Mathematics Commons^™

Solving Equations (And Systems Of Equations) Under Uncertainty: How Different Practical Problems Lead To Different Mathematical And Computational Formulations, Vladik Kreinovich

Departmental Technical Reports (CS)

Many practical problems are naturally reduced to solving systems of equations. There are many efficient techniques for solving well-defined systems of equations, i.e., systems in which we know the exact values of all the parameters and coefficients. In practice, we usually know these parameters and coefficients with some uncertainty -- uncertainty usually described by an appropriate granule: interval, fuzzy set, rough set, etc. Many techniques have been developed for solving systems of equations under such granular uncertainty. Sometimes, however, practitioners use previously successful techniques and get inadequate results. In this -- mostly pedagogical -- paper, we explain that to obtain …

From Tertullian's Credo Quia Absurdum To Bohr's Crazy Theories: A Rational Explanation Of A Seemingly Irrational Idea, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

At first glance, Tertullian's idea -- that absurdity of a statement makes it more believable -- sounds irrational, maybe appropriate for theology but definitely not for science. However, somewhat surprisingly, a similar idea was successfully used by the Nobelist Niels Bohr in theoretical physics -- an epitome of rationality in science. In this paper, we show that this Tertullian-Bohr idea actually has a simple rational explanation. Specifically, if previous attempts to construct a theory which is consistent with what is perceived as common sense were unsuccessful, this implies that a true theory much contradict common sense -- and thus, the …

Towards Selecting The Best Abstraction For A Patrolling Game, Anjon Basak, Chris Kiekintveld, Vladik Kreinovich

Departmental Technical Reports (CS)

When the number of possible strategies is large, it is not computationally feasible to compute the optimal strategy for the original game. Instead, we select our strategy based on an approximate approximate description of the original game. The quality of the resulting strategy depends on which approximation we select. In this paper, on an example of a simple game, we show how to find the optimal approximation, the approximation whose use results in the best strategy.

Lower Bound For Ranks Of Invariant Forms, Harm Derksen, Zach Teitler

Mathematics Faculty Publications and Presentations

We give a lower bound for the Waring rank and cactus rank of forms that are invariant under an action of a connected algebraic group. We use this to improve the Ranestad-Schreyer-Shafiei lower bounds for the Waring ranks and cactus ranks of determinants of generic matrices, Pfaffians of generic skew-symmetric matrices, and determinants of generic symmetric matrices.

Review: A Short Introduction To De Branges-Rovnyak Spaces, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

How To Predict Nesting Sites?, Stephen Escarzaga, Craig Tweedie, Vladik Kreinovich

Departmental Technical Reports (CS)

How to predict nesting sites? Usually, all we know is the past nesting sites, and the fact that the birds select a site which is optimal for them (in some reasonable sense), but we do not know the exact objective function describing this optimality. In this paper, we propose a way to make predictions in such a situation.

Why It Is Healthy To Regularly Challenge Authority: An Algorithmic Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One way to make group decisions is to select the best decision maker(s) in the group as the authority, and to follow his or her decisions. At first glance, it seems that if the selected authority is indeed the best decision maker, it is beneficial for everyone to obey his or her authority. However, history shows that in many cases, challenges to the authority (even to the authority of the best decision maker) were beneficial to the group. In this paper, we provide an algorithmic explanation for this phenomenon. The main idea behind this explanation is that most practical general …

Interval Methods For Data Fitting Under Uncertainty: A Probabilistic Treatment, Vladik Kreinovich, Sergey P. Shary

Departmental Technical Reports (CS)

How to estimate parameters from observations subject to errors and uncertainty? Very often, the measurement errors are random quantities that can be adequately described by the probability theory. When we know that the measurement errors are normally distributed with zero mean, then the (asymptotically optimal) Maximum Likelihood Method leads to the popular least squares estimates. In many situations, however, we do not know the shape of the error distribution, we only know that the measurement errors are located on a certain interval. Then the maximum entropy approach leads to a uniform distribution on this interval, and the Maximum Likelihood Method …

Simplest Innovations Are, Empirically, The Most Promising: An Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Many examples show that the simplest innovation are the most promising. In this paper, we provide a theoretical explanation for this empirical observation.

Differentialgeometry In Brno, Ian M. Anderson

Presentations

This page will provide files supporting Ian Anderson's presentations in Brno, December 2015. The files can be found and downloaded from "Additional Files", below.

