients of the spherical cap windows along with their associated angular orders and concentration factors. If you ever need to access these directly, they are stored in the class attributes tapers, orders and eigenvalues. By default, theta should be provided in degrees, but this can be input in radians by specifying the optional parameter theta_degrees=False. If you are curious to see what these windows look like, you can plot them using the built in method plot_windows(). Let's plot the first 35:

In [5]:
fig, axes = capwin.plot_windows(35)

As is seen, the windows are centered at the north pole, the concentration factor is noted above the window, and almost all of these windows are very well localized. If you want to know how many windows have concentration factors larger than a specified value, you can use the method number_concentrated():

In [6]:
capwin.number_concentrated(0.99)

Out[6]:
34

If you are really curious about the windows, you can return an SHGrid class instance of an individual window using the method to_shgrid(), you can return the spherical harmonic coefficients of individual windows using to_array() and to_shcoeffs(), and you can also return as a numpy array the power spectra of one or more windows using the method spectra(). If you want to plot the power spectra of the windows, this can be done using the built in method plot_spectra():

In [7]:
fig, axes = capwin.plot_spectra(15)

In general, we will not perform localized spectral analyses at the north pole, so let's rotate the windows so that they are centered at 45 degrees north and 90 degrees east. This is easily accomplished using the rotate() method. To speed things up, we will rotate only the first 50 best localized windows, and not all 900 of them:

In [8]:
capwin.rotate(clat=45., clon=90., nwinrot=50)

fig, axes = capwin.plot_windows(15)

In rotating the windows, the spherical harmonic coefficients of the initial tapers centered at the north pole are not modified, but a second set of rotated coefficients are created and stored in the attribute coeffs. If you ever forget how you constructed your windows, you can always use the info() method to print out all the metadata:

In [9]:
capwin.info()

kind = 'cap'
theta = 30.000000 degrees
lwin = 29
nwin = 900
clat = 45.000000 degrees
clon = 90.000000 degrees
nwinrot = 50
dj_matrix is stored
Taper weights are not set.

Next, let's calculate the localized power spectrum at two different locations, one in the northern hemisphere and the other in the southern hemisphere. We will use all 34 windows that have concentration factors greater than 0.99:

In [10]:
k = capwin.number_concentrated(0.99)

mtse_north, sd_north = capwin.multitaper_spectrum(clm, k)
mtse_south, sd_south = capwin.multitaper_spectrum(clm, k, clat=-55., clon=90.)

If you don't provide the central latitude and longitude of the analysis with the parameters clat and clon, the coefficients that were created previously using the rotate() method will be employed. If these coefficients are not available, the analysis will be performed at the north pole.

multitaper_spectrum returns a power spectrum whose maximum degree is ldata - lwin. This is because localized degrees beyond this limit depend upon coefficients of the global data beyond ldata, and these are not known. If the global function was truly zero beyond ldata, you could simply construct the spherical harmonic coefficients of clm to have zeros beyond that degree.

When a function is multiplied by a window, the power spectrum of the localized function is modified. For the case of stationary and random data, the expectation of this biasing effect can be estimated using two methods. First, we could calculate the "coupling matrix" using the method coupling_matrix(). The expectation of the windowed power spectrum is then simply the multiplication of this matrix by the global spectrum. If you are interested, you can plot the coupling matrix using the built in method plot_coupling_matrix():

In [11]:
fig, ax = capwin.plot_coupling_matrix(ldata)

Here, however, we will estimate the expectation of the windowed spectrum using biased_spectrum() and the global power spectra used to create the data in the northern and southern hemispheres:

In [12]:
power_north_biased = capwin.biased_spectrum(power_north, k)
power_south_biased = capwin.biased_spectrum(power_south, k)

Note that this function returns a spectrum with a maximum degree ldata+lwin. In calculating the expectation of the biased power spectrum from the global spectrum, it is assumed implicitly that the global power spectrum is exactly zero for all degrees greater than ldata.

Finally, lets plot the global power spectra, the localized spectra, and the localized expectations. Assuming that the data are unknown above degree ldata, we plot only the valid localized spectral estimates up to degree ldata - lwin.

In [13]:
degrees2 = np.arange(ldata+capwin.lwin+1)
degrees3 = np.arange(ldata-capwin.lwin+1)

fig, ax = plt.subplots(1,1)
ax.plot(degrees, power_north, '-k',
degrees, power_south, '--k',
degrees2, power_north_biased, '-r',
degrees2, power_south_biased, '--r',
degrees3, mtse_north, '-b',
degrees3, mtse_south, '--b')
ax.set(yscale='log', xlabel='degree', ylabel='power', xlim=(0,200-capwin.lwin), ylim=(1.e-8, 1.))

Out[13]:
[None,
(1e-08, 1.0),
<matplotlib.text.Text at 0x113602a20>,
(0, 171),
<matplotlib.text.Text at 0x1136cb978>]

As is seen, the expectation of the localized spectra (red) are significantly biased at low degrees in comparison to the unwindowed global fields (black). This is not necessarily a problem, because this effect is quantifiable. The actual localized power spectra (blue) are found to closely resemble the expected value, especially for degrees greater than the window bandwidth of 29.

In this example, we calculated only the localized power spectrum of a single function. If you were interested in the localized cross-power spectrum of two functions, this could be caluculated using the method multitaper_cross_spectrum().

## Arbitrary localization windows¶

We next demonstrate how to perform a localized spectral analysis over an irregular region. For this example, we will first create a function whose power spectrum is different over the oceans and landmass of Earth, we will then calculate windows that localize these two regions, and finally we will perform a multitaper spectral analysis similar to what we did with the spherical cap localization windows above.

First, let's read in the spherical harmonic coefficients of Earth's topography (referenced to mean sea level):

In [14]:
topo_coeffs = pyshtools.SHCoeffs.from_file('../ExampleDataFiles/srtmp300.msl', 300)
topo = topo_coeffs.expand()
fig, ax = topo.plot()

Next, create a boolean mask that is True for elevations that are greater than zero:

In [15]:
land_mask = pyshtools.SHGrid.from_array(topo.data > 0)

format: plain


text:
# Show that $\mathbb{Q}$ is finitely generated $\mathbb{Q}[x_1,x_2,\dots]$-module

Let $$R=\mathbb{Q}[x_1,x_2,\dots]$$ and $$M=\mathbb{Q}$$. Show that $$M$$ is finitely generated $$R$$-module.

First of all, I don't understand how is $$M$$ an $$R$$-module; Indeed $$f(x_1,x_2,\dots)=x_1\in R, 1\in M$$ but $$1\cdot f(x_1,x_2,\dots)=x_1\notin \mathbb{Q}=M$$.

