Mathematics Commons^™

Unit Rectangle Visibility Graphs, Alice M. Dean, Joanna A. Ellis-Monaghan, Sarah J. Hamilton, Greta Pangborn

Mathematics, Statistics and Computer Science Faculty Research and Publications

Over the past twenty years, rectangle visibility graphs have generated consider- able interest, in part due to their applicability to VLSI chip design. Here we study unit rectangle visibility graphs, with fixed dimension restrictions more closely modeling the constrained dimensions of gates and other circuit components in computer chip applications. A graph G is a unit rectangle visibility graph (URVG) if its vertices can be represented by closed unit squares in the plane with sides parallel to the axes and pairwise disjoint interiors, in such a way that two vertices are adjacent if and only if there is a non-degenerate …

Pendugaan Parameter Regresi Logistik Dengan Jaringan Syaraf Tiruan, Anik Djuraidah

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Logistic regression can be mapped equivalent to artificial neural network (ANN) without hidden layer with logistic as activation function, hence logistic regression is subset of ANN. The result study on binary and poly-chotomous response data show that parameter estimation values of ANN and logistic regression are similar. In comparison with ANN, logistic regression has standard procedure for estimation and testing parameter.
Keyword : logistic regression, generalized linear model, artificial neural network, activation function, hidden layer

Masalah Norm Minimum Pada Ruang Hilbert Dan Aplikasinya, Karyati Karyati, Dhoriva Urwatul Wutsqa

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

In this paper, will be discussed about the minimum norm in the pre- Hilbert Space, Hilbert space and its modification, and its application. The results are: Let X be a pre-Hilbert space and M is a sub space of X. If an element is fixed, then : . If there is such that , then is unique. Let H be a Hilbert space and M be a closed sub space of H . If , then there is a unique element such that , . Let X be a Hilbert space , M be a closed sub space of X …

Inversi Dan Titik-Titik Harmonis, Himmawati Puji, Caturiyati Caturiyati

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Given a circle centre O and radius r in , the inversion in this circle is the mapping defined by , where lies on the straight line through O and A, and on the same side of O as A, and . It will be investigated the property of inversion related to four harmonic points. The result is that the cross-ratio of any four coplanar points A, B, C, D is invariant under inversion. Hence, the inversion preserves the four harmonic points.
Keywords : inversion, cross ratio, four harmonic points.

On The Convergence Theorems Of The Mcshane Integral For Riesz-Spaces-Valued Functions Defined On Real Line, Muslim Ansori, Yosephus D. Sumanto, Novi Rustiana Dewi

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

This paper is a partial result of our researchs in the main topic "On The McShane Integral for Riesz-Spaces-valued Functions Defined on the space ". We have constructed McShane integral for Riesz-spaces-valued functions defined on the space by a technique involving double sequences and proved some basic properties which coincides with the McShane Integral for Banach-spaces valued functions defined on real line. Further, we construct some convergence theorems involving uniformly convergence theorems, monotone convergence theorems and Fatou's lemma in the sense of this integral.
Keywords : Riesz Space, McShane Integral

Menghitung Nilai Probabilitas Pada Distribusi Normal Multivariate, Jaka Nugraha

PYTHAGORAS : Jurnal Matematika dan Pendidikan Matematika

Menghitung nilai probabilitas variabel random yang mempunyai distribusi multivariat normal, merupakan salah satu kendala dalam model probit. Persamaan probabilitas dalam model probit tidak berbentuk persamaan tertutup dan harus diselesaikan secara numerik maupun simulasi. Metode Gezn merupakan metode yang paling efektif untuk menghitung nilai probabilitas normal multivariat. Metode ini banyak diimplementasikan dalam beberapa "package" pada program R. Metode ini juga telah diimplementasikan dalam model multinomial probit yang populer disebut dengan simulator Geweke-Hajivassiliou-Keane (GHK).
Kata kunci : model multinomial probit, faktor Cholesky, random utiliti, deret Taylor

Review Of The Triumph Of Numbers By I. B. Cohen, H L. Vacher

Numeracy

I. Bernard Cohen, The Triumph of Numbers: How Counting Shaped Modern Life. (New York: W.W. Norton & Company, 2005). 209 pp. $24.95 (USA). ISBN 0-393-05769-0.

The premier historian of science ends his career telling how the world has become awash in numbers—“how numbers entered the conduct of life and of government, the understanding of nature, and the analysis of societies.” The stories begin with Kepler and end with Florence Nightingale. In between, major players include Galileo, Harvey, Leeuwenhoek, and Halley; Graunt and Petty; Jefferson and Franklin; Lavoisier, Sinclair, Pinel and Louis; Guerry and Quetelet. The book tells of the spread …

Birds–Dead And Deadly: Why Numeracy Needs To Address Social Construction, Joel Best

