text:
# Preface

The book "Programming Basics with C#" introduces the readers with writing programming code at a beginners level (basic coding skills), working with development environment (IDE), using variables and data, operators and expressions , working with console (reading input data and printing output), using conditional statements (if, if-else , switch-case), loops (for, while, do-while, foreach) and methods (declaring and calling methods, passing parameters, and returning value).

The programming language C# and the development environment Visual Studio are used. All examples are given in C#, which is a modern, general purpose programming language, a good choice for beginners.

This book is the official textbook for the free Programming Basics course for absolute beginners at the Software University (SoftUni): https://softuni.bg/courses/programming-basics.

The curriculum provides basic training for a deeper study of programming and prepares readers for the entrance exam in SoftUni.

 This book only gives you the first steps to programming. It covers very basic skills that you have to develop for years, in order to reach a high enough level and start working as a programmer

The book is also used as unofficial textbook for school programming courses in professional high schools, studying the professions "Programmer", "Application Programmer" and "System Programmer", as well as an additional training tool in the initial programming courses at secondary schools, mathematical and professional high schools in Bulgaria, with profile "Informatics and Information Technologies".

## Who Is This Book Intended For?

That book is suitable for any beginners in programming who want to try what programming is and learn the main constructions for creating programming code that are used in software development, regardless of the programming language and the technologies used. The book gives a solid basis of practical skills that you can use in any future training in programming and software development.

The free course for beginners in SoftUni is suitable for students (5th grade and up), university students and workers having any other professions, who want to gain technical knowledge and check if programming is what they like to do, and understand if they would like to develop in the software development field.

A new group starts each month. The "Programming Basics" course at SoftUni is organized regularly using a number of different programming languages as basis. So, just check it out! The course is free and you can quit any time you like. Signing up for free on-site or online training is available via the SoftUni application form: https://softuni.bg/apply.

## Why Did We Choose C#?

For this book, we choose the C# language because it is a modern programming language for high-level programming, open source, easy to learn and suitable for beginners. Using C# is widespread, with a well-developed ecosystem, numerous libraries and technology frameworks, and accordingly, it gives many perspectives for development. C# combines paradigms of procedural, object-oriented and functional programming in a modern way with easy syntax. In this book, we will use C# language and Visual Studio development environment, which are available for free from Microsoft.

As we will explain later, the programming language that we start with, does not make a significant difference, but we still need to use some programming language, and in this book we choose C# specifically. The book can also be found mirrored in other programming languages such as Java and JavaScript (see https://csharp-book.softuni.org).

## Programming Is Learned by a Lot of Writing, Not Reading!

If someone thinks they will read a book and learn to program without writing code and solving problems, this is definitely a delusion. Programming needs a lots of practice, with code writing every day and solving hundreds, even thousands of problems, seriously and persistently for years.

You need to solve а lot of problems, to make mistakes, to fix, to search for solutions and information from the Internet, to try, to experiment, to find better solutions, to get used to the code, syntax, the programming language, the development environment, to search for errors and debugging the broken code, the algorithmic thinking, breaking the problems into smaller parts, gaining experience and raising your skills every day, because when you learn to write code, this is only the first step to the profession of the "software engineer". You have a lot to learn, really!

We advise the reader, as a minimum, to try out all the examples from the book, to play with them, to change them and test them. Even more important than the examples are the exercises because they develop the programmer's practical skills.

You need to solve all the problems in the book because programming is learned with practice! The exercises after each topic are carefully selected to cover in depth the learning material. Тhe purpose of solving all the problems is to provide complete set of skills for writing programming code at a beginners level (which is the purpose of this book). During the courses in SoftUni we purposefully focus on practice and problem solving, and in most courses code writing occupies over 70% of the entire course.

 Solve all the exercises in the book. Otherwise you won't learn anything! Programming is learned by writing a lot of code and solving thousands of problems!


text:
# About Lindahl equilibrium and Pareto Optimality

Let an economy with 20 consumers, one private good $x_2$ and one public good $x_1$. The public good is produced using the private good as input with the following technology $x_1=g(z)=z^{1/2}$, where $z$ is units of private good. TheUtility function of the consumer "i" is: $$U(x_1,x_{2i})=ln(x_1)+ln(x_{2i})$$ the aggregate endowment of private good is $\sum_{i=1}^{20}w_i=20$. My problem is en the section b)

a)Obtain the pareto optimal allocation.

Here, I have the following lagrangian:

$$Max_{x_1,x_{2i},z}20ln(x_1)+\sum_{i=1}^{20}ln(x_{2i})+\lambda_1(40-\sum_{i=1}^{20}x_{2i}-z)+\lambda_2(z^{1/2}-x_1)$$

with CPO's:

$$x_1:20/x_1=\lambda_2$$ $$x_{2i}:1/x_{2i}=\lambda_1$$ $$z:-\lambda_1+\frac{1}{2}\lambda_2z^{-1/2}=0$$ $$\lambda_1: 40=\sum_{i=1}^{20}x_{2i}+z$$ $$\lambda_2:z^{1/2}=x_1$$

Where the solution $x_{2i}*=4/3$, $x_1*=\sqrt{\frac{40}{3}}$, $z*=\frac{40}{3}$ is pareto optimal.

b)Obtain the Lindahl equilibrium allocation with $·p_i=p_j \hspace{0.3cm} \forall i\neq j$. Here each consumer maximize his utility function subject to a restriction that has to be with a personalized price; and the firm which produce the public good maximize benefits. So the problem of consumer is: $$Max_{x_1,x_{2i}}ln(x_1)+ln(x_{2i})+\lambda_1(w_i-x_{2i}-p_ix_1)$$

The CPO's:

$$x_1:1/x_1=\lambda_1p_i$$ $$x_{2i}:1/x_{2i}=\lambda_1$$ $$\lambda_1:(w_i=x_{2i}+p_ix_1)$$

So, from the first and the second CPO: $x_{2i}=x_1p_i$ substituting in the third $x_{2i}=\frac{w_i}{2}$ Here is my problem. In order to obtain the Pareto allocation in a) $x_{2i}=\frac{w_i}{2}=\frac{4}{3}$ so , it must be $w_i=8/3$ for each consumer $i$ but $\sum_{i=1}^{20}w_i=20\frac{8}{3}=\frac{160}{3} \neq 40$ So What is happening?

format: plain


text:
# Let G be a group such that $|G| = pk$, where $p$ is a prime, $k < p$.

The question is

Let $G$ be a group such that $|G| = pk$, where $p$ is a prime, $k < p$. Then $G$ contains a normal subgroup of order $p$.

It is easy to use Cauchy's Theorem to see that there exists a subgroup $H$ of $G$ with order $p$, but how to continue from here? Thanks.

• To add on, this is 1st year Group Theory, so Sylow's Theorem is not expected – Bernoulli Jun 13 '17 at 20:52
• I saw sylow theorems in my first year group theory lecture though – user370967 Jun 13 '17 at 20:59
• @Bernoulli, I added a different proof. – Sahiba Arora Jun 13 '17 at 21:18
• Thank you very much everybody. You are very helpful. – Bernoulli Jun 15 '17 at 20:24
• math.stackexchange.com/questions/1932206/… you can also check this, I think it can be useful. – MOVZBL Jun 17 '17 at 16:58

Let $n_p$ be the number of subgroups of order $p$. Then by Sylow's theorem $$n_p | k$$ and$$n_p\equiv1 \ mod \ p$$ As $k<p$, therefore $n_p =1$. Hence, the group is normal.

Edit You mentioned you don't know Sylow's so I'm adding a different proof. From future please mention what you know about the subject in the question itself.

Let $H$ be a subgroup of order $p$, $g \in G$ and $K=gHg^{-1}$. Then $|K|=p$. Now $$|HK|=\frac{|H||K|}{|H \cap K|}$$ If $|H \cap K|= 1$, then $|HK|=p^2$. But $|G| < p^2$, therefore $|H \cap K|\neq 1$. This forces $|H \cap K|= p$ which shows $H =K$. As $g \in G$ was arbitrary, therefore $H$ is normal.

Don't know where you are in learning group theory, but I would consider the Sylow Theorems.

suppose $H=<h>$ and $S=<s>$ are distinct subgroups of order $p$. consider the complex $HS$. since $$|HS| \le pk \lt p^2$$ there must be indices $a\ne b,c \ne d$ in $[0,p-1] \cap \mathbb{N}$ such that: $$h^as^c = h^bs^d$$ but this gives $$h^{a-b} = s^{c-d}$$ from which it follows (since $a-b$ is invertible in $\mathbb{Z}_p$) that $H$ and $S$ are the same subgroup, counter to our assumption.

since the subgroup of order $p$ guaranteed by Cauchy's theorem is unique, it is normal. can you show that it is in fact a characteristic subgroup?

• $HS$ has more elements then $G$ what is point of rest of the argument ? – mesel Jun 14 '17 at 2:17
• you try to avoid using the fact $|HK|=p^2$ ? – mesel Jun 14 '17 at 2:18


text:
# Cloning repositories

So far we’ve only dealt with git repos which exist entirely locally - you’ve created a repo, added commits and navigated the history, all on your local machine. These are all important skills, but a powerful aspect of version control is in keeping a remote copy of your files somewhere else. Most commonly, this somewhere else will be a specific hosting service like GitHub, but in principle it can be any external computer you have access to or even a different location on your local machine (although this is less likely to be useful).

This allows you both to back up your files in case something happens to your local copy, and to share your code with others, so it’s very important that we learn to interact with non-local versions of repositories. We’ll be going into detail on a variety of ways to do this in later lessons, but for now the first thing you’ll need to know about is cloning a repository.

### What is cloning and why do I care?

Cloning means creating a new repository locally which is based on a remote one somewhere else. This is a vital part of collaboration with git because it allows you to make a copy of somebody else’s repo and to work on it locally without affecting that person’s copy.

Often this will mean each of you working on seperate parts of a paper or code at the same time (and combining your changes later). Today, you’ll be cloning this repository containing all the notebooks we’re working from for this summer school. Again, this means you will have your own copy and can freely change any of the files locally without worrying about interfering with the original versions.

### How do I clone a repo?

The syntax for cloning a repo is

git clone <location_of_remote_repo>

which means we need to know where the repo we’re cloning is. This will often be a github.com URL that looks something like https://github.com/<username>/<repo-name>.git, where username is the name of some GitHub user and repo-name is the name of the specific repo you want to clone. (Note the significance of this: repositories hosted on GitHub belong to users, so different users can own different versions and you can choose which one you want to clone.)

Before we run this command, note that it will create a new folder in the current directory for the repo you’re cloning, complete with the .git and all the history. This means that the rules we’ve discussed previously about not creating repos within repos still apply, so make sure that you are not inside a git repo when you clone a new one.