Is this a mistake in the question.

Assuming it's a mistake we need to change $$R\leftrightarrow M$$. I still don't know how to solve it because we need to find a finite basis $$\{m_1,\dots ,m_n\}\subseteq M$$ s.t. $$M=\{\sum_{i=1}^nr_im_i:r_i\in R\}$$.

The netural guess is to detemine $$m_i:=x_i$$ but this way $$x_{n+1}\notin \operatorname{span} \{x_1,\dots,x_n\}$$.

• Turning it around, the polynomial ring over a field is not finitely generated over this field. – Wuestenfux Aug 29 at 12:00

An $$R$$-module $$M$$ is an abelian group equipped with a ring homomorphism $$\varphi:\ R\ \longrightarrow\ \operatorname{End}(M).$$ In this particular case, a ring homomorphism $$\varphi:\ \Bbb{Q}[x_1,x_2,\ldots]\ \longrightarrow\ \operatorname{End}(\Bbb{Q}),$$ is uniquely determined by where the indeterminates $$x_i$$ are mapped, and an endomorphism of $$\Bbb{Q}$$ (as an abelian group!) is uniquely determined by where $$1\in\Bbb{Q}$$ is mapped. So $$\varphi$$ is uniquely determined by the values $$(\varphi(x_i))(1)\in\Bbb{Q}$$.
Note that here $$\varphi(x_i)$$ is an endomorphism of $$\Bbb{Q}$$ for each $$i$$. In your notation $$(\varphi(x_i))(1)=1\cdot x_i$$. Recall that the '$$\cdot$$' in $$1\cdot f(x_i)$$ stands for the 'multiplication' defined by the $$R$$-module structure on $$M$$; it is not the regular multiplication $$1\cdot f(x_i)\in\Bbb{Q}[x_1,x_2,\ldots]$$ because we are not in $$\Bbb{Q}[x_1,x_2,\ldots]$$, we are in $$\Bbb{Q}$$ with a $$\Bbb{Q}[x_1,x_2,\ldots]$$-module structure.
• I understand that there's an equivalent defenition for an $R$-module. But still, how could $\mathbb{Q}$ be a $\mathbb{Q}[x_1,x_2,...]$-module if $1\in \mathbb{Q}, x_1\in \mathbb{Q}[x_1,...]$ but $1\cdot x_1=x_1\notin \mathbb{Q}$? – J. Doe Aug 29 at 12:18
• The dot in the multiplication $1\cdot x_1$ is not multiplication in $\Bbb{Q}[x_1,x_2,\ldots]$. It denotes the module action of $\Bbb{Q}[x_1,x_2,\ldots]$ on $\Bbb{Q}$. When getting familiar with modules, it can be very illustrative to make this difference explicit by not writing $1\cdot x_1$, but in stead writing $\varphi_{x_i}(1)$, where $\varphi$ is the module homomorphism described above, and $\varphi_{x_i}:=\varphi(x_i)\in\operatorname{End}(\Bbb{Q})$. – Inactive - avoiding CoC Aug 29 at 12:21
• As a simpler example, the ring homomorphism $$\varphi:\ \Bbb{Q}[x]\ \longrightarrow\ \operatorname{End}(\Bbb{Q}):\ x\ \longmapsto\ (q\ \mapsto\ 2q),$$ defines a $\Bbb{Q}[x]$-module structure on $\Bbb{Q}$. With this structure you have $q\cdot x=\varphi_x(q)=2q$, and so in particular $1\cdot x=2$. – Inactive - avoiding CoC Aug 29 at 12:24
• To complete the answer, let $T:=\{\sum_{i=1}^n(\varphi(r_i))(m_i):r_i\in R\}$. We want to find $m_1,\dots,m_n\in\mathbb{Q}$ s.t. $\mathbb{Q}=T$. Now, we know that $\operatorname{id}_{\mathbb{Q}},0_{\operatorname{End}(M)}\in \operatorname{Im}(\varphi)$. Hence, if we choose for example $n=1,m_1=1$ then we have $0,1\in T$. But how can we choose $n,m_1,\dots,m_n$ s.t. $\forall q\in\mathbb{Q}, q\in T$? – J. Doe Aug 29 at 12:55
• You already note that $\operatorname{id}_{\Bbb{Q}}\in\operatorname{Im}(\varphi)$; indeed necessarily $\operatorname{id}_{\Bbb{Q}}=\varphi(1)$, for $1\in\Bbb{Q}[x_1,x_2,\ldots]$. Because $\varphi$ is a ring homomorphism it follows that $\varphi(q)=q\varphi(1)=q\cdot\operatorname{id}_{\Bbb{Q}}$ for all $q\in\Bbb{Q}\subset\Bbb{Q}[x_1,x_2,\ldots]$, and hence $$q=q\cdot\operatorname{id}_{\Bbb{Q}}(1)=(\varphi(q))(1).$$ So not only is $\Bbb{Q}$ finitely generated over $\Bbb{Q}[x_1,x_2,\ldots]$, it is cyclic because it is generated by $1\in\Bbb{Q}$. – Inactive - avoiding CoC Aug 29 at 13:13


text:
# $\frac{\pi^2\csc^2(\pi/x)}{x^2}= \sum_{n=-\infty}^\infty\frac{1+(xn)^2}{(1-(xn)^2)^2}$. Where can I find some more series of this class?

After reading Show $\sum_{n=0}^\infty\frac{1}{a^2+n^2}=\frac{1+a\pi\coth a\pi}{2a^2}$ and noodling around on wolfram alpha, I discovered

\begin{align} &\coth(x \pi)=\frac{x}{\pi}\sum_{n=-\infty}^\infty\frac{1}{x^2+n^2} & \cot(x \pi)= \frac{x}{\pi}\sum_{n=-\infty}^\infty\frac{1}{x^2-n^2} \\ & \text{csch}(x \pi )=\frac{x}{\pi} \sum_{n=-\infty}^\infty{\frac{(-1)^n }{x^2+n^2}} &\csc(x \pi)= \frac{x}{\pi} \sum_{n=-\infty}^\infty{\frac{(-1)^n }{x^2-n^2}} \\ & \tanh(x \pi)=\frac{4x}{\pi}\sum_{n=-\infty}^\infty{\frac{1}{(2n+1)^2+4x^2}} &\tan(x \pi) = \frac{4x}{\pi}\sum_{n=-\infty}^\infty{\frac{1}{(2n+1)^2-4x^2}} \end{align}

I suspect (but don't know for sure) that these can all be justified by milking the techniques from the link above.

