text: National Oceanic and Atmospheric Administration There is a lot of water for photosynthesis production. The earth-atmosphere energy balance is the balance between incoming energy from the Sun and outgoing energy from the Earth. Light-colored objects and surfaces, like snow and clouds, tend to reflect most sunlight, while darker objects and surfaces, like the ocean, forests, or soil, tend to absorb more sunlight. Reflection factors (r), absorption factors (a) and transmission factors (t) can be between 0 and 1 (0 -100%). 3b. Is the surface translucent or opaque? Absorption factor α The absorption factor is … A light yellow block and a dark blue box are next to each other in full sunlight on a summer day. Yes. The insolation (incoming solar energy) received on a daily basis depends primarily on 1) the angle of the Sun above the horizon (solar elevation angle, solar incidence angle), 2) the length of time the surface is exposed to the Sun, and 3) atmospheric conditions. Even if the earth were fully covered by clouds and they absorbed all the incident sunlight, that would only account for 3.7*10-5 %, or less than 4 parts in ten million. Click card to see definition Interesting that if you don’t use up that 10–30% as electricity, that becomes heat too. Remember that about 29 percent of incoming sunlight is reflected back to space by bright particles in the atmosphere or bright ground surfaces, which leaves about 71 percent to be absorbed by the atmosphere (23 percent) and the land (48 percent). A. Water selectively scatters and absorbs certain wavelengths of visible light. Sunlight, also called sunshine, solar radiation that is visible at Earth’s surface. What is the word equation for cellular respiration? Reflected solar radiation is the part of incident solar radiation reflected from the earth's surface due to the albedo effect. Of the sun’s energy that reaches Earth’s atmosphere, 30 percent is reflected back into outer space, 47 percent is absorbed by Earth’s surface and converted into heat energy, 23 percent drives the hydrological (water) cycle, less than one percent creates winds and ocean currents, and only 0.03 percent is captured by plants and used in photosynthesis. We can indirectly see this energy radiate into the atmosphere as heat, rising from a hot road, creating shimmers on hot sunny days. The nineteen percent of the sun's energy that is absorbed by the atmosphere helps to warm the air. It is to converted light C. It is reflected back to the sun <---D. It is converted to electricity 3. clouds. For photosynthesis, plants use approximately 0.023 percent of sunlight energy. What percentage of the light incident on the surface is transmitted? All objects reflect some insolation, and the percentage of insolation that is reflected by an object is termed its albedo. Through calculations determining the solar energy to the Earth , it can be concluded that the average value for the amount of energy absorbed by the Earth is approximately $238 \frac{\textrm{W}}{\textrm{m}^2}$ . This is a very small percentage that plants need to make food when compared to the water cycle’s use of solar energy, which is 23 percent. What is the word equation for the process of photosynthesis? The warmth of the air helps keep the surface of the earth warm. Take water, for instance. One way to harness that energy lies in understanding how materials absorb and reflect sunlight, then selecting for the job those materials that are most efficient and cost-effective. If the photosynthetic production is limited, the dissolved oxygen level in the water will decrease 13. A 0% albedo would mean none of the solar radiation is reflection and thus all … The more particles present in the water, the less photosynthetically active radiation that will be received by plants and phytoplankton. absorbed by Earth's surface and converted into heat energy, 23 percent drives the hydrological (water) cycle, less. The earth-atmosphere energy balance is the balance between incoming energy from the Sun and outgoing energy from the Earth. In other words, about 30 percent of incoming solar radiation is reflected back into space and 70 percent is absorbed. Material: Albedo: snow. Longwave radiation from the atmosphere into space. 2) the angle at which the ray of light strikes the surface. A substance with a high albedo will reflect a high percentage of the solar radiation striking it. What percentage of the energy stored as biomass in plants is transferred, on average, to the next trophic level of the food chain? The sum of the three factor is always 1. Click the red dots to see examples of land … Earth’s heat engine does more than simply move heat from one part of the surface to another; it also moves heat from the Earth’s surface and lower atmosphere back to space. … We can indirectly see this energy radiate into the atmosphere as heat, rising from a hot road, … What is meant by the term 'gross primary productivity'? ... Only about 8 percent of light falling perpendicularly on a sheet of glass is reflected (half of this from the rear surface), but at large angles of incidence almost all the incoming light is reflected at the front surface. When sunlight hits water, not all of it penetrates the surface, and the deeper you go the larger percentage of light that has been deflected, reflected, or absorbed. Yes. According to the second law of thermodynamics, the biomass stored in plants cannot all be used to feed other organisms. The albedo of a body is crucial for the percentage of absorbed sunlight. Chemical makeup of the substance. 2. Estuaries, swamps and marshes, tropical rain forests, and temperate rain forests. It measures the degree of reflection of materials in different spectral ranges. GPP in these areas differ due to the climate (cold/dry in the west versus wet/warm in the southeast). What causes this loss of solar energy? This is the reason why we are sweating more wearing a black shirt in summer. There is not enough water for photosynthesis. Longwave radiation from clouds into space. In the absence of clouds, absorption happens mainly at the surface. This flow of incoming and outgoing energy is Earth’s energy budget. (write only number) * - 16814204 US Dept of Commerce The open ocean and tropical/temperate rain forests. Use arrows to show energy flow. Sea ice has a bright surface; 80 percent of the sunlight that strikes it is reflected back into space. The force exerted on 1 m 2 surface area will be close to? Depending on molecular makeup, some substances, like coal, absorb light; others, like glass, transmit it. https://quizlet.com/330558861/primary-productivity-apes-flash-cards Of the sun's energy that reaches Earth's atmosphere, 30. percent is reflected back into outer space, 47 percent is. See … 1) the color of the substance. This animation shows a molecule of CO 2 absorbing an incoming infrared photon (yellow arrows). The other 70% of the radiation is absorbed. Of the 340 watts per square meter of solar energy that falls on the Earth, 29% is reflected back into space, primarily by clouds, but also by other bright surfaces and the atmosphere itself. Earth's surface is heated by energy from the Sun. … For the energy budget at Earth’s surface to balance, processes on the ground must get rid of the 48 percent of incoming solar energy that the ocean and land surfaces … Most albedos are sensitive to the angle at which sunlight strikes the surface. The amount that is reflected or absorbed depends on Earth’s surface and atmosphere. The earth-atmosphere energy balance is achieved as the energy received from the Sun balances the energy lost by the Earth back into space. How much percentage of energy is absorbed by plants from the sun? clouds. 5 0 W / m 2 energy density of sunlight is normally incident on the surface of a solar panel. The energy from the photon causes the CO 2 molecule to vibrate. The table below lists values of albedo for different materials in the visible range of light. Bright white clouds are responsible for reflecting a lot of sunlight back into space before it ever reaches Earth's surface. Absorptivity of a solar cell is about 90%, so around 10% of sunlight is reflected off. When sunlight hits water, not all of it penetrates the surface, and the deeper you go the larger percentage of light that has been deflected, reflected, or absorbed. It is expressed as a percentage of reflected insolation to incoming insolation and zero percent is total absorption while 100% is the total reflection. Not all gas molecules are able to absorb IR radiation. was reflected to space, 13 percent was absorbed by the atmosphere and clouds, and the remaining 47 percent was absorbed at the earth's surface. In your opinion, is the surface receiving the light or dark in color? (c = 3 × 1 0 8 m / s) That which penetrates the water’s surface is attenuated by absorption and conversion to other forms of energy, such as heat that warms or evaporates water, or is used by plants to fuel photosynthesis. The albedo is the reflection coefficient c. Values for c are generally between 0 and 1 or expressed as a percentage. Heat required by the processes of evaporation and sublimation and therefore removed from the surface. Which of the following is best at reflecting sunlight back into space? The observed increase in solar radiation absorbed in the Arctic since 2000 aligns with the steady decrease in Arctic sea ice during the same period. By contrast, the average surface temperature of the Earth is 59°F (15°C). Energy absorption by the atmosphere stores more energy near its