So, with that in mind, go to the command line and navigate to the directory in which you want to clone the notebooks repo. You may want to create a directory to keep git repos in, but any non-repo directory will do (e.g. your home directory). If you change your mind you can move the repo later so don’t worry about this too much now. Once you’ve done that, run the clone command:

git clone https://github.com/OpenAstronomy/rcsc18_lessons.git

You should see some output while the files copy onto your machine. Once this finishes, you can run ls and you should be able to see the new folder. Move into that folder now and run git log and you’ll see that you have access to the full history of the master branch of the repo.

### Remotes

There is one final thing to note which you don’t need to worry about too much now but which will become relevant later. Local repos can have one or more remote versions associated with them. This can be set up manually (more on that later), but the git clone command automatically sets the remote repo we’ve cloned as being associated with our local version. To see this you can use the following command:

git remote

origin

This means we have one remote which has been named origin (because it’s where we got the repo from). you can see more detail on this by using the ‘verbose’ version of this command:

git remote -v

origin	https://github.com/OpenAstronomy/rcsc18_lessons.git (fetch)
origin	https://github.com/OpenAstronomy/rcsc18_lessons.git (push)

We don’t need to go into why there are two versions of this remote - the main thing to note is that the remote knows the URL it came from. Again, we’ll cover ways in which we can use this information in later lessons.


text:
• Editorial Board +
• For Contributors +
• Journal Search +
Journal Search Engine
ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.16 No.4 pp.455-464
DOI : https://doi.org/10.7232/iems.2017.16.4.455

# Fuzzy Risk Analysis Using Fuzzy Sampling Method: Case Study of Design a Reconfigurable Multi-Agent Supply Chain Network under Risk

Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Faculty of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran
Industrial Engineering Department and Center of Excellence for the Optimization of Advanced Production and Service Systems, Iran University of Science and Technology, Tehran, Iran
Corresponding Author, mjtarokh@kntu.ac.ir
20170717 20170805 20170821

## ABSTRACT

First step of reconfigurable supply chain network developing is understanding of risk affects. Categorizing of risk module and results of risk events considered with gathering and analyzing of data from network design parameters. These obtained data have probability distribution that shows uncertainty in parameters. In the literatures supply chain risk categorized based on occurrences rate or frequency and period or duration time and also place of occurrence. Deal with uncertainty and complexity of risk, our proposed fuzzy method can solve these problems in two aspects. Also described a fuzzy based sampling method (FLHS) that developed and used in this paper can improve our results even more than previous works. This paper suggests a novel modelling and simulation method of fuzzy sampling and fuzzy analysis system to address the dynamic risks effects in the especially the consideration of uncertainty risk event system behavior in different operational conditions.

## 1.INTRODUCTION

Risk is defined as a future development or event that might adversely impact the achievement of corporate goals. Moeinzadeh and Hajfathaliha (2009) argues that risk management is an entrepreneurial need, which should be established by any company. Most developed countries also “support” this need by further regulation requiring risk management systems to contain the risk on a company level. But there seems to be no regulation demanding risk management which covers the supply chain and consequently, companies are free to extend the scope of risk management beyond the company level and develop inter- organizational approaches to managing risk.

Risk management has a long history among the academics and practitioners and it is a currently debated topic in the area of supply chain and in our case study especially HCSC management. The topic derives its importance due to several industry trends currently in place: market globalizations, increase use of outsourcing, short product lifecycle, unpredictable demand, uncertain supply and pressure for lean production.

In order to be more efficient, firms have adopted strategies such as outsourcing, global partnerships and lean practices. Although such strategies have tremendous abilities to improve the efficiencies but simultaneously they make the firms vulnerable to market uncertainties, dependencies and disruptions. Moreover, natural calamities and manmade crises have also put negative impact on strategic, operational and tactical performance of supply chains. These factors have triggered the interest of academia and industry to consider the risk issues as prime concerns. To capture the more fine-grained elements of diversified risk issues related to the supply chain (Udbye, 2014; Marzbanrad et al., 2015) employ a multi-layered top town taxonomy to classify and codify the literature and put forward the probable dimensions for future research.

In today’s global marketplace, individual firms do not compete as independent entities rather as an integral part of a supply chain. Peidro et al. (2009), proposes a fuzzy mathematical programming model for supply chain planning which considers supply, demand and process uncertainties. The model has been formulated as a fuzzy mixed-integer linear programming model where data are ill-known and modelled by triangular fuzzy numbers. The fuzzy model provides the decision maker with alternative decision plans for different degrees of satisfaction.

Fuzzy logic can be a powerful tool for managers to use instead of traditional mathematical models when measuring the of supply chains responsive. The flexibility of the model allows the decision maker to introduce vagueness, uncertainty, and subjectivity into the evaluation system. Responsiveness measurement represents a critically important decision that often involves subjective information. Fuzzy logic models provide a reasonable solution to these common decision situations. After extensive exploration of the literature, Omar et al. (2015) recommend an outcome of developing a Fuzzy logic framework in measuring qualitative aspects of supply chain responsiveness.

In recent years many methodologies have been developed in terms of quantitative measures but most of them merely focus on the control mechanism based on reported measures whereas the qualitative aspect of the work is still unexplored. Fuzzy logic can be a powerful tool for managers to use instead of traditional mathematical models when evaluating the performance of supply chains. The flexibility of the model allows the decision maker to introduce vagueness, uncertainty, and subjectivity into the evaluation system. Performance evaluations represent a critically important decision that often involves subjective information. Fuzzy logic models provide a reasonable solution to these common decision situations. After extensive exploration of the literature, we recommend an outcome of exploring Fuzzy logic approach in evaluating qualitative aspects of performance of supply chain management (Omar et al., 2015).

One of the essential tools for uncertainty bounding is the fuzzy logic and, therefore, the main objective of (Li et al., 2016b) is the analysis of the literature about the application of fuzzy logic in performance measurement systems operating within uncertainty environments with the aim of categorizing, conceptualizing and classifying the works written so far.

Explain a pricing model at farm level by consensus using stakeholder dialogue approach which is based on balancing the fuzzy risk utility preference that will be faced by all levels of the supply chain members. Fuzzy risk utility optimization was used to get consensus of supply chain stakeholder dialogue while basic risk utility function was derived by using fuzzy regression approach (Li et al., 2016a).

Managing risk has become a critical component of SC management. Different types of SC vulnerability management methodologies have been proposed for managing SC risk, most offer only point-based solutions that deal with a limited set of risks. Feyzioglu et al. (2007) research aims to reinforce SC risk management by proposing an integrated approach. SC risks are identified and a risk index classification structure is created. Then we develop a SC risk assessment approach based on the analytic network process (ANP) and the VIKOR methods under the fuzzy environment where the vagueness and subjectivity are handled with linguistic terms parameterized by triangular fuzzy numbers.

A combined fuzzy analytical hierarchy process (AHP) to calculate the weight of each risk criterion and sub-criterion and technique for order performance by similarity to ideal solution (TOPSIS) methodology to rank and assess the risks associated with implementation of (GSCM) practices under the fuzzy environment (Nazam et al., 2015; Wen and Xi, 2007; Malmir et al., 2013).

As the essential components in formulations, pharmaceutical excipients directly affect the safety, efficacy, and stability of drugs. Recently, safety incidents of pharmaceutical excipients posing seriously threats to the patients highlight the necessity of controlling the potential risks. Hence, it is indispensable for the industry to establish an effective risk assessment system of supply chain. An AHP-fuzzy comprehensive evaluation model was developed based on the analytic hierarchy process and fuzzy mathematical theory, which quantitatively assessed the risks of supply chain (Li et al., 2016b).

Using the method of fuzzy multi-criteria lattice-order decision-making to evaluate the potential risks through ranking and structuring the risks. Normalizing the fuzzy risk evaluation matrix, through triangular fuzzy number calculation and comparing each risk with the positive ideal risk (PIR) and negative ideal risk (NIR), making supply chain enterprise’ main risks’ ranking more reasonable so that the enterprise can take corresponding measure to the high rank risks, without doubt that such work can greatly help the supply chain risk management (Wen and Xi, 2007).

Aqlana and Lam (2015) research presents an integrated framework for supply chain risk assessment. The framework consists of three main components: survey, Bow-Tie analysis, and fuzzy inference system (FIS). Due to increase in customer environmental awareness, competitiveness and strict governmental policies, the approach of incorporating green supply chain management (GSCM), healthcare supply chain (HCSC) to conserve resources and sustainable production, is gradually becoming more imperative for organizations. However, the successful accomplishment of green supply chain (GSC) production HCSC services and business activities is relatively difficult due to involvement of different risks. These risks and their respective sources have a tendency to disturb the GSC functioning, and thereby, decline in the ecological-economic performance. Therefore, identification of risks and their subsequent analysis in the GSC are very important to know and understand. The present research analyzes the risks relevant to adoption and effective implementation of GSC practices at industrial viewpoint. A two-phase research approach has been proposed and used in (Ceryno et al., 2013). In the first phase, six categories of risks and twenty-five specific risks, associated with the GSC, were identified. The basis of identification of the risks was literature and inputs received from experts from industries. Experts’ opinion has been collected from the officials and managers of four Indian poly product-manufacturing companies. In the second phase, the fuzzy analytic hierarchy process (fuzzy AHP), a qualitative and quantitative analysis was used to analyze the identified risks for determining of their priority of concern.

## 2.DESIGN A RECONFIGURABLE MULTI-AGENT HEALTHCARE SUPPLY CHAIN NETWORK UNDER RISK

First step for developing of a reconfigurable healthcare supply chain network is understanding of risk affects. Categorizing of risk module and results of risk events considered with gathering and analyzing of data from network design parameters. These obtained data have probability distribution that shows uncertainty in parameters. In the literatures healthcare supply chain risk categorized based on occurrences rate or frequency and period or duration time and also place of occurrence as detailed as following:

• Risk frequency: 3 level of frequency high (6 times in year), medium (4 times in year) and low (2 times in year)

• Risk duration: 3 level of period happens: high (13- 15 days), medium (6-8 days) and low (0-2 days)

• Risk place: it happens in one of these layers of healthcare supply chain: source, production site, storage, or customer layer.

All possible states for risk occurrence is multiplication of 3, 3 and 4 that equals 36 states. However to consider of all possible states of risk events we need check all of these 36 states. Even though we consider for example 4 layer in risk place item maybe some who consider 2 or more layers than or method. Based on optional or scientific experimental every company can use different levels of risk module, but what happens in each category if a company want to use customized level of category? Or especially uses many further levels of category? Can we test any contribution of risk categories?

Organizations commonly develop and rely on rules as a primary tool for managing risk, equating compliance with overall effective risk management. While complying with rules may be adequate to manage certain types of risks, history has demonstrated that not all types of risk can be effectively dealt with through compliance-focused risk management. This article presents a new framework for defining and addressing an organization’s risks that expands beyond rules-based models.