We should be able to derive a few more identities. For example,

$$\Big(\cot(x \pi) \Big)'= \Big(\frac{x}{\pi} \sum_{n=-\infty}^\infty{\frac{1}{x^2-n^2}} \Big )'$$

$$\Big(\pi csc(\pi x)\Big)^2= \sum_{n=-\infty}^\infty\frac{x^2+n^2}{(x^2-n^2)^2}$$

And after some manipulations we can find

$$\frac{\pi^2\csc^2(\pi/x)}{x^2}= \sum_{n=-\infty}^\infty\frac{1+(xn)^2}{(1-(xn)^2)^2}$$ Lovely. We can write then $$\frac{\pi^2}{9}=\sum_{n=-\infty}^\infty {\frac{1+(6n)^2}{(1-(6n)^2)^2}}$$ I have a feeling at this point that this must be a well-studied subject and I wonder where I can find some more identities of this class. Does anyone have a link/resource where I can read more on these. I don't really need their derivations if they are just the techniques of the link above + elementary calculus techniques. I am just looking for a well organized list that I can refer to.

• $+1$ just for the "go go gadget calculus," because I get the reference. XD – Frpzzd Sep 15 '18 at 23:54
• Also... How do you render $\csch$? – Mason Sep 15 '18 at 23:58
• You can always use \operatorname{csch} – MPW Sep 16 '18 at 0:09
• This and This seem like they could be good resources. – Mason Sep 21 '18 at 23:27

I don’t have a list, but I can present the method to make a list systematically.

Let $P(x,n),Q(x,n)$ be two polynomials of $x,n$.

Suppose $$Q(x,r_1(x))=Q(x,r_2(x))=\cdots=Q(x,r_k(x))=0$$ for all $x$.

Suppose the sum $$S(x)=\sum^\infty_{n=-\infty}\frac{P(x,n)}{Q(x,n)}$$ converges whenever $r_{(\cdot)}(x)\not\in\mathbb Z$.

Then, by residue theorem, $$S(x)=-\pi\sum^k_{n=1}\operatorname*{Res}_{z=r_n(x)}\frac{\cot(\pi z)P(x,z)}{Q(x,z)}$$

(It is an issue that for some $x$, we might have $r_p(x)=r_q(x)$. When two or more $r$ functions take the same value, the residue should only be evaluated once.)

There is some nice things to see here:

$$\tanh(x \pi)=\frac{4x}{\pi}\sum_{n=-\infty}^\infty{\frac{1}{(2n+1)^2+4x^2}}$$

$$\Big(\tanh(x \pi) \Big)'= \Big( \frac{1}{\pi}\sum_{n=-\infty}^\infty{\frac{4x}{(2n+1)^2+4x^2}} \Big)'$$

$$\pi\operatorname{sech}^2(\pi x)=\frac{1}{\pi}\sum_{n=-\infty}^{\infty}\frac{4\left(4n^2+4n-4x^2+1\right)}{\left(4n^2+4n+4x^2+1\right)^2}$$

Which is nice: taking $x=0$ we have

$$\pi^2=\sum_{n=-\infty}^{\infty}\frac{4}{4n^2+4n+1}=8\Big(1+\sum_{n=1}^\infty{\frac{1}{4n^2+4n+1}}\Big)$$

Interesting. I wonder if we can use this to demonstrate Takebe Kenko's somewhat similar looking (this can be found- with a tiny typo in denominator- on the last page of this):

$$\pi^2=4\Big(1+\sum_{n=1}^{\infty} \frac{2^{2n+1}(n!)^2}{(2n+2) !} \Big)$$


text:
# A-level Physics/Forces, Fields and Energy/Electromagnetism

## Magnetic Force on a Current

The formula below calculates the force being undergone by a current in a magnetic field.

${\displaystyle F=BIL\sin(\theta )}$

F is the force being undergone by the current - measured in Newtons(N).

B is the magnetic field strength (or flux density) of the field the charge is in (I.e The number of magnetic field lines per unit area) - measured in Teslas (T).

I is current of the current - measured in amperes (A).

L is the length of conductor in the magnetic field - measured in meters (m)

θ is the angle the current makes with the magnetic field - measured in either radians or degrees (° or C)

The force undergone by the current is at its maximum magnitude when the current vector is perpendicular to the magnetic field vector (ie. Force is maximum when θ = 90°) as Sin(90°) = 1. However the force undergone by the current is at a magnitude of 0 N when the current vector is parallel to the magnetic field vector (ie. Force is 0 N when θ = 0°) as Sin(0°) = 0.

The direction of the Force may be found by application of the Right-hand rule rule as follows:

1. The index finger points in the direction of the velocity vector, v.
2. The middle finger points in the direction of the magnetic field vector B.
3. The thumb points in the direction of the cross product of v and B, which is equal to the force vector, F.

For example, for a positively charged particle moving to the north, in a region where the magnetic field points west, the resultant force points up.

## Magnetic Force on a moving charge

F = BqV

F is the force being undergone by the charge - measured in Newtons (N)

B is the magnetic field strength (or flux density) of the field the charge is in (I.e No. of magnetic lines of force from magnet per unit area) - measured in Teslas (T)

q is the charge of the charge - measured in Coulombs (C).

v is the velocity of the charge - measured in meters per second (ms-1)

The direction of the Force may be determined using the Right-hand rule.

## Orbiting charges

As stated by the Right-hand rule, the direction of the force experienced by a charge entering a magnetic field (assuming the direction of magnetic field vector and the velocity vector of the charge are not the same) would be perpendicular to the plane of the direction of the velocity and magnetic field vectors.

Due to this, as the charge particle's velocity changes due to the force, the force vector also changes. This causes a circular motion of the charge particle inside the magnetic field. Due to this, the charge's path has a radius and a centripetal force. These are described by:

${\displaystyle r={\frac {mv}{Bq}}}$

r is the radius of the charge's path - measured in metres (m)

m is the mass of the charge - measured in kilograms (kg)

v is the velocity of the charge - measured in meters per second (ms-1)

B is the magnetic field strength (or flux density) of the field the charge is in (I.e No. of magnetic lines of force from magnet per unit area) - measured in Teslas (T)

q is the charge of the charge - measured in Coulombs (C).

