Algebra Commons^™

Decoding Book Barcode Images, Yizhou Tao

CMC Senior Theses

This thesis investigated a method of barcode reconstruction to address the recovery of a blurred and convoluted one-dimensional barcode. There are a lot of types of barcodes used today, such as Code 39, Code 93, Code 128, etc. Our algorithm applies to the universal barcode, EAN 13. We extend the methodologies proposed by Iwen et al. (2013) in the journal article "A Symbol-Based Algorithm for Decoding barcodes." The algorithm proposed in the paper requires a signal measured by a laser scanner as an input. The observed signal is modeled as a true signal corrupted by a Gaussian convolution, additional noises, …

Numerical Experiments For Finding Roots Of The Polynomials In Chebyshev Basis, M. S. Solary

Applications and Applied Mathematics: An International Journal (AAM)

Root finding for a function or a polynomial that is smooth on the interval [a; b], but otherwise arbitrary, is done by the following procedure. First, approximate it by a Chebyshev polynomial series. Second, find the zeros of the truncated Chebyshev series. Finding roots of the Chebyshev polynomial is done by eigenvalues of a nXn matrix such as companion or comrade matrices. There are some methods for finding eigenvalues of these matrices such as companion matrix and chasing procedures.We derive another algorithm by second kind of Chebyshev polynomials.We computed the numerical results of these methods for some special and ill-conditioned …

Some Pre-Filters In Eq-Algebras, M. Behzadi, L. Torkzadeh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the notion of an obstinate prefilter (filter) in an EQ-algebra ξ is introduced and a characterization of it is obtained by some theorems. Then the notion of maximal prefilter is defined and is characterized under some conditions. Finally, the relations among obstinate, prime, maximal, implicative and positive implicative prefilters are studied.

Effective Modified Hybrid Conjugate Gradient Method For Large-Scale Symmetric Nonlinear Equations, Jamilu Sabi'u, Mohammed Y. Waziri

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we proposed hybrid conjugate gradient method using the convex combination of FR and PRP conjugate gradient methods for solving Large-scale symmetric nonlinear equations via Andrei approach with nonmonotone line search. Logical formula for obtaining the convex parameter using Newton and our proposed directions was also proposed. Under appropriate conditions global convergence was established. Reported numerical results show that the proposed method is very promising.

Investigation Of Finite Groups Through Progenitors, Charles Baccari

Electronic Theses, Projects, and Dissertations

The goal of this presentation is to find original symmetric presentations of finite groups. It is frequently the case, that progenitors factored by appropriate relations produce simple and even sporadic groups as homomorphic images. We have discovered two of the twenty-six sporadic simple groups namely, M₁₂, J₁ and the Lie type group Suz(8). In addition several linear and classical groups will also be presented. We will present several progenitors including: 2^*12: 2² x (3 : 2), 2^*11: PSL₂(11), 2^*5: (5 : 4) which have produced the homomorphic images: …

An Introduction To Lie Algebra, Amanda Renee Talley

Electronic Theses, Projects, and Dissertations

An (associative) algebra is a vector space over a field equipped with an associative, bilinear multiplication. By use of a new bilinear operation, any associative algebra morphs into a nonassociative abstract Lie algebra, where the new product in terms of the given associative product, is the commutator. The crux of this paper is to investigate the commutator as it pertains to the general linear group and its subalgebras. This forces us to examine properties of ring theory under the lens of linear algebra, as we determine subalgebras, ideals, and solvability as decomposed into an extension of abelian ideals, and nilpotency, …

Distributive Residuated Frames And Generalized Bunched Implication Algebras, Nikolaos Galatos, Peter Jipsen

Mathematics, Physics, and Computer Science Faculty Articles and Research

We show that all extensions of the (non-associative) Gentzen system for distributive full Lambek calculus by simple structural rules have the cut elimination property. Also, extensions by such rules that do not increase complexity have the finite model property, hence many subvarieties of the variety of distributive residuated lattices have decidable equational theories. For some other extensions, we prove the finite embeddability property, which implies the decidability of the universal theory, and we show that our results also apply to generalized bunched implication algebras. Our analysis is conducted in the general setting of residuated frames.

Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Roots Of Early Group Theory In The Works Of Lagrange, Janet Heine Barnett

Abstract Algebra

No abstract provided.

Inquiry Into Saving [Mathematics], Jeanne Funk

Open Educational Resources

‘Inquiry Into Saving’ is an assignment originally designed for MAT117, which is a course for students who have been placed in basic skills mathematics and who can apply a college level course in Algebra and Trigonometry to their program. These students should, ideally, be early in their LaGuardia career, though that is frequently not the case. All, however, are novices of mathematics. The assignment was vetted and revised based on feedback from the Inquiry and Problem Solving in STEM CTL seminar and a charrette not affiliated with the seminar. Revisions addressed connections to the Inquiry and Problem Solving/Written competency/ability pair, …

World Population Dynamics: Modeling Involving Polynomial Functions [Mathematics], Mangala Kothari

Open Educational Resources

In this Inquiry and Problem Solving Assignment students are expected to reflect on their analysis and compare their results with the actual population by conducting their own elementary level research such as searching databases, gathering information and interpreting. Students are expected to comment on the scope of the mathematical model and connect their learning in context to the real-world problem. The assignment includes open-ended questions such as: Write a paragraph about the dynamics of population for the world. What could be some of the possible parameters that contribute to the change in population size? Reflect on what you learned by …

Neutrosophic N -Structures Applied To Bck/Bci-Algebras, Florentin Smarandache, Young Bae Jun, Hashem Bordbar

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic N -structures with applications in BCK/BC I-algebras is discussed. The notions of a neutrosophic N -subalgebra and a (closed) neutrosophic N -ideal in a BCK/BC I-algebra are introduced, and several related properties are investigated. Characterizations of a neutrosophic N -subalgebra and a neutrosophic N -ideal are considered, and relations between a neutrosophic N -subalgebra and a neutrosophic N -ideal are stated. Conditions for a neutrosophic N -ideal to be a closed neutrosophic N -ideal are provided.

