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Articles 1 - 16 of 16
Full-Text Articles in Education
The Convergence Of Two Algorithms For Compressed Sensing Based Tomography, Xiezhang Li, Jiehua Zhu
The Convergence Of Two Algorithms For Compressed Sensing Based Tomography, Xiezhang Li, Jiehua Zhu
Department of Mathematical Sciences Faculty Publications
The constrained total variation minimization has been developed successfully for image reconstruction in computed tomography. In this paper, the block component averaging and diagonally-relaxed orthogonal projection methods are proposed to incorporate with the total variation minimization in the compressed sensing framework. The convergence of the algorithms under a certain condition is derived. Examples are given to illustrate their convergence behavior and noise performance.
Cycles, The Degree Distance, And The Wiener Index, Daniel Gray, Hua Wang
Cycles, The Degree Distance, And The Wiener Index, Daniel Gray, Hua Wang
Department of Mathematical Sciences Faculty Publications
The degree distance of a graph G is D'(G)=(1/2)∑ni=1∑nj=1(di+dj)Li ,j, where di and dj are the degrees of vertices vi, vj ∈ V (G), and Li,j is the distance between them. The Wiener index is defined as W(G)=(1/2)∑ni=1 ∑nj-1Li, j. An elegant result (Gutman; Klein, Mihalic, Plavsic and Trinajstic) is known regarding their correlation, that D'(T)=4W(T)-n(n-1)for a tree T with n vertices. In …
Generalized Diamond-Alpha Dynamic Opial Inequalities, Nuriye Atasever, Billûr Kaymakçalan, Goran Lesaja, Kenan Taş
Generalized Diamond-Alpha Dynamic Opial Inequalities, Nuriye Atasever, Billûr Kaymakçalan, Goran Lesaja, Kenan Taş
Department of Mathematical Sciences Faculty Publications
We establish some new dynamic Opial-type diamond alpha inequalities in time scales. Our results in special cases yield some of the recent results on Opial's inequality and also provide new estimates on inequalities of this type. Also, we introduce an example to illustrate our result.
Balance With Unbounded Complexes, Edgar E. Enochs, Sergio Estrada, Alina Iacob
Balance With Unbounded Complexes, Edgar E. Enochs, Sergio Estrada, Alina Iacob
Department of Mathematical Sciences Faculty Publications
Given a double complex X there are spectral sequences with the E2 terms being either HI (HII(X)) or HII(HI(X)). But if HI(X)=HII(X)=0, then both spectral sequences have all their terms 0. This can happen even though there is nonzero (co)homology of interest associated with X. This is frequently the case when dealing with Tate (co)homology. So, in this situation the spectral sequences may not give any information about the (co)homology of interest. In this article, we …
Formulæ For The Number Of Partitions Of N Into At Most M Parts (Using The Quazi-Polynomial Ansatz), Andrew Sills, Doron Zeilberger
Formulæ For The Number Of Partitions Of N Into At Most M Parts (Using The Quazi-Polynomial Ansatz), Andrew Sills, Doron Zeilberger
Department of Mathematical Sciences Faculty Publications
The purpose of this short article is to announce, and briefly describe, a Maple package, PARTITIONS, that (inter alia) completely automatically discovers, and then proves, explicit expressions (as sums of quasi-polynomials) for pm(n) for any desired m. We do this to demonstrate the power of “rigorous guessing” as facilitated by the quasi-polynomial ansatz.
Generalized Borcea-Voisin Construction, Jimmy Dillies
Generalized Borcea-Voisin Construction, Jimmy Dillies
Department of Mathematical Sciences Faculty Publications
C. Voisin and C. Borcea have constructed mirror pairs of families of Calabi-Yau threefolds by taking the quotient of the product of an elliptic curve with a K3 surface endowed with a non-symplectic involution. In this paper, we generalize the construction of Borcea and Voisin to any prime order and build three and four dimensional Calabi-Yau orbifolds. We classify the topological types that are obtained and show that, in dimension 4, orbifolds built with an involution admit a crepant resolution and come in topological mirror pairs. We show that for odd primes, there are generically no minimal resolutions and the …
Lecture Hall Sequences, Q-Series, And Asymmetric Partition Identities, Sylvie Corteel, Carla D. Savage, Andrew Sills
Lecture Hall Sequences, Q-Series, And Asymmetric Partition Identities, Sylvie Corteel, Carla D. Savage, Andrew Sills
Department of Mathematical Sciences Faculty Publications
We use generalized lecture hall partitions to discover a new pair of q-series identities. These identities are unusual in that they involve partitions into parts from asymmetric residue classes, much like the little Göllnitz partition theorems. We derive a two-parameter generalization of our identities that, surprisingly, gives new analytic counterparts of the little Göllnitz theorems. Finally, we show that the little Göllnitz theorems also involve “lecture hall sequences,” that is, sequences constrained by the ratio of consecutive parts.
