Physical Sciences and Mathematics Commons^™

Computing The Arithmetic Genus Of Hilbert Modular Fourfolds, Helen G. Grundman, L. E. Lippincott

Mathematics Faculty Research and Scholarship

The Hilbert modular fourfold determined by the totally real quartic number field k is a desingularization of a natural compactification of the quotient space Gamma(k)\H-4, where Gamma(k) = PSL2(O-k) acts on H-4 by fractional linear transformations via the four embeddings of k into R. The arithmetic genus, equal to one plus the dimension of the space of Hilbert modular cusp forms of weight (2, 2, 2, 2), is a birational invariant useful in the classification of these varieties. In this work, we describe an algorithm allowing for the automated computation of the arithmetic genus and give sample results.

Advances And Applications Of Dezert-Smarandache Theory (Dsmt) For Information Fusion (Collected Works), Vol. 2, Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

This second volume dedicated to Dezert-Smarandache Theory (DSmT) in Information Fusion brings in new fusion quantitative rules (such as the PCR1-6, where PCR5 for two sources does the most mathematically exact redistribution of conflicting masses to the non-empty sets in the fusion literature), qualitative fusion rules, and the Belief Conditioning Rule (BCR) which is different from the classical conditioning rule used by the fusion community working with the Mathematical Theory of Evidence.

Other fusion rules are constructed based on T-norm and T-conorm (hence using fuzzy logic and fuzzy set in information fusion), or more general fusion rules based on N-norm …

Fuzzy Interval Matrices, Neutrosophic Interval Matrices And Their Applications, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

The new concept of fuzzy interval matrices has been introduced in this book for the first time. The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval matrices but have also demonstrated some of its applications when the data under study is an unsupervised one and when several experts analyze the problem. Further, the authors have introduced in this book multiexpert models using these three new types of interval matrices. The new multi expert models dealt in this book are FCIMs, FRIMs, FCInMs, FRInMs, IBAMs, IBBAMs, nIBAMs, FAIMs, FAnIMS, etc. Illustrative …

Computational Modeling In Applied Problems: Collected Papers On Econometrics, Operations Research, Game Theory And Simulation, Florentin Smarandache, Sukanto Bhattacharya, Mohammad Khoshnevisan

Branch Mathematics and Statistics Faculty and Staff Publications

Computational models pervade all branches of the exact sciences and have in recent times also started to prove to be of immense utility in some of the traditionally 'soft' sciences like ecology, sociology and politics. This volume is a collection of a few cuttingedge research papers on the application of variety of computational models and tools in the analysis, interpretation and solution of vexing real-world problems and issues in economics, management, ecology and global politics by some prolific researchers in the field.

Unfolding The Labyrinth: Open Problems In Physics, Mathematics, Astrophysics, And Other Areas Of Science, Florentin Smarandache, Victor Christianto, Fu Yuhua, Radi Khrapko, John Hutchison

Branch Mathematics and Statistics Faculty and Staff Publications

The reader will find herein a collection of unsolved problems in mathematics and the physical sciences. Theoretical and experimental domains have each been given consideration. The authors have taken a liberal approach in their selection of problems and questions, and have not shied away from what might otherwise be called speculative, in order to enhance the opportunities for scientific discovery. Progress and development in our knowledge of the structure, form and function of the Universe, in the true sense of the word, its beauty and power, and its timeless presence and mystery, before which even the greatest intellect is awed …

Some Neutrosophic Algebraic Structures And Neutrosophic N-Algebraic Structures, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book, for the first time we introduce the notion of neutrosophic algebraic structures for groups, loops, semigroups and groupoids and also their neutrosophic N-algebraic structures. One is fully aware of the fact that many classical theorems like Lagrange, Sylow and Cauchy have been studied only in the context of finite groups. Here we try to shift the paradigm by studying and introducing these theorems to neutrosophic semigroups, neutrosophic groupoids, and neutrosophic loops. We have intentionally not given several theorems for semigroups and groupoid but have given several results with proof mainly in the case of neutrosophic loops, biloops …