${\displaystyle F={\frac {mv^{2}}{r}}}$

F is the centripetal force being undergone by the charge - measured in Newtons (N)

m is the mass of the charge - measured in kilograms (kg)

v is the velocity of the charge - measured in meters per second (ms-1)

r is the radius of the charge's path - measured in metres (m)

## Parallel Current Carrying Conductors

F/l=k (I1 I2)/d

Where F = Force; Newtons N

l = Length of the current carrying conductors parallel to each other.

k = constant; mu0/2p = 2 x 10-7 SI Units

I1 and I2 are current carrying conductors respectively

d = distance between the current carrying conductors (mm)

## Quick note

Radius is large for more massive, faster particles. Radius is smaller when the magnetic field strength is large


text:
## Thursday, October 07, 2010

### How the eye wires up

Nature has some fun articles about the measurements that are unmasking the neural circuitry of the retina:
Field, G. et al. Nature 467, 673-677 (2010)

Adam Mann: How the eye wires up (Nature)

Mapping color vision in HD (NSF)
The NSF article also features an amusing comment that the tiny, multi-electrode retinal readout system was inspired by the particle detectors used to search for the Higgs boson: that's how I found this article in the first place. ;-)

Signals from hundreds of cells are evaluated simultaneously.

Click to zoom in (by a lot). Credit: Zina Redetsky, NSF

These analyses of the neural network show how they're capable to selectively amplify the color when it's needed, and so forth. The popular articles are not enough for me to understand the details. But it's clear that there's a lot of stuff to study here - and the neural networks are kind of remotely analogous to computers and digital cameras, too.

The World Wide Web was invented at CERN and the particle detectors are becoming useful to study the functioning of the eye which may be useful for many applications in the future. These are clearly not real-world applications of the W-bosons, Z-bosons, or Higgs bosons themselves - and chances are that these particles will never have a real-world application. But they're applications of the technological insights that people naturally and almost inevitably acquire when they're trying to find the most profound truths about the elementary particles. ;-)

It is not a coincidence that such new technologies are pioneered in abstract fields such as particle physics. It's simply because particle physics forces the physicists and engineers to push the technological edge to the realm of the "previously impossible". Those folks have to make advances that would be "uneconomic" - and no one would be thinking about them - if the profitability in some everyday situations were the only issue.

However, what is useful and profitable in the everyday life is changing, too. So we shouldn't be surprised that many things that belonged among the abstract ideas in the past are getting - or will be getting - a part of the "bread and butter" life for much wider sets of professional right now or in the future.

After all, this is true about portions of pure mathematics, too. Lie groups and Calabi-Yau manifolds used to be "just pure, abstract mathematics" at some points of the history, too. And many mathematical structures that are still viewed as "abstract" today will become a part of the "required physics toolkit" in the future - although we can't be quite certain which of them before they actually do.

America builds its ATLAS detector

The ATLAS detector is a part of the LHC collider at CERN - the Center of Europe for the Research of Nuclei. Many nations - mostly European nations - have built it. However, America is more efficient. It can build it, too.

Actually, one person - an artist named Josef Kristofoletti - was enough to build or paint America's own ATLAS detector. See the three galleries: click Set 1, Set 2, Set 3.

Reuters announced that the work has been completed today.


text:
# Latex twoside format with non linear page numbering

I have the following problem:

I need to make a Latex document, where the first part is numbered with roman numbers and the 2nd part in numbered with Arabic numbers. The Arabic numbers should start with 1 again. Moreover, I have to add some empty pages which do not add to the page counting in between. All this messes up my margins for the twoside setup.

Here is an example:

\documentclass[11pt, bibliography=totoc, twoside]{article}
\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage{abstract}
\usepackage{graphicx}
\graphicspath{{images/}{../images/}}
\usepackage{enumitem}
\usepackage{natbib}
\usepackage[onehalfspacing]{setspace}

\usepackage{subfiles}
\usepackage{siunitx}
\sisetup{per-mode=fraction}
\usepackage{amsmath}
\usepackage[many]{tcolorbox}

\usepackage{float}
\usepackage{acronym}
\usepackage{geometry}
\usepackage{hyperref}
\usepackage{fancyhdr}

\usepackage{blindtext}
\usepackage{xcolor}
\usepackage{booktabs}
\usepackage{listings}
\usepackage{tabularx}
\usepackage{ltablex}
\usepackage{caption}

\makeatletter
\makeatother

\definecolor{TU_blue}{RGB}{0, 102, 153}

\fancyhf{}
\fancyfoot[C]{\thepage}
\pagestyle{fancy}

\title{dummy}
\author{my name}
\date{December 2019}

\begin{document}

\maketitle

\pagestyle{fancy}
\pagenumbering{Roman}

\section*{Acknowledgements}
\blindtext

\section*{Abstract}
\blindtext

\section*{Abstract German}
\blindtext

\tableofcontents
\newpage

\section*{List of Abbreviations}
\markboth{List of Abbreviations}{LIST OF ABBREVIATIONS}
\begin{acronym}\itemsep0pt
\acro{ABC}{Alphabet}
\end{acronym}
\newpage

\listoffigures
\newpage

\listoftables
\newpage

\pagenumbering{arabic}
\section{Introduction}
\blindtext
\newpage

\section{Section 2}
\blindtext[4]
\subsection{subsection 2.1}
\blindtext[4]
\subsection{subsection 2.2}
\blindtext[4]
\subsection{subsection 2.3}
\blindtext[4]
\subsection{subsection 2.4}
\blindtext[4]
\newpage

\blindtext
\newpage

\end{document}

The Title page, Acknowledgements, Abstract, Abstract German should all be on the right side. However, they should be numbered without empty pages.

Starting from "Contents" the text should appear on both sides. Both sides "List of Tables" and "Introduction" are formated as a left page.

One additional minor question because I confused myself a lot at the moment: The first page should be the right page, am I right?

Your MWE should me more minimalistic. A lot of packages are not needed in your example.

Please: Ask yourself, what type of document to prepare. This is a different question as how your document should look like.

In your MWE you defined a document with two-sided layout. Two-sided layout is the default for a class like book.

Regardless of the class (article or book) you should prepare a document which is unambiguous. One cannot stress this point too much. If you prepare a document with a two-sided layout, every page has to have a consecutive pagenumber! You can decide, to not print out the number, but the number is still in existence, hence the next page is the next higher number.

The Title page, Acknowledgements, Abstract, Abstract German should all be on the right side.

This leads me to the assumption, that an article is not the correct choice. Instead you should choose a report or even a book-class. The standard LaTeX classes, as well as those replacements of KOMA-Script, start a new chapter on a right hand side, which of course could also be identified by its odd page number.

But what do you mean with

However, they should be numbered without empty pages.

