SUBQUOTIENTS OF A FINITE PRODUCT AND THEIR SELF-HOMOTOPY EQUIVALENCES

In the present work we introduce a composition formula of the pathway fractional integration operator with finite product of generalized K-Wright function and K4-function. The obtained results are in terms of generalized Wright function.Certain special cases of the main results given here are also considered to correspond with some known and new (presumably) pathway fractional integral formulas.

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Inventory lot sizing policies for a closed-loop hybrid system over a finite product life cycle

Computers & Industrial Engineering ◽

10.1016/j.cie.2020.106340 ◽

2020 ◽

Vol 142 ◽

pp. 106340 ◽

Cited By ~ 3

Author(s):

Hong Sun ◽

Xiaodong Xia ◽

Biyu Liu

Keyword(s):

Life Cycle ◽

Hybrid System ◽

Product Life Cycle ◽

Closed Loop ◽

Lot Sizing ◽

Finite Product ◽

Product Life

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A TAIL CONE VERSION OF THE HALPERN–LÄUCHLI THEOREM AT A LARGE CARDINAL

Journal of Symbolic Logic ◽

10.1017/jsl.2017.55 ◽

2019 ◽

Vol 84 (02) ◽

pp. 473-496 ◽

Cited By ~ 1

Author(s):

JING ZHANG

Keyword(s):

Level Set ◽

Rational Numbers ◽

Large Cardinals ◽

Large Cardinal ◽

Linear Orders ◽

Partition Relation ◽

Finite Product

AbstractThe classical Halpern–Läuchli theorem states that for any finite coloring of a finite product of finitely branching perfect trees of height ω, there exist strong subtrees sharing the same level set such that tuples in the product of the strong subtrees consisting of elements lying on the same level get the same color. Relative to large cardinals, we establish the consistency of a tail cone version of the Halpern–Läuchli theorem at a large cardinal (see Theorem 3.1), which, roughly speaking, deals with many colorings simultaneously and diagonally. Among other applications, we generalize a polarized partition relation on rational numbers due to Laver and Galvin to one on linear orders of larger saturation.

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On p-adic Integral Representation of q-Bernoulli Numbers Arising from Two Variable q-Bernstein Polynomials

Symmetry ◽

10.3390/sym10100451 ◽

2018 ◽

Vol 10 (10) ◽

pp. 451 ◽

Cited By ~ 2

Author(s):

Dae Kim ◽

Taekyun Kim ◽

Cheon Ryoo ◽

Yonghong Yao

Keyword(s):

Integral Representation ◽

Bernstein Polynomials ◽

Bernoulli Polynomials ◽

Bernoulli Numbers ◽

Finite Product ◽

Bernoulli Numbers And Polynomials ◽

Special Values ◽

Invariant Integrals ◽

Evaluation Problem ◽

Double Integrals

The q-Bernoulli numbers and polynomials can be given by Witt’s type formulas as p-adic invariant integrals on Z p . We investigate some properties for them. In addition, we consider two variable q-Bernstein polynomials and operators and derive several properties for these polynomials and operators. Next, we study the evaluation problem for the double integrals on Z p of two variable q-Bernstein polynomials and show that they can be expressed in terms of the q-Bernoulli numbers and some special values of q-Bernoulli polynomials. This is generalized to the problem of evaluating any finite product of two variable q-Bernstein polynomials. Furthermore, some identities for q-Bernoulli numbers are found.

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On the endomorphism near-ring of a free group

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091500003655 ◽

1980 ◽

Vol 23 (1) ◽

pp. 103-121 ◽

Cited By ~ 1

Author(s):

R. Warwick Zeamer

Keyword(s):