surface than it would if there was no atmosphere. The reflected radiation simply bounces off of Earth's atmosphere and is re-emitted into space. Reflected Solar Radiation. What is the relationship between net primary productivity and gross product productivity? Whether light is absorbed, reflected or transmitted by a substance depends on . This loss of sunlight decreases the rate of photosynthesis. What percent of the sunlight is reflected and/or absorbed? Condensation /Deposition of water vapor (heat is released into the atmosphere by process). Approximately 30% is reflected back to space while the rest is absorbed by clouds, oceans and land masses. Absorbed longwave radiation from earth's surface. Materials That Absorb & Reflect Solar Energy. Absorbed shortwave radiation by gases in the atmosphere. In this investigation, however, we'll focus only on sunlight that actually reaches the surface, and on how that solar energy is reflected or absorbed by different types of land cover. Learning Lesson: Canned Heat. In other words, about 30 percent of incoming solar radiation is reflected back into space and 70 percent is absorbed. The principles of absorption can be transferred to daily life: A black t-shirt absorbs more sunlight than a white one. Of the sun’s energy that reaches Earth’s atmosphere, 30 percent is reflected back into outer space, 47 percent is absorbed by Earth’s surface and converted into heat energy, 23 percent drives the hydrological (water) cycle, less than one percent creates winds and ocean currents, and only 0.03 percent is captured by plants and used in photosynthesis. Overall, our planet reflects about 30% of the sunlight that strikes it. 60-90%. Please Contact Us. In general, when the angle of incidence of the solar energy is 90 ° the solar panel's absorptivity of the solar energy is about 90 % indicating that around 10 % of the sunlight is reflected. National Weather Service Visible sunlight makes up about 40 percent of the total energy Earth receives from the sun. Over the whole surface of the Earth, about 30 percent of incoming solar energy is reflected back to space. In terms of visible colors, darker colors have a lower albedo, that is, they absorb more insolation, and lighter colors have a … glucose + oxygen → carbon dioxide + water + the sun's energy. Some places on Earth receive more than 4,000 hours per year of sunlight (more than 90 percent of the maximum possible), as in the Sahara; others receive less than 2,000 hours, as in regions of frequent storminess, such as Scotland and Iceland. A sensor aboard NASA’s Terra satellite is now collecting detailed measurements of how much sunlight the … Absorbed shortwave radiation from the sun. After a silicon surface was treated with Lin's new nanoengineered reflective coating, however, the material absorbed 96.21 percent of sunlight … Electromagnetic radiationis made up of electromagnetic waves that are defined by their wavelength and frequency. It absorbs frequencies of sunlight except those that make your eyes see the yellow color. When sunlight reaches Earth, it can be reflected or absorbed. The climate is too cold for photosynthesizing plants to live. Light from a chromatic light source strikes a surface. Greenhouse warming is enhanced during nights when the sky is overcast. Transparent, translucent and … Overall, our planet reflects about 30% of the sunlight that strikes it. This huge gain in absorption was consistent across the entire spectrum of sunlight, from UV to visible light and infrared, and moves solar power a … a. Through the photosynthesis process, sunlight is used to convert carbon dioxide and water into a carbohydrate (glucose) and oxygen. Sunlight that is not absorbed can be scattered by molecules and particulates suspended in the water. Albedo varies from 0% for a theoretical black object that reflects no light to 100% for a perfectly white, smooth one; no common objects have these end-member values. The 0.03 percent of the sun’s energy captured by plants … 3) the chemical makeup of the substance. Tundras, the open ocean, desert scrubs, and the extreme desert. of EECS Energy is Conserved Thus, the power absorbed by the load (i.e., the power delivered to the load) is simply: P abs P inc P ref or, rearranging, we find: P inc P abs P ref This equation is simply an expression of the conservation of energy The rest of the energy Earth receives from the sun is not visible. A sensor aboard NASA’s Terra satellite is now collecting detailed measurements of how much sunlight the earth’s surface reflects back up into the atmosphere. What is the 10-meter … See Section 1.3. What also happens to this heat energy? Draw a food web, including two primary producers, three primary consumers, two secondary consumers, two decomposers, and respiration energy loss. 50%. The numbers in this article rely most heavily on direct satellite observations of reflected sunlight and thermal infrared energy radiated by the atmosphere and the surface. … What percentage of the Sun's energy does Earth's surface absorb directly or indirectly? Light Spectrum. Of the sun's energy that reaches Earth's atmosphere, 30. percent is reflected back into outer space, 47 percent is. Reflected Solar Radiation. When the Sun is at an angle of 40° or higher, the albedo of water is fairly constant (around 0.06), but as the sun goes down, the albedo increases dramatically, so at 10° it is about 0.5, and between 0.9 and 1.0 at sunset or sunrise. The transmitted or reflected radiation can be regular (1), scattered (2) or completely diffuse (3). Albedo varies from 0% for a theoretical black object that reflects no light to 100% for a perfectly white, smooth one; no common objects have these end-member values. What percentage of the Sun's energy is scattered or reflected back into space? For example, nitrogen (N 2) and oxygen (O 2), which make up more than 90% of Earth's atmosphere, do not absorb infrared photons. It is refracted back to the sun B. CO 2 molecules can vibrate in ways that simpler nitrogen and oxygen molecules cannot, which allows CO 2 … If Earth was completely covered in ice, its albedo would be about 0.84, meaning it would reflect most (84 percent) of the sunlight that hit it. Under partly cloudy skies, some heat is allowed to escape and some remains trapped. In terms of visible colors, darker colors have a lower albedo, that is, they absorb more insolation, and lighter colors have a "high albedo," or higher rates of reflection. Most albedos are sensitive to the angle at which sunlight strikes the surface. 1/27/2012 Incident Reflected and Absorbed Power present 6/12 Jim Stiles The Univ. Color of the substance. Energy released from the Sun is emitted as shortwave light and ultraviolet energy. Longwave radiation emitted to space by clouds. The amount of sunlight is dependent on the extent of the daytime cloud cover. However, since the Earth is much cooler than the Sun, its radiating energy is much weaker (long wavelength) infrared energy. The balance between the incoming sunlight to that directly reflected … Write the equation. A 100% albedo (highest albedo possible) would be all the solar radiation being reflected away. This ability to absorb and re-emit infrared energy is what makes CO 2 an effective heat-trapping greenhouse gas. The spectrum of solar light at the Earth's surface is mostly spread across the visible and near-infrared ranges with a small part in the near-ultraviolet. absorbed by Earth's surface and converted into heat energy, 23 percent drives the hydrological (water) cycle, less. After a silicon surface was treated with Lin’s new nanoengineered reflective coating, however, the material absorbed 96.21 percent of sunlight shone upon it — meaning that only 3.79 percent of the sunlight was reflected and unharvested. The albedo is the reflection coefficient c. Values for c are generally between 0 and 1 or expressed as a percentage. The Moon's albedo is 0.136, meaning only 13.6% of incident sunlight is reflected from the lunar surface. The exact percentage of light that reaches a certain depth depends on several factors. Longwave radiation emitted by the surface. Despite low population density, the total volume near the surface allows for high production of photosynthesis. The Earth receives energy radiated from the sun; at noon on a sunny day, it amounts to 1,000 watts per square meter. 1.2K views From convective currents (rising air warms the atmosphere). Shortwave radiation reflected back to space by clouds. Take water, for instance. ... sunlight is absorbed by plants, through the chlorophyll which is found in the chloroplasts. The Earth's albedo is one of the main factors that determine the amount of sunlight absorbed into the climate system. What is the reflectance, absorptance, and transmittance values? About 50 percent is infrared energy, nine percent is ultraviolet (UV) energy, and one percent is X-rays or microwaves. about 30%; lost energy is scattered by the atmosphere, reflected from clouds and Earth's surfaces. For photosynthesis, plants use approximately 0.023 percent of sunlight energy. Heat energy from the earth can be trapped by clouds leading to higher temperatures as compared to nights with clear skies. Some of the Sun’s radiant energy is reflected at the ocean surface and does not enter the ocean. This heating effect is called the greenhouse effect. —Light colors reflect light back into space, while dark colors absorb heat, warming the Earth. 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text:
# Math Help - Homomorphisms and Factor Rings