As explained above, you can suppress the page numbers to be printed on otherwise empty pages. KOMA-Script does that by default.

Or did you mean, that an empty page should not be counted? This would lead to page numbers, which could be even-numbered, even for a right hand page. Are you sure, you will break all traditions? I would strongly advise against that!

Starting from "Contents" the text should appear on both sides. Both sides "List of Tables" and "Introduction" are formated as a left page.

I have no clue, what you mean. Do you describe the result of your LaTeX code? If so, are you ok with it?

Both standard LaTeX classes (report and book) as well as those KOMA replacements are able to open new chapters also on a left hand side, if the previous chapter happens to end on a right hand page. Just insert the class-option openany in your \documentclass command. The default for report, scrreprt, book and scrbook is to open new chapters on a right handed (odd numbered) page. Hence, the default option is openright.

Again, either option you choose will than treat every chapter throughout the complete in the same way, it treated previous chapters in the document. That is, no expceptions will be made! The same rule (either openany or openright) will apply. And that is a good decision.

One additional minor question because I confused myself a lot at the moment: The first page should be the right page, am I right?

Yes, you are. 1 happens to be an odd number. The traditional rule says, in book-printing any odd numbers are right handed pages.

I modified your MWE by deleting all unneeded packages. I added a bibliography database, containing one book and added a \cite command in the text as well. More important, I switched from article class to a very mighty scrbook from KOMA-Script classes.

As "your" document is now of type book, I upgraded the sectioning commands to be one level higher: \section was changed into \chapter and so forth.

I added the \frontmatter and \mainmatter commands, to automatically switch between roman and arabic pagenumberings and deleted your similar attempts. \frontmatter and \mainmatter are special to the book classes, they are not available in article or report classes (neither LaTeX or KOMA-Script). But using \frontmatter also changes the numbering of \chapter: they won't get a number, but will be incorporated in the table of contents. Easy-peasy. :-)

Please read the acronym manual carefully about its possibilities. You can automatically get a list of abbreviations with kind help of makeindex ...

In the end of your document, I added the \appendix command, to end the normal document and start the appendencies. As you can see, this command again changes the treatment of the sectioning commands as \chapter. This time, the chapters won't get numbers, but Letters.

I also added a bibliography by \printbibliography. This assumes, you are working with BibLaTeX and the biber binary. The KOMA-Script class options liststotoc and bibtotoc make sure, that your list of figures and list of tables as well as your bibliography will be listed in the table of contents. Again easy-peasy. :-)

I hope, you can life with my assumptions and modifications based on them. Here is my "improved" MWE. I don't wont to be rude if I give you the advise: "keep it simple, keep it plain". Start to write your document. Don't worry about the layout to much (at least in the beginning of the process). Be assured, LaTeX will produce high quality documents (from the point of typographic view).

Have fun in writing! The rest will come step by step. I am sure.

\documentclass[11pt, openright, liststotoc, twoside]{scrbook}
% \documentclass[11pt, openright, twoside]{book}
% \documentclass[11pt, openany, twoside]{book}

\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage{acronym}
\usepackage{blindtext}

%% Needed for the bibliography
\usepackage[backend=biber,style=numeric]{biblatex}
\begin{filecontents}{\jobname.bib}
@Manual{class:scrguide,
title =    {{KOMA-Script}},
author =   {Kohm, Markus},
month =    May,
year =     2016,
url =      {http://www.komascript.de/~mkohm/scrguide.pdf},
langid =   {ngerman},
note =     {Bestandteil der Online-Dokumentation von \LaTeX,
Datei \texttt{scr\-guide.pdf}},
keywords =     {manual},
}
\end{filecontents}
\bibliography{\jobname}

%% Maybe you don't need this in KOMA any more?
% \usepackage{fancyhdr}
% \fancyhf{}
% \fancyfoot[OL]{\thepage}
% \fancyfoot[ER]{\thepage}
% \pagestyle{fancy}

\title{dummy}
\author{my name}
\date{December 2019}

\begin{document}

%% Frontmatter starts the preliminaries and uses roman pagenumbers
\frontmatter

\maketitle

\chapter{Acknowledgements}
\blindtext

\chapter{Abstract}
\section*{German}
\blindtext[4]
\section*{English}
\blindtext[7]

\tableofcontents
\listoffigures
%% only needed in book.cls.  KOMA class option "liststotoc" add these
%% entries automagically
\listoftables
%% only needed in book.cls.  KOMA class option "liststotoc" add these
%% entries automagically

%% New: print the nomenclature/abbreviations here.  See package
%% acroynm handbook (texdoc acronym)!
% \printnomenclature

\chapter{List of Abbreviations}
\begin{acronym}\itemsep0pt
\acro{ABC}{Alphabet}
\end{acronym}

%% Here ends the preliminaries and the normal document starts.  The
%% \mainmatter command switches the page numbers to be arabic.
\mainmatter
\chapter{Introduction}
\blindtext

\chapter{Section 2}
\blindtext[4]
\section{subsection 2.1}
\blindtext[4]
\section{subsection 2.2}
\blindtext[4]
\section{subsection 2.3}
\blindtext[4]
\cite{class:scrguide}
\blindtext[3][2]

\section{subsection 2.4}
\blindtext[4]

%% What should this command be good for?
% \newpage

%% End of the document.  Start the appendencies
\appendix

\chapter{Some Appendix}
\blindtext[6]

\chapter{Next Appendix}

\section{First Subappendix}
\blindtext[4]

\section{Another Subappendix}
\blindtext[7]

%% Finally the bibliography
\printbibliography{}

%% Same as above!
% \newpage

\end{document}


text:
• Browse all
Studying Parton Energy Loss in Heavy-Ion Collisions via Direct-Photon and Charged-Particle Azimuthal Correlations

The collaboration
Phys.Rev.C 82 (2010) 034909, 2010.

Abstract
Charged-particle spectra associated with direct photon ($\gamma_{dir}$) and $\pi^0$ are measured in $p$+$p$ and Au+Au collisions at center-of-mass energy $\sqrt{s_{_{NN}}}=200$ GeV with the STAR detector at RHIC. A hower-shape analysis is used to partially discriminate between $\gamma_{dir}$ and $\pi^0$. Assuming no associated charged particles in the $\gamma_{dir}$ direction (near side) and small contribution from fragmentation photons ($\gamma_{frag}$), the associated charged-particle yields opposite to $\gamma_{dir}$ (away side) are extracted. At mid-rapidity ($|\eta|<0.9$) in central Au+Au collisions, charged-particle yields associated with $\gamma_{dir}$ and $\pi^0$ at high transverse momentum ($8< p_{T}^{trig}<16$ GeV/$c$) are suppressed by a factor of 3-5 compared with $p$ + $p$ collisions. The observed suppression of the associated charged particles, in the kinematic range $|\eta|<1$ and $3< p_{T}^{assoc} < 16$ GeV/$c$, is similar for $\gamma_{dir}$ and $\pi^0$, and independent of the $\gamma_{dir}$ energy within uncertainties. These measurements indicate that the parton energy loss, in the covered kinematic range, is insensitive to the parton path length.