Neutrosophic Commutative N-Ideals In Bck-Algebras, Florentin Smarandache, Seok-Zun Song, Young Bae Jun

Branch Mathematics and Statistics Faculty and Staff Publications

The notion of a neutrosophic commutative N -ideal in BCK-algebras is introduced, and several properties are investigated. Relations between a neutrosophic N -ideal and a neutrosophic commutative N -ideal are discussed. Characterizations of a neutrosophic commutative N -ideal are considered.

On A Frobenius Problem For Polynomials, Ricardo Conceição, R. Gondim, M. Rodriguez

Math Faculty Publications

We extend the famous diophantine Frobenius problem to a ring of polynomials over a field~k. Similar to the classical problem we show that the n = 2 case of the Frobenius problem for polynomials is easy to solve. In addition, we translate a few results from the Frobenius problem over ℤ to k[t] and give an algorithm to solve the Frobenius problem for polynomials over a field k of sufficiently large size.

“Wrong” Side Interpolation By Positive Real Rational Functions, Daniel Alpay, Izchak Lewkowicz

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using polynomial interpolation, along with structural properties of the family of rational positive real functions, we here show that a set of m nodes in the open left half of the complex plane, can always be mapped to anywhere in the complex plane by rational positive real functions whose degree is at most m. Moreover we introduce an easy-to-find parametrization in R2m+3 of a large subset of these interpolating functions.

Predicting Locations Of Pollution Sources Using Convolutional Neural Networks, Yiheng Chi, Nickolas D. Winovich, Guang Lin

The Summer Undergraduate Research Fellowship (SURF) Symposium

Pollution is a severe problem today, and the main challenge in water and air pollution controls and eliminations is detecting and locating pollution sources. This research project aims to predict the locations of pollution sources given diffusion information of pollution in the form of array or image data. These predictions are done using machine learning. The relations between time, location, and pollution concentration are first formulated as pollution diffusion equations, which are partial differential equations (PDEs), and then deep convolutional neural networks are built and trained to solve these PDEs. The convolutional neural networks consist of convolutional layers, reLU layers …

Efficiently Representing The Integer Factorization Problem Using Binary Decision Diagrams, David Skidmore

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

Let p be a prime positive integer and let α be a positive integer greater than 1. A method is given to reduce the problem of finding a nontrivial factorization of α to the problem of finding a solution to a system of modulo p polynomial congruences where each variable in the system is constrained to the set {0,...,p − 1}. In the case that p = 2 it is shown that each polynomial in the system can be represented by an ordered binary decision diagram with size less than 20.25log₂(α)³ + 16.5log₂(α)² + …

Π-Operators In Clifford Analysis And Its Applications, Wanqing Cheng

Graduate Theses and Dissertations

In this dissertation, we studies Π-operators in different spaces using Clifford algebras. This approach generalizes the Π-operator theory on the complex plane to higher dimensional spaces. It also allows us to investigate the existence of the solutions to Beltrami equations in different spaces.

Motivated by the form of the Π-operator on the complex plane, we first construct a Π-operator on a general Clifford-Hilbert module. It is shown that this operator is an L^2 isometry. Further, this can also be used for solving certain Beltrami equations when the Hilbert space is the L^2 space of a measure space. This idea is …

Ideal Containments Under Flat Extensions And Interpolation On Linear Systems In P2, Solomon Akesseh

Department of Mathematics: Dissertations, Theses, and Student Research

Fat points and their ideals have stimulated a lot of research but this dissertation concerns itself with aspects of only two of them, broadly categorized here as, the ideal containments and polynomial interpolation problems.

Ein-Lazarsfeld-Smith and Hochster-Huneke cumulatively showed that for all ideals I in k[Pⁿ], I^(mn) ⊆ I^m for all m ∈ N. Over the projective plane, we obtain I⁽⁴⁾< ⊆ I². Huneke asked whether it was the case that I⁽³⁾ ⊆ I². Dumnicki, Szemberg and Tutaj-Gasinska show that if I is the saturated homogeneous radical ideal of the 12 …

Stable Cohomology Of Local Rings And Castelnuovo–Mumford Regularity Of Graded Modules, Luigi Ferraro

Department of Mathematics: Dissertations, Theses, and Student Research

This thesis consists of two parts:

1) A bimodule structure on the bounded cohomology of a local ring (Chapter 1),

2) Modules of infinite regularity over graded commutative rings (Chapter 2).

Chapter 1 deals with the structure of stable cohomology and bounded cohomology. Stable cohomology is a $\mathbb{Z}$-graded algebra generalizing Tate cohomology and first defined by Pierre Vogel. It is connected to absolute cohomology and bounded cohomology. We investigate the structure of the bounded cohomology as a graded bimodule. We use the information on the bimodule structure of bounded cohomology to study the stable cohomology algebra as a trivial extension …