Wreath Product ◽

Free Group ◽

The Other ◽

Finite Support ◽

Finite Product ◽

Prime Factorization ◽

Infinite Rank ◽

One To One ◽

Almost All ◽

Countably Infinite

Suppose F is an additively written free group of countably infinite rank with basis T and let E = End(F). If we add endomorphisms pointwise on T and multiply them by map composition, E becomes a near-ring. In her paper “On Varieties of Groups and their Associated Near Rings” Hanna Neumann studied the sub-near-ring of E consisting of the endomorphisms of F of finite support, that is, those endomorphisms taking almost all of the elements of T to zero. She called this near-ring Φω. Now it happens that the ideals of Φω are in one to one correspondence with varieties of groups. Moreover this correspondence is a monoid isomorphism where the ideals of φω are multiplied pointwise. The aim of Neumann's paper was to use this isomorphism to show that any variety can be written uniquely as a finite product of primes, and it was in this near-ring theoretic context that this problem was first raised. She succeeded in showing that the left cancellation law holds for varieties (namely, U(V) = U′(V) implies U = U′) and that any variety can be written as a finite product of primes. The other cancellation law proved intractable. Later, unique prime factorization of varieties was proved by Neumann, Neumann and Neumann, in (7). A concise proof using these same wreath product techniques was also given in H. Neumann's book (6). These proofs, however, bear no relation to the original near-ring theoretic statement of the problem.

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Unified integrals involving product of multivariable polynomials and generalized Bessel functions

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v38i6.39291 ◽

2019 ◽

Vol 38 (6) ◽

pp. 73-83

Author(s):

K. S. Nisar ◽

D. L. Suthar ◽

Sunil Dutt Purohit ◽

Hafte Amsalu

Keyword(s):

Bessel Function ◽

Bessel Functions ◽

General Character ◽

Polynomial Functions ◽

Finite Product ◽

Generalized Bessel Function ◽

Integral Formulas ◽

Generalized Bessel Functions ◽

Multivariable Polynomial ◽

Integral Formulae

The aim of this paper is to evaluate two integral formulas involving a finite product of the generalized Bessel function of the first kind and multivariable polynomial functions which results are expressed in terms of the generalized Lauricella functions. The major results presented here are of general character and easily reducible to unique and well-known integral formulae.

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Stability of maxima of random variables defined on a Markov chain

Advances in Applied Probability ◽

10.2307/1426000 ◽

1972 ◽

Vol 4 (2) ◽

pp. 285-295 ◽

Cited By ~ 13

Author(s):

Sidney I. Resnick

Keyword(s):

Markov Chain ◽

Regularity Condition ◽

Sufficient Conditions ◽

Random Variables ◽

Necessary And Sufficient Conditions ◽

Finite Markov Chain ◽

Finite Product ◽

Normalizing Constants ◽

Necessary And Sufficient

Consider maxima Mn of a sequence of random variables defined on a finite Markov chain. Necessary and sufficient conditions for the existence of normalizing constants Bn such that are given. The problem can be reduced to studying maxima of i.i.d. random variables drawn from a finite product of distributions πi=1mHi(x). The effect of each factor Hi(x) on the behavior of maxima from πi=1mHi is analyzed. Under a mild regularity condition, Bn can be chosen to be the maximum of the m quantiles of order (1 - n-1) of the H's.

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On Soft Separation Axioms and Their Applications on Decision-Making Problem

Mathematical Problems in Engineering ◽

10.1155/2021/8876978 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

T. M. Al-shami

Keyword(s):

Decision Making ◽

Topological Spaces ◽

Topological Properties ◽

Finite Product ◽

Separation Axioms ◽

Decision Making Problem ◽

Weak Structure

In this work, we introduce new types of soft separation axioms called p t -soft α regular and p t -soft α T i -spaces i = 0,1,2,3,4 using partial belong and total nonbelong relations between ordinary points and soft α -open sets. These soft separation axioms enable us to initiate new families of soft spaces and then obtain new interesting properties. We provide several examples to elucidate the relationships between them as well as their relationships with e -soft T i , soft α T i , and t t -soft α T i -spaces. Also, we determine the conditions under which they are equivalent and link them with their counterparts on topological spaces. Furthermore, we prove that p t -soft α T i -spaces i = 0,1,2,3,4 are additive and topological properties and demonstrate that p t -soft α T i -spaces i = 0,1,2 are preserved under finite product of soft spaces. Finally, we discuss an application of optimal choices using the idea of p t -soft T i -spaces i = 0,1,2 on the content of soft weak structure. We provide an algorithm of this application with an example showing how this algorithm is carried out. In fact, this study represents the first investigation of real applications of soft separation axioms.

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