• #### Figure 2

Data from Figure 2

10.17182/hepdata.101353.v1/t1

The $z_{T}$ dependence of $\pi^{0}-h^{\pm}$ near side and away-side associated particle yields. The errors denoted 'syst' are systematic errors correlated...

• #### Figure 3 (upper panel)

Data from Figure 3 (upper panel)

10.17182/hepdata.101353.v1/t2

The $z_{T}$ dependence of away-side associated-particle yields for $\pi^{0}-h^{\pm}$ triggers and $\gamma_{dir}$ triggers. The errors denoted 'syst' are systematic errors...

• #### Figure 3 (lower panel)

Data from Figure 3 (lower panel)

10.17182/hepdata.101353.v1/t3

The $z_{T}$ dependence $I_{AA}$ for $\pi^{0}-h^{\pm}$ triggers and $\gamma_{dir}$ triggers. The errors denoted 'syst' are systematic errors correlated in $z_{T}$....

• #### Figure 4

Data from Figure 4

10.17182/hepdata.101353.v1/t4

$I_{AA}$ as a function of $p_{T}$ for $\gamma_{dir}$ triggers, measured in 0-10% Au+Au collisions. The associated charged particles have \$z_{T}...


text:
# [OS X TeX] Miscellaneous Questions

KHALID NADIRI khalid.nadiri at gmail.com
Mon Nov 29 13:43:45 EST 2010

Thanks Alan.  I've created a BibTex bibliography via BibDesk and have exported it to the folder where my article is saved.  When I try to run the BibTex file in my LaTeX file using the \bibliography{bib file name} command, my references do not show up.  Any idea what might be going on here? I've tried re-running the LaTeX file several times to make sure the BibTex file is compiling properly.

Thanks,

Khalid

On Nov 29, 2010, at 1:03 PM, Alan Munn wrote:

> On Nov 29, 2010, at 12:58 PM, KHALID NADIRI wrote:
>
>> Hey everyone,
>>
>> LaTex novice here.  Have a few very basic questions.  Any help would be much appreciated.
>>
>> 1. Does one have to download BibTex in addition to BibDesk? BibTex does not come with the full MacTex package, correct?
>
> No, bibtex is part of your TeXLive distribution. (MacTeX) so you don't have to download anything else. BiBDesk is a bibliography management system which is (more or less) independent of bibtex (although it does assume you have it for doing previews etc.).
>
>>
>> 2. If I wanted to change the item and paragraph spacing in a list per the syntax below, but wanted to specify different symbols for the labels of each item and sub-item (e.g., filled-in bullets for one item, open bullets for a sub-item, etc.), how would I change the syntax below?
>>
>> \renewenvironment{itemize}{
>> \begin{list}{}{
>>   \setlength{\leftmargin}{1.5em}
>>   \setlength{\itemsep}{0.25em}
>>   \setlength{\parskip}{0pt}
>>   \setlength{\parsep}{0.25em}
>> }
>> }{
>> \end{list}
>> }
>>
>>
> The best way to do this is to use the enumitem package, which allows easy customization of all list parameters.  If you are using TeXShop as your editor, you can find the package documentation by using the "Show Help For Package" menu item in the Help menu.
>
> Alan
>
> --
> Alan Munn
> amunn at gmx.com
>
>
>
>
> ----------- Please Consult the Following Before Posting -----------
> TeX FAQ: http://www.tex.ac.uk/faq
> List Reminders and Etiquette: http://email.esm.psu.edu/mac-tex/
> List Archive: http://tug.org/pipermail/macostex-archives/
> TeX on Mac OS X Website: http://mactex-wiki.tug.org/
> List Info: http://email.esm.psu.edu/mailman/listinfo/macosx-tex
>

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://email.esm.psu.edu/pipermail/macosx-tex/attachments/20101129/00b19fb3/attachment.html>

More information about the MacOSX-TeX mailing list


text:
## 闪烁时间 / fundus-vessel-segmentation-tmbe .gitee-modal { width: 500px !important; }

Explore and code with more than 6 million developers，Free private repositories ！：）
This repository doesn't specify license. Without author's permission, this code is only for learning and cannot be used for other purposes.
Notice: Creating folder will generate an empty file .keep, because not support in Git

#Retinal Vessel Segmentation Created by José Ignacio Orlando at Pladema Institute (Facultad de Ciencias Exactas, UNCPBA, Tandil, Argentina) and CONICET (Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina), under the supervision of Matthew B. Blaschko (KU Leuven, Belgium).

##Introduction This code corresponds to our paper published at IEEE TBME 2016. It allows you to perform vessel segmentation in color fundus images.

##License Our code is released under the MIT Licence (refer to the LICENSE file for details).

##Citing If you find our code useful for your research, please cite:

@article{orlando2016discriminatively,
title={A discriminatively trained fully connected Conditional Random Field model for blood vessel segmentation in fundus images},
author={Orlando, Jos{\'e} Ignacio and Prokofyeva, Elena and Blaschko, Matthew},
journal={Biomedical Engineering, IEEE Transactions on},
year={2016},
publisher={IEEE}
}
@incollection{orlando2014learning,
title={Learning fully-connected CRFs for blood vessel segmentation in retinal images},
author={Orlando, Jos{\'e} Ignacio and Blaschko, Matthew},
booktitle={Medical Image Computing and Computer-Assisted Intervention--MICCAI 2014},
pages={634--641},
year={2014},
publisher={Springer}
}

There are also some third party libraries included in our code. If you use it, please cite:

• Responses to 2D Gabor wavelets by Soares et al. J. V. Soares et al.: Retinal vessel segmentation using the 2-D Gabor wavelet and supervised classification. IEEE Transactions on Medical Imaging, vol. 25, no. 9, 2006

• Line detectors by Nguyen et al. U. T. Nguyen et al.: An effective retinal blood vessel segmentation method using multi-scale line detection. Pattern Recognition, vol. 46, no. 3, pp. 703–715, 2013.