Central to this framework is the idea that an organization’s risks can be broken down into the following three categories:

• Internal risks, relative to an organization, that can be controlled (e.g. the risk of employee misconduct)

• Strategic risks taken on by an organization in the pursuit of value (e.g. the risk associated with an investment in developing a new product line)

• External risks, relative to an organization, that are largely beyond control (e.g. the risk of impact from a natural disaster, like an earthquake)

For each risk category, the authors of this Harvard Business Review article discuss risk management mechanisms that have actually been put to effective use in the field by various organizations. Below is a summary of the risk management techniques discussed in the article for each category of risk.

Agents in our method contributed as five section, we want to use optimized risk values for gaining better results, and aim of our approach is reduction procedure that adapted to difference values of risk.

Firstly we should prove that variety in risk value is better than fixed one and in follow we mixed fuzzy approach to gaining better results and more precise than previous proved values. I.e. using fuzzy approach to different ranges of risk in every category.

### 2.1.Multi-Agent Simulation Model

A multi-agent system showed in Figure 1 has several properties that described in following sections.

Predefined assumptions in Multi-Agent Simulation (MAS):

• 1. Risk event occurs just once in every time

• 2. If risk event happens, production of that node stopped

• 3. The time for service one day after of the time for request

• 4. Time of reception between two nodes is one day

• 5. None of productions accepted in failure state

• 6. Initial price unit for ith day:

• 7. No request needed for not demand request

• 8. There is no direct path from company nodes to customer nodes

• 9. Cost of holding for every day equals 20% cost of movement

• 10. Prediction request for all nodes done with movement medium in 7 days period

• 11. Penalty cost for production equals with cost of 100 unit

• 12. Total action cost equals with summation of costs for move, hold and penalty

### 2.2.Multi-Agent Simulation Procedure

Study results on parameters of network including risks events simulated based on following steps:

• 1. Designing optimized configuration of healthcare supply chain based on cost values from mixed integer programming (MIP) model.

• 2. After computing optimize configuration of network MAS model obtained. Assume all of parameters are deterministic else consumer requests in each node

• 3. Simulation process done based on this model in order to observations of cost values, requests, facilities and node capacities.

• 4. In every loop just one risk event can occur.

Requests in each node as commonly distributed with 20% standard deviation of deterministic values for problem.

As a results of probability distribution, theoretical probability distributions are a good view to implementation but in our case it is not applicable because of following reasons.

• 1. Gathered data is not continues. So to fit data for theoretical methods, data relaxation is needed.

• 2. Some information related to costs of supply, production and warehouse are restricted. In MAS model lower bound for price of goods is 70% of mean price.

• 3. Problem of this research solved by numerical assumptions.

A sample developing of experimental distribution to optimization module

As shown in Figure 2, process of sample production to optimization module contains steps that first of it is risk analysis. With information about risk we can find that uncertain parameter in data base. Next step is using local uncertain parameter related to that kind of risk and configuration. Simulation of these processes done and obtained results sent to random sample generator step. In this step experimental probability distribution used to configuration of network.

Random optimization module of network is second main part of reconfigurable supply chain network as shown in Figure 3. Task of this part is designing new configuration in risk event time. Two entry is needed for implementation of this module. First one is a list of contain all possible nodes as like available producers, potential customers and present facilities in supply chain. Second important one in optimization under uncertainty is related data of probability distribution to parameters of network design.

Main idea for random optimization module of network is recognizing of potential risk in every loop of system. In this case deterministic model of healthcare supply chain based on MIP used for implementation of that model possibly is not sufficient for making decisions on nondeterministic environment, so our proposed method is using a two-step model based on risk events.

Mathematical model can be referred as a problem of reconfigurable supply chain under risk (SRR). Random optimization module composed three part that important part of this module is two-step random programming model for SRR problem. Also a Fuzzy Latin Hypercube Sampling (FLHS) method used to reducing of variance and execution time in this part of module. (FLHS is a sampling method that wrote by authors of this paper and under process)

Assumptions for formulation of random programming model for SRR problem:

• 1. HCSCN contains four layers (producer, company, warehouse and consumer) and production service form producers to consumers is continues.

• 2. Only one kind of production can be provided by HCSC.

One of important risk analysis approaches is fuzzy concept that encounter with uncertainty (Wen and Xi, 2007).

Optimized model of SRR and consecutively SRR with fuzzy modeling of SRR formulated as following:(1)

$M i n z = ∑ i ∈ F c 0 i ( y i , 1 − y i , 1 y i , 0 ) + ∑ i ∈ F c c i ( y i , 0 − y i , 1 y i , 0 ) ∑ i ∈ W l i c r i y i + ∑ i ∈ P c b i , y i , 1 + ∑ i ∈ W c b i ( y i , 1 + y i ) + E [ Q ( y 1 , Y , ξ ( ω k ) ) ] y i , 1 + y i ≤ 1 ∀ i ∈ W ∑ i ∈ F c 0 i ( y i , 1 − y i , 1 y i , 0 ) + ∑ i ∈ F c c i ( y i , 0 − y i , 1 y i , 0 ) + ∑ i ∈ W l i c r i y i ≤ b Y 1 ∈ { 0 , 1 } | F | Y ∈ { 0 , 1 } | W |$
(1)

where $Q ( ( Y 1 , Y , ξ ( ω k ) ) )$ is the optimal value of the following problem:(2)

$M i n ∑ ( i j ) ∈ A q ( ω k ) i j x i j + ∑ j ∈ c g j u j ∑ i ∈ N x i j − ∑ l ∈ N x j l = 0 ; ∀ j ∈ F ∑ i ∈ W x i j + u j ≥ d ( ω k ) j : ∀ j ∈ C ∑ J ∈ P x i j ≤ s ( ω k ) i ; ∀ i ∈ S r j ( ∑ i ∈ s x i j ) ≤ m ( ω k ) i ; ∀ j ∈ P r j ( ∑ i ∈ p x i j ) ≤ m ( ω k ) j ( y j , 1 + y j ) ; ∀ j ∈ W X ∈ R + | A | , U ∈ R + | C |$
(2)

Main problems:

• 1. Sampling model

• 2. Risk uncertainty

First problem discussed in another literature under processing (we use brief notation here):

## 3.PROPOSED FUZZY LHS SAMPLING

In argued method each element just belongs to one category, but in our approach each element include in all groups with one exception that membership values are different. For example consider age ranges.

When we categories such samples with LHS method, some errors raised for computing values like variance, mean, etc. in fuzzy approach precision level make up better. In fact each element is member of every category with a probability between 0 and 1. Our new approach is a combination of fuzzy and LHS. In this approach we assume that linguistic variables comprised as five parts and modeled in trapezoid.

Like stratified and LHS method we choose some random elements from each stratum for sampling, and then we identify the neighborhood of LHS to modeling fuzzy. Let $n 1 , n 2 , ⋯ , n m$ be the number of elements in each of the m sampled LHS. Let $X ¯ 1 , X ¯ 2 , ⋯ , X ¯ m$ be the means of the sampled LHS. The relative uncertainty itself can also be used without the subsequent statistical testing particularly if enough is known about the parameter being evaluated. Variance reduction techniques are methods that attempt to reduce the variance, i.e., the dispersion associated with the variations, of the parameter being evaluated. This can result in one of two outcomes. Either the variance is reduced for the same number of sampling or the number of sampling can be reduced for the same variance, the comparison of both being made when no variance reduction techniques are used. This therefore either increases the confidence in the results or reduces the computational burden. There are many forms of variance reduction techniques and a specialized text should be consulted if full details of all techniques are needed. This algorithm provides reduced variances and standard errors comparison with other traditional methods. Schematic of proposed method is shown in Figure 4.

Steps that are used for programming with use of fuzzy-LHS method are mentioned in following algorithm (Figure 4):

• Determine number of dimensions for problem

• Select m (No. of points) random elements from each set of LHS

• Determine neighborhood of selected point between sets of LHS

• Calculate membership values for each LHS

• Calculate mean value, variance, max confidence and min confidence from formulas

• Calculate values for each LHS with effect of LHS neighbors

• Calculate values with effect of element neighbors in each LHS

• Calculate values with effect of both element neighbors and LHS neighbors

## 4.PROPOSED METHOD FOR FUZZY RISK

As noted previously there are K-types of risks and must be implemented in simulations but in every risk types it’s unknown that exact values. For example consider risk duration parameter that vary from 0 to N days, if it is modeled in classic approach you should compute all of possible durations but it is not applicable or time consuming procedure. Another risk parameters have same conditions. This situations always occurred in real world problems, our approach to deal with this problem is choosing one of following solutions:

• 1. Discrete constrained approach

• 2. Fuzzy continues approach

From computational complexity view first approach is time consuming because there are many states that you should consider, and also it has low precision rate because lack of real information. So to encounter this problems our proposed method is using fuzzy logic.

Following steps transfers crisp values of risk parameters to fuzzy sets:

• 1. Determine lower and upper bound of risk types for each periods

• 2. Estimation or prediction of critical values for risk parameters in each period (like low, medium and high)

• 3. Create fuzzy demonstration for each boundary of critical values

Result fuzzy view for risk duration and risk frequency showed in Figure 5 and Figure 6 respectively. In this view by choosing every point of domain value it can be decidable that risk event happens, but in traditional discrete view it is not decidable. Choosing triangular or trapezoid view depends on risk values, i.e. if our risk parameter has range of values we should select trapezoid and if it has fixed numbers (countable) modeled as triangular view.

Properties of membership values for fuzzy demon- stration are very simple. Each point of domain belongs to 3 set with different membership values and sum of these membership values are 1.(4)

$μ ( x ) = μ low ( x ) + μ medium ( x ) + μ high ( x ) = 1$
(3)

$e.g. μ duration ( 5 ) = { μ low ( 5 ) = ˜ 0.3 μ medium ( 5 ) = ˜ 0.7 μ high ( 5 ) = ˜ 0.0$
(4)

That means if a risk duration event happens 5 days of a period time, simply by including risk event in system there can be configured for risk event. Efficiency of this approach arisen when you want to model discrete values in period cycle i.e. when your decisions made on points that have membership values equal to 1. In this case its computations done just for one point whereas all of them. And here if your model have 3 level of risk events in worst case with changing all of risk event parameters you should apply 3 parameters to system.

We have implemented our algorithm in MATLAB®, which has been resented in Appendix A1.

## 5.RESULTS AND EXPERIENCES

Formulation of this model for three types of companies and applying risk event summarized in Table 1.