1. ## Homomorphisms and Factor Rings

Let R and R' be rings and let N and N' be ideals of R and R' respectively.

Let $\phi$ be a homomorphism of R into R'.

Show that $\phi$ induces a natural homomorphism $\phi_* : R/N \rightarrow R'/N'$ if $\ \ \phi [N] \subseteq N'$

2. ## Re: Homomorphisms and Factor Rings

well, what do we have to work with?

we are given the homomorphism φ:R-->R', the ideal N of R and the ideal N' of R', and that φ(N) is a subset of N'.

so the natural thing to do is define: φ*(r+N) = φ(r)+N'.

whenEVER you define things on cosets, it is imperative that you verify that the definition depends ONLY on the coset r+N, and not on "r".

so we must check that if r'+N = r+N, that φ*(r+N) = φ*(r'+N).

if r+N = r'+N, this means r-r' is in N. since φ maps N inside N', φ(r-r') is in N'. since φ is a homomorphism, φ(r-r') = φ(r)-φ(r').

so we have φ(r)-φ(r') is in N', hence φ(r)+N' = φ(r')+N', that is: φ*(r+N) = φ*(r'+N), as desired.

now all that is left to do is verify that φ* is a ring homomorphism. you can do this.

3. ## Re: Homomorphisms and Factor Rings

Thanks Deveno ... appreciate your help.

WIll now work through the post

Peter

format: plain


text:
## How do you specify the entry file?

General discussion about LÖVE, Lua, game development, puns, and unicorns.
NetherGranite
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Posts: 30
Joined: Wed Jul 11, 2018 11:08 pm

### How do you specify the entry file?

How does one go about telling love2d to use a different file than main.lua? Please do not tell me to use states; I am looking to make two separate applications that use the same set of libraries. Currently I am syncing all of my libraries using git subtrees, but it is a very painful process.

Ulydev
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### Re: How do you specify the entry file?