Numeracy

Sociologists use the term social construction to refer to the processes by which people assign meaning to their world. This paper argues that numeracy education needs to address social construction. In particular, thinking critically about the statistics the news media report regarding social issues requires understanding the competitive nature of the social problems marketplace, and the social forces that allow questionable numbers to receive widespread public attention. Such critiques must incorporate more than assessing how the numbers were calculated; they must consider the social construction of particular statistics. Two recent examples—claims about the number of birds killed flying into windows, …

Development Of Case Stories By Interviewing Students About Their Critical Moments In Science, Math, And Engineering Classes, Vicki V. May, Thomas H. Luxon, Kathy Weaver, Rachel Esselstein, Cynthia Char

Numeracy

Dartmouth’s Critical Moments project is designed to promote discussions among faculty and graduate students about the retention of students, particularly women and minorities, in science, math, and engineering (SME) disciplines. The first phase of the ongoing project has been the development of four case stories, which are fictionalized composites drawn from surveys and interviews of real Dartmouth students. The surveyed population was 125 students in general chemistry. Of the 77 who agreed to be interviewed, 61 reported having experienced a critical moment – i.e., a positive or negative event or time that had a significant impact on the student’s academic …

Teachers Talk: Pressure Points In The K-8 Mathematics Curriculum, Kim Rheinlander, Dorothy Wallace, Wells Morrison, Daniel Ansari, Donna Coch, B. Venus Williams

Numeracy

Forty K-8 teachers participated in small, in-depth, facilitated discussions about "pressure points" in the curriculum. We define a pressure point as a topic, skill, or concept that is crucial to future mathematics learning but which many or most students do not master to the extent expected at a given grade level. They are issues that persist from one grade level to the next; eventually they impair the ability of students to succeed in technical disciplines. The teachers identified a number of pressure points; we focus on an understanding of place value and "reasonableness" of answer as two examples that were …

Scientifically Based Research In Quantitative Literacy: Guidelines For Building A Knowledge Base, Richard L. Scheaffer

Numeracy

Research in quantitative literacy (QL) is in its infancy, so now is the time to begin a regimen for healthy growth into adulthood. As a new discipline still defining itself, QL has the opportunity to build a sound infrastructure for accumulating a solid body of interconnected research that will serve the discipline well in years to come. To that end, much can be learned from recent studies of the weaknesses of mathematics education research and recommendations on how to overcome them. Mathematics education lacks a strong research foundation, one that is scientific, cumulative, interconnected, and intertwined with teaching practice. These …

Evolution Of Numeracy And The National Numeracy Network, Bernard L. Madison, Lynn Arthur Steen

Numeracy

The National Numeracy Network grew from heightened awareness of the complex and sophisticated nature of quantitative literacy and the resulting need for interdisciplinary attention to education for quantitative literacy in schools and colleges. This complexity and sophistication applies especially to the US where it is fueled by an agile economy and the needs of a democratic society. This paper describes the environment surrounding the National Numeracy Network’s establishment, some of its activities, and some complementary and synergistic actions by other professional societies. The paper concludes with a sample of quantitative literacy programs in colleges and universities

The Scope Of Numeracy, H L. Vacher, Dorothy Wallace

Numeracy

No abstract provided.

Existence And Nonexistence Results For A Class Of Quasilinear Elliptic Systems, Said El Manouni

Mathematics and System Engineering Faculty Publications

Using variational methods, we prove the existence and nonexistence of positive solutions for a class of -Laplacian systems with a parameter.

Decomposition, Packings And Coverings Of Complete Digraphs With A Transitive-Triple And A Pendant Arc., Janice Gail Lewenczuk

Electronic Theses and Dissertations

In the study of design theory, there are eight orientations of the complete graph on three vertices with a pendant edge, K₃∪{e}. Two of these are the 3-circuit with a pendant arc and the other six are transitive triples with a pendant arc. Necessary and sufficient conditions are given for decompositions, packings and coverings of the complete digraph with each of the six transitive triples with a pendant arc.

Chromatic Number Of The Alphabet Overlap Graph, G(2, K , K-2)., Jerry Brent Farley

Electronic Theses and Dissertations

A graph G(a, k, t) is called an alphabet overlap graph where a, k, and t are positive integers such that 0 ≤ t < k and the vertex set V of G is defined as, V = {v : v = (v₁v₂...v_k); v_i ∊ {1, 2, ..., a}, (1 ≤ i ≤ k)}. That is, each vertex, v, is a word of length k over an alphabet of size a. There exists an edge between two vertices u, …

Packings And Coverings Of Various Complete Digraphs With The Orientations Of A 4-Cycle., Melody Elaine Cooper

Electronic Theses and Dissertations

There are four orientations of cycles on four vertices. Necessary and sufficient conditions are given for covering complete directed digraphs D_v, packing and covering complete bipartite digraphs, D_m,n, and packing and covering the complete digraph on v vertices with hole of size w, D(v,w), with three of the orientations of a 4-cycle, including C₄, X, and Y.