• Efficient inference in fully connected CRF by Krahenbul and Koltun (C++ implementation) P. Krahenbuhl and V. Koltun: Efficient inference in fully connected CRFs with Gaussian edge potentials. Advances in Neural Information Processing Systems, 2012, pp. 109–117. (if you use the MEX function that wraps this code please also cite our IEEE TMBE and MICCAI papers)

• Graph-cut for local neighborhood based CRF inference Y. Boykov and V. Kolmogorov: An experimental comparison of mincut/max-flow algorithms for energy minimization in vision. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 9, pp. 1124–1137, 2004.

##Contents

###Requirements

1. Set up MEX compiler according to your OS.
2. Compile the Fully Connected CRF wrapper doing:
mex ./CRF/CRF_1.0/fullyCRFwithGivenPairwises.cpp ./CRF/CRF_1.0/densecrf.cpp ./CRF/CRF_1.0/util.cpp
mex ./CRF/CRF_1.0/pairwisePart.cpp ./CRF/CRF_1.0/densecrf.cpp ./CRF/CRF_1.0/util.cpp

###Using the code Check out the user_manual.pdf file!

One of the first steps in automatic fundus image analysis is the segmentation of the retinal vasculature, which provides valuable information related to several diseases. In this work, we present an extensive description and evaluation of our method for blood vessel segmentation in fundus images based on a discriminatively trained, fully connect... spread retract

No release


text:
(Requires Analytica Enterprise, Optimizer, or Power Player)

Returns the contents a text file «filename» as a text value. «filename» may be the name of a file in the Current Data Directory (initially, the directory containing the model), or a path relative to the Current Data Directory , or an absolute pathname.

If it can't find a file with that name, by default, it opens a file browser dialog to let the user select another file. Set optional parameter, «showDialog» to True (1) to show the file browser dialog, using «filename» as default, even if the file exists. Set «showDialog» to False (0) to never show it. If it can't find the file, it shows an error message.

You can specify the caption for the title bar of the file browser dialog titlebar in the optional «title» parameter.

ADE never shows the file browser dialog, no matter what the parameter values.

## Treating End-of-line

There are three common standards in text-files to identify newlines:

• Windows files usually use the two-character sequence CRLF -- Chr(10) Chr(13)
• Unix files use a single LF character -- Chr(10)
• Macintosh OS files use a single CR character -- Chr(13)

Occasional Windows-based programs use one of the other standards.

ReadTextFile insulates you from worrying about which standard is used by converting each to the Unix standard, a single LF -- Chr(10).

If a file contains inconsistent line breaks -- e.g. including more than one examples of LF, CRLF, and CR -- it converts LF and CRLF to a single LF, and leaves CR -- Chr(13) -- as is.

When evaluated in the Analytica Decision Engine (ADE) and a dialog needs to be shown to the end-user, it calls IAdeUICallbacks::GetFilename(...). From within that callback, the parent application can interact with the end-user to resolve the file path, and a web applications can instruct the end-user to upload a file. Once complete, the callback returns the full path to the file which is then read. To receive this callback, the parent application must have previously registered the callback with ADE using CAEngine::SetCallbackObject( ). If it has not registered a callback and the file doesn't exist, returns an empty text.


text:
My Math Forum Covariance and correlation coefficient

 Algebra Pre-Algebra and Basic Algebra Math Forum

November 23rd, 2010, 04:35 PM   #1
Newbie

Joined: Nov 2010

Posts: 11
Thanks: 0

Covariance and correlation coefficient

Hi all,

If anybody knows how to work with joint probability function of multiple random variables, please take a look at this problem and see if you can give me any pointers.

I know you first need to find the marginal pdf of both U and V to get their respective means and variances. Then you need to find the expected value of X and Y (EXY) by double integration. Following, you use all the obtained results in the covariance formula in the second attachment below.

Then finally, you use the obtained covariance of X and Y to find the correlation coefficient in the third attachment below.

I hope my explanation is somewhat clear.

What I need help with is the mechanics of the problem. Is anybody familiar?

Thanks for looking.

knp
Attached Images
 Correlation Coefficient.jpg (9.5 KB, 160 views) Covariance.jpg (10.6 KB, 160 views) C and CC.jpg (18.1 KB, 160 views)

November 23rd, 2010, 07:31 PM   #2
Senior Member

Joined: Oct 2010
From: Changchun, China

Posts: 492
Thanks: 14

Re: Covariance and correlation coefficient

The domain on the u-v plane is shown as the following:

[attachment=0:238ndci0]1.JPG[/attachment:238ndci0]

As the joint probability function is

$f(u,v)=\begin{cases}\frac{1}{64}e^{-\frac{v}{8}} &0\leq u\leq v\leq +\infty\\0=&\text{otherwise}\end{cases} \text{ (i)}=$

the marginal probability functions are

$f_{\small{U}}(u)=\begin{cases}\int_u^{+\infty}\fra c{1}{64}e^{-\frac{v}{8}}\;d v &0\leq u\leq +\infty\\0=&\text{otherwise}\end{cases}=\begin{cases}\frac{1} {8}e^{-\frac{u}{8}} &0\leq u\leq +\infty\\\text{ }\\0=&\text{otherwise}\end{cases}\text{ (ii)}=$

$f_{\small{V}}(v)=\begin{cases}\int_0^{v}\frac{1}{6 4}e^{-\frac{v}{8}}\;d u &0\leq v\leq +\infty\\0=&\text{otherwise}\end{cases}=\begin{cases}\frac{1} {64}ve^{-\frac{v}{8}} &0\leq v\leq +\infty\\\text{ }\\0=&\text{otherwise}\end{cases}\text{ (iii)}=$ .