LÖVE automatically reads a main.lua file at the root, but nothing prevents you from require-ing any other file from there. You could go for an architecture like this:

/
main.lua
lib/
app1/
main.lua
app2/
main.lua

and then require your libraries from the main.lua of each app. just my 2 cents

pgimeno
Party member
Posts: 2479
Joined: Sun Oct 18, 2015 2:58 pm

### Re: How do you specify the entry file?

Or zip them into different .love files. For example:

application1.love - contains main.lua for application1
application2.love - contains main.lua for application2

zorg
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### Re: How do you specify the entry file?

Besides, you'd usually have the libraries NOT have their entrypoints called main.lua, since, you know, they're libraries? After that, i personally would just zip download the libs and hard-include them into my projects, instead of messing around with the nightmarish git subtrees stuff... people might disagree with me on this though
Me and my stuff True Neutral Aspirant. Why, yes, i do indeed enjoy sarcastically correcting others when they make the most blatant of spelling mistakes. No bullying or trolling the innocent tho.

NetherGranite
Prole
Posts: 30
Joined: Wed Jul 11, 2018 11:08 pm

### Re: How do you specify the entry file?

Ulydev wrote:
Fri Aug 24, 2018 12:07 pm
LÖVE automatically reads a main.lua file at the root, but nothing prevents you from require-ing any other file from there.
Unfortunately, I am looking to create two applications that can operate independently of each other. This approach would result in only a single window that can only switch between the two. Maybe a good solution is to take this approach and then inform the user that they may open multiple instances of this application.
pgimeno wrote:
Fri Aug 24, 2018 1:50 pm
Or zip them into different .love files. For example:

application1.love - contains main.lua for application1
application2.love - contains main.lua for application2
That is actually a really good idea. If I cannot find a better solution, I will adopt a workflow that supports this. The only downside is that the end user will have two copies of the libraries shared between the applications, but the libraries in mine are not too big.
zorg wrote:
Fri Aug 24, 2018 3:45 pm
Besides, you'd usually have the libraries NOT have their entrypoints called main.lua, since, you know, they're libraries? After that, i personally would just zip download the libs and hard-include them into my projects, instead of messing around with the nightmarish git subtrees stuff... people might disagree with me on this though
Sorry, I think you misunderstood me because I was not clear. I was talking about the entry points of applications, not libraries. I only brought up the libraries to explain why I wanted to be able to specify the entry point of applications.

pgimeno
Party member
Posts: 2479
Joined: Sun Oct 18, 2015 2:58 pm

### Re: How do you specify the entry file?

I have a folder with several Lua files, and I have a main.lua like this:

Code: Select all

local f = arg[2]:gsub('%.lua\$','')
table.remove(arg, 2)
require(f)

Then I run: love . filename.lua

Maybe it helps?

zorg
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### Re: How do you specify the entry file?

NetherGranite wrote:
Sat Aug 25, 2018 3:32 am
Unfortunately, I am looking to create two applications that can operate independently of each other.
...
That is actually a really good idea. If I cannot find a better solution, I will adopt a workflow that supports this. The only downside is that the end user will have two copies of the libraries shared between the applications, but the libraries in mine are not too big.
...
Sorry, I think you misunderstood me because I was not clear. I was talking about the entry points of applications, not libraries. I only brought up the libraries to explain why I wanted to be able to specify the entry point of applications.
Let me elaborate; i wanted to highlight that it's the same thing. I myself usually hate the fact how i have about 20 versions of the visual C redistributable packages installed on my computer because that piece of shit library is included in tons of games and even non-game applications, and each of them need a slightly different version. (I'd be less salty if there'd be a way for it to function like in linux, having one C runtime actually kinda baked into the OS itself, and everything relying on that... to my knowledge anyway)

In contrast to those 500MB+ compiled binaries, lua project libraries really don't have that big of a footprint for you to need to only have them in one place, and not allow yourself the luxury of using separate project directories with main.lua-s in them for separate projects.

If you're really space-conscious, then just symlink in the library folders into both project folders; that can work on windows too, and similar solutions exist on OSX and unix/linux systems. When it comes to versioning though, care not whether git or whatever you use actually pulls the files and uploads them or indexes them; that shouldn't worry you.
Me and my stuff True Neutral Aspirant. Why, yes, i do indeed enjoy sarcastically correcting others when they make the most blatant of spelling mistakes. No bullying or trolling the innocent tho.

bobbyjones
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### Re: How do you specify the entry file?

Edit 2: What i was recommending would have used luasocket to download a core libs folder from whatever website hosts the source. I was going to use github as my source in my example but the lack of ssl support in love2d would have made that impossible. Even if I did find a website that allowed the downloading of files through http it wouldn't really be secure anyways.
Do you frequently have great ideas but immediately lose them? Check out the MVP for my website called IdeaVault. It is designed to solve that problem. Desktop browsers only currently.

NetherGranite
Prole
Posts: 30
Joined: Wed Jul 11, 2018 11:08 pm

### Re: How do you specify the entry file?

bobbyjones wrote:
Mon Aug 27, 2018 2:37 am
If the goal is to just share libraries you could write a loading screen that downloads "NetherGraniteUtils" from a website into a save directory when the identity is set to "NetherGraniteUtils" this will create a folder in the save location called NetherGraniteUtils that all of your games can reference. As long as they set their identity to "NetherGraniteUtils".
That is actually very interesting idea, thanks for taking the time to explain it.

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# What variables do I have to take into consideration when I homebrew armour?

The variables that are clear to me are shown in the Armor-table (PHB 145):

1. Type of armour: Light, Medium, Heavy (also limits Dex mods).
2. Cost, commonly displayed in GP.
3. Armour Class.
4. Strength prerequisite.
5. State of disadvantage on Stealth checks.
6. Weight.

A description of the armour is also necessary. Considerations of which classes have access to the armour types seems necessary. Considerations of worldbuilding implications seem optional. Considerations of the feats that grant access to armours and improve the efficiency of armours (PHB 167-168) appears necessary.

Have I missed any important variables, such as specific class feature interactions with armour?

# What I'm going to do with this:

I will homebrew (a) mundane armour, replacing those listed on the PHB's armor-table, which will then later translate to (b) magic armours that have an existing type of mundane armour as their base type. While I'm most interested in mundane armour, I'm also interested in other properties. The focus here is variables to consider before the process of brewing.