Numerics Of Stochastic Systems With Memory (Mittag-Leffler Institute Seminar), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

Existence Of Positive Definite Noncoercive Sums Of Squares, Gregory C. Verchota

Mathematics - All Scholarship

Positive definite forms

f 2 R[x₁, . . . , x_n] which are sums of squares of forms of R[x₁, . . . , x_n] are constructed to have the additional property that the members of any collection of forms whose squares sum to f must share a nontrivial complex root in Cⁿ.

Reed-Solomon Codes Construction & Decoding, Samuel J. Parsons

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

Mathematically Modeling Pcr: An Asymptotic Approximation With Potential For Optimization, Martha J. Garlick

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

A mathematical model for PCR (Polymerase Chain Reaction) is developed using the law of mass action. Differential equations are written from the chemical equations, preserving the detail of the complementary DNA single strand being extended one bas e pair at a time. The equations for the annealing stage are solved analytically. The method of multiple scales is used to approximate solutions for the extension stage. A map is then developed from the solutions to simulate PCR. The advantage of this model is the ability to use the map to optimize the process. Our results suggest that dynamically optimizing the extension …

On The Asymptotic Stability Of Linear Volterra Difference Equations Of Convolution Type, Saber Elaydi, E Messina, A Vecchio

Mathematics Faculty Research

We show that the condition |a| + |∑^+∞_l=0b_l| < 1 is not necessary, though sufficient, for the asymptotic stability of x_n+1 = ax_n + ∑^+∞_l=0b_n-lx_l. We prove the existence of a class of Volterra difference equations (VDEs) that violate this condition but whose zero solutions are asymptotically stable.

A New Family Of Pr Two Channel Filter Banks, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

A new family of multidimensional dimensional (MD) perfect reconstruction (PR) two channel filter banks with finite impulse response (FIR) filters induced from systems of biorthogonal MD scaling functions and wavelets are introduced. One of the advantages of this construction is that the biorthogonal scaling functions and wavelets are easy to establish due to the interpolatory property of the scaling functions to start with. The other advantage is that all filters can be centrosymmetric or bi-linear phase. Examples of two dimensional (2D) bi-linear phase PR twochannel FIR filter banks will be demonstrated.

Recounting Determinants For A Class Of Hessenberg Matrices, Arthur T. Benjamin, Mark A. Shattuck

All HMC Faculty Publications and Research

We provide combinatorial interpretations for determinants which are Fibonacci numbers of several recently introduced Hessenberg matrices. Our arguments make use of the basic definition of the determinant as a signed sum over the symmetric group.

Effective Structure Theorems For Quadratic Spaces Via Height, Lenny Fukshansky

CMC Faculty Publications and Research

Lecture given at the Second International Conference on The Algebraic and Arithmetic Theory of Quadratic Forms, December 2007.

Bidimensional Pr Qmf With Fir Filters, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

Multidimensional perfect reconstruction (PR) quadrature mirror filter (QMF) banks with finite impulse response (FIR) filters induced from systems of biorthogonal multivariate scaling functions and wavelets are investigated. In particular, bivariate scaling functions and wavelets with dilation as an expansive integer matrix whose determinant is two in absolute value are considered. Demonstrative quincunxial examples are explicitly given and new FIR filters are constructed.

Uniform Weighted Compact / Non-Compact Schemes For Shock / Boundary Layer Interaction, Peng Xie

Mathematics Dissertations - Archive

The critical problem of CFD is perhaps an accurate approximation of derivatives for a given discrete data set. Based on our previous work on the weighted compact scheme (WCS), a uniform weighted compact / non-compact scheme (UWCNC) has been developed. Similar to WENO, three high order candidates, left, right, and central, are constructed by using Hermite polynomials. According to the smoothness, three weights are derived and assigned to each candidate. The weights will lead the scheme to be upwind-biased when approaching the shock or other discontinuities but quickly becomes central, compact, and of high order just off the shock. Therefore, …

Teaching Time Savers: The Exam Practically Wrote Itself!, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

When I first started teaching, creating an exam for my upper division courses was a genuinely exciting process. The material felt fresh and relatively unexplored (at least by me), and I remember often feeling pleasantly overwhelmed with what seemed like a vast supply of intriguing and engrossing exam-ready problems. Crafting the perfect exam, one that was noticeably inviting, exceedingly fair, and unavoidably illuminating, was a real joy.

On Progenitively Koszul Commutative Rings, Paul Russell Stern

Mathematics Dissertations - Archive

This paper introduces and identifies classes of progenitively Koszul rings. A progenitively Koszul ring is a commutative ring that admits a Koszul complex A=K(R) that is formal, and such that the homology algebra H(A) generated by A is a Koszul algebra. Local complete intersections, which yield exterior algebras (an example of a Koszul algebra) for their homology algebras, serve as a prototype. It is shown that the local complete intersections occupy only a small portion of the class of progenitively Koszul rings. The material in Chapter 1 will cover basic definitions and facts regarding free resolutions differential graded algebras, homology, …

Markov Semigroups And Estimating Functions, With Applications To Some Financial Models, Jerome A Goldstein, Rosa Maria Mininni, Silvia Romanelli

Communications on Stochastic Analysis

No abstract provided.