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Local Rings Of Embedding Codepth At Most 3 Have Only Trivial Semidualizing Complexes, Saeed Nasseh, Sean Sather-Wagstaff

Department of Mathematical Sciences Faculty Publications

We prove that a local ring R of embedding codepth at most 3 has at most two semidualizing complexes up to shift-isomorphism, namely, R itself and a dualizing R-complex if one exists.

Exponentiated Kumaraswamy-Dagum Distribution With Applications To Income And Lifetime Data, Shujiao Huang, Broderick O. Oluyede

Department of Mathematical Sciences Faculty Publications

A new family of distributions called exponentiated Kumaraswamy-Dagum (EKD) distribution is proposed and studied. This family includes several well known sub-models, such as Dagum (D), Burr III (BIII), Fisk or Log-logistic (F or LLog), and new sub-models, namely, Kumaraswamy-Dagum (KD), Kumaraswamy-Burr III (KBIII), Kumaraswamy-Fisk or Kumaraswamy-Log-logistic (KF or KLLog), exponentiated Kumaraswamy-Burr III (EKBIII), and exponentiated Kumaraswamy-Fisk or exponentiated Kumaraswamy-Log-logistic (EKF or EKLLog) distributions. Statistical properties including series representation of the probability density function, hazard and reverse hazard functions, moments, mean and median deviations, reliability, Bonferroni and Lorenz curves, as well as entropy measures for this class of distributions and the …

The Apostles And Brothers Of Jesus, Andrew Sills

Department of Mathematical Sciences Faculty Publications

Excerpt: The Talpiot tomb, a tomb excavated outside Jerusalem in 1980 and brought to worldwide public attention in 2007, contained ten ossuaries, six of which were inscribed with names. The English equivalents of the names are Jesus son of Joseph, two Marys, a rare diminutive form of Joseph, a diminutive of Matthew, and a Judah son of Jesus. Because of the similarities between this collection of names and certain names appearing in the Christian New Testament, some are curious as to whether the Talpiot tomb may have once interred the remains of Jesus of Nazareth and some of his relatives. …

Mathematical Model Of Dynamic Protein Interactions Regulating P53 Protein Stability For Tumor Suppression, Hua Wang, Guang Peng

Department of Mathematical Sciences Faculty Publications

In the field of cancer biology, numerous genes or proteins form extremely complex regulatory network, which determines cancer cell fate and cancer cell survival. p53 is a major tumor suppressor that is lost in more than 50% of human cancers. It has been well known that a variety of proteins regulate its protein stability, which is essential for its tumor suppressive function. It remains elusive how we could understand and target p53 stabilization process through network analysis. In this paper we discuss the use of random walk and stationary distribution to measure the compound effect of a network of genes …

Multiple Solutions Of A P(X)-Laplacian Equation Involving Critical Nonlinearities, Yuan Liang, Xianbin Wu, Qihu Zhang, Chunshan Zhao

Department of Mathematical Sciences Faculty Publications

In this paper, we consider the existence of multiple solutions for the following p(x)-Laplacian equations with critical Sobolev growth conditions

−div(|∇u| p(x)−2 ∇u) + |u| ^p(x)−2 u = f(x, u) in Ω,

u = 0 on ∂Ω.

We show the existence of infinitely many pairs of solutions by applying the Fountain Theorem and the Dual Fountain Theorem respectively. We also present a variant of the concentration-compactness principle, which is of independent interest.

Discrete Fourier Restriction Associated With Kdv Equations, Yi Hu, Xiaochun Li

Department of Mathematical Sciences Faculty Publications

In this paper, we consider a discrete restriction associated with KdV equations. Some new Strichartz estimates are obtained. We also establish the local well-posedness for the periodic generalized Korteweg-de Vries equation with nonlinear term $F(u)\p_x u$ provided F∈C5 and the initial data ϕ∈Hs with s>1/2.

Comparing The Effects Of Interactive And Noninteractive Complementary Nutrients On Growth In A Chemostat, James P. Braselton, Martha L. Abell, Lorraine Braselton

Department of Mathematical Sciences Faculty Publications

We compare the effects of interactive and noninteractive complementary nutrients on the growth of an organism in the chemostat. We also compare these two situations to the case when the nutrients are substitutable. In previous studies, complementary nutrients have been assumed to be noninteractive. However, more recent research indicates that some complementary nutrient relationships are interactive. We show that interactive complementary and substitutable nutrients can lead to higher population densities than do noninteractive complementary nutrients. We numerically illustrate that if the washout rate is high, an organism can persist at higher densities when the complementary nutrients are interactive than when …

Rock-Paper-Scissors In The Chemostat, James P. Braselton, Martha L. Abell, Lorraine Braselton

Department of Mathematical Sciences Faculty Publications

Rock-Paper-Scissors is a game played by two players to determine a single winner. Biological relationships of Rock-Paper-Scissors are documented. In this paper, we form a continuous model of Rock-Papers-Scissors in the chemostat that coincides with the biology of such relationships. The basic models that we develop coincide with the observed phenomena. Because the model involves a system of seven nonlinear differential equations, global results are difficult to obtain. We present several numerical studies that are the result of a substantial number of numerical trials to illustrate the various possibilities that might occur in the context of the problem discussed here.

