The Generalized Reciprocal Super Catalan Matrix,
2016
TÜBİTAK
The Generalized Reciprocal Super Catalan Matrix, Emrah Kiliç, Talha Arikan
Turkish Journal of Mathematics
The reciprocal super Catalan matrix studied by Prodinger is further generalized, introducing two additional parameters. Explicit formulae are derived for the $LU$-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use $q$-analysis and to leave the justification of the necessary identities to the $q$-version of Zeilberger's celebrated algorithm.
On Congruences Related To Central Binomial Coefficients, Harmonic And Lucasnumbers,
2016
TÜBİTAK
On Congruences Related To Central Binomial Coefficients, Harmonic And Lucasnumbers, Si̇bel Koparal, Neşe Ömür
Turkish Journal of Mathematics
In this paper, using some combinatorial identities, we present new congruences involving central binomial coefficients and harmonic, Catalan, and Fibonacci numbers. For example, for an odd prime $p$, we have \begin{eqnarray*} \sum\limits_{k=1}^{\left( p-1\right) /2}\left( -1\right) ^{k}\binom{2k}{k}% H_{k-1} &\equiv &\frac{2^{p}}{p}\left( 2F_{p+1}-5^{\left( p-1\right) /2}-1\right) ({\rm mod\ }p), \\ \sum\limits_{k=0}^{\left( p-1\right) /2}\frac{H_{k}C_{k}}{\left( -4\right) ^{k}} &\equiv &2\frac{Q_{p+1}}{p}-\frac{2^{p+1}}{p}\left( 1+2^{\left( p+1\right) /2}\right) ({\rm mod\ }p), \end{eqnarray*}% and for $\left( \frac{5}{p}\right) =1,$% \begin{equation*} \sum\limits_{k=1}^{\left( p-1\right) /2}\binom{2k}{k}\frac{H_{k-1}F_{k}}{% \left( -4\right) ^{k}}\equiv \frac{1}{p}\left( F_{2p+1}-F_{p+2}\right) -% \frac{2^{p}}{p}F_{p-1}({\rm mod\ }p), \end{equation*} where $\left\{ F_{n}\right\} $ is the Fibonacci sequence and $\left\{ Q_{n}\right\} $ is the Pell-Lucas sequence.
Factorizations Related To The Reciprocal Pascal Matrix,
2016
TÜBİTAK
Factorizations Related To The Reciprocal Pascal Matrix, Helmut Prodinger
Turkish Journal of Mathematics
The reciprocal Pascal matrix has entries $\binom{i+j}{j}^{-1}$. Explicit formul$\ae{}$ for its LU-decomposition, the LU-decomposition of its inverse, and some related matrices are obtained. For all results, $q$-analogues are also presented.
Lagrangian Description, Symplectization, And Eulerian Dynamics Of Incompressible Fluids,
2016
TÜBİTAK
Lagrangian Description, Symplectization, And Eulerian Dynamics Of Incompressible Fluids, Hasan Gümral
Turkish Journal of Mathematics
Eulerian dynamical equations in a three-dimensional domain are used to construct a formal symplectic structure on time-extended space. Symmetries, invariants, and conservation laws are related to this geometric structure. The symplectic structure incorporates dynamics of helicities as identities. The generator of the infinitesimal dilation for symplectic two-form can be interpreted as a current vector for helicity. Symplectic dilation implies the existence of contact hypersurfaces. In particular, these include contact structures on the space of streamlines and on the Bernoulli surfaces.
Some Upper Bounds On The Dimension Of The Schur Multiplierof A Pair Of Nilpotent Lie Algebras,
2016
TÜBİTAK
Some Upper Bounds On The Dimension Of The Schur Multiplierof A Pair Of Nilpotent Lie Algebras, Behrouz Edalatzadeh
Turkish Journal of Mathematics
Let $(L,N)$ be a pair of Lie algebras where $N$ is an ideal of the finite dimensional nilpotent Lie algebra $L$. Some upper bounds on the dimension of the Schur multiplier of $(L,N)$ are obtained without considering the existence of a complement for $N$. These results are applied to derive a new bound on the dimension of the Schur multiplier of a nilpotent Lie algebra.
Problems In Matricially Derived Solid Banach Sequence Spaces,
2016
TÜBİTAK
Problems In Matricially Derived Solid Banach Sequence Spaces, Peter D. Johnson, Faruk Polat
Turkish Journal of Mathematics
Let $\mathbb{F}^\mathbb{N}$ denote the vector space of all scalar sequences. If $A$ is an infinite matrix with nonnegative entries and $\lambda$ is a solid subspace of $\mathbb{F}^\mathbb{N}$, then $ sol-A^{-1}(\lambda)=\{x\in \mathbb{F}^\mathbb{N} : A x \in \lambda\} $ is also a solid subspace of $\mathbb{F}^\mathbb{N}$ that, under certain conditions on $A$ and $\lambda$, inherits a solid topological vector space topology from any such topology on $\lambda$. Letting $\Lambda_0=\lambda$ and $\Lambda_m=sol-A^{-1}(\Lambda_{m-1})$ for $m>0$, we derive an infinite sequence $\Lambda_0, \Lambda_1, \Lambda_2,...$ of solid subspaces of $\mathbb{F}^\mathbb{N}$ from the inputs $A$ and $\lambda$. For $A$ and $\lambda$ confined to certain classes, we …
Existence Of Positive Solutions For Difference Systems Coming From A Model For Burglary,
2016
TÜBİTAK
Existence Of Positive Solutions For Difference Systems Coming From A Model For Burglary, Tianlan Chen, Ruyun Ma
Turkish Journal of Mathematics
In this paper, we use the Brouwer degree to prove existence results of positive solutions for the following difference systems: $$\aligned &{D}_k\Delta^2(A_{k-1}-A^0_{k-1})-(A_{k}-A^0_{k})+N_kf(k, A_{k})=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta^2N_{k-1}+\Delta[g(k, A_{k}, \Delta A_{k-1})N_k]-w^2(N_k-1)=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta A_{1}=0=\Delta A_{n-1},\ \ \Delta N_{1}=0=\Delta N_{n-1}, \endaligned\eqno $$ where the assumptions on $w,\ D_k, A_k^0, f$, and $g$ are motivated by some mathematical models for the burglary of houses.
A Generalization Of Turaev’S Virtual String Cobracket And Self-Intersections Of Virtual Strings,
2016
University of Pennsylvania
A Generalization Of Turaev’S Virtual String Cobracket And Self-Intersections Of Virtual Strings, Patricia Cahn
Mathematics Sciences: Faculty Publications
Previously we defined an operation µ that generalizes Turaev’s cobracket for loops on a surface. We showed that, in contrast to the cobracket, this operation gives a formula for the minimum number of self-intersections of a loop in a given free homotopy class. In this paper we consider the corresponding question for virtual strings, and conjecture that µ gives a formula for the minimum number of self-intersection points of a virtual string in a given virtual homotopy class. To support the conjecture, we show that µ gives a bound on the minimal self-intersection number of a virtual string which is …
Small Sample Confidence Bands For The Survival Functions Under Proportional Hazards Model,
2016
Missouri University of Science and Technology
Small Sample Confidence Bands For The Survival Functions Under Proportional Hazards Model, Emad Mohamed Abdurasul
Doctoral Dissertations
"In this work, a saddlepoint-based method is developed for generating small sample confidence bands for the population survival function from the Kaplan-Meier (KM), the product limit (PL), and Abdushukurov-Cheng-Lin (ACL) survival function estimators, under the proportional hazards model. In the process the exact distribution of these estimators is derived and developed mid-population tolerance bands for said estimators. The proposed saddlepoint method depends upon the Mellin transform of the zero-truncated survival estimator which is derived for the KM, PL, and ACL estimators. These transforms are inverted via saddlepoint approximations to yield highly accurate approximations to the cumulative distribution functions of the …
Chebyshev Inversion Of The Radon Transform,
2016
University of South Carolina
Chebyshev Inversion Of The Radon Transform, Jared Cameron Szi
Theses and Dissertations
In its two-dimensional form, the Radon transform of an image (function) is a collection of projections of the image which are parameterized by a set of angles (from the positive x-axis) and distances from the origin. Computational methods of the Radon transform are important in many image processing and computer vision problems, such as pattern recognition and the reconstruction of medical images. However, computability requires the construction of a discrete analog to the Radon transform, along with discrete alternatives for its inversion. In this paper, we present discrete analogs using classical methods of Chebyshev polynomial reconstruction, along with a new …
On A Constant Associated With The Prouhet-Tarry-Escott Problem,
2016
University of South Carolina
On A Constant Associated With The Prouhet-Tarry-Escott Problem, Maria E. Markovich
Theses and Dissertations
For n a positive integer, the Prouhet-Tarry-Escott Problem asks for two different sets of n positive integers for which the sum of the kth powers of the elements of one set is equal to the sum of the kth powers of the elements of the second set for each positive integer k < n. For n > 12, it is not known whether such sets exist. I will give some background on this problem and then show how Newton polygons can be used to determine information on the size of the 2-adic value of a certain constant associated with the problem.
Binary Quartic Forms Over Fp,
2016
University of South Carolina
Binary Quartic Forms Over Fp, Daniel Thomas Kamenetsky
Theses and Dissertations
Let Vp denote the five dimensional vector space of binary quartic forms over the finite field Fp, with p a prime greater than 3. There is a natural action of the group GL1(Fp)×GL2(Fp) on Vp. This action partitions Vp into orbits, the number of which increases with p. In this thesis, we determine explicitly, for a given p, the number of orbits under the action of GL1(Fp) × GL2(Fp) on Vp. Moreover, we determine the size of each orbit and the general structure of the forms each orbit contains. We also introduce an application of understanding these orbits to the …
A Linear Matrix Inequality-Based Approach For The Computation Of Actuator Bandwidth Limits In Adaptive Control,
2016
Missouri University of Science and Technology
A Linear Matrix Inequality-Based Approach For The Computation Of Actuator Bandwidth Limits In Adaptive Control, Daniel Robert Wagner
Masters Theses
"Linear matrix inequalities and convex optimization techniques have become popular tools to solve nontrivial problems in the field of adaptive control. Specifically, the stability of adaptive control laws in the presence of actuator dynamics remains as an important open control problem. In this thesis, we present a linear matrix inequalities-based hedging approach and evaluate it for model reference adaptive control of an uncertain dynamical system in the presence of actuator dynamics. The ideal reference dynamics are modified such that the hedging approach allows the correct adaptation without being hindered by the presence of actuator dynamics. The hedging approach is first …
Modeling Daily Electricity Load Curve Using Cubic Splines And Functional Principal Components,
2016
Missouri University of Science and Technology
Modeling Daily Electricity Load Curve Using Cubic Splines And Functional Principal Components, Abdelmonaem Salem Jornaz
Doctoral Dissertations
"Forecasting electricity load is very important to the electric utilities as well as producers of power because accurate predictions can cut down costs by avoiding power shortages or surpluses. Of specific interest is the 24-hour daily electricity load profile, which provides insight into periods of high demand and periods where the use of electricity is at a minimum. Researchers have proposed many approaches to modeling electricity prices, real-time load, and day-ahead demand, with varying success. In this dissertation three new approaches to modeling and forecasting the 24-hour daily electricity load profiles are presented. The application of the proposed methods is …
Boundary Control Of Parabolic Pde Using Adaptive Dynamic Programming,
2016
Missouri University of Science and Technology
Boundary Control Of Parabolic Pde Using Adaptive Dynamic Programming, Behzad Talaei
Doctoral Dissertations
"In this dissertation, novel adaptive/approximate dynamic programming (ADP) based state and output feedback control methods are presented for distributed parameter systems (DPS) which are expressed as uncertain parabolic partial differential equations (PDEs) in one and two dimensional domains. In the first step, the output feedback control design using an early lumping method is introduced after model reduction. Subsequently controllers were developed in four stages; Unlike current approaches in the literature, state and output feedback approaches were designed without utilizing model reduction for uncertain linear, coupled nonlinear and two-dimensional parabolic PDEs, respectively. In all of these techniques, the infinite horizon cost …
Pointwise And Uniform Convergence Of Fourier Series On Su(2),
2016
Missouri University of Science and Technology
Pointwise And Uniform Convergence Of Fourier Series On Su(2), Donald Forrest Myers
Doctoral Dissertations
"Let f be a Lipschitz function on the special unitary group SU (2). We prove that the Fourier partial sums of f converge to f uniformly on SU (2), thereby extending theorems of Caccioppoli, Mayer, and a special case of Ragozin. Pointwise convergence theorems for the Fourier series of functions on SU (2), due to Liu and Qian, were obtained by Clifford algebra techniques. We obtain similar versions of these theorems using simpler proof techniques: classical harmonic analysis and group theory"--Abstract, page iii.
A Partition Function Connected With The Göllnitz-Gordon Identities,
2016
Georgia Southern University
A Partition Function Connected With The Göllnitz-Gordon Identities, Nicolas A. Smoot
College of Graduate Studies: Theses & Dissertations
Nearly a century ago, the mathematicians Hardy and Ramanujan established their celebrated circle method to give a remarkable asymptotic expression for the unrestricted partition function. Following later improvements by Rademacher, the method was utilized by Niven, Lehner, Iseki, and others to develop rapidly convergent series representations of various restricted partition functions. Following in this tradition, we use the circle method to develop formulas for counting the restricted classes of partitions that arise in the Gollnitz-Gordon identities. We then show that our results are strongly supported by numerical tests. As a side note, we also derive and compare the asymptotic behavior …
Gorenstein Projective (Pre)Covers,
2016
Georgia Southern University
Gorenstein Projective (Pre)Covers, Michael J. Fox
College of Graduate Studies: Theses & Dissertations
The existence of the Gorenstein projective precovers is one of the main open problems in Gorenstein Homological algebra. We give sufficient conditions in order for the class of Gorenstein projective complexes to be special precovering in the category of complexes of R-modules Ch(R). More precisely, we prove that if every complex in Ch(R) has a special Gorenstein flat cover, every Gorenstein projective complex is Gorenstein flat, and every Gorenstein flat complex has finite Goenstein projective dimension, then the class of Gorenstein projective complexes, GP(C), is special precovering in Ch(R).
Series 07,
2016
Illinois Mathematics and Science Academy
Series 08,
2016
Illinois Mathematics and Science Academy