I'm solely interested in variables from the RAW. I'm currently unhappy with the flavour of armours and some of the balancing. I'm not trying to homebrew how armours function as a system. So to restructure that system, I require your expertise in analysing that system and its components to keep it functioning without breaking it by not considering variables that are integral to that system.

## What I'm looking for in your answers:

A variable described (in one sentence), then a brief explanation about why this variable is to be considered for home-brewing armour, followed by the next variable until the finite number of variables is exhausted. The best answer is the one that is most comprehensive, exhaustive and correct (RAW).

This is an example of a good answer that is further improved by its comments which I paraphrase:

The material of the armour is significant because there are classes that restrict wearing specific materials and spells that affect specific materials and creatures which have abilities that affect the material.

• Past comments asking for clarity on the question have been moved to chat. – V2Blast Jun 15 at 18:21

## The most important thing to consider is maximum attainable AC.

There is a clear hierarchy in the standard armor sets in the PHB. Heavy armor grants the best potential AC, while Medium and Light armor provide less but roughly equal AC, albeith with light armor requiring much higher dexterity to accomplish said maximum. Plate grants 18 AC versus 17 AC from both half plate (15+2) and studded leather (12+5).

Low level armor follows a similar pattern, albeit with medium armor performing a bit better. Chain mail provides 16, as does scale mail (14+2), while studded leather provides 15 AC(12+3) with the maximum starting dexterity of 16.

In general, no armor should allow for a higher maximum AC than the three top-tier armors of each category. An exception could be made for armor with a significant drawback, or armor only usable with a specific class feature or feat, in which case the bonus AC should be considered a part of that feature.

The reason this maximum is so important is the bounded AC of 5th edition. Getting even +1 AC is a very rare thing, and AC becomes exponentially more powerful the higher your AC already is. For example, say you have a high level Paladin, who has taken the defense fighting style, adamantine plate armor, a +3 shield, constantly uses Shield of Faith, and through whatever means (feat or 1 class level) also has access to the Shield spell. All told, they have a base AC of 24, an enhanced AC of 26, and a emergency AC of 31.

If you allowed that player to get an extra +1 AC on top of all of that, you might think, "Well, there's only a 5% chance each time they're attacked the AC will even matter, so it's not a big bonus." However, that's not how the math actually works out.

Let's say for example an balor tries to attack this paladin. At this level the paladin probably has plenty of low level spell slots to burn on this kind of thing, so we'll use 31 AC as the target. The balor has +14 to hit, which means they need to roll a 17 to hit through the shield spell. In other words, in 16 out of 20 cases, the balor does 0 damage. In the other four cases (17-20) it does normal damage (no crits due to adamantine). On average, that means the balor does 4/20 = 20% of it's attack damage per attack.

Now lets say the paladin is able to buy some fancy form of armor that grants an extra point of AC over plate. Now their AC with everything is 32, and the balor needs to roll a 18 to hit, and our formula changes to: 3/20 = 15% of it's attack damage per attack. That 5% smaller chance to be hit actually translates into 25% less damage taken overall. If they could somehow squeeze out an extra +1 AC on top of that, 2/20 = 10% attack damage, or half as much damage taken compared to when they had just 2 AC less.

# Whether it is made of metal

Armor: Light armor, medium armor, shields (druids will not wear armor [....] made of metal) - PHB p65

• Druids also care a lot about whether their opponent's armor is made of metal, because of their Heat Metal spell. – Ryan Thompson May 23 at 0:57
• @RyanThompson their AC comes up much more often than a mediocre spell. – András May 23 at 9:40
• There are also some creatures with special abilities (and a spell) that work better on a target wearing metal armor. Gray Ooze, Lava Child, Rust Monster, and the spell Shocking Grasp among others. – guildsbounty May 23 at 16:51

# Magical Effects or Special Properties

One of the major things to consider are any magical effects or special properties the item possesses. Chapter 7 of the Dungeon Master’s Guide (DMG) focuses on treasure and rewards, including magical items.

Pages 141-143 detail special properties an item may possess. Whilst this section of the book is focusing on magical items, you as the DM could rule an item has one of these special properties but is not magical. For example, a helmet may have been designed for a cloud giant, making it too large for a medium sized creature to use. Plate armour that's not properly fitted may have the painful property. A shield may have an in-built compass or sundial.

# Size and Shape

Following up from that, the size and shape of a weapon or piece of armour may be something to consider. Pages 140 and 141 of the DMG state, under "Wearing or Wielding Items", that:

In most cases, a magic item that's meant to be worn can fit a creature regardless of size or build. Many magic garments are made to be easily adjustable, or the: magically adjust themselves to the wearer.

Rare exceptions exist. If the story suggests a good reason for an item to fit only creatures of a certain size or shape, you can rule that it doesn't adjust. For example, armor made by the drow might fit elves only. Dwarves might make item only useable by Dwarf-sized and dwarf-shaped characters.

When a nonhumanoid tries to wear an item, use your discretion as to whether the item functions as intended. A ring placed on a tentacle might work, but a yuan-ti with a snakelike tail instead of legs can't wear boots

Again, this is only considering magical items. A non-magical item will not will not magically adjust its size or shape (though an armour smith may be able to adjust the piece for you, for a fee). Below is a variant rule from page 144 of the Player’s Handbook which details how size may be important for armour:

### Variant: Equipment Sizes

In most campaigns, you can use or wear any equipment that you find on your adventures, within the bounds of common sense. For example, a burly half-orc won't fit in a halfling's leather armour, and a gnome would be swallowed up in a cloud giant's elegant robe.

The DM can impose more realism. For example, a suit of plate armour made for one human might not fit another one without significant alterations, and a guard's uniform might be visibly ill-fitting when an adventurer tries to wear it as a disguise.

Using this variant, when adventurers find armour, clothing. and similar items that are made to be worn, they might need to visit an armour smith, tailor, leatherworker, or similar expert to make the item wearable. The cost for such work varies from 10 to 40 percent of the market price of the item. The DM can either roll 1d4 x 10 or determine the increase in cost based on the extent of the alterations required.