Here efficiency of proposed method should be discussed in two aspects from view of comparison point. Firstly our sampling method must be challenged with following formula and secondly risk event and it`s efficiency.(5)

$Eff FLHS = Var min Var FLHS × Time min Time FLHS$
(5)

where Varmin is minimum value of variance for sampling methods and Timemin is the needed time for computation of sampling method. Comparative results of fuzzy risk event showed in Table 2.

Estimation of risk events and analysis in our method and traditional methods with and without fuzzy view showed that for this kind of uncertainty using fuzzy approach is a good solution. Also Figure 7 shows smooth improving in comparison with other algorithms.

Simulations based on fuzzy both in sampling and risk events have significant improvement and more precise than other methods and also it is very close to optimal values (these values obtained from estimation values and best conditions).

## 6.CONCLUSIONS AND FUTURE WORKS

Fuzzy concept have many features that suitable to real world problems, in fact uncertainty is a big deal problem that can be reduced using fuzzy approach. In this paper we modeled a healthcare supply chain network that have risk event, as a result of this event we must reconfigure our network to include risk parameters and hence described model have 3 types of risk it is so complicated to compute and redesign network. Then in study of uncertainty occurrence we used fuzzy model to reduce errors, even we used a sampling method that has contribution of fuzzy model. Finally we see that composition of fuzzy sampling and fuzzy risk modeling has a significance improvements in results and more accuracy than other mentioned works.

## Figure

An example configuration of healthcare supply chain network.

Procedure of control agent from risk analysis to optimization module.

MAS schema.

Flowchart of proposed sampling method.

Risk duration item modeling in fuzzy approach.

Risk frequency item modeling in fuzzy approach.

Fuzzy risk with fuzzy sampling in compare to others.

## Table

Parameters value range

Summary of fuzzy risk event comparative results

Sample MATLAB code.

## REFERENCES

1. AqlanaF. LamS. (2015) A fuzzy-based integrated framework for supply chain risk assessment. , Int. J. Prod. Econ., Vol.161 ; pp.54-63
2. CerynoP. ScavardaL. KlingebielK. YA1/4zgA1/4lecG. (2013) Supply chain risk management: A content analysis approach. , International Journal of Industrial Engineering and Management, Vol.4 (3) ; pp.141-150[IJIEM].
3. FeyziogluO. BuyukozkanG. ErsoyM.S. (2007) Supply chain risk analysis with fuzzy cognitive maps. , Industrial Engineering and Engineering Management, IEEE International Conference on, Sheffield,
4. LiC. RenJ. WangH. (2016) A system dynamics simulation model of chemical supply chain transportation risk management systems. , Comput. Chem. Eng., Vol.89 (9) ; pp.71-83a
5. LiM. DuY. WangQ. SunC. LingX. YuB. (2016) Risk assessment of supply chain for pharmaceutical excipients with AHP-fuzzy comprehensive evaluation. , Drug Dev. Ind. Pharm., Vol.42 (4) ; pp.676-684b
6. MalmirM. EsfahaniM.J. EmamiM. (2013) An investigation of relation between organizational justice and professional commitment of staff: A case study of public organization in Kermanshah., ; pp.1333-1338
7. MarzbanradJ. SoleimaniG. Mahmoodi-kM. RabieeM. (2015) Development of fuzzy anti-roll bar controller for improving vehicle stability. , J. Vibroeng., Vol.17 (7) ; pp.3856-3864
8. MoeinzadehP. HajfathalihaA. (2009) A combined fuzzy decision making approach to supply chain risk assessment. , World Academy of Science, Engineering and Technology International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, Vol.3 (12) ; pp.1631-1647
9. NazamM. XuJ. TaoZ. AhmadJ. HashimM. (2015) A fuzzy AHP-TOPSIS framework for the risk assessment of green supply chain implementation in the textile industry. , International Journal of Supply and Operations Management IJSOM, Vol.2 (1) ; pp.548-568
10. OmarS. WaweruM. RimiruR. (2015) Fuzzy logic framework for qualitative evaluation of supply chain responsiveness. , Int. J. Eng. Sci., Vol.4 (8) ; pp.37-48[IJES].
11. PeidroD. MulaJ. PolerR. VerdegayJ. (2009) Fuzzy optimization for supply chain planning under supply, demand and process uncertainties. , Fuzzy Sets Syst., Vol.160 (18) ; pp.2640-2657
12. UdbyeA. (2014) Supply Chain Risk Management in India: An Empirical Study of Sourcing and Operations Disruptions, heir Frequency, Severity, Mitigation Methods, and Expectations,
13. WenL. XiZ. (2007) Supply chain risk evaluation based on fuzzy multi-criteria lattice-order decisionmaking , Automation and Logistics, IEEE International Conference,
 오늘하루 팝업창 안보기 닫기


text:
# §25.13 Periodic Zeta Function

The notation $F\left(x,s\right)$ is used for the polylogarithm $\mathrm{Li}_{s}\left(e^{2\pi ix}\right)$ with $x$ real:

 25.13.1 $F\left(x,s\right)=\sum_{n=1}^{\infty}\frac{e^{2\pi inx}}{n^{s}},$ ⓘ Defines: $F\left(\NVar{x},\NVar{s}\right)$: periodic zeta function Symbols: $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm, $n$: nonnegative integer, $x$: real variable and $s$: complex variable Permalink: http://dlmf.nist.gov/25.13.E1 Encodings: TeX, pMML, png See also: Annotations for §25.13 and Ch.25

where $\Re s>1$ if $x$ is an integer, $\Re s>0$ otherwise.

$F\left(x,s\right)$ is periodic in $x$ with period 1, and equals $\zeta\left(s\right)$ when $x$ is an integer. Also,

 25.13.2 $F\left(x,s\right)=\frac{\Gamma\left(1-s\right)}{(2\pi)^{1-s}}\*\left(e^{\pi i(% 1-s)/2}\zeta\left(1-s,x\right)+e^{\pi i(s-1)/2}\zeta\left(1-s,1-x\right)\right),$ $0, $\Re s>1$,
 25.13.3 $\zeta\left(1-s,x\right)=\frac{\Gamma\left(s\right)}{(2\pi)^{s}}\left(e^{-\pi is% /2}F\left(x,s\right)+e^{\pi is/2}F\left(-x,s\right)\right),$ $0, $\Re s>0$.


text:
Category:Fresnel Cosine Integral Function

The Fresnel cosine integral function is the real function $\R \to \R$ defined by:
$\ds \map {\operatorname C} x = \sqrt {\frac 2 \pi} \int_0^x \cos u^2 \rd u$


text:
for Journals by Title or ISSN for Articles by Keywords help

Publisher: Springer-Verlag (Total: 2354 journals)

 Algebras and Representation Theory   [SJR: 0.868]   [H-I: 20]   [1 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1572-9079 - ISSN (Online) 1386-923X    Published by Springer-Verlag  [2354 journals]
• Varieties of Characters
• Authors: Sean Lawton; Adam S. Sikora
Pages: 1133 - 1141
Abstract: Let G be a connected reductive affine algebraic group. In this short note we define the variety of G-characters of a finitely generated group Γ and show that the quotient of the G-character variety of Γ by the action of the trace preserving outer automorphisms of G normalizes the variety of G-characters when Γ is a free group, free abelian group, or a surface group.
PubDate: 2017-10-01
DOI: 10.1007/s10468-017-9679-y
Issue No: Vol. 20, No. 5 (2017)

• Differential Modules over Quadratic Monomial Algebras
• Authors: Torkil Stai
Pages: 1239 - 1247
Abstract: We compare the so-called clock condition to the gradability of certain differential modules over quadratic monomial algebras. These considerations show that a stably hereditary or gentle one-cycle algebra is piecewise hereditary if and only if the orbit category of its bounded derived category with respect to a positive power of the shift functor is triangulated.
PubDate: 2017-10-01
DOI: 10.1007/s10468-017-9684-1
Issue No: Vol. 20, No. 5 (2017)

• Irreducible Characters of p -group of Order ≤ p 5
• Authors: S. K. Prajapati; M. R. Darafsheh; M. Ghorbani
Pages: 1289 - 1303
Abstract: P. Hall introduced the concept of isoclinism of groups to classify p-groups. It is well-known that two isoclinic nilpotent groups have the same nilpotency class. In this paper using the classification of James of p-groups of order at most p 5 via their isoclinism classes, the degrees of irreducible characters with their frequencies are found. To do this we use the concept of generalized Camina pairs. We also investigate that whether a nonlinear irreducible character can be obtained as a product of two other nonlinear irreducible characters of same degree.
PubDate: 2017-10-01
DOI: 10.1007/s10468-017-9687-y
Issue No: Vol. 20, No. 5 (2017)

• A Combinatorial Categorification of the Tensor Product of the
Kirillov-Reshetikhin Crystal B 1,1 and a Fundamental Crystal
• Authors: Henry Kvinge; Monica Vazirani
Abstract: We use Khovanov-Lauda-Rouquier (KLR) algebras to categorify a crystal isomorphism between a fundamental crystal and the tensor product of a Kirillov-Reshetikhin crystal and another fundamental crystal, all in affine type. The nodes of the Kirillov-Reshetikhin crystal correspond to a family of “trivial” modules. The nodes of the fundamental crystal correspond to simple modules of the corresponding cyclotomic KLR algebra. The crystal operators correspond to socle of restriction and behave compatibly with the rule for tensor product of crystal graphs.
PubDate: 2017-11-24
DOI: 10.1007/s10468-017-9747-3

• A Generalized Dade’s Lemma for Local Rings
• Authors: Petter Andreas Bergh; David A. Jorgensen
Abstract: We prove a generalized Dade’s Lemma for quotients of local rings by ideals generated by regular sequences. That is, given a pair of finitely generated modules over such a ring with algebraically closed residue field, we prove a sufficient (and necessary) condition for the vanishing of all higher Ext or Tor of the modules. This condition involves the vanishing of all higher Ext or Tor of the modules over all quotients by a minimal generator of the ideal generated by the regular sequence.
PubDate: 2017-11-23
DOI: 10.1007/s10468-017-9751-7

• Some Methods of Computing First Extensions Between Modules of Graded Hecke
Algebras
• Authors: Kei Yuen Chan
Abstract: In this paper, we establish connections between the first extensions of simple modules and certain filtrations of of standard modules in the setting of graded Hecke algebras. The filtrations involved are radical filtrations and Jantzen filtrations. Our approach involves the use of information from the Langlands classification as well as some deeper understanding on some structure of some modules. Such module arises from the image of a Knapp-Stein type intertwining operator and is a quotient of a generalized standard module. As an application, we compute the Ext-groups for irreducible modules in a block for the graded Hecke algebra of type C 3, assuming the truth of a version of Jantzen conjecture.
PubDate: 2017-11-22
DOI: 10.1007/s10468-017-9742-8

• Several Generalizations of the Wedderburn-Artin Theorem with Applications
• Authors: M. Behboodi; A. Daneshvar; M. R. Vedadi
Abstract: We say that an R-module M is virtually semisimple if each submodule of M is isomorphic to a direct summand of M. A nonzero indecomposable virtually semisimple module is then called a virtually simple module. We carry out a study of virtually semisimple modules and modules which are direct sums of virtually simple modules . Our study provides several natural generalizations of the Wedderburn-Artin Theorem and an analogous to the classical Krull-Schmidt Theorem. Some applications of these theorems are indicated. For instance, it is shown that the following statements are equivalent for a ring R: (i) Every finitely generated left (right) R-module is virtually semisimple; (ii) Every finitely generated left (right) R-module is a direct sum of virtually simple R-modules; (iii) $$R\cong {\prod }_{i = 1}^{k} M_{n_{i}}(D_{i})$$ where k,n 1,…,n k ∈ ℕ and each D i is a principal ideal V-domain; and (iv) Every nonzero finitely generated left R-module can be written uniquely (up to isomorphism and order of the factors) in the form R m 1 ⊕… ⊕ R m k where each R m i is either a simple R-module or a virtually simple direct summand of R.
PubDate: 2017-11-20
DOI: 10.1007/s10468-017-9748-2

• Külshammer Ideals of Graded Categories and Hochschild Cohomology
• Authors: Yury Volkov; Alexandra Zvonareva
Abstract: We generalize the notion of Külshammer ideals to the setting of a graded category. This allows us to define and study some properties of Külshammer type ideals in the graded center of a triangulated category and in the Hochschild cohomology of an algebra, providing new derived invariants. Further properties of Külshammer ideals are studied in the case where the category is d-Calabi-Yau.
PubDate: 2017-11-20
DOI: 10.1007/s10468-017-9746-4

• On the Classification of Almost Square-Free Modular Categories
• Authors: Jingcheng Dong; Sonia Natale
Abstract: Let $$\mathcal {C}$$ be a modular category of Frobenius-Perron dimension d q n , where q > 2 is a prime number and d is a square-free integer. We show that $$\mathcal {C}$$ must be integral and nilpotent and therefore group-theoretical. In the case where q = 2, we describe the structure of $$\mathcal {C}$$ in terms of equivariantizations of group-crossed braided fusion categories.
PubDate: 2017-11-16
DOI: 10.1007/s10468-017-9750-8

• The Real Spectrum of a Noncommutative Ring and the Artin-Lang Homomorphism
Theorem
• Authors: Igor Klep
Abstract: Let R be a noncommutative ring. Two epimorphisms $$\alpha_{i}:R\to (D_{i},\leqslant_{i}),\quad i = 1,2$$ from R to totally ordered division rings are called equivalent if there exists an order-preserving isomorphism ϕ : (D 1, ⩽ 1) → (D 2, ⩽ 2) satisfying ϕ ∘ α 1 = α 2. In this paper we study the real epi-spectrum of R, defined to be the set of all equivalence classes (with respect to this relation) of epimorphisms from R to ordered division rings. We show that it is a spectral space when endowed with a natural topology and prove a variant of the Artin-Lang homomorphism theorem for finitely generated tensor algebras over real closed division rings.
PubDate: 2017-11-14
DOI: 10.1007/s10468-017-9745-5

• Restricted Lie Algebras via Monadic Decomposition
• Authors: Alessandro Ardizzoni; Isar Goyvaerts; Claudia Menini
Abstract: We give a description of the category of restricted Lie algebras over a field $$\Bbbk$$ of prime characteristic by means of monadic decomposition of the functor that computes the $$\Bbbk$$ -vector space of primitive elements of a $$\Bbbk$$ -bialgebra.
PubDate: 2017-11-02
DOI: 10.1007/s10468-017-9734-8

• Levi Subgroup Actions on Schubert Varieties, Induced Decompositions of
their Coordinate Rings, and Sphericity Consequences
• Authors: Reuven Hodges; Venkatramani Lakshmibai
Abstract: Let L w be the Levi part of the stabilizer Q w in G L N (for left multiplication) of a Schubert variety X(w) in the Grassmannian G d,N . For the natural action of L w on $$\mathbb {C}[X(w)]$$ , the homogeneous coordinate ring of X(w) (for the Plücker embedding), we give a combinatorial description of the decomposition of $$\mathbb {C}[X(w)]$$ into irreducible L w -modules; in fact, our description holds more generally for the action of the Levi part L of any parabolic subgroup Q that is contained in Q w . This decomposition is then used to show that all smooth Schubert varieties, all determinantal Schubert varieties, and all Schubert varieties in G2,N are spherical L w -varieties.
PubDate: 2017-10-28
DOI: 10.1007/s10468-017-9744-6

• A Quantum Analog of Generalized Cluster Algebras
• Authors: Liqian Bai; Xueqing Chen; Ming Ding; Fan Xu
Abstract: We define a quantum analog of a class of generalized cluster algebras which can be viewed as a generalization of quantum cluster algebras defined in Berenstein and Zelevinsky (Adv. Math. 195(2), 405–455 2005). In the case of rank two, we extend some structural results from the classical theory of generalized cluster algebras obtained in Chekhov and Shapiro (Int. Math. Res. Notices 10, 2746–2772 2014) and Rupel (2013) to the quantum case.
PubDate: 2017-10-24
DOI: 10.1007/s10468-017-9743-7

• Irreducible Modules Over Witt Algebras W n $\mathcal {W}_{n}$ and Over
ð–˜ ð–‘ n + 1 ( ℂ ) $\mathfrak {sl}_{n+1}(\mathbb {C})$
• Authors: Haijun Tan; Kaiming Zhao
Abstract: In this paper, by using the “twisting technique” we obtain a class of new modules A b over the Witt algebras $$\mathcal {W}_{n}$$ from modules A over the Weyl algebras $$\mathcal {K}_{n}$$ (of Laurent polynomials) for any $$b\in \mathbb {C}$$ . We give necessary and sufficient conditions for A b to be irreducible, and determine necessary and sufficient conditions for two such irreducible $$\mathcal {W}_{n}$$ -modules to be isomorphic. Since $$\mathfrak {sl}_{n+1}(\mathbb {C})$$ is a subalgebra of $$\mathcal {W}_{n}$$ , all the above irreducible $$\mathcal {W}_{n}$$ -modules A b can be considered as $$\mathfrak {sl}_{n+1}(\mathbb {C})$$ -modules. For a class of such $$\mathfrak {sl}_{n+1}(\mathbb {C})$$ -modules, denoted by Ω1−a (λ 1, λ 2, ⋯ ,λ n ) where $$a\in \mathbb {C}, \lambda _{1},\lambda _{2},\cdots ,\lambda _{n} \in \mathbb {C}^{*}$$ , we determine necessary and sufficient conditions for these $$\mathfrak {sl}_{n+1}(\mathbb {C})$$ -modules to be irreducible. If the $$\mathfrak {sl}_{n+1}(\mathbb {C})$$ -module Ω1−a (λ 1, λ 2,⋯ ,λ n ) is reducible, we prove that it has a unique nontrivial submodule W 1−a (λ 1, λ 2,...λ n ) and the quotient module is the finite dimensional $$\mathfrak {sl}_{n+1}(\mathbb {C})$$ -module with highest weight mΛ n for some non-negative integer $$m\in \mathbb {Z}_{+}$$ . We also determine necessary and sufficient conditions for two $$\mathfrak {sl}_{n+1}(\mathbb {C})$$ -modules of the form Ω1−a (λ 1, λ 2,⋯ ,λ n ) or of the form W 1−a (λ 1, λ 2,...λ n ...
PubDate: 2017-10-19
DOI: 10.1007/s10468-017-9738-4

• The Injective Leavitt Complex
• Authors: Huanhuan Li
Abstract: For a finite quiver Q without sinks, we consider the corresponding finite dimensional algebra A with radical square zero. We construct an explicit compact generator for the homotopy category of acyclic complexes of injective A-modules. We call such a generator the injective Leavitt complex of Q. This terminology is justified by the following result: the differential graded endomorphism algebra of the injective Leavitt complex of Q is quasi-isomorphic to the Leavitt path algebra of Q. Here, the Leavitt path algebra is naturally $$\mathbb {Z}$$ -graded and viewed as a differential graded algebra with trivial differential.
PubDate: 2017-10-13
DOI: 10.1007/s10468-017-9741-9

• Dedualizing Complexes of Bicomodules and MGM Duality Over Coalgebras
• Authors: Leonid Positselski
Abstract: We present the definition of a dedualizing complex of bicomodules over a pair of cocoherent coassociative coalgebras $$\mathcal {C}$$ and $$\mathcal {D}$$ . Given such a complex $$\mathcal {B}^{\bullet }$$ , we construct an equivalence between the (bounded or unbounded) conventional, as well as absolute, derived categories of the abelian categories of left comodules over $$\mathcal {C}$$ and left contramodules over $$\mathcal {D}$$ . Furthermore, we spell out the definition of a dedualizing complex of bisemimodules over a pair of semialgebras, and construct the related equivalence between the conventional or absolute derived categories of the abelian categories of semimodules and semicontramodules. Artinian, co-Noetherian, and cocoherent coalgebras are discussed as a preliminary material.
PubDate: 2017-10-12
DOI: 10.1007/s10468-017-9736-6

• τ -Tilting Modules Over One-Point Extensions by a Projective Module
• Authors: Pamela Suarez
Abstract: Let A be the one point extension of an algebra B by a projective B-module. We prove that the extension of a given support τ-tilting B-module is a support τ-tilting A-module; and, conversely, the restriction of a given support τ-tilting A-module is a support τ-tilting B-module. Moreover, we prove that there exists a full embedding of quivers between the corresponding poset of support τ-tilting modules.
PubDate: 2017-10-07
DOI: 10.1007/s10468-017-9737-5

• Mutation of Torsion Pairs in Triangulated Categories and its Geometric
Realization
• Authors: Yu Zhou; Bin Zhu
Abstract: We introduce and study mutation of torsion pairs, as a generalization of mutation of cluster tilting objects, rigid objects and maximal rigid objects. It is proved that any mutation of a torsion pair is again a torsion pair. A geometric realization of mutation of torsion pairs in the cluster category of type A n or A ∞ is given via rotation of Ptolemy diagrams.
PubDate: 2017-10-06
DOI: 10.1007/s10468-017-9740-x

• Irreducible Morphisms Between Modules over a Repetitive Algebras
• Authors: Hernán Giraldo
Abstract: We describe the irreducible morphisms in the category of modules over a repetitive algebra. We find three special canonical forms: The first canonical form happens when all the component morphisms are split monomorphisms, the second when all the component morphisms are split epimorphisms and the third when there is exactly one irreducible component map. Also, we obtain the same result for the irreducible homomorphisms in the stable category of modules over a repetitive algebra.
PubDate: 2017-10-05
DOI: 10.1007/s10468-017-9733-9

• Division Algebras with Left Algebraic Commutators
• Authors: M. Aaghabali; S. Akbari; M. H. Bien
Abstract: Let D be a division algebra with center F and K a (not necessarily central) subfield of D. An element a ∈ D is called left algebraic (resp. right algebraic) over K, if there exists a non-zero left polynomial a 0 + a 1 x + ⋯ + a n x n (resp. right polynomial a 0 + x a 1 + ⋯ + x n a n ) over K such that a 0 + a 1 a + ⋯ + a n a n = 0 (resp. a 0 + a a 1 + ⋯ + a n a n ). Bell et al. proved that every division algebra whose elements are left (right) algebraic of bounded degree over a (not necessarily central) subfield must be centrally finite. In this paper we generalize this result and prove that every division algebra whose all multiplicative commutators are left (right) algebraic of bounded degree over a (not necessarily central) subfield must be centrally finite provided that the center of division algebra is infinite. Also, we show that every division algebra whose multiplicative group of commutators is left (right) algebraic of bounded degree over a (not necessarily central) subfield must be centrally finite. Among other results we present similar result regarding additive commutators under certain conditions.
PubDate: 2017-10-03
DOI: 10.1007/s10468-017-9739-3

JournalTOCs
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
Email: journaltocs@hw.ac.uk
Tel: +00 44 (0)131 4513762
Fax: +00 44 (0)131 4513327

Home (Search)
Subjects A-Z
Publishers A-Z
Customise
APIs


text:
# Noetherian ring has an associated prime ideal

Question

Let $$R$$ be a Noetherian ring. Show that there is a prime ideal $$\mathfrak{p}$$ and a monomorphism of $$R$$-modules $$f:R/\mathfrak{p}\to R$$.

Attempt

I considered the set of ideals $$\{I< R: \exists \text{ monomorphism } f:R/I\to R\}$$ which is not empty hence has a maximal element, say $$\mathfrak{p}$$.

How can I show that $$\mathfrak{p}$$ is prime?

• Suppose you have two elements not in $\mathfrak p$ whose product is. CAn you construct a larger ideal adimitting a monomorphism $R/I\to I$? – Brandon Apr 3 at 19:24
• @Brandon That is exactly what I was trying to do, but I can't – giannispapav Apr 3 at 19:36
• Any associated prime of $R$ does the job for $p$. At least one exists as $R$ is Noetherian. – Youngsu Apr 3 at 20:35
• Suppose $ab\in\mathfrak p$, $a\notin\mathfrak p$ and $b\notin\mathfrak p$. Then $a\in(\mathfrak p:b)$, so $\mathfrak p\subsetneq(\mathfrak p:b)\subsetneq R$. On the other side, $R/(\mathfrak p:b)$ is isomorphic to the cyclic submodule of $R/\mathfrak p$ generated by the residue class of $b$. Now restrict the injective morphism $R/\mathfrak p\to R$ to this submodule and find an injective morphism $R/(\mathfrak p:b)\to R$, a contradiction. – user26857 Apr 3 at 21:13
• @user26857 Thank you very much! – giannispapav Apr 4 at 4:19

I would go about this in a different way. For a commutative ring $$R$$, prime ideal $$\mathfrak p \subset R$$, and $$R$$-module $$M$$, the following are equivalent:
(1) there is an injective $$R$$-module homomorphism $$R/\mathfrak p \to M$$;
(2) there is an element $$u\in M$$ with $$\mathrm{Ann}_R(u):= \{r \in R : ru = 0\} = \mathfrak p$$.
To see why (2) implies (1), notice that the $$R$$-module homomorphism $$R\to M$$ given by $$r\mapsto ru$$ has kernel $$\mathfrak p$$. So we'll go about this problem by trying to satisfy (2). Since $$\mathrm{Ann}_R(0) = R$$, we need to assume $$M\ne 0$$ if we want there to be such a prime ideal, and we obviously need $$R \ne 0$$ too (if we want any prime ideals at all). For us, $$M=R$$, but let's keep it general. $$R \ne 0$$ is Noetherian and $$M \ne 0$$ is an $$R$$-module.
It is in fact true that any nonzero element of $$M$$ has a nonzero multiple with prime annihilator. Let $$0\ne u \in M$$. Let $$\mathcal S = \{I \subset R : I = \mathrm{Ann}_R(ru) \text{ for some } r\in R \text{ with } ru \ne 0\}$$. Notice that if $$I\in \mathcal S$$, then $$I \ne R$$, since $$1\notin \mathrm{Ann}_R(ru)$$ when $$ru \ne 0$$. Zorn's lemma tells us there's a maximal element $$\mathfrak p \in \mathcal S$$ under containment, and $$\mathfrak p = \mathrm{Ann}_R(ru)$$ for some $$r\in R$$ with $$ru\ne 0$$. Suppose $$a,b \in R-\mathfrak p$$ are such that $$ab\in \mathfrak p$$. Then $$bru \ne 0$$ and $$\mathrm{Ann}_R(bru) \in \mathcal S$$ contains $$a$$ as well as $$\mathfrak p$$, contradicting maximality of $$\mathfrak p$$ in $$\mathcal S$$. So $$\mathfrak p$$ is prime.


text:
# How to write the following vector

I have written a vector

\begin{align}
\textbf{\underline w} &= \begin{bmatrix}
\textbf{0} \\
\textbf{v} \\
\textbf{0}
\end{bmatrix}
\end{align}

However I want to write the number of elements in the vector too. That is I want to write it like 0_{1\times 4} then v_{1\times 5} and so on.

Is it possible to write that in the vector w ?

How to do it?

• Although this is a personnal opition, I would not use such notations. Why would w be underlined and not v ? – BambOo Sep 1 '18 at 16:17
You should use \mathbf, not \textbf.
$$\underline{\mathbf{w}}= \begin{bmatrix} \mathbf{0}_{1\times 4}\\ \mathbf{v}_{1\times 5}\\ \mathbf{0}_{1\times 4} \end{bmatrix}$$


text:
# All Questions

398 views

### Forcing unifom axis scaling on a list plot [duplicate]

I'm trying to draw a ListPlot where the x and y axis have the same scale. My data is ...
97 views

### Plot integration curve of a system of ODEs

I'm really n00b in Mathematica, so please bear with me, as this seems to be my only option to learn how to do what I wany to do. I have a system of two differential equations: ...
415 views

### Transparency rendering problems in Mathematica 10 (Mac)

For some weird reason, they apparently changed the styling of contours in ContourPlot for 10.0. Here is a comparison of the results for V9 and V10 (first 9, then 10): ...
146 views

### How can I rewrite my code to make it simpler?

Two months ago,I written a function IRobot to caculate the $I_{xx},I_{yy},I_{zz}$ and $I_{xy},I_{xz},I_{yz}$,shown as below: ...
81 views

1k views

### How to get the new font in Mathematica 10?

Trying out Mathematica 10 and I still get the Courier font, not the new font shown in all of the examples on Wolfram's website. Anybody have any ideas how to get the new font working? Running on Mac ...
734 views

### Error changing Dataset using Part

bug present as of 10.0.2 In the new guide Computation With Structured Datasets we can find this part, on how to change a Dataset But if we create a Dataset ...
214 views

### Fitting data to a Poisson distribution

I'm trying to fit a Poisson Distribution to data produced in a lab. I've successfully made a Histogram of the data, which looks like: However, when I try to fit the Poisson Distribution using: ...
792 views

### How to disable the small pop-up windows when mouse is over a Mathematica command in V10?

In version 10, when the mouse is over a Mathematica command, a small pop-up window comes up that one can click on for help on the command. Is there an option to disable this feature? Screen shot: ...
92 views

### How to make a function that can return the box with information?

In the version 10, a lot of functions returned a box with brief information which is very useful. For example: Interpolation[{1, 2, 3, 5, 8, 5}] So what's ...
63 views

### Keep batch-mode kernel alive

I made a small HTTP server using jlink that works when running with the frontend. Now I need to keep a stand-alone math kernel alive after all functions have evaluated for the server to stay up. All ...
35 views

### StringCases: return list of outputs for each of several patterns

According to the documentation, StringCases[{s1, s2, ...}, p] returns {StringCases[s1, p], StringCases[s2, p], ...} but, ...
2k views

### How to make use of Associations?

I have been curious about it for long. Now that Mathematica 10 arrives, I think it's time to ask the question: How the new Association data structure would be used ...
95 views

### How to combine different EventHandlers? [duplicate]

Here are two very nice programs I got from the nice guys here helping me to solve my questions. The first one can be used to change the positions of the vertices and to delete the unwanted edges of a ...
139 views

### How can estimate the PSF function to deblur an image of plate licence of a car

I want to deblur a blurred image of a plate licence of a car. I need to deblured it. I have used the ImageDeconvolve[] function and Sharpen but the problem is still difficult because I need to ...
711 views

### Replace interior of matrix with zeros

I have f.e. the following square matrix: ...
117 views

### Integral over geometric region [duplicate]

I'd like to calculate this integral $$\int_E y\ dydz$$ where $E = \{ (x,y,z) \in R^3 : z^2+6 < y^2 < 5z \}$ By hand i've got $\frac{1}{12}$ but i'm not sure, and i'd like to verify this ...
140 views

### How can I use NestWhileList instead of While in this case?

OK, the problem occurred when I challenged with Project Euler No. 10 The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. Find the sum of all the primes below two million. My code is: ...
61 views

### How to use a scheduled event in a cloud notebook to read data files on a desktop

I don't know even how to attempt this, or if it's possible. I would like to be able to examine conditions, data, status of email server on my work desktop from the programming cloud. I recognize that ...
381 views

### How to estimate the matrix condition number in the 2-Norm?

The Mathematica documentation say it is possible to estimate the Matrix condition number in norm 1, 2, Infinity. But the 2-Norm raise a message. This is an extract from reference documentation ...
41 views

### Constrain Fit to make a fit that remains positive over the range of my independent variable

For example, say I have the following data. ...
99 views

### Coloring a set of polygons, each polygon to have a specific color

In addition to my previus post, regarding plotting the surface of a Möbius strip, I now realised, that some of the eigenmodes for a Möbius strip are either oscillations of a scalar field OR a vector ...
89 views

### Plotting multiple curves with multiple axes (>2) on the same plot

I'm attempting to generate a graph that depicts mulitple time series, measured in different units (but with a common time scale) on the same graph. This is a generalization of the familiar ...
94 views

### What is wrong with combining two programs with event handlers?

I can delete the unwanted nodes of a RandomGraph by double-clicking on them from the first program, and I can change the positions of the nodes by dragging them ...
58 views

### Enlarging a contour plot

I just started using Mathematica, and when I entered the following: ...
88 views

### Returning ancillary computation results from a function

Suppose I want to implement a function to solve a very basic Elliptic problem using Finite Element of some degree (It's just an example). Normally the user of my function is only interested to the ...
106 views

### Piecewise conditions with a parametric PDE

I'm using ParametricNDsolve to check best fit of a model (function Eb1) with some data, and I have four free parameters I want to test. I can easily construct a Parametric solution between the two ...
62 views

### FindFit is producing a list of imaginary numbers when there is non

I am trying to find the fit of an equation to some data and mathematica thinks there is a list of imaginary values. My data is all real positive number. ...
45 views

### Sort a multidimensional list row-wise [closed]

Suppose I have a multidimensional list as shown below: RandomInteger[{1,10},{3,7}] I obtain the results:  \left( \begin{array}{ccccccc} 3 & 8 ...
179 views

### LinearSolve failing to find solution to system of linear equations of 64 variables

I've got a 64x64 Matrix L for which I want to find the solution to the matrix equation L . x == rho. L is defined as ...


text: Let $f(x) = 3x^3-7x^2+5x+6$. The maximum value of $f(x)$ over the interval $[0,2]$ is ________ (up to one decimal place).


text:
5

# Accelerated from rest through a potential = difference to a In a linear accclerator; protons are proton beam enters a region of uniform magnetic ~speed of fapproxim...