The files include:

(1) DifferentialGeometryUSU.mla: This is the Maple Library Archive file which provides all the DifferentialGeometry functionality. Here are Installation Instructions.

(2) DifferentialGeometry.help : this is the latest version of the DifferentialGeometry documentation. Copy this file to the same directory used for DifferentialGeometryUSU.mla (from step (1)).

Apply Data Clustering To Gene Expression Data, Abdullah Jameel Abualhamayl Mr.

Electronic Theses, Projects, and Dissertations

Data clustering plays an important role in effective analysis of gene expression. Although DNA microarray technology facilitates expression monitoring, several challenges arise when dealing with gene expression datasets. Some of these challenges are the enormous number of genes, the dimensionality of the data, and the change of data over time. The genetic groups which are biologically interlinked can be identified through clustering. This project aims to clarify the steps to apply clustering analysis of genes involved in a published dataset. The methodology for this project includes the selection of the dataset representation, the selection of gene datasets, Similarity Matrix Selection, …

In Honor And Memory Of Professor Lajos Takács, Aliakbar M. Haghighi, Sri G. Mohanty

Applications and Applied Mathematics: An International Journal (AAM)

This issue of AAM is dedicated to honoring and remembering Professor Lajos Takács. While wrapping up the manuscript of my book (co-authored by Dr. Dimitar Mishev): Delayed and Network Queues, I went back to celebrate his 1962 book, Introduction to the Theory of Queues, where he gives an example illustrating a waiting time paradox, where the waiting time of a passenger waiting for a bus at a bus stop is infinite, while, in reality, he will wait a finite unit of time before a bus arrive. I sent Professor Takács an e-mail on December 4, 2015, inquiring if he had …

Independent Monopoly Size In Graphs, Ahmed M. Naji, N. D. Soner

Applications and Applied Mathematics: An International Journal (AAM)

In a graph G = (V;E), a set D ⊆V (G) is said to be a monopoly set of G if every vertex v ∈V-D has at least d(v)/ 2 neighbors in D. The monopoly size of G, denoted mo(G), is the minimum cardinality of a monopoly set among all monopoly sets in G. The set D ⊆ V (G) is an independent monopoly set in G if it is both a monopoly set and an independent set in G. The number of vertices in a minimum independent monopoly set in a graph G is the independent monopoly size of …

On The Stability Of A Pexiderized Functional Equation In Intuitionistic Fuzzy Banach Spaces, Nabin C. Kayal, Pratap Mondal, T. K. Samanta

Applications and Applied Mathematics: An International Journal (AAM)

During the last few decades several researchers have been devoted to establishing stability of different kinds of functional equations, differential equations, functional differential equations, fractional differential equations, etc. under different sufficient conditions in different spaces like Banach spaces, Banach modules, fuzzy Banach spaces etc. In this paper, we remain confined in the discussion of stability of functional equations in intuitionistic fuzzy Banach spaces. Ulam was the first person who introduced an open question concerning the stability of a group homomorphism in an international conference. Thereafter several researchers have replied and are still replying to this open question in different contexts. …

The Shifted Jacobi Polynomial Integral Operational Matrix For Solving Riccati Differential Equation Of Fractional Order, A. Neamaty, B. Agheli, R. Darzi

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we have applied Jacobi polynomial to solve Riccati differential equation of fractional order. To do so, we have presented a general formula for the Jacobi operational matrix of fractional integral operator. Using the Tau method, the solution of this problem reduces to the solution of a system of algebraic equations. The numerical results for the examples presented in this paper demonstrate the efficiency of the present method.

Numerical Solution Of Linear Fredholm Integro-Differential Equations By Non-Standard Finite Difference Method, Pramod K. Pandey

Applications and Applied Mathematics: An International Journal (AAM)

In this article we consider a non-standard finite difference method for numerical solution of linear Fredholm integro-differential equations. The non-standard finite difference method and the repeated / composite trapezoidal quadrature method are used to transform the Fredholm integro-differential equation into a system of non-linear algebraic equations. The numerical experiments on some linear model problems show the simplicity and efficiency of the proposed method. It is observed from the numerical experiments that our method is convergent and second order accurate.

Group Decision Making Using Comparative Linguistic Expression Based On Hesitant Intuitionistic Fuzzy Sets, Ismat Beg, Tabasam Rashid

Applications and Applied Mathematics: An International Journal (AAM)

We introduce a method for aggregation of experts’ opinions given in the form of comparative linguistic expression. An algorithmic form of technique for order preference is proposed for group decision making. A simple example is given by using this method for the selection of the best alternative as well as ranking the alternatives from the best to the worst.

