97,603 research outputs found
An extension of Sheffer polynomials
No full textSheffer [Some properties of polynomial sets of type zero, Duke Math. J. 5 (1939), pp.590-622] studied polynomial sets zero type and many authors investigated various properties and its applications. In the sequel to the study of Sheffer Polynomials, an attempt is made to generalize the Sheffer polynomials by using partial differential operator
Joshua Davis: Author of Spare Parts
No full textCitation: K-State First (2016). Joshua Davis: Author of Spare Parts [Flier]. Manhattan, Kansas: K-State First.Flyer advertising Joshua Davis's author talk at Kansas State University
Approximation with king type generalized Szász-Sheffer operators
No full textBu tezde genelleştirilmiş Szász-Sheffer operatörlerinin bazı yaklaşım özellikleri verildi ve lineer fonksiyonları koruyan King tip genelleştirmesi tanımlandı. Bu genelleştirmede, belirli koşulları sağlayan sınırsız diziler yardımı ile daha iyi bir yaklaşım derecesi elde edildi. King tipi operatörlerin yakınsama oranının genelleştirilmiş Szász-Sheffer operatörlerinden daha iyi olduğu ispatlandı ve King tipi operatörlerin yaklaşımlarının Szász-Sheffer operatörlerinden daha iyi olduğu grafikler ile gösterildi. İntegrallenebilir fonksiyonlara yaklaşmak için, genelleştirilmiş Szász-Sheffer-Kantorovich operatörleri tanımlanarak bu operatörün yaklaşım derecesi, süreklilik modülü, Lipschitz sınıfından fonksiyonlar ve Peetre- fonksiyoneli cinsinden verildi. Ayrıca Szász-Sheffer-Kantorovich operatörleri için asimptotik yaklaşım formülü Voronovskaja tip teorem ile elde edildi. Aynı zamanda Szász-Sheffer-Kantorovich operatörlerin King tip genelleştirmesi tanımlandı. King tipi operatörlerin Szász-Sheffer-Kantorovich operatörlerinden daha iyi bir yaklaşım oranına sahip olduğu ispatlanarak bu sonuç grafikler ile gösterildi. Son olarak iki değişkenli genelleştirilmiş Szász-Sheffer-Kantorovich operatörleri tanımlanarak tam süreklilik modülü ve kısmi süreklilik modülü yardımıyla yaklaşım hızları elde edildi. Ayrıca Peetre- fonksiyoneli ve Lipschitz sınıfından fonksiyonlara yaklaşımı ile ilgili bir sonuç elde edildi.In this thesis, some approximation properties of generalized Szász-Sheffer operators are given and the King type generalization of these operators which preserves linear functions is introduced. It is proved that the rate of convergence of the King type operators is better than generalized Szász-Shefferoperators. It is supported by graphs that the approximation of King type operators is better than Szász-Sheffer operators. In order to approximate integrable functions, the generalized Szász-Sheffer-Kantorovich operators are defined. The degree of approximation of these operators is given in terms of modulus of continuity and also by means of Lipschitz class and the Petree's K-functional. In addition, the asymptotic approximation formula is obtained by Voronovskaja type theorem for Szász-Sheffer-Kantorovich operators. Moreover, the King type generalization of the Szász-Sheffer-Kantorovich operators is introduced. It is proved that the King type operators have a better order of approximation than Szász-Sheffer-Kantorovich operators and this result is illustrated by graphics. Finally, bivariate Szász-Sheffer-Kantorovich operators are introduced and the degree of approximation for the bivariate case is investigated by using the complete and partial moduli of continuity. The rate of convergence is obtained by means of a Lipschitz type function and the Peetre's K-functional
King tip genelleştirilmiş Szász-Sheffer operatörleri ile yaklaşım