# How It's Used

For armour, this seems fairly obvious, you wear it and gain the AC bonus. However, certain design features, told to the players when describing the armour, may warrant a special feature, as described above. For example, gauntlets with spikes on the knuckles may add +1 damage (piercing) to an unarmed strike.

A parrying dagger or sword breaker (it doesn’t actually break swords) may grant increased AC as they are used, mechanically speaking, like a shield. However, they would still have the 1d4 piercing damage a dagger does.

# Roleplaying Elements

Finally, whilst not a hard-and-fast rule, you could make your items more interesting by attaching roleplay elements to them.

For example, a fun idea could be to offer the player’s a normal shield with a yellow square painted in the centre, taking inspiration from Heraldry and Abatements. Whilst the yellow square does not offer any mechanical advantages or disadvantages, in history, a person with a big yellow blotch on their shield was easily identified as a coward. This could lead to some unique roleplaying opportunities, such as people mocking the owner of the shield. Or, wearing armour bearing alliance to an enemy army, a cult of necromancers or the Thieves Guild may cause guards of a city to attack or arrest you. It could also be done in reverse, giving the player’s the weapon or armour that an ancient hero once owned, again, allowing for unique roleplaying opportunities.

Based off the question, I could not really tell if you had implicitly covered this, but have you considered the rarity of the armor?

You listed the cost (in GP), which should pretty easily determine the rarity of the armor. I am pretty sure you are considering this, but how likely are the players to just come across this armor in a normal enemy encounter or in some slightly out of the way storage room?

Is this armor one-of-a-kind, a dime-a-dozen, or somewhere in between?

$$\\begin{array}{|l|c|c|r|} \hline \textbf{Rarity} & \textbf{Character Level} & \textbf{Bonus} & \textbf{Value} \\ \hline \text{Common} & \text{1st or higher} & – & 50–100\,\text{gp} \\ \text{Uncommon} & \text{1st or higher} & – & 101–500\,\text{gp} \\ \text{Rare} & \text{5th or higher} & +1 & 501–5,000\,\text{gp} \\ \text{Very rare} & \text{11th or higher} & +2 & 5,001–50,000\,\text{gp} \\ \text{Legendary} & \text{17th or higher} & +3 & 50,001+\,\text{gp} \\ \hline \end{array} \$$

With all the considerations you listed, I am sure you are already determining if the armor is balanced, but balance is definitely something that it seems a lot of people overlook until it is too late and a player breaks the game with some minor detail.

I hope this helps you as you create the armor!

• Welcome to rpg.se! Take the tour and visit the help center if you haven't already. This is a good answer, you could possibly improve it by cited some of the rules on rarity as well. Thanks for contributing and happy gaming! – linksassin May 22 at 5:17

## Which enchantments are valid on the armor.

Many magical items in the DMG call out specific types of armor that they might be found on. If you homebrew armor, you'll have to make decisions on which armor-types might be enchanted with which options.

For example, Mithral Armor requires (medium or heavy, but not hide), which is a fancy way of saying "primarily made of metal", but if your new armor type is a Medium armor made from plants, then it likely wouldn't qualify for this "enchantment", which really is more like a special material.

Another example, Demon Armor is a form of Plate armor, which means you won't be able to use the enchantment if you replace the existing armor types, unless you decide which new type(s) will be allowed to hold it.

Another thing to remember is how core armors are balanced.

If you include an type of light armor with an AC of 13 + Dexterity bonus as a step above studded leather (before enhancements), regardless of price tag, you have effectively rendered medium armor and the Medium Armor Master feat useless, because there is an intentional design reason that the best non-magical armor in 5e is 1 point weaker than mage armor.

That reason: to give Strength-based builds a defensive advantage over Dexterity-based ones ones to compensate for Dexterity's other defensive benefits. This supports Strength-based fighters and paladins, which in turn supports the trope of the plate-clad tank you see defending their allies from the front lines in most video games or fantasy fiction.

• I think you may be onto something here with regard to how feats interact - but the way you've stated it now involves a lot of supposition regarding design reasons that you haven't supported (and not sure you can). But focusing on making sure feats still interact appropriately may be helpful to OP> – NautArch May 22 at 16:43
• either way: the important part is to consider feat interactions and to consider the balance against other published armors. i made the mistake of accidentally slaughtering medium armor when i made Spidersilk. which was a light armor that provided an AC of 13 + Dexterity Bonus, had no Stealth Disadvantage, had no weight and Didn't require proficiency as a nonmagical Alternative to mage armor for Fey mages. it ended up being mostly used by Rogues and Rangers. – Umbrie Shadowsong May 24 at 2:03

At risk of missing what you're trying to accomplish, the Angry GM basically rewrote the entire armor table for one of his campaigns. It may have some of the insight you're looking for.

My own personal guidelines from trying to create a more satisfactory weapons table are this:

Use the given armors to try to establish base costs for each feature (this covers type, AC, cost, weight, stealth, Str reqs, etc). I.E., Light/medium/heavy armors should have a point budget of X, each point of AC above Y costs Z points, various features give +/-W points.

Don't sweat the edge cases too much. Perfect game balance in a complicated game like D&D is a myth; that's why Blizzard is always tweaking WoW and Overwatch.

• While the intent of the resource is entirely different from mine, it has excellent insight into the components that make the armour system. – Akixkisu May 23 at 22:26


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# 17. Analyzing inventories over three years. The following information relates to the activities...

17.   Analyzing inventories over three years. The following information relates to the activities of Funtime, Inc., a manufacturer of toys (amounts in millions of euros):

 2013 2012 2011 Sales. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . €5,970 €5,650 €5,179 Cost of Goods Sold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,193 3,038 2,806 Average Inventory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 380 415

a.   Compute the inventory turnover for each year.

b.   Compute the average number of days that inventories are held each year.

c.    Compute the cost of goods sold to sales percentage for each year.

d.   How well has Funtime managed its inventories over the three years?

 a. Calculation of inventory turnover ratio: Particulars 2013 2012 2011 Cost of goods sold(A) 3193 3038 2806 Average inventory(B) 406 380 415 Inventory turnover ratio(A/B) 7.86453202 7.994736842 6.761445783


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# Thread: Using series to evaluate integrals

1. ## Using series to evaluate integrals

Use series to approximate the integral from 0 to 1 of...

