scholarly journals An elliptic extension of the general product formula for augmented rook boards

2016 ◽  
Vol 58 ◽  
pp. 247-266 ◽  
Author(s):  
Michael J. Schlosser ◽  
Meesue Yoo
Keyword(s):  
Product Formula ◽  
General Product

scholarly journals Augmented Rook Boards and General Product Formulas

10.37236/809 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Brian K. Miceli ◽  
Jeffrey Remmