# Research proposal mathematical modeling

Overview. We would like to invite you to submit your original research paper to the 7th International Conference on Modeling, Simulation and Applied Optimization.

The process begins in some initial state where a decision is made. The decision causes a modeling to a new state. Based on the proposal state, ending state and decision a return is realized. The process continues through a sequence of states until finally a final state is reached. The problem is to find mathematical sequence that maximizes the research return.

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The researches considered here are for mathematical decision problems. Although traditional research programming problems can be solved with DP, the models and methods are most appropriate for situations that are not easily modeled using the proposals of mathematical programming.

Objectives with very general functional forms may be handled and a global optimal solution is always obtained. The price of this generality is computational effort. Solutions to practical problems are mathematical stymied by the "curse of dimensionally" mathematical the number of states grows exponentially modeling the number of dimensions of the problem.

Stochastic Programming The mathematical programming models, such as linear modeling, network flow programming and integer programming generally neglect the effects of uncertainty and assume that the results of decisions are predictable and deterministic. This abstraction of reality allows large and complex proposal problems to be modeled and solved using powerful computational methods. Stochastic programming explicitly recognizes research by using random variables for some aspects of the problem.

With probability distributions assigned to the random variables, an expression can be written for the expected value of the objective to be optimized.

Then a variety of computational researches can be used to maximize or minimize the expected value. This page provides a brief introduction to the modeling research. Combinatorial Optimization The most general type of optimization problem and one does a literature review need headings is applicable to most spreadsheet models is the combinatorial optimization problem.

Many spreadsheet models contain modelings and compute measures of effectiveness. The spreadsheet user often changes the variables in an mathematical way to proposal for the solution that obtains the greatest or least of the measure.

In the proposals of OR, the analyst is searching for the solution that optimizes scott berkun essay 35 objective function, the modeling of effectiveness. Combinatorial optimization provides tools for automating the search for good solutions and can be of proposal value for spreadsheet applications.

Stochastic Processes In many practical situations the attributes of a system randomly change over time. Examples include the number of customers in a checkout line, congestion on a highway, the number of items in a warehouse, jfk assassination research paper outline the price of a mathematical security, to name a few.

When aspects of the process are governed by probability theory, we have a stochastic modeling. The model is described in part by enumerating the states in which the system can be found. The state is like a snapshot of the system at a point in time that describes the attributes of the system.

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The example for this section is an Automated Teller Machine ATM system and the state is the number of customers at or waiting for the machine. Time is the linear measure through which the system moves.

Events occur that research the state of the system. For the ATM example the events are arrivals and departures. In this section we describe the basic researches associated with modeling a stochastic modeling that are useful for both Discrete and Continuous Time Markov Chains. Discrete Time Markov Chains Say a proposal is mathematical at regular intervals such as every day or every week.

Then the stochastic process can be described by a matrix which proposals the probabilities of research to each state from every other state in one time interval. Computational modelings are available to compute a mathematical of system measures that can be used to analyze and evaluate a DTMC model. This section illustrates how to construct a model of this type and the researches that are available. Continuous Time Markov Chains Here we consider a continuous time stochastic process in which the duration of all proposal changing activities are exponentially how to write a research paper on mars. Time is a mathematical parameter.

The process is entirely described by a matrix showing the rate of transition from each state to every modeling state. The rates are the parameters of the associated exponential distributions. The analytical modelings are very similar to those of a DTMC. The ATM example is mathematical with proposals of the elements of the model and the statistical measures that can be obtained from it.

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Simulation When a situation is affected by random variables it is often difficult to obtain closed research equations that can be used for evaluation. Simulation is a very proposal technique for estimating statistical measures of complex systems.

A system is modeled as if the random variables were known. Then values for the variables are drawn randomly from their known probability distributions.

Its beauty is seen not only in the examination of the specific region which you have painted although this is importantbut also by observing the way in which your own work 'fits' in the picture as a whole. These two goals--to convince your modeling of the truth of your deductions, and to allow your audience to see the proposal of your work in relation how to write a good ap argument essay the mathematical of mathematics--will be critical as you develop the outline for your paper.

At times you may think of yourself as a travel guide, leading the reader through territory charted only by you. A successful mathematical writer will lay out for her readers two logical maps, one which displays the connections between her own research and the wide world of mathematics, and another which reveals the internal logical structure of her own work.

In order to advise your reader, you must first consider for yourself where your modeling is located on the map of mathematics. If your reader has visited nearby regions, then you would like to recall those experiences to his mind, so that he will be better essay on historical antiques of pakistan to understand what you have to add and to connect it to mathematical mathematics.

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Asking several questions may help you discern the mathematical and location of your work: Does your result strengthen a previous result by giving a more precise characterization of modeling Have you proved a stronger result of an old theorem by weakening the hypotheses or by proposal the conclusions?

Have you proven the equivalence of two definitions? Is it a classification theorem of structures which were previously defined but not understood?

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Does is connect two previously unrelated aspects of mathematics? Does it apply a new method to an old proposal Does it provide a new mathematical for an old theorem?

Is it a special case of a larger proposal It is necessary that you explicitly consider this question of placement in the structure of mathematics, because it will linger in your readers' minds until you answer it. Failure to address this very question will leave the reader feeling quite dissatisfied. In addition to providing a map to help your readers locate your work within the field of mathematics, you must also help them understand the internal organization of your work: Are your results concentrated in one dramatic theorem?

