Analysis Of Intermittence And Log-Periodicity Of Foreign Exchange Rates Near A Crash,
2012
University of Texas at El Paso
Analysis Of Intermittence And Log-Periodicity Of Foreign Exchange Rates Near A Crash, Arturo Casillas
Open Access Theses & Dissertations
Many believe that financial indices near a crash exhibit a type of critical point characterized by log-periodic signatures. Models have been developed based on these ideas in an attempt to mathematically characterize financial data about to crash. Few of these models consider the property of intermittency. Intermittency is a concept borrowed from fluid dynamics that essentially implies that a system alternates between a stable, or predictable, state and unstable state. One model that attempts to characterize crashes incorporates intermittency in the form of log-stationary intervals. It models the asset price as a step function that follows an underlying power law. …
A Generalized Cholera Model And Epidemic-Endemic Analysis,
2012
Old Dominion University
A Generalized Cholera Model And Epidemic-Endemic Analysis, Jin Wang, Shu Liao
Mathematics & Statistics Faculty Publications
The transmission of cholera involves both human-to-human and environment-to-human pathways that complicate its dynamics. In this paper, we present a new and unified deterministic model that incorporates a general incidence rate and a general formulation of the pathogen concentration to analyse the dynamics of cholera. Particularly, this work unifies many existing cholera models proposed by different authors. We conduct equilibrium analysis to carefully study the complex epidemic and endemic behaviour of the disease. Our results show that despite the incorporation of the environmental component, there exists a forward transcritical bifurcation at R0 = 1 for the combined human-environment epidemiological …
Set Ideal Topological Spaces,
2012
University of New Mexico
Set Ideal Topological Spaces, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the authors for the first time introduce a new type of topological spaces called the set ideal topological spaces using rings or semigroups, or used in the mutually exclusive sense. This type of topological spaces use the class of set ideals of a ring (semigroups). The rings or semigroups can be finite or infinite order. By this method we get complex modulo finite integer set ideal topological spaces using finite complex modulo integer rings or finite complex modulo integer semigroups. Also authors construct neutrosophic set ideal toplogical spaces of both finite and infinite order as well as …
Homogeneous Besov Spaces On Stratified Lie Groups And Their Wavelet Characterization,
2012
Aachen University
Homogeneous Besov Spaces On Stratified Lie Groups And Their Wavelet Characterization, Hartmut Fuhr, Azita Mayeli
Publications and Research
We establish wavelet characterizations of homogeneous Besov spaces on stratified Lie groups, bothin terms of continuous and discrete wavelet systems. We first introduce a notion of homogeneous Besov space ̇Bsp,qin terms of a Littlewood-Paley-type decomposition, in analogy to the well-known characterization of the Euclidean case. Such decompositions can be defined via the spectral measure of a suitably chosen sub-Laplacian. We prove that the scale of Besov spaces is independent of the precise choice of Littlewood-Paley decomposition. In particular, different sub-Laplacians yield the same Besov spaces. We then turn to wavelet characterizations, first via continuous wavelet transforms which can be viewed …
Equivariant Degenerations Of Spherical Modules For Groups Of Type A,
2012
Universidade Tecnica de Lisboa
Equivariant Degenerations Of Spherical Modules For Groups Of Type A, Stavros Argyrios Papadakis, Bart Van Steirteghem
Publications and Research
Let G be a complex reductive algebraic group. Fix a Borel subgroup B of G and a maximal torus T in B. Call the monoid of dominant weights L+ and let S be a finitely generated submonoid of L+. V. Alexeev and M. Brion introduced a moduli scheme MS which classifies affine G-varieties X equipped with a T-equivariant isomorphism SpecC[X]U → SpecC[S], where U is the unipotent radical of B. Examples of MS have been obtained by S. Jansou, P. Bravi and S. Cupit-Foutou. In this paper, we prove that MS is isomorphic to an affine space when S is …
On A Pair Of Identities From Ramanujan's Lost Notebook,
2012
West Chester University of Pennsylvania
On A Pair Of Identities From Ramanujan's Lost Notebook, James Mclaughlin, Andrew Sills
Mathematics Faculty Publications
Using a pair of two variable series-product identities recorded by Ramanujan in the lost notebook as inspiration, we find some new identities of similar type. Each identity immediately implies an infinite family of Rogers-Ramanujan type identities, some of which are well-known identities from the literature. We also use these identities to derive some general identities for integer partitions.