No full textBu tezde genelleştirilmiş Szász-Sheffer operatörlerinin bazı yaklaşım özellikleri verildi ve lineer fonksiyonları koruyan King tip genelleştirmesi tanımlandı. Bu genelleştirmede, belirli koşulları sağlayan sınırsız diziler yardımı ile daha iyi bir yaklaşım derecesi elde edildi. King tipi operatörlerin yakınsama oranının genelleştirilmiş Szász-Sheffer operatörlerinden daha iyi olduğu ispatlandı ve King tipi operatörlerin yaklaşımlarının Szász-Sheffer operatörlerinden daha iyi olduğu grafikler ile gösterildi. İntegrallenebilir fonksiyonlara yaklaşmak için, genelleştirilmiş Szász-Sheffer-Kantorovich operatörleri tanımlanarak bu operatörün yaklaşım derecesi, süreklilik modülü, Lipschitz sınıfından fonksiyonlar ve Peetre- fonksiyoneli cinsinden verildi. Ayrıca Szász-Sheffer-Kantorovich operatörleri için asimptotik yaklaşım formülü Voronovskaja tip teorem ile elde edildi. Aynı zamanda Szász-Sheffer-Kantorovich operatörlerin King tip genelleştirmesi tanımlandı. King tipi operatörlerin Szász-Sheffer-Kantorovich operatörlerinden daha iyi bir yaklaşım oranına sahip olduğu ispatlanarak bu sonuç grafikler ile gösterildi. Son olarak iki değişkenli genelleştirilmiş Szász-Sheffer-Kantorovich operatörleri tanımlanarak tam süreklilik modülü ve kısmi süreklilik modülü yardımıyla yaklaşım hızları elde edildi. Ayrıca Peetre- fonksiyoneli ve Lipschitz sınıfından fonksiyonlara yaklaşımı ile ilgili bir sonuç elde edildi.In this thesis, some approximation properties of generalized Szász-Sheffer operators are given and the King type generalization of these operators which preserves linear functions is introduced. It is proved that the rate of convergence of the King type operators is better than generalized Szász-Shefferoperators. It is supported by graphs that the approximation of King type operators is better than Szász-Sheffer operators. In order to approximate integrable functions, the generalized Szász-Sheffer-Kantorovich operators are defined. The degree of approximation of these operators is given in terms of modulus of continuity and also by means of Lipschitz class and the Petree's K-functional. In addition, the asymptotic approximation formula is obtained by Voronovskaja type theorem for Szász-Sheffer-Kantorovich operators. Moreover, the King type generalization of the Szász-Sheffer-Kantorovich operators is introduced. It is proved that the King type operators have a better order of approximation than Szász-Sheffer-Kantorovich operators and this result is illustrated by graphics. Finally, bivariate Szász-Sheffer-Kantorovich operators are introduced and the degree of approximation for the bivariate case is investigated by using the complete and partial moduli of continuity. The rate of convergence is obtained by means of a Lipschitz type function and the Peetre's K-functional
Steven Johnson Author Talk Poster
No full textK-State Book NetworkA poster advertising an author talk by Steven Johnson at Kansas State University on September 3, 2014. Steven Johnson's book "The Ghost Map" was the 2014-2015 common book
Combinatorial identities involving the central coefficients of a Sheffer matrix
No full textGiven m ∈ N, m ≥ 1, and a Sheffer matrix S = [s_{n,k}]_{n,k}≥0, we obtain the exponential generating series for the coefficients binomial(a+(m+1)n,a+mn)^{−1}*s_{a+(m+1)n,a+mn}. Then, by using this series, we obtain two general combinatorial identities, and their specialization to r-Stirling, r-Lah and r-idempotent numbers. In particular, using this approach, we recover two well known binomial identities, namely Gould’s identity and Hagen-Rothe’s identity. Moreover, we generalize these results obtaining an exchange identity for a cross sequence (or for two Sheffer sequences) and an Abel-like identity for a cross sequence (or for an s-Appell sequence). We also obtain some new Sheffer matrices
