Mathematics Commons^™

On The Slow Growth And Approximation Of Entire Function Solutions Of Second-Order Elliptic Partial Differential Equations On Caratheodory Domains, Devendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we consider the regular, real-valued solutions of the second-order elliptic partial differential equation. The characterization of generalized growth parameters for entire function solutions for slow growth in terms of approximation errors on more generalized domains, i.e., Caratheodory domains, has been obtained. Moreover, we studied some inequalities concerning the growth parameters of entire function solutions of above equation for slow growth which have not been studied so far.

How To Make Machine Learning Robust Against Adversarial Inputs, Gerardo Muela, Christian Servin, Vladik Kreinovich

Departmental Technical Reports (CS)

It has been recently shown that it is possible to "cheat" many machine learning algorithms -- i.e., to perform minor modifications of the inputs that would lead to a wrong classification. This feature can be used by adversaries to avoid spam detection, to create a wrong identification allowing access to classified information, etc. In this paper, we propose a solution to this problem: namely, instead of applying the original machine learning algorithm to the original inputs, we should first perform a random modification of these inputs. Since machine learning algorithms perform well on random data, such a random modification ensures …

Heat Source Thermoelastic Problem In A Hollow Elliptic Cylinder Under Time-Reversal Principle, Pravin Bhad, Vinod Varghese, Lalsingh Khalsa

Applications and Applied Mathematics: An International Journal (AAM)

The article investigates the time-reversal thermoelasticity of a hollow elliptical cylinder for determining the temperature distribution and its associated thermal stresses at a certain point using integral transform techniques by unifying classical orthogonal polynomials as the kernel. Furthermore, by considering a circle as a special kind of ellipse, it is seen that the temperature distribution and the comparative study of a circular cylinder can be derived as a special case from the present mathematical solution. The numerical results obtained are accurate enough for practical purposes.

Iterative Solution Of Fractional Diffusion Equation Modelling Anomalous Diffusion, A. Elsaid, S. Shamseldeen, S. Madkour

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we study the fractional diffusion equation with spatial Riesz fractional derivative. The continuation of the solution of this fractional equation to the solution of the corresponding integer order equation is proved. The series solution is obtained based on properties of Riesz fractional derivative operator and utilizing the optimal homotopy analysis method (OHAM). Numerical simulations are presented to validate the method and to show the effect of changing the fractional derivative parameter on the solution behavior.

Study On The Q-Conjugacy Relations For The Janko Groups, Ali Moghani

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider all the Janko sporadic groups J₁, J₂, J₃ and J₄ (with orders 175560, 604800, 50232960 and 86775571046077562880, respectively) with a new concept called the markaracter- and Q-conjugacy character tables, which enables us to discuss marks and characters for a finite group on a common basis of Q-conjugacy relationships between their cyclic subgroups. Then by using GAP (Groups, Algorithms and Programming) package we calculate all their dominant classes enabling us to find all possible Q-conjugacy characters for these sporadic groups. Finally, we prove in a main theorem that all twenty …

Why Product "And"-Operation Is Often Efficient: One More Argument, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is an empirical fact that the algebraic product is one the most efficient "and"-operations in fuzzy logic. In this paper, we provide one of the possible explanations of this empirical phenomenon.

Towards An Algebraic Description Of Set Arithmetic, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To describe the state of the world, we need to describe the values of all physical quantities. In practice, due to inevitable measurement inaccuracy, we do not know the exact values of these quantities, we only know the sets of possible values for these quantities. On the class of such uncertainty-related sets, we can naturally define arithmetic operations that transform, e.g., uncertainty in a and b into uncertainty with which we know the sum a + b.

In many applications, it has been useful to reformulate the problem in purely algebraic terms, i.e., in terms of axioms that the basic …

Why The Presence Of Point-Wise ("Punctate") Calcifications Or Linear Configurations Of Calcifications Makes Breast Cancer More Probable: A Geometric Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When a specialist analyzes a mammogram for signs of possible breast cancer, he or she pays special attention to point-wise and linear-shaped calcifications and point-wise and linear configurations of calcification -- since empirically, such calcifications and combinations of calcifications are indeed most frequently associated with cancer. In this paper, we provide a geometric explanation for this empirical phenomenon.

Why Most Bright Stars Are Binary But Most Dim Stars Are Single: A Simple Qualitative Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that most visible stars are binary: they have a nearby companion star, and these two stars orbit around each other. Based on this fact, until recently, astronomers believed that, in general, most stars are binary. A few years ago, a surprising paper showed that while most bright stars are indeed binary, most dim stars are single. In this paper, we provide a simple qualitative explanation for this empirical fact.

The History Of Algorithmic Complexity, Audrey A. Nasar

Publications and Research

This paper provides a historical account of the development of algorithmic complexity in a form that is suitable to instructors of mathematics at the high school or undergraduate level. The study of algorithmic complexity, despite being deeply rooted in mathematics, is usually restricted to the computer science curriculum. By providing a historical account of algorithmic complexity through a mathematical lens, this paper aims to equip mathematics educators with the necessary background and framework for incorporating the analysis of algorithmic complexity into mathematics courses as early on as algebra or pre-calculus.

Ua66 Ogden College Of Science & Engineering Newsletter, Wku Ogden College Of Science & Engineering

Ogden College of Science & Engineering Publications

Newsletter created by and about WKU Ogden College of Science & Engineering.