## Question

###### Accelerated from rest through a potential = difference to a In a linear accclerator; protons are proton beam enters a region of uniform magnetic ~speed of fapproximately 1Sx1O' m/s The follow semicircular path. Determine the field B. shown below, that causes the beam to 0.3 m. The charge of the magnitude sfthe field that is required to cause an arc of radius the mass of the proton 1.67*10-27 kg: proton is 1.60 x 10-IPC, and proton hca Reeioll Mugnetic hole Feld EPositive Qult ol Hge

accelerated from rest through a potential = difference to a In a linear accclerator; protons are proton beam enters a region of uniform magnetic ~speed of fapproximately 1Sx1O' m/s The follow semicircular path. Determine the field B. shown below, that causes the beam to 0.3 m. The charge of the magnitude sfthe field that is required to cause an arc of radius the mass of the proton 1.67*10-27 kg: proton is 1.60 x 10-IPC, and proton hca Reeioll Mugnetic hole Feld E Positive Qult ol Hge

#### Similar Solved Questions

##### Estiniata iron Eq {11.67 vvlusTothanonc f ~cuier?& P #25088C&mj 8Q baiz
Estiniata iron Eq {11.67 vvlusTothanonc f ~cuier?& P #25088C&mj 8Q baiz...
##### Find the general solution of the given system. -1 X' = -4x(t)
Find the general solution of the given system. -1 X' = -4 x(t)...
##### 4 Use Hh itegral Tect o the Seni es ; to detcrmine iF Hho sr e conveyges Or #ivergs 96 k+) k_|K= 2
4 Use Hh itegral Tect o the Seni es ; to detcrmine iF Hho sr e conveyges Or #ivergs 96  k+) k_| K= 2...
##### Provide both resonance structures of the enolate formed when the following ketone is treated with baseUse resonance arrow between resonance structures. Include curved arrow(s) and lone pairs in your answer,
Provide both resonance structures of the enolate formed when the following ketone is treated with base Use resonance arrow between resonance structures. Include curved arrow(s) and lone pairs in your answer,...
##### Dx = as follows: 1+37 7 sin {Use the Residue Theorem to show thatFix R > 1, and consider Jc 142 where C is the positively oriented contour containing the positive real axis from 0 to R, the arc of the circle 2 = Reio with 0 â‚¬ [0, 2], and the line segment from Re2ri/7 back to 0.
dx = as follows: 1+37 7 sin { Use the Residue Theorem to show that Fix R > 1, and consider Jc 142 where C is the positively oriented contour containing the positive real axis from 0 to R, the arc of the circle 2 = Reio with 0 â‚¬ [0, 2], and the line segment from Re2ri/7 back to 0....
##### We CANT draw the graphs of two different functions with the same domain and range and sharingthose x-intercepts, BECAUSE
We CANT draw the graphs of two different functions with the same domain and range and sharing those x-intercepts, BECAUSE...
##### Find the limit of the sequence or determine that it diverges_ 10.1 n+2 f 4=3, 0,41 a+O (2) (24 Vzn+1 (F1)" 7+3n Vn'+4 0 +4
Find the limit of the sequence or determine that it diverges_ 10.1 n+2 f 4=3, 0,41 a+O (2) (24 Vzn+1 (F1)" 7+3n Vn'+4 0 +4...
##### Problem 2 With R Iv â‚¬ R " 2 0} denoting the set of all non-ncgalive real numhers; prove that the square root function delined by f (r) Vz from the metric space (R+,di) (o the same metric space d,) is continuous everywhere on i Specilically: for eaeh f â‚¬ R+ und cach 0. delermine # 6 (.such that for ech / â‚¬ R. ir d,(r,") 6 , then d,(V1v < e
Problem 2 With R Iv â‚¬ R " 2 0} denoting the set of all non-ncgalive real numhers; prove that the square root function delined by f (r) Vz from the metric space (R+,di) (o the same metric space d,) is continuous everywhere on i Specilically: for eaeh f â‚¬ R+ und cach 0. delermine # 6 ...
##### Muller's ratchet is an explanation for sexual reproduction thatargues that genetic load is purged more quickly from asexual populationsargues asexuals will take over any population if their mutation rate is high enough argues sex is beneficial because it purges genetic load. argues that asexual genotypes will always have higner ftness than sexual genotypes:
Muller's ratchet is an explanation for sexual reproduction that argues that genetic load is purged more quickly from asexual populations argues asexuals will take over any population if their mutation rate is high enough argues sex is beneficial because it purges genetic load. argues that asexu...
##### [dgtt o ! ddrEY218ZISUArange in order of smallest to largest653c , 6m 52cm, 6km, 6Om, 6km 52m, 6km Sm 2cmWhat is the weight of the book? What is the weight of the purse? Give each weight in the form kgThe amount of water in the jug can fill 3 glasses What is the capacity of each glass if all the glasses are the same size?Find the equivalent measures: (show your thinking) 0.65 km 70.63 cn 16,75 #= 015,63 km 6 km 54m
[dgtt o ! ddrEY 218 ZISU Arange in order of smallest to largest 653c , 6m 52cm, 6km, 6Om, 6km 52m, 6km Sm 2cm What is the weight of the book? What is the weight of the purse? Give each weight in the form kg The amount of water in the jug can fill 3 glasses What is the capacity of each glass if all t...
##### Ine Rudubon Soccty 4i Lrormols State Unltcrail (FSU Rolanning anaual funa (tu FPn--thon ne rluy AA Amvino; 4J50 tl 0( rent 0 tte feciliy Jor Unc Qvene=chatt ILOegrLiAa DtlyaereWme doxnLnnaaoJunanaVallors35000Wntc 00tFoen#umoCollanRix) 881Umepronit {unctica Fx) dolla 1P{*) 70r 35000Aaduban Societypreak LvrnHow mjny {Lving;ZeminathrelaLLno #civing?pastntWhat pront
Ine Rudubon Soccty 4i Lrormols State Unltcrail (FSU Rolanning anaual funa (tu FPn--thon ne rluy AA Amvino; 4J50 tl 0( rent 0 tte feciliy Jor Unc Qvene= chatt ILOegrLi Aa Dtlyaere Wme doxn Lnnaao Junana Vallors 35000 Wntc 00t Foen#umo Collan Rix) 881 Ume pronit {unctica Fx) dolla 1 P{*) 70r 35000 Aad...
##### IUPAC name for the following 1. (6 pts) Provide thename for the following 2. (4 pts) Provide the Common
IUPAC name for the following 1. (6 pts) Provide the name for the following 2. (4 pts) Provide the Common...
##### Charge Q1 18.41 mC is placed R = 32.65 cm to the left of charge Qz 76.23 mC, shown in the figure. Both charges are held stationary. Point A is located R3 9.795 cm to the right of Q1- particle with a charge of q =3.051 pC and a mass of 32.31 g is placed at rest at a distance Rz 29.39 cm above Q2. If the particle were to be released from rest; calculating its exact path would be a challenging problem However; it is possible to make some definite predictions about the future motion of the particleI
Charge Q1 18.41 mC is placed R = 32.65 cm to the left of charge Qz 76.23 mC, shown in the figure. Both charges are held stationary. Point A is located R3 9.795 cm to the right of Q1- particle with a charge of q =3.051 pC and a mass of 32.31 g is placed at rest at a distance Rz 29.39 cm above Q2. If ...
##### 7. For the preceding problem you should find that thcre anc significant difierences among the thrcc trcatmcnts, The primary reason for the significance is tat the mcan for Ireatment III is substantially larger than the means for the other [WO treatments To create the following dita, Ie started with the values frOm prablem 6 and subtracted 3 Points| Itoeach score in uceument IIL Nolice tal subtracting # constant causcs the mean t0 change bul has no influence on the variability of te samplc. In th
7. For the preceding problem you should find that thcre anc significant difierences among the thrcc trcatmcnts, The primary reason for the significance is tat the mcan for Ireatment III is substantially larger than the means for the other [WO treatments To create the following dita, Ie started with ...
##### Determine whether the pair of lines is parallel, perpendicular, or neither. \begin{aligned} &y=\frac{2}{5} x-4\\ &y=-\frac{2}{5} x+4 \end{aligned}
Determine whether the pair of lines is parallel, perpendicular, or neither. \begin{aligned} &y=\frac{2}{5} x-4\\ &y=-\frac{2}{5} x+4 \end{aligned}...
##### Mathematical induction is a method of proving that a statement $P(n)$ is true for all__________numbers $n .$ In Step 1 we prove that_________is true.
Mathematical induction is a method of proving that a statement $P(n)$ is true for all__________numbers $n .$ In Step 1 we prove that_________is true....
##### In a 1.50 L buffer solution, there are 0.054 M ammonia and 0.072M of ammonium chloride. What would be the pH if 0.018 L of 2.73 MHCl is added to the solution? pKa of ammonium ion is9.25. Keep 2 decimal places in your answer.
In a 1.50 L buffer solution, there are 0.054 M ammonia and 0.072 M of ammonium chloride. What would be the pH if 0.018 L of 2.73 M HCl is added to the solution? pKa of ammonium ion is 9.25. Keep 2 decimal places in your answer....
##### B) (Relativistic mechanics) Consider the Hamilton-functionH( . p) = T(p) + V() = cVm?e + p? kxwhere m (the mass) , c (speed of light) and k are constants, find the Hamilton equations; find the solution p(t) of the Hamilton equations for p(O) = 0_ find the velocity i(t) with _(0) = 0 as a function of time; find the linear Taylor expansion in time of the velocity i(t), dliscuss the convergence O divergence of i(t) for t = O_ draw a sketch of i(t). How does this differ from the result in a)? find t
b) (Relativistic mechanics) Consider the Hamilton-function H( . p) = T(p) + V() = cVm?e + p? kx where m (the mass) , c (speed of light) and k are constants, find the Hamilton equations; find the solution p(t) of the Hamilton equations for p(O) = 0_ find the velocity i(t) with _(0) = 0 as a function ...
##### Determine whether the series ES-2 in(n-y is convergent or divergent (S points)
Determine whether the series ES-2 in(n-y is convergent or divergent (S points)...
##### 13. [-/6.66 Points]DETAILSSCALC8 16.6.041_MY NOTESFind the area of the surface The part of the plane x + 2y + 32 = 1 that lies inside the cylinder x2 + v2 = 4Need Help?Read ItWalchkt14 [-/6.66 Points]DETAILSSCALC8 16.6.514.XP.MY NOTESFind the area of the surface_The part of the surface 2 = 3 + Sx + 2y2 that lies above the triangle with vertices (0, 0), (0, 1), (2, 1).Need Help?Read It15. [~/6.76 Points]DETAILSSCALC8 16.6.515.XP.MI_MY NOTESFind the area of the surface_The part of the paraboloid X
13. [-/6.66 Points] DETAILS SCALC8 16.6.041_ MY NOTES Find the area of the surface The part of the plane x + 2y + 32 = 1 that lies inside the cylinder x2 + v2 = 4 Need Help? Read It Walchkt 14 [-/6.66 Points] DETAILS SCALC8 16.6.514.XP. MY NOTES Find the area of the surface_ The part of the surface...