Sum Formula Of Multiple Hurwitz-Zeta Values, Jianqiang Zhao

Department of Mathematical Sciences Faculty Publications

Let s1,⋯,sd be d positive integers and define the multiple t-values of depth d byt(s1,⋯,sd)=∑n1>⋯>nd≥11(2n1−1)s1⋯(2nd−1)sd,which is equal to the multiple Hurwitz-zeta value 2−wζ(s1,⋯,sd;−12,⋯,−12) where w=s1+⋯+sd is called the weight. For d≤n, let T(2n,d) be the sum of all multiple t-values with even arguments whose weight is 2n and whose depth is d. In 2011, Shen and Cai gave formulas for T(2n,d) for d≤5 in terms of t(2n), t(2)t(2n−2) and t(4)t(2n−4). In this short note we generalize their results to arbitrary depth by using the theory of symmetric functions established by Hoffman (2012).

Exponential Kleisli Monoids As Eilenberg-Moore Algebras, Dirk Hofmann, Frédéric Mynard, Gavin J. Seal

Department of Mathematical Sciences Faculty Publications

Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This result generalizes the classical identification of exponentiable topological spaces as those whose lattice of open subsets forms a continuous lattice.

The Mc-Dagum Distribution And Its Statistical Properties With Applications, Broderick O. Oluyede, Sasith Rajasooriya

Department of Mathematical Sciences Faculty Publications

In this paper, a new class of distributions called Mc-Dagum distribution is proposed. This class of distributions contains several distributions such as beta-Dagum, beta-Burr III, beta-Fisk, Dagum, Burr III and Fisk distributions as special cases. The hazard function, reverse hazard function, moments, mean residual life function, Renyi entropy and Fisher information are obtained. Lorenz, Bonferroni and Zenga curves are derived. Maximum likelihood estimates of the model parameters and numerical examples are given to illustrate the usefulness of the proposed class of distributions.

Distance-Based Graph Invariants Of Trees And The Harary Index, Stephan G. Wagner, Hua Wang, Xiao-Dong Zhang

Department of Mathematical Sciences Faculty Publications

Introduced in 1947, the Wiener index W(T) = ∑{u,v}⊆V(T) d(u, v) is one of the most thoroughly studied chemical indices. The extremal structures (in particular, trees with various constraints) that maximize or minimize the Wiener index have been extensively investigated. The Harary index H(T) = ∑{u,v}⊆V(T) , introduced in 1993, can be considered as the 'reciprocal analogue' of the Wiener index. From recent studies, it is known that the extremal structures of the Harary index and the Wiener index coincide in many instances, i.e., the graphs that maximize the Wiener index minimize the Harary index and vice versa. In this …

Extremal Values Of Ratios: Distance Problems Vs. Subtree Problems In Trees, László A. Székely, Hua Wang

Department of Mathematical Sciences Faculty Publications

The authors discovered a dual behaviour of two tree indices, the Wiener index and the number of subtrees, for a number of extremal problems [Discrete Appl. Math. 155 (3) 2006, 374-385; Adv. Appl. Math. 34 (2005), 138-155]. Barefoot, Entringer and Székely [Discrete Appl. Math. 80 (1997), 37-56] determined extremal values of σT(w)/σT(u), σT(w)/σT(v), σ(T)/σT(v), and σ(T)/σT(w), where T is a tree on n vertices, v is in the centroid of …

Numerical Studies Of The Generalized L₁ Greedy Algorithm For Sparse Signals, Fangjun Arroyo, Edward Arroyo, Xiezhang Li, Jiehua Zhu

Department of Mathematical Sciences Faculty Publications

The generalized l₁ greedy algorithm was recently introduced and used to reconstruct medical images in computerized tomography in the compressed sensing framework via total variation minimization. Experimental results showed that this algorithm is superior to the reweighted l₁-minimization and l₁ greedy algorithms in reconstructing these medical images. In this paper the effectiveness of the generalized l₁ greedy algorithm in finding random sparse signals from underdetermined linear systems is investigated. A series of numerical experiments demonstrate that the generalized l₁ greedy algorithm is superior to the reweighted l₁-minimization and l₁ greedy algorithms …

Greedy Trees, Subtrees And Antichains, Eric Ould Dadah Andriantiana, Stephan G. Wagner, Hua Wang

Department of Mathematical Sciences Faculty Publications

Greedy trees are constructed from a given degree sequence by a simple greedy algorithm that assigns the highest degree to the root, the second-, third-, ... highest degrees to the root's neighbors, and so on.

They have been shown to maximize or minimize a number of different graph invariants among trees with a given degree sequence. In particular, the total number of subtrees of a tree is maximized by the greedy tree. In this work, we show that in fact a much stronger statement holds true: greedy trees maximize the number of subtrees of any given order. This parallels recent …

Rademacher's Infinite Partial Fractions Conjecture Is (Almost Certainly) False, Andrew Sills, Doron Zeilberger

Department of Mathematical Sciences Faculty Publications

In his book Topics in Analytic Number Theory, Hans Rademacher conjectured that the limits of certain sequences of coefficients that arise in the ordinary partial fraction decomposition of the generating function for partitions of integers into at most N parts exist and equal particular values that he specified. Despite being open for nearly four decades, little progress has been made towards proving or disproving the conjecture, perhaps in part due to the difficulty in actually computing the coefficients in question. In this paper, we present a recurrence (alias difference equation) which provides a fast algorithm for calculating the Rademacher …

On Q-Analogs Of Wostenholme Type Congruences For Multiple Harmonic Sums, Jianqiang Zhao

Department of Mathematical Sciences Faculty Publications

Multiple harmonic sums are iterated generalizations of harmonic sums. Recently Dilcher has considered congruences involving q-analogs of these sums in depth one. In this paper we shall study the homogeneous case for arbitrary depth by using generating functions and shuffle relations of the q-analog of multiple harmonic sums. At the end, we also consider some non-homogeneous cases.