((e^x)-1)/x dx

Write out 4 terms but do not add them.

Any help would be GREATLY appreciated....

2. Originally Posted by TwentyBucks
Use series to approximate the integral from 0 to 1 of...

((e^x)-1)/x dx

Write out 4 terms but do not add them.

Any help would be GREATLY appreciated....
The integral you gave is not a good integral.
Because the function is not defined on [0,1]
That means we need to appeal to improper integrals.

You can write out e^x as 4 terms:

e^x = 1+x+x^2/2 + x^3/6

Then,

e^x - 1 = x+x^2/2 + x^3/6

Thus,

(e^x-1)/x = 1 + x/2 + x^2 / 6

Now this is a polynomial you can integrate this easily.

3. That's all I had to do? I thought I needed to find a series to represent the whole function...

Thanks so much for the help.

4. Originally Posted by TwentyBucks
That's all I had to do? I thought I needed to find a series to represent the whole function...

Thanks so much for the help.
the question said to do only the first 4 terms, so there was no need to find the series to represent the "whole" function


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2 deleted 6 characters in body

I guess you are considering normal singularities. In this case your statement follows from you can probably use [Kollar-Mori, Birational geometry of algebraic varieties, Corollary 5.21 p. 161]. For the reader's covenience, let me write the complete statement.

Proposition. Let $x \in X$ be a germ of a normal singularity.

(1) $x \in X$ is Kawamata Log Terminal if and only if it is a cyclic quotient of an index $1$ canonical singularity $0 \in Y$ by an action which is fixed point free in codimension $1$ (that is, $\textrm{Sing}(X)$ has codimension at least $2$).

(2) If $x \in X$ is terminal (resp. canonical) then it is a cyclic quotient of an index $1$ terminal (resp. canonical) singularity $0 \in Y$ by an action which is fixed point free in codimension $2$ (that is, $\textrm{Sing}(X)$ has codimension at least $3$).

1

I guess you are considering normal singularities. In this case your statement follows from [Kollar-Mori, Birational geometry of algebraic varieties, Corollary 5.21 p. 161]. For the reader's covenience, let me write the complete statement.

Proposition. Let $x \in X$ be a germ of a normal singularity.

(1) $x \in X$ is Kawamata Log Terminal if and only if it is a cyclic quotient of an index $1$ canonical singularity $0 \in Y$ by an action which is fixed point free in codimension $1$ (that is, $\textrm{Sing}(X)$ has codimension at least $2$).

(2) If $x \in X$ is terminal (resp. canonical) then it is a cyclic quotient of an index $1$ terminal (resp. canonical) singularity $0 \in Y$ by an action which is fixed point free in codimension $2$ (that is, $\textrm{Sing}(X)$ has codimension at least $3$).


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# Don’t Photoshop it…MATLAB it! Image Effects with MATLAB (Part 2)

I'd like to welcome back guest blogger Brett Shoelson for the continuation of his series of posts on implementing image special effects in MATLAB. Brett, a contributor for the File Exchange Pick of the Week blog, has been doing image processing with MATLAB for almost 20 years now.

### Contents

#### imadjust as an Image Enhancement Tool

In my previous post in this guest series, I introduced my image adjustment GUI, and used it to enhance colors in modified versions of images of a mandrill and of two zebras. For both of those images, I operated on all colorplanes uniformly; i.e., whatever I did to the red plane, I also did to green and blue. The calling syntax for imadjust is as follows:

imgOut = imadjust(imgIn,[low_in; high_in],[low_out; high_out],gamma);

The default inputs are:

imgOut = imadjust(imgIn,[0; 1],[0; 1],1);

Different input parameters will produce different effects. In fact, imadjust should often be the starting point for simply correcting illumination issues with an image:

URL = 'https://blogs.mathworks.com/pick/files/DrinkingZebra1.jpg';
enhanced = imadjust(img,[0.00; 0.35],[0.00; 1.00], 1.00);
subplot(1,2,1);imshow(img);title('Original');

You may recall that when I modified the image of two zebras in my previous post, I not only increased low_out, but I also reversed (and tweaked) the values for low_out and high_out:

imgEnhanced = imadjust(imgEnhanced,[0.30; 0.85],[0.90; 0.00], 0.90);

In reversing those input values, I effectively reversed the image. In fact, for a grayscale image, calling

imgOut = imadjust(imgIn,[0; 1],[1; 0],1); % Note the reversal of low_out and high_out

is equivalent to calling imgOut = imcomplement(imgIn):

img = imread('cameraman.tif');
img1 = imadjust(img,[0.00; 1.00],[1.00; 0.00], 1.00);
img2 = imcomplement(img);
assert(isequal(img1,img2))% No error is thrown!
figure;subplot(1,2,1);imshow(img);xlabel('Original image courtesy MIT');
subplot(1,2,2);imshow(img1);

Now recognize that ImadjustGUI calls imadjust behind the scenes, using the standard syntax. If you read the documentation for imadjust carefully, you will learn that the parameter inputs low_in, high_in, low_out, high_out, and gamma need not be scalars. In fact, if those parameters are specifed appropriately as 1-by-3 vectors, then imadjust operates separately on the red, green, and blue colorplanes:

newmap = imadjust(map,[low_in; high_in],[low_out; high_out],gamma)
% ...transforms the colormap associated with an indexed image.
% If low_in, high_in, low_out, high_out, and gamma are scalars, then the
% same mapping applies to red, green, and blue components.
%
% Unique mappings for each color component are possible when low_in and
% high_in are both 1-by-3 vectors, low_out and high_out are both 1-by-3 vectors,
% or gamma is a 1-by-3 vector.

That works for adjusting colormaps; it also works for adjusting images. As a result, you can readily reverse individual colorplanes of an input RGB image, and in doing, create some cool effects!

#### Andy Warhol Meets an Elephant

Andy Warhol famously created iconic images of Marilyn Monroe and other celebrities, casting them in startling, unexpected colors, and sometimes tiling them to create memorable effects. We can easily produce similar effects by reversing and saturating individual colorplanes of RGB images. (I wrote ImadjustGUI to facilitate, interactively, those plane-by-plane intensity adjustments.)