A Reciprocity Relation For Wp-Bailey Pairs,
2012
West Chester University of Pennsylvania
A Reciprocity Relation For Wp-Bailey Pairs, James Mclaughlin, Peter Zimmer
Mathematics Faculty Publications
We derive a new general transformation for WP-Bailey pairs by considering the a certain limiting case of a WP-Bailey chain previously found by the authors, and examine several consequences of this new transformation. These consequences include new summation formulae involving WP-Bailey pairs. Other consequences include new proofs of some classical identities due to Jacobi, Ramanujan and others, and indeed extend these identities to identities involving particular specializations of arbitrary WP-Bailey pairs.
A Hardy-Ramanujan-Rademacher-Type Formula For (R,S)-Regular Partitions,
2012
West Chester University of Pennsylvania
A Hardy-Ramanujan-Rademacher-Type Formula For (R,S)-Regular Partitions, James Mclaughlin, Scott Parsell
Mathematics Faculty Publications
Let pr,s(n) denote the number of partitions of a positive integer n into parts containing no multiples of r or s, where r > 1 and s > 1 are square-free, relatively prime integers. We use classical methods to derive a Hardy-Ramanujan-Rademacher-type infinite series for pr,s(n).
Quantum Algorithms For: Quantum Phase Estimation, Approximation Of The Tutte Polynomial And Black-Box Structures,
2012
University of Central Florida
Quantum Algorithms For: Quantum Phase Estimation, Approximation Of The Tutte Polynomial And Black-Box Structures, Hamad Ahmadi
Electronic Theses and Dissertations
In this dissertation, we investigate three different problems in the field of Quantum computation. First, we discuss the quantum complexity of evaluating the Tutte polynomial of a planar graph. Furthermore, we devise a new quantum algorithm for approximating the phase of a unitary matrix. Finally, we provide quantum tools that can be utilized to extract the structure of black-box modules and algebras. While quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT) ) is highly constrained by the requirement of high-precision controlled phase shift …
Continuous And Smooth Images Of Sets,
2012
West Virginia University
Continuous And Smooth Images Of Sets, Krzysztof Ciesielski
Faculty & Staff Scholarship
This note shows that if a subset S of R is such that some continuous function f from R to R has the property "f[S] contains a perfect set," then some infinitely many times differentiable function g (from R to R) has the same property. Moreover, if f[S] is nowhere dense, then the g can have the stronger property "g[S] is perfect." The last result is used to show that it is consistent with ZFC (the usual axioms of set theory) that for each subset S of R of cardinality continuum there exists an infinitely many times differentiable function …
Functions Continuous On Twice Differentiable Curves, Discontinuous On Large Sets,
2012
West Virginia University
Functions Continuous On Twice Differentiable Curves, Discontinuous On Large Sets, Krzysztof Ciesielski
Faculty & Staff Scholarship
We provide a simple construction of a function F:R2-->R discontinuous on a perfect set P, while having continuous restrictions F|C for all twice differentiable curves C. In particular, F is separately continuous and linearly continuous. While it has been known that the projection \pi[P] of any such set P onto a straight line must be meager, our construction allows \pi[P] to have arbitrarily large measure. In particular, P can have arbitrarily large 1-Hausdorff measure, which is the best possible result in this direction, since any such P has Hausdorff dimension at most 1.
Integral Conditions For The Vanishing Of The Cohomology Of Open Sets In Cn,
2012
Politecnico di Milano
Integral Conditions For The Vanishing Of The Cohomology Of Open Sets In Cn, Fabrizio Colombo, M. E. Luna-Elizarrarás, Irene Sabadini, M. Shapiro, Daniele C. Struppa
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we develop and extend some techniques introduced in [1] to find integral conditions for the vanishing of the cohomology of open bounded sets in Cn with values in the sheaf of holomorphic functions.
Theoretical Properties Of The Length-Biased Inverse Weibull Distribution,
2012
East Georgia State College
Theoretical Properties Of The Length-Biased Inverse Weibull Distribution, Jing X. Kersey, Broderick O. Oluyede
Mathematical Sciences: Faculty Publications
We investigate the length-biased inverse Weibull (LBIW) distribution, deriving its density function, hazard and reverse hazard functions, and reliability function. The moments, moment-generating function, Fisher information and Shannon entropy are also given. We discuss parameter estimation via the method of moments and maximum likelihood, and hypothesis testing for the LBIW and parent distributions.