Theoretical Properties Of The Length-Biased Inverse Weibull Distribution, Jing X. Kersey, Broderick O. Oluyede
Theoretical Properties Of The Length-Biased Inverse Weibull Distribution, Jing X. Kersey, Broderick O. Oluyede
Department of 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.
Estimation Of Parameters In Weighted Generalized Beta Distribution Of The Second Kind, Yuan Ye, Broderick O. Oluyede, Marvis Pararai
Estimation Of Parameters In Weighted Generalized Beta Distribution Of The Second Kind, Yuan Ye, Broderick O. Oluyede, Marvis Pararai
Department of 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) …
Weighted Generalized Beta Distribution Of The Second Kind, Yuan Ye, Broderick O. Oluyede, Marvis Pararai
Weighted Generalized Beta Distribution Of The Second Kind, Yuan Ye, Broderick O. Oluyede, Marvis Pararai
Department of 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 …
On Some Order 6 Non-Symplectic Automorphisms Of Elliptic K3 Surfaces, Jimmy J. Dillies
On Some Order 6 Non-Symplectic Automorphisms Of Elliptic K3 Surfaces, Jimmy J. Dillies
Department of Mathematical Sciences Faculty Publications
We classify primitive non-symplectic automorphisms of order 6 on K3 surfaces. We show how their study can be reduced to the study of non-symplectic automorphisms of order 3 and to a local analysis of the fixed loci. In particular, we determine the possible fixed loci and show that when the Picard lattice is fixed, K3 surfaces come in mirror pairs.
Full Newton-Step Interior-Point Method For Linear Complementarity Problems, Goran Lesaja, Antre M. Drummer, Ljiljana Miletić
Full Newton-Step Interior-Point Method For Linear Complementarity Problems, Goran Lesaja, Antre M. Drummer, Ljiljana Miletić
Department of Mathematical Sciences Faculty Publications
In this paper we consider an Infeasible Full Newton-step Interior-Point Method (IFNS-IPM) for monotone Linear Complementarity Problems (LCP). The method does not require a strictly feasible starting point. In addition, the method avoids calculation of the step size and instead takes full Newton-steps at each iteration. Iterates are kept close to the central path by suitable choice of parameters. The algorithm is globally convergent and the iteration bound matches the best known iteration bound for these types of methods.
Structure Of Colored Complete Graphs Free Of Proper Cycles, Vincent E. Coll, Colton Magnant, Kathleen Ryan
Structure Of Colored Complete Graphs Free Of Proper Cycles, Vincent E. Coll, Colton Magnant, Kathleen Ryan
Department of Mathematical Sciences Faculty Publications
For a fixed integer m, we consider edge colorings of complete graphs which contain no properly edge colored cycle Cm as a subgraph. Within colorings free of these subgraphs, we establish global structure by bounding the number of colors that can induce a spanning and connected subgraph. In the case of smaller cycles, namely C4,C5, and C6, we show that our bounds are sharp.
Cotorsion Pairs In C(R-Mod), Diego Bravo, Edgar E. Enochs, Alina Iacob, Overtoun M. G. Jenda, Juan Rada
Cotorsion Pairs In C(R-Mod), Diego Bravo, Edgar E. Enochs, Alina Iacob, Overtoun M. G. Jenda, Juan Rada
Department of 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 …
Estimating Population Exposure To Fine Particulate Matter In The Conterminous U.S. Using Shape Function-Based Spatiotemporal Interpolation Method: A County Level Analysis, Lixin Li, Xingyou Zhang, James B. Holt, Jie Tian, Reinhard Piltner
Estimating Population Exposure To Fine Particulate Matter In The Conterminous U.S. Using Shape Function-Based Spatiotemporal Interpolation Method: A County Level Analysis, Lixin Li, Xingyou Zhang, James B. Holt, Jie Tian, Reinhard Piltner
Department of Mathematical Sciences Faculty Publications
This paper investigates spatiotemporal interpolation methods for the application of air pollution assessment. The air pollutant of interest in this paper is fine particulate matter PM2.5. The choice of the time scale is investigated when applying the shape function-based method. It is found that the measurement scale of the time dimension has an impact on the quality of interpolation results. Based upon the result of 10-fold cross validation, the most effective time scale out of four experimental ones was selected for the PM2.5 interpolation. The paper also estimates the population exposure to the ambient air pollution of …
Theoretical Properties Of The Weighted Generalized Rayleigh And Related Distributions, Xueheng Shi, Broderick O. Oluyede, Marvis Pararai
Theoretical Properties Of The Weighted Generalized Rayleigh And Related Distributions, Xueheng Shi, Broderick O. Oluyede, Marvis Pararai
Department of 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.