Use (ii) and (iii), the expectations are

$E(U)=\int_0^{+\infty}u.\frac{1}{8}e^{-\frac{u}{8}}\;d u=8$

$E(V)=\int_0^{+\infty}v.\frac{1}{64}ve^{-\frac{v}{8}}\;d v=16$

Also, the variances are

$D(U)=E(U^2)-[E(U)]^2=\int_0^{+\infty}u^2.\frac{1}{8}e^{-\frac{u}{8}}\;d u-8^2=64$

$D(V)=E(V^2)-[E(V)]^2=\int_0^{+\infty}v^2.\frac{1}{64}ve^{-\frac{u}{8}}\;d v-16^2=128$

And the covariance is

$\text{Cov}(U,V)=E(UV)-E(U)E(V)=\iint_{\small{0\leq u\leq v\leq+\infty}}uv.\frac{1}{64}e^{-\frac{v}{8}}\;d ud v -8\times16=\int_0^{+\infty}\frac{1}{64}ve^{-\frac{v}{8}}dv\int_0^vudu-128=64$

The correlation cofficient is

$\rho_{\small{UV}}=\frac{\text{Cov}(U,V)}{\sqrt{D(U )D(V)}}=\frac{64}{\sqrt{64\times128}}=\frac{\sqrt{ 2}}{2}\approx 0.7071$
Attached Images
 1.JPG (7.3 KB, 151 views)

 November 23rd, 2010, 08:13 PM #3 Senior Member     Joined: Oct 2010 From: Changchun, China Posts: 492 Thanks: 14 Re: Covariance and correlation coefficient I have corrected some mistakes in the above. Please have a check
 November 23rd, 2010, 08:15 PM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Covariance and correlation coefficient I vaguely thought the correlation coefficient should be 0 < r ? 1, but I wasn't gonna question you, when I wasn't sure.
 November 23rd, 2010, 08:27 PM #5 Newbie   Joined: Nov 2010 Posts: 11 Thanks: 0 Re: Covariance and correlation coefficient I'm not quite sure how you obtained 0.7071 for the correlation coefficient. Am I missing something here? The rest of the problem looks great.
November 23rd, 2010, 08:42 PM   #6
Senior Member

Joined: Oct 2010
From: Changchun, China

Posts: 492
Thanks: 14

Re: Covariance and correlation coefficient

Quote:
 Originally Posted by knp I'm not quite sure how you obtained 0.7071 for the correlation coefficient. Am I missing something here? The rest of the problem looks great.
the standard deviation $\sigma_{\small{X}}=\sqrt{D(X)}$, this is from my text book

November 23rd, 2010, 09:20 PM   #7
Senior Member

Joined: Oct 2010
From: Changchun, China

Posts: 492
Thanks: 14

Re: Covariance and correlation coefficient

Quote:
 Originally Posted by MarkFL I vaguely thought the correlation coefficient should be 0 < r ? 1, but I wasn't gonna question you, when I wasn't sure.

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post honeysyd Advanced Statistics 3 January 9th, 2014 06:23 PM playthious Advanced Statistics 0 December 1st, 2011 07:37 PM matmul Advanced Statistics 1 October 24th, 2011 08:11 AM daivinhtran Algebra 4 May 14th, 2011 12:35 PM goldgrill Advanced Statistics 0 December 3rd, 2007 11:22 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top


text:
# Crate lazy_regex[−][src]

Expand description

Use the regex! macro to build regexes:

• they’re checked at compile time
• they’re wrapped in once_cell lazy static initializers so that they’re compiled only once
• they can hold flags as suffix: let case_insensitive_regex = regex!("ab*"i);
• regex creation is less verbose

This macro returns references to normal instances of regex::Regex so all the usual features are available.

You may also use shortcut macros for testing a match, replacing with concise closures, or capturing groups as substrings in some common situations:

Some structs of the regex crate are reexported to ease dependency managment.

## Build Regexes

use lazy_regex::regex;

// build a simple regex
let r = regex!("sa+$"); assert_eq!(r.is_match("Saa"), false); // build a regex with flag(s) let r = regex!("sa+$"i);
assert_eq!(r.is_match("Saa"), true);

// you can use a raw literal
let r = regex!(r#"^"+$"#); assert_eq!(r.is_match("\"\""), true); // or a raw literal with flag(s) let r = regex!(r#"^\s*("[a-t]*"\s*)+$"#i);
assert_eq!(r.is_match(r#" "Aristote" "Platon" "#), true);

// there's no problem using the multiline definition syntax
let r = regex!(r#"(?x)
(?P<name>\w+)
-
(?P<version>[0-9.]+)
"#);
assert_eq!(r.find("This is lazy_regex-2.2!").unwrap().as_str(), "lazy_regex-2.2");
// (look at the regex_captures! macro to easily extract the groups)

// this line wouldn't compile because the regex is invalid:
// let r = regex!("(unclosed");

Supported regex flags: i, m, s, x, U.

## Test a match

use lazy_regex::regex_is_match;

let b = regex_is_match!("[ab]+", "car");
assert_eq!(b, true);

doc: regex_is_match!

## Extract a value

use lazy_regex::regex_find;

let f_word = regex_find!(r#"\bf\w+\b"#, "The fox jumps.");
assert_eq!(f_word, Some("fox"));

doc: regex_find!

## Capture

use lazy_regex::regex_captures;

let (_, letter) = regex_captures!("([a-z])[0-9]+"i, "form A42").unwrap();
assert_eq!(letter, "A");

let (whole, name, version) = regex_captures!(
r#"(\w+)-([0-9.]+)"#, // a literal regex
"This is lazy_regex-2.0!", // any expression
).unwrap();
assert_eq!(whole, "lazy_regex-2.0");
assert_eq!(name, "lazy_regex");
assert_eq!(version, "2.0");

There’s no limit to the size of the tuple. It’s checked at compile time to ensure you have the right number of capturing groups.

You receive "" for optional groups with no value.

doc: regex_captures!

## Replace with captured groups

use lazy_regex::regex_replace_all;

let text = "Foo8 fuu3";
let text = regex_replace_all!(
r#"\bf(\w+)(\d)"#i,
text,
|_, name, digit| format!("F<{}>{}", name, digit),
);
assert_eq!(text, "F<oo>8 F<uu>3");

The number of arguments given to the closure is checked at compilation time to match the number of groups in the regular expression.

## Shared lazy static

When a regular expression is used in several functions, you sometimes don’t want to repeat it but have a shared static instance.

The regex! macro, while being backed by a lazy static regex, returns a reference.

If you want to have a shared lazy static regex, use the lazy_regex! macro:

use lazy_regex::*;

pub static GLOBAL_REX: Lazy<Regex> = lazy_regex!("^ab+\$"i);

Like for the other macros, the regex is static, checked at compile time, and lazily built at first use.

doc: lazy_regex!

## Macros

Return an instance of once_cell::sync::Lazy<regex::Regex> that you can use in a public static declaration.

Return a lazy static Regex checked at compilation time and built at first use.

Extract captured groups as a tuple of &str.

Extract the leftmost match of the regex in the second argument, as a &str

Test whether an expression matches a lazy static regular expression (the regex is checked at compile time)

Replaces the leftmost match in the second argument with the value returned by the closure given as third argument.

Replaces all non-overlapping matches in the second argument with the value returned by the closure given as third argument.

## Structs

Captures represents a group of captured strings for a single match.

A value which is initialized on the first access.

A compiled regular expression for matching Unicode strings.

A configurable builder for a regular expression.