-- 0.021258--


text:
Solved

# Trying to import specific rows from excel to sql table. But: System.Data.OleDb.OleDbException: No value given for one or more required parameters.

Posted on 2013-11-25
1,262 Views
Hi,
I have workable code to import excel data into sql table, but only as [Sheet1$]. But, I'm trying to choose specific rows to be imported like [Sheet1$A3:C3]. And, of course not working, and getting an error: System.Data.OleDb.OleDbException: No value given for one or more required parameters.
So, I would like someone to check if this is actual correct procedure, or something else...Or, maybe my approach is totally wrong.

Private strConnection As String = "<MyServerConnection>"
Protected Sub btnSend_Click(ByVal sender As Object, ByVal e As EventArgs)
Dim path As String = fileuploadExcel.PostedFile.FileName
Dim excelConnectionString As String = (Convert.ToString("Provider=Microsoft.ACE.OLEDB.12.0;Data Source=") & path) + ";Extended Properties=Excel 12.0;Persist Security Info=False"
Dim excelConnection As New OleDbConnection(excelConnectionString)
Dim cmd As New OleDbCommand("Select [ID],[FirstName],[SecondName] from [Sheet1$A3:C3]", excelConnection) excelConnection.Open() Dim dReader As OleDbDataReader dReader = cmd.ExecuteReader() Dim sqlBulk As New SqlBulkCopy(strConnection) sqlBulk.DestinationTableName = "test" sqlBulk.WriteToServer(dReader) excelConnection.Close() End Sub Thank you in advance for help. 0 Question by:dejandejanovic • 2 4 Comments LVL 38 Assisted Solution Jim P. earned 150 total points ID: 39676447 Does it take excessive time? Or is there some other reason for wanting to change? My suggestion would be to import the data to a staging table and then move the rows you want to the final table. You don't state what the DB system you are using in your question. But if it is SQL and you use TRUNCATE TABLE it resets the table each time and shouldn't cause excessive growth. 0 LVL 51 Accepted Solution Mark Wills earned 350 total points ID: 39676509 For me, this works via SQL Server : Select * FROM OPENROWSET('Microsoft.ACE.OLEDB.12.0', 'Excel 12.0;Database=c:\ee\TEST.xlsx;HDR=NO;IMEX=1', 'SELECT * FROM [Sheet1$A1:C10]') as a

So, it shouldn't be an oledb problem per se. But you might want to triple check your command line syntax and make sure of the single quotes etc.

But lets also think outside the box...

well, as part of the select statement, you can use the "WHERE" clause.

the A:C is taken care of by the column names (might want to add in ";HDR=NO;IMEX=1" to make very sure, then columns are F1, F2...etc ) so, it becomes a matter of identifying row=3, and you could select top 3 to make sure it doesn't go further and then only exclude the first two rows in the "where".

Couple of strategies... One is to use the "where" to identify the contents in that row number, next would be to loop and count the rows and only post the three field values (ie don't make SQL read the excel sheet just yet), add in a datatable, load into that and then foreach datarow count rows.

Where and how are you using this ?

There is an example similar to yours in : http://www.mssqltips.com/sqlservertip/2176/dynamically-find-where-table-data-starts-in-excel-using-ssis/
0

LVL 51

Assisted Solution

Mark Wills earned 350 total points
ID: 39676532
Ummm, just on reflection, if you are excluding the first row, then how will it be getting its field names ? Try HDR=NO and then use F1,F2,F3 or in the select use F1 as ID, F2 as Firstname etc...
0

Author Closing Comment

ID: 39678833
@Mark_Wills,
OPENROWSET works perfect for my solutions. Thanks again, to all posts.
0

## Featured Post

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

### Suggested Solutions

IntroductionWhile developing web applications, a single page might contain many regions and each region might contain many number of controls with the capability to perform  postback. Many times you might need to perform some action on an ASP.NET po…
If you have heard of RFC822 date formats, they can be quite a challenge in SQL Server. RFC822 is an Internet standard format for email message headers, including all dates within those headers. The RFC822 protocols are available in detail at:   ht…
This Micro Tutorial will give you a basic overview how to record your screen with Microsoft Expression Encoder. This program is still free and open for the public to download. This will be demonstrated using Microsoft Expression Encoder 4.
Learn how to create flexible layouts using relative units in CSS.  New relative units added in CSS3 include vw(viewports width), vh(viewports height), vmin(minimum of viewports height and width), and vmax (maximum of viewports height and width).


text:
# Solution to differential equations $y(0)=1$ and $y^{(n)}=y+1$

When I was solving some differential equations, I asked myself the following: Is there a function has the following: $$y'=y+1$$ $$y''=y+1$$ $$y'''=y+1$$ $$......$$ $$......$$

If the initial value is $$y(0)=1$$

• What about $y=2e^x-1$? Dec 14, 2014 at 12:51
• @Amzoti how does this only work for the first one? For any $k$, $y^{(k)} = 2e^x$ and $y(0) = 1$ so I think this one work. Dec 14, 2014 at 13:01

Well you have that $$y'=y''=y^{(3)}\cdots$$ and the only function that is a derivative of itself is $ae^{x}$ for some $a$ so $y'=ae^x$ and $$y=y'-1=ae^x-1$$ Since $y(0)=1$ we have that $$y(0)=ae^0-1=a-1=1$$ so $a=2$ hence our function is $\boxed{y(x)=2e^x-1}$

• +1, although the edge case mentioned doesn't need special consideration, since the function $y'=0$ is of the form $y'=ae^x$ with $a=0$. Dec 14, 2014 at 15:12
• @PeterOlson Yes you're right,corrected,Thanks Dec 14, 2014 at 21:57

All your differential equations after the first one are implied by the first equation. If $y'=y+1$ then differentiation of it gives $y''=y'$ and further differentiation gives the successive equations. So it is really just about solving the first equation with the given initial value, and this you can do.

The solution to $$y' = y + 1,\ y(0)=1$$ is $y = 2e^x -1$ which can be found from your method of choice for first-order non-homogeneous ODEs. Now let's see what the derivatives look like

$$y' = 2e^x$$

$$y'' = 2e^x$$

$$y''' = 2e^x$$

We can clearly see $y^{(k+1)} = y^{(k)}\ \forall k\in\mathbb{Z},k\geq1$. Therefor all $n$th-derivatives of $y$ are equal by induction, and as $y'$ satisfies the conditions so do all $y^{(k)}$.

Edit:

If you're interested, here's how you could solve this using annihilators, my method of choice for simple problems like this (I prefer Laplace for harder ones). First re-arrange the equation to say:

$$y'-y=1$$

We find the general solution, $y_c$ by setting the RHS to $0$:

$$y_c'-y_c = 0$$

For which we assume $y_c = Ce^{mx} \Rightarrow mCe^{mx}-Ce^{mx} = 0 \Rightarrow m = 1$ so therefor $y_c = Ce^x$. We need to find $y_p$ now.

As $D$ annihilates $1$, assume $y_p = a$. Then $y' = 0$ and thus $0 - a = 1$ so $a=-1$. All together we have $y = Ce^x-1$. Further

$$y(0) = Ce^0 - 1 = 1 \Rightarrow C = 2 \therefore y= 2e^x -1$$


text:
# INFORMS Open Forum

## Reminder: 2022 Edelman Competition Submission Deadline is October 21st

• #### 1.  Reminder: 2022 Edelman Competition Submission Deadline is October 21st

Posted 10-19-2021 13:21

The purpose of the Franz Edelman competition is to bring forward, recognize and reward outstanding examples of operations research, management science, and advanced analytics in practice in the world, It attests to the contributions of operations research and analytics in both the profit and non-profit sectors. Since its inception, cumulative benefits from Edelman finalist projects has topped the $292 billion mark. Edelman finalist teams have improved organizational efficiency, increased profits, brought better products to consumers, helped foster peace negotiations, and saved lives. First prize is accompanied by a$10,000 honorarium.

For more detailed information on the award, click here.  If you have questions, please reach out to us at awards@informs.org.

------------------------------
Christy Blevins
INFORMS
Catonsville MD
------------------------------


text:
# ODE--y''+(y')^2=2e^(-y)

• October 15th 2008, 02:47 AM
petition Edgecombe
ODE--y''+(y')^2=2e^(-y)
Could someone help me solve this?

$y''+(y')^2=2e^{-y}$

So far I've got $v\frac{dv}{dy}+v^2=2e^{-y}$ with $v=y'$, which I also cannot solve.
• October 15th 2008, 04:51 AM
mr fantastic
Quote:

Originally Posted by petition Edgecombe
Could someone help me solve this?

$y''+(y')^2=2e^{-y}$

So far I've got $v\frac{dv}{dy}+v^2=2e^{-y}$ with $v=y'$, which I also cannot solve.

Divide by v and re-arrange to recognise that it's a Bernoulli DE: Bernoulli differential equation - Wikipedia, the free encyclopedia

So make the substitution w = v^2.
• October 15th 2008, 08:03 PM
petition Edgecombe
We haven't covered Bernoulli eqns yet, that's why I was stuck.