Local Fractional Variational Iteration Method For Solving Nonlinear Partial Differential Equations Within Local Fractional Operators, Hossein Jafari, Hassan K. Jassim

Applications and Applied Mathematics: An International Journal (AAM)

In this article, the local fractional variational iteration method is proposed to solve nonlinear partial differential equations within local fractional derivative operators. To illustrate the ability and reliability of the method, some examples are illustrated. A comparison between local fractional variational iteration method with the other numerical methods is given, revealing that the proposed method is capable of solving effectively a large number of nonlinear differential equations with high accuracy. In addition, we show that local fractional variational iteration method is able to solve a large class of nonlinear problems involving local fractional operators effectively, more easily and accurately, and …

Two-Dimensional 1-Meixner Random Vectors And Their Semi-Quantum Operators, Gabriela Popa, Aurel I Stan

Communications on Stochastic Analysis

No abstract provided.

A Poisson Shot-Noise Process Of Pulses And Its Scaling Limits, Mine Çaglar

Communications on Stochastic Analysis

No abstract provided.

Solving A Class Of Linear Skorokhod Stochastic Differential Equations, Karl-Heinz Fichtner, Steffen Klaere, Volkmar Liebscher

Communications on Stochastic Analysis

No abstract provided.

Large Deviations For Stochastic Tidal Dynamics Equation, Murugan Suvinthra, Sivaguru S Sritharan, Krishnan Balachandran

Communications on Stochastic Analysis

No abstract provided.

On The Lévy-Khinchin Decomposition Of Generating Functionals, Uwe Franz, Malte Gerhold, Andreas Thom

Communications on Stochastic Analysis

No abstract provided.

White Noise Analysis For The Canonical Lévy Process, Rolando D Navarro Jr., Frederi G Viens

Communications on Stochastic Analysis

No abstract provided.

Krylov-Veretennikov Formula For Functionals From The Stopped Wiener Process, Georgii V Riabov

Communications on Stochastic Analysis

No abstract provided.

Doob's Decomposition Theorem For Near-Submartingales, Hui-Hsiung Kuo, Kimiaki Saitô

Communications on Stochastic Analysis

No abstract provided.

Maximal Class P-Groups With Large Character Degree Gaps, Michael Slattery

Mathematics, Statistics and Computer Science Faculty Research and Publications

In Mann (More on normally monomial p-groups, 2015), he proves some bounds on the size of gaps between character degrees of maximal class p-groups. In this note we construct a family of examples that shows that one of these bounds is sharp.

Analysis Of Water Quality In New Jersey, Kaitlyn Scrudato

Theses, Dissertations and Culminating Projects

Numerous diseases can occur when swimming or fishing in contaminated water. It is important that the quality of water is being monitored prior to recreational activities. To model the quality of the water at any given time with available predictors, data from bodies of water across New Jersey from 1999 to 2013 was collected from the database STORET. The water quality parameters studied were Escherichia coli (E. coli) and enterococcus with the predictors as Dissolved oxygen (DO), pH, Salinity, Temperature, Total Dissolved Solids (TDS) and Total Suspended Solids (TSS). The data was broken down by habitat type. The habitat types …

Multiplier Operator On Framed Hilbert Spaces, Haodong Li

All Theses

Very often the operators that we study appear most naturally in highly non-diagonal representation. The main goal of spectral theory is to solve this problem by exhibiting for many operators a natural orthonormal basis with respect to which the operators have diagonal representations. However, this can be done only for certain classes of operators. The most important such class is probably the class of compact operators. The problem is that it is often hard to tell whether an operator is compact looking at its non-diagonal representation. In this thesis, we will study a class of operators for which we can …

The Classical Theory Of Rearrangements, Monica Josue Agana

Boise State University Theses and Dissertations

One type of conditionally convergent series that has long been considered by mathematicians is the Alternating Harmonic Series and its sum under various types of rearrangements. The purpose of this thesis is to introduce results from the classical theory of rearrangements dating back to the 19th and early 20th century. We will look at results by mathematicians such as Ohm, Riemann, Schlömilch, Pringsheim, and Sierpiński. In addition, we show examples of each classical result by applying the Alternating Harmonic Series under the different types of rearrangements, and also introducing theorems by Lévy and Steinitz, and Wilczyński which are modern extensions …