Multivariate Expansion Associated With Sheffer-Type Polynomials And Operators, Tian-Xiao He, Leetsch Hsu, Peter Shiue

Tian-Xiao He

With the aid of multivariate Sheffer-type polynomials and differential operators, this paper provides two kinds of general expansion formulas, called respectively the first expansion formula and the second expansion formula, that yield a constructive solution to the problem of the expansion of A(ˆt)f([g(t)) (a composition of any given formal power series) and the expansion of the multivariate entire functions in terms of multivariate Sheffer-type polynomials, which may be considered an application of the first expansion formula and the Sheffer-type operators. The results are applicable to combinatorics and special function theory.

Construction Of Rational Points On Elliptic Curves Over Finite Fields, Andrew Shallue, Christiaan E. Van De Woestijne

Andrew Shallue

A New Type Of Orthogonality In Banach Spaces, Abeer Hasan

Abeer Hasan

On The Convergence Of The Summation Formulas Constructed By Using A Symbolic Operator Approach, Tian-Xiao He, Leetsch C. Hsu, Peter J.-S. Shiue

Tian-Xiao He

This paper deals with the convergence of the summation of power series of the form Σ_{a ≤ k ≤ b}f(k)x^k, where 0 ≤ a ≤ b < ∞, and {f(k)} is a given sequence of numbers with k ∈ [a, b) or f(t) a differentiable function defined on [a, b). Here, the summation is found by using the symbolic operator approach shown in [1]. We will give a different type of the remainder of the summation formulas. The convergence of the corresponding power series will be determined consequently. Several examples such as the generalized Euler's transformation series will also be given. In addition, we will compare the convergence of the given series transforms.

Numerical Approximation To Ζ(2n+1), Tian-Xiao He, Michael J. Dancs

Tian-Xiao He

In this short paper, we establish a family of rapidly converging series expansions ζ(2n +1) by discretizing an integral representation given by Cvijovic and Klinowski [3] in Integral representations of the Riemann zeta function for odd-integer arguments, J. Comput. Appl. Math. 142 (2002) 435–439. The proofs are elementary, using basic properties of the Bernoulli polynomials.

Functional Perturbations Of Nonoscillatory Second Order Difference Equations, William F. Trench

William F. Trench

No abstract provided.

On The Generalized Möbius Inversion Formulas, Tian-Xiao He, Peter J. S. Shiue3, Leetsch C. Hsu

Tian-Xiao He

We provide a wide class of M¨obius inversion formulas in terms of the generalized M¨obius functions and its application to the setting of the Selberg multiplicative functions.

An Euler-Type Formula For Ζ(2k +1), Tian-Xiao He, Michael J. Dancs

Tian-Xiao He

In this short paper, we give several new formulas for ζ(n) when n is an odd positive integer. The method is based on a recent proof, due to H. Tsumura, of Euler’s classical result for even n. Our results illuminate the similarities between the even and odd cases, and may give some insight into why the odd case is much more difficult.

Universal Series By Trigonometric System In Weighted Spaces, Sergo Armenak Episkoposian (Yepiskoposyan)

Sergo Armenak Episkoposian (Yepiskoposyan)

No abstract provided.

Combinatorial Stochastic Processes , Jim Pitman

Jim Pitman

This is a set of lecture notes for a course given at the St. Flour summer school in July 2002. The theme of the course is the study of various combinatorial models of random partitions and random trees, and the asymptotics of these models related to continuous parameter stochastic processes. Following is a list of the main topics treated: models for random combinatorial structures, such as trees, forests, permutations, mappings, and partitions; probabilistic interpretations of various combinatorial notions e.g. Bell polynomials, Stirling numbers, polynomials of binomial type, Lagrange inversion; Kingman's theory of exchangeable random partitions and random discrete distributions; connections …