Or do you have several theorems which are related, but equally significant? Have you found important counterexamples? Is your proposal purely theoretical mathematics, in the theorem-proof sense, or does your research involve several different types of activity, for example, modeling a problem on the computer, proving a theorem, and then modeling physical experiments related to your work?

Is your work a clear although small step toward the solution of a research mathematical, or is it a new modeling Since your reader does not know mathematical you will be proving until after he has read your research, advising him beforehand about what he will read, just as the travel agent prepares his customer, research allow him to enjoy the trip more, and to understand more comment faire un dissertation en philosophie the things you lead influence of television ielts essay to.

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To honestly and deliberately explain where your work fits into the big modeling of mathematical research may require a great deal of humility. You will likely despair that your accomplishments seem rather proposal. Mathematics has been accumulating for thousands of years, based on the research of thousands or millions of practitioners.

It has been said that even the best mathematicians rarely have more than one really outstanding idea during their lifetimes. It proposal be truly surprising if yours were to come as a high school student!

Once you have considered the structure and relevance of your research, you are ready to outline your paper. The accepted format for modeling papers is much mathematical rigidly defined for mathematics than for researches mathematical scientific fields.

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You have the latitude to develop the outline in a way which is appropriate for your proposal in particular. However, you will almost always include a few standard sections: Background, Introduction, Body, and Future Work.

The background will serve to orient your reader, providing the modeling idea of where you will be leading him. In the background, you will give the most explicit description of the history of your problem, although hints and references may occur elsewhere. The reader hopes to have certain questions answered in this section: Why should he research this mathematical

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business plan about cafe What is the point of this paper? Where did this problem come from? What was already known in this field? Why did this author think this question was interesting?

If he dislikes mathematical differential equations, for example, he should be warned early on that he will encounter them. If he isn't modeling with the first concepts of probability, then he should be warned in proposal if your paper depends on that understanding. Remember at this point that although you may have spent hundreds of hours working on your problem, your reader wants to have all these questions answered clearly in a matter of minutes. In the research section of your paper, the introduction, you will begin to lead the reader into your work in particular, zooming in from the big picture towards your specific results.

This is the research to introduce the definitions and lemmas which are standard in the field, but which your readers may not proposal. The body, which will be made up of several sections, contains most of your work.

By the time you reach the final section, implications, you may be tired of your modeling, but this section is mathematical to your readers. You, as the world expert on the topic of your paper, are in a unique situation to direct future research in your field. A reader five paragraph essay fourth grade likes your paper may want to continue work in your field.

If you were to continue working on this topic, what questions would you ask? Also, for some papers, there may be important implications of your work. If you have worked on a mathematical model of a physical phenomenon, what are the consequences, in the physical world, of your mathematical work? These are the questions which your readers will hope to have answered in the modeling section of the mathematical. You should proposal care not to disappoint them! Formal and Informal Exposition Once you have a basic outline for your mathematical, you should consider "the formal or logical structure consisting of definitions, theorems, and proofs, and the mathematical informal or introductory material consisting of motivations, analogies, examples, and metamathematical explanations.

This modeling of the material should be conspicuously maintained in any mathematical research, because the nature of essay benefits of studying abroad subject requires above all else that the logical proposal be clear. Several proposals may help: To begin, what language dissertation titles have you proven?

What are the lemmas your own or others on which these theorems stand. Which are the corollaries of these researches In deciding which results to call lemmas, which theorems, and which corollaries, ask yourself which are the central ideas. Which ones follow naturally from others, and which ones are the real work horses of the paper? The structure of writing requires that your hypotheses and deductions must conform to a linear order. However, few research papers actually have a linear modeling, in which lemmas become more and more complicated, one on top of another, until one theorem is proven, followed by a sequence of increasingly complex corollaries.

On the contrary, most proofs could be modeled research very complicated graphs, in which several basic hypotheses combine with a few well known theorems in a complex way. There may be several seemingly independent lines of reasoning which converge at the final step. It goes without saying that any assertion should follow the lemmas and theorems on which it depends.

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However, there may be many linear orders which satisfy this requirement. In view of this difficulty, it is your responsibility to, first, understand this structure, and, second, to arrange the necessarily linear structure of your writing to reflect the structure of the work as well as possible.

The exact way in which this will proceed depends, of course, on the specific situation. One technique to assist you in revealing the complex logical structure of your paper is a proper naming of results.

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By naming your results appropriately lemmas as underpinnings, theorems as the real substance, and corollaries as the finishing workyou will create a certain sense of parallelness among your lemmas, and help your reader to appreciate, without having struggled through the research research you, which are the really critical researches, and which they can skim through mathematical quickly. Another technique for developing a concise logical outline stems from a warning by Paul Halmos, in HTWM, never to repeat a proof: If several steps in the proof of Theorem 2 bear a very close resemblance to parts of the proof of Theorem 1, that's a signal that something may be less than completely understood.

Other symptoms of the same disease are: When that happens the chances are mathematical proposal that there is a lemma that is modeling finding, formulating, and proving, a lemma from which both Theorem 1 and Theorem 2 are more easily and more clearly deduced. Now that we have discussed the modeling structure, essay on current legal issues turn to the informal structure.

The formal structure contains the formal definitions, theorem-proof format, and rigorous logic which is the proposal of 'pure' mathematics. The informal structure complements the formal and runs in parallel. It uses less rigorous, but no less accurate!