#### Reading and Pre-Processing the Elephant

First, of course, we read and display the elephant:

URL = 'https://blogs.mathworks.com/pick/files/ElephantProfile.jpg';
img = imread(URL);

He's a wrinkly old fellow (below left). I'd like to bring out those wrinkles by enhancing contrast in the image. There are a few ways to do that, but I learned about my favorite way by reading through the "Gray-Scale Morphology" section of DIPUM, 2nd Ed. Specifically, the authors of this (most excellent) book indicated (on page 529) that one could combine topat and bottomhat filters to enhance contrast. (I built the appropriate combination of those filters behind the "Contrast Enhancement" button of MorphTool.) So, using MorphTool-generated code:

SE = strel('Disk',18);

Now, operating with imadjust plane by plane, reversing the red and blue planes, and modifying the gamma mapping, I can easily find my way to several interesting effects. For instance:

imgEnhanced1 = imadjust(imgEnhanced,[0.00 0.00 0.00; 1.00 0.38 0.40],[1.00 0.00 0.70; 0.20 1.00 0.40], [4.90 4.00 1.70]);
imgEnhanced2 = imadjust(imgEnhanced,[0.13 0.00 0.30; 0.75 1.00 1.00],[0.00 1.00 0.50; 1.00 0.00 0.27], [5.90 0.80 4.10]);

So, two more of those interesting effects, and then we can compose the four-elephants image above:

imgEnhanced3 = imadjust(img,[0.20 0.00 0.09; 0.83 1.00 0.52],[0.00 0.00 1.00; 1.00 1.00 0.00], [1.10 2.70 1.00]);
imgEnhanced4 = imadjust(img,[0.20 0.00 0.00; 0.70 1.00 1.00],[1.00 0.90 0.00; 0.00 0.90 1.00], [1.30 1.00 1.00]);

I also wanted to flip two of those enhanced images. fliplr makes it easy to flip a 2-dimensional matrix, but it doesn't work on RGB images. So I flipped them plane-by-plane, and concatenated cat the flipped planes in the third ( z -) dimensioninto new RGB images:

r = fliplr(imgEnhanced2(:,:,1));
g = fliplr(imgEnhanced2(:,:,2));
b = fliplr(imgEnhanced2(:,:,3));
imgEnhanced2 = cat(3,r,g,b);
CompositeImage = [imgEnhanced1 imgEnhanced2; imgEnhanced3 imgEnhanced4]; % (Images 2 and 4 are flipped plane-by-plane.)

#### Next Up: Put Me In the Zoo!

All images except "cameraman" copyright Brett Shoelson; used with permission.

Published with MATLAB® R2012b

|


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# Is there a term for an algebraic structure with two binary operators that are closed under a set?

For example, let's say we're using the operators +, and *, and the set {0,1,2}

The Cayley tables look like this:

* 0 1 2    + 0 1 2
0 0 0 1    0 1 2 0
1 1 2 1    1 0 1 0
2 0 0 2    2 1 2 2

These Cayley tables are totally random, but the point is that the algebraic structure isn't necessarily like any other common type of algebraic structure with two binary operators (e.a. field, ring, boolean algebra). The two operators just obey closure, so it's basically an abstraction of a magma to more than one operator.

Is there a specific, agreed upon name for this in mathematics yet? The most obvious thing to me would be to call this a bimagma, then to call something similar with three binary operators a trimagma, then in general a n-magma. Do these structures have a common, agreed upon name?

• If the two operations do not talk to each other, via something like distributivity or Jacobi's identity, then they're just that, two separate operations. – lhf Jun 10 '14 at 1:36
• Is that true though? There may be properties like distributivity or Jacobi's identity that the two operators obey, or there may not be, that's the point. Shouldn't all that information be derivable from the Cayley tables anyway? – Nathan BeDell Jun 10 '14 at 1:41
• I haven't seen a term for this sort of structure before, but I do like the "$n$-magma" idea. – Malice Vidrine Jun 10 '14 at 1:55
• As @lhf suggests, there's really no point in making a specific term for a set with multiple operations unless they are related somehow. Just like if a set is a group under two different operations, you merely speak of it as two separate groups, not as one double-group. There must be some relation between the two operations in order for it to make sense to bunch them together. – 6005 Jun 10 '14 at 14:31
• @Sintrastes: Hi! Yeah I had seen that page...but I don't know much of it indeed. Bigroupoid is the word: I would swear some authors were using it decades ago (R.H. Bruck, 1958? I should check again and again...) while I never heard/read bimagma. But this is the way to follow ;) – MattAllegro Jun 13 '14 at 13:00

## 1 Answer

From Burris, Sankappanavar A Course in Universal Algebra page 26 (42 of the pdf): "An algebra A is unary if all of its operations are unary, and it is mono-unary if it has just one unary operation."

Although from what I read it is not clear whether or not in practice this terminology has been extended before, an algebra with two binary operators could be called di-binary.


text:
Open Access

# Non-Archimedean unitary operators

### Abstract

We describe a subclass of the class of normal operators on Banach spaces over non-Archimedean fields (A. N. Kochubei, J. Math. Phys. 51 (2010), article 023526) consisting of operators whose properties resemble those of unitary operators. In particular, an analog of Stone's theorem about one-parameter groups of unitary operators is proved.

### Article Information

 Title Non-Archimedean unitary operators Source Methods Funct. Anal. Topology, Vol. 17 (2011), no. 3, 219-224 MathSciNet MR2857725 Copyright The Author(s) 2011 (CC BY-SA)

### Authors Information

Anatoly N. Kochubei
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

### Citation Example

Anatoly N. Kochubei, Non-Archimedean unitary operators, Methods Funct. Anal. Topology 17 (2011), no. 3, 219-224.

### BibTex

@article {MFAT590,
AUTHOR = {Kochubei, Anatoly N.},
TITLE = {Non-Archimedean unitary operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {17},
YEAR = {2011},
NUMBER = {3},
PAGES = {219-224},
ISSN = {1029-3531},
MRNUMBER = {MR2857725},
URL = {http://mfat.imath.kiev.ua/article/?id=590},
}