Positive Bernstein-Sheffer Operators
No full textAbstractLet h(t) = Σn ≥ 1hntn, h1 > 0, and exp(xh(t)) = Σn ≥ 0Pn(x) tn/n!. For f ∈ C[0,1], the associated Bernstein-Sheffer operator of degree n is defined by Bhnf(x) = Pn− 1 Σnk = 0f(k/n)(nk) Pk(x) Pn − k(1 − x) where pn = pn(1). We characterize functions h for which Bhn is a positive operator for all n ≥ 0. Then we give a necessary and sufficient condition insuring the uniform convergence of Bhnf to f. When h is a polynomial, we give an upper bound for the error ∥ f − Bhnf ∥∞. We also discuss the behavior of Bhnf when h is a series with a finite or infinite radius of convergence
On the approximation properties of Bernstein-Sheffer operator
No full text前言主要介绍一维Bernstein算子的研究成果和各类Bernstein型算子的推广 2Sheffer序列的定义及其有关性质利用幂级数G(t)=DD(n=0DD)g ntn(g0)H(t)=t+ht2和exH(t)=DD(n=0DD)P n(x)S X(tnn!SX)G(x)exH(t)=DD(n=0DD)Sn(x)SX( t nn!SX)定义并给出了Sheffer序列Pn(x)Sn(x)及其具体表 示式证明了 HTH定理2.1HT当h0时对x(01有SX(Pn(x)Pn+1 (x) SX)SX(1xSX) HTH定理2.2HT当h0时对x(01有SX(Pn-2(x)P ...Bernstein-Sheffer operator is defined as B H n(f(t),x)=SX(1 P n(1) SX)DD(n k=0 DD)f JB((SX(k n SX)JB))JB((n k JB))P n(x)P n-k (1-x)(P n(1)0) This thesis includes six sections. Section 1 is an introduction in which some results about 1-dimention and various others Bernstein operators are introduced.Bernstein operator is generalized in a different perspective. Section 2 presents the definatio...学位：理学硕士院系专业：数学系_基础数学学号：19952300
The Sheffer B-type 1 Orthogonal Polynomial Sequences
No full textIn 1939, I.M. Sheffer proved that every polynomial sequence belongs to one and only one type. Sheffer extensively developed properties of the B-Type 0 polynomial sequences and determined which sets are also orthogonal. He subsequently generalized his classification method to the case of arbitrary B-Type k by constructing the generalized generating function A(t)exp[xH1(t) + · · · + xk+1Hk(t)] = ∑∞n=0 Pn(x)tn, with Hi(t) = hi,iti + hi,i+1t i+1 + · · · , h1,1 ≠ 0. Although extensive research has been done on characterizing polynomial sequences, no analysis has yet been completed on sets of type one or higher (k ≥ 1). We present a preliminary analysis of a special case of the B-Type 1 (k = 1) class, which is an extension of the B-Type 0 class, in order to determine which sets, if any, are also orthogonal sets. Lastly, we consider an extension of this research and comment on future considerations. In this work the utilization of computer algebra packages is indispensable, as computational difficulties arise in the B-Type 1 class that are unlike those in the B-Type 0 class
Shifting Property for Riordan, Sheffer and Connection Constants Matrices.
No full textWe study the shifting property of a matrix and a sequence , i.e., the identity
\begin{displaymath} \sum_{k=0}^n r_{n,k} h_{k+1} = \sum_{k=0}^n r_{n+1,k+1} h_k \, , \end{displaymath}
when R is a Riordan matrix, a Sheffer matrix (exponential Riordan matrix), or a connection constants matrix (involving symmetric functions and continuants). Moreover, we consider the shifting identity for several sequences of combinatorial interest, such as the binomial coefficients, the polynomial coefficients, the Stirling numbers (and their q-analogues), the Lah numbers, the De Morgan numbers, the generalized Fibonacci numbers, the Bell numbers, the involutions numbers, the Chebyshev polynomials, the Stirling polynomials, the Hermite polynomials, the Gaussian coefficients, and the q-Fibonacci numbers
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