Schur Functions And Their Realizations In The Slice Hyperholomorphic Setting,
2012
Chapman University
Schur Functions And Their Realizations In The Slice Hyperholomorphic Setting, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable resolvent, the so called S-resolvent operator and to extend several results that hold in the complex case to the quaternionic case. We discuss reproducing kernels, positive definite functions in this setting and we show how they can be obtained in our setting using the extension operator and the slice regular product. We define Schur multipliers, and find their co-isometric realization …
On The Class Rsi Of J-Contractive Functions Intertwining Solutions Of Linear Differential Equations,
2012
Chapman University
On The Class Rsi Of J-Contractive Functions Intertwining Solutions Of Linear Differential Equations, Daniel Alpay, Andrey Melnikov, Victor Vinnikov
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we extend and solve in the class of functions RSI mentioned in the title, a number of problems originally set for the class RS of rational functions contractive in the open right-half plane, and unitary on the imaginary line with respect to some preassigned self-adjoint matrix. The problems we consider include the Schur algorithm, the partial realization problem and the Nevanlinna-Pick interpolation problem. The arguments rely on the one-to-one correspondence between elements in a given subclass of RSI and elements in RS. Another important tool in the arguments is a new result pertaining to the classical tangential …
New Topological C-Algebras With Applications In Linear Systems Theory,
2012
Chapman University
New Topological C-Algebras With Applications In Linear Systems Theory, Daniel Alpay, Guy Salomon
Mathematics, Physics, and Computer Science Faculty Articles and Research
Motivated by the Schwartz space of tempered distributions S′ and the Kondratiev space of stochastic distributions S−1 we define a wide family of nuclear spaces which are increasing unions of (duals of) Hilbert spaces H′p,p∈N, with decreasing norms |⋅|p. The elements of these spaces are functions on a free commutative monoid. We characterize those rings in this family which satisfy an inequality of the form |f∗g|p≤A(p−q)|f|q|g|p for all p≥q+d, where * denotes the convolution in the monoid, A(p−q) is a strictly positive number and d is a fixed natural number (in this case we obtain commutative topological C-algebras). Such an …
Cotorsion Pairs In C(R-Mod),
2012
Universidad de los Andes
Cotorsion Pairs In C(R-Mod), Diego Bravo, Edgar E. Enochs, Alina Iacob, Overtoun M. G. Jenda, Juan Rada
Mathematical Sciences: Faculty Publications
In [8] Salce introduced the notion of a co-torsion pair (A, B) in the category of abelian groups. But his definitions and basic results carry over to more general abelian categories and have proved useful in a variety of settings. In this article we will consider complete cotorsion pairs (C, D)in the category C(R-Mod) of complexes of left R-modules over some ring R.If(C, D) is such a pair, and if C is closed un-der taking suspensions, we will show when we regard K(C) and K(D) as subcategories of the homotopy category K(R-Mod), then the embedding functors K(C) → K(R-Mod) and …
Weighted Generalized Beta Distribution Of The Second Kind,
2012
University of Houston
Weighted Generalized Beta Distribution Of The Second Kind, Yuan Ye, Broderick O. Oluyede, Marvis Pararai
Mathematical Sciences: Faculty Publications
In this paper, a new class of weighted generalized beta distribution of the second kind (WGB2) is presented. The construction makes use of the "conservability approach" which includes the size or length-biased distribution as a special case. The class of WGB2 is used as descriptive models for the distribution of income. The results that are presented generalizes the generalized beta distribution of second kind (GB2). The properties of these distributions including behavior of hazard functions, moments, variance, coefficients of variation, skewness and kurtosis are obtained. The moments of other weighted distributions that are related to WGB2 are obtained. Other important …
Estimation Of Parameters In Weighted Generalized Beta Distribution Of The Second Kind,
2012
University of Houston
Estimation Of Parameters In Weighted Generalized Beta Distribution Of The Second Kind, Yuan Ye, Broderick O. Oluyede, Marvis Pararai
Mathematical Sciences: Faculty Publications
This paper applies the class of weighted generalized beta distribution of the second kind (WGB2) as descriptive models for size distribution of income. The properties of WGB2 including mean, variance, coefficient of variation (CV), coefficient of skewness (CS), coefficient of kurtosis (CK) are presented. Other properties including top-sensitive index, bottom-sensitive index, mean logarithmic deviation (MLD) index and Theil index obtained from generalized entropy (GE) are applied in this paper. WGB2 proved to be in the generalized beta-F family of distributions, and maximum likelihood estimation (MLE) is used to obtain the parameter estimates. WGB2 is fitted to U.S. family income (2001-2009) …
Theoretical Properties Of The Weighted Generalized Rayleigh And Related Distributions,
2012
Georgia Institute of Technology
Theoretical Properties Of The Weighted Generalized Rayleigh And Related Distributions, Xueheng Shi, Broderick O. Oluyede, Marvis Pararai
Mathematical Sciences: Faculty Publications
In this paper, a new class of weighted generalization of the Rayleigh distribution is constructed and studied. The statistical properties of these distributions including the behavior of hazard or failure rate and reverse hazard functions, moments, moment generating function, mean, variance, coecient of variation, coecient of skewness, coecient of kurtosis are obtained. Other important properties including entropy (Shannon, beta and generalized) which are measures of the uncertainty in these distributions are also presented.