• Ogden College Hall Taking Shape on TIme & on Budget
• Alumni Focus: Dr. Talia McKinney Collins
• WKU Research Foundation Launches New Website
• French, Jackson. Stemshot Rocketry Competition
• Agriculture
• Architectural & Manufacturing Sciences
• Grants & Publications
• Dr. Noah Ashley Receives NIH Grant
• Biology - News & Notes
• WKU Chemistry Welcomes Dr. Lawrence Hill & Dr. David Wolfgang
• Gary Kwong Receives McNally Award
• Student Teams Compete in National Engineering Contests Over the Summer
• Geology Major Conducts Research in Ethiopia - Deborah Flynn
• Geography & Geology
• WKU Meterology Launches White Squirrel …

When Invading, Cancer Cells Do Not Divide: A Geometric (Symmetry-Based) Explanation Of An Empirical Observation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In general, malignant tumors are known to grow fast, cancer cells that form these tumors divide and spread around. Tumors also experience the process of metastasis, when cancer cells invade neighboring organs. A recent experiment has shown that, contrary to the previous assumptions, when cancer cells are invading, they stop dividing. In this paper, we provide a geometric explanation for this empirical phenomenon.

Birth Mass Is The Key To Understanding The Negative Correlation Between Lifespan And Body Size In Dogs, Rong Fan, Gayla R. Olbricht, Xavior Baker, Chen Hou

Mathematics and Statistics Faculty Research & Creative Works

Larger dog breeds live shorter than the smaller ones, opposite of the mass-lifespan relationship observed across mammalian species. Here we use data from 90 dog breeds and a theoretical model based on the first principles of energy conservation and life history tradeoffs to explain the negative correlation between longevity and body size in dogs. We found that the birth/adult mass ratio of dogs scales negatively with adult size, which is different than the weak interspecific scaling in mammals. Using the model, we show that this ratio, as an index of energy required for growth, is the key to understanding why …

Going For Gold In The International Math Olympiad, Queena N. Lee-Chua

Mathematics Faculty Publications

In July 2016, two high school students in the Philippine team garnered gold at the 57th International Mathematics Olympiad (IMO) in Hong Kong, capping a three-decade long quest for the top prize in the most prestigious high school math competition in the world. The four other team members also brought home honors, boosting our country to its highest rank ever, 17th out of 109 countries. This article discusses the history of the Philippine participation in the IMO, and examines the critical factors that have led to the victory. For Philippine team participants in general, these include: institutionalized and refined search …

Reduction Of A Nilpotent Intuitionistic Fuzzy Matrix Using Implication Operator, Riyaz A. Padder, P. Murugadas

Applications and Applied Mathematics: An International Journal (AAM)

A problem of reducing intuitionistic fuzzy matrices is examined and some useful properties are obtained with respect to nilpotent intutionistic fuzzy matrices. First, reduction of irreflexive and transitive intuitionistic fuzzy matrices are considered, and then the properties are applied to nilpotent intutionistic fuzzy matrices. Nilpotent intuitionistic fuzzy matrices are intuitionistic fuzzy matrices which signify acyclic graphs, and the graphs are used to characterize consistent systems. The properties are handy for generalization of various systems with intuitionistic fuzzy transitivity.

Solution Of A Cauchy Singular Fractional Integro-Differential Equation In Bernstein Polynomial Basis, Avipsita Chatterjee, Uma Basu, B. N. Mandal

Applications and Applied Mathematics: An International Journal (AAM)

This article proposes a simple method to obtain approximate numerical solution of a singular fractional order integro-differential equation with Cauchy kernel by using Bernstein polynomials as basis. The fractional derivative is described in Caputo sense. The properties of Bernstein polynomials are used to reduce the fractional order integro-differential equation to the solution of algebraic equations. The numerical results obtained by the present method compares favorably with those obtained earlier for the first order integro-differential equation. Also the convergence of the method is established rigorously.

Density-Dependent Leslie Matrix Modeling For Logistic Populations With Steady-State Distribution Control, Bruce Kessler, Andrew Davis

Mathematics Faculty Publications

The Leslie matrix model allows for the discrete modeling of population age-groups whose total population grows exponentially. Many attempts have been made to adapt this model to a logistic model with a carrying capacity (see [1], [2], [4], [5], and [6]), with mixed results. In this paper we provide a new model for logistic populations that tracks age-group populations with repeated multiplication of a density-dependent matrix constructed from an original Leslie matrix, the chosen carrying capacity of the model, and the desired steady-state age-group distribution. The total populations from the model converge to a discrete logistic model with the same …

Why Growth Of Cancerous Tumors Is Gompertzian: A Symmetry-Based Explanation, Pedro Barragan Olague, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that the growth of a cancerous tumor is well described by the Gompertz's equation. The existing explanations for this equation rely on specifics of cell dynamics. However, the fact that for many different types of tumors, with different cell dynamics, we observe the same growth pattern, make us believe that there should be a more fundamental explanation for this equation. In this paper, we show that a symmetry-based approach indeed leads to such an explanation: indeed, out of all scale-invariant growth dynamics, the Gompertzian growth is the closest to the linear-approximation exponential growth model.

What Is The Best Way To Add Large Number Of Integers: Number-By-Number As Computers Do Or Lowest-Digits-Than-Next-Digits-Etc As We Humans Do?, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When we need to add several integers, computers add them one by one, while we usually add them digit by digit: first, we add all the lowest digits, then we add all next lowest digits, etc. Which way is faster? Should we learn from computers or should we teach computers to add several integers our way?

In this paper, we show that the computer way is faster. This adds one more example to the list of cases when computer-based arithmetic algorithms are much more efficient than the algorithms that we humans normally use.

Yes- And No-Gestures Explained By Symmetry, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In most cultures, "yes" is indicate by a vertical head movement (nod), while "no" is indicated by a left-right movement (shake). In this paper, we show that basic symmetries can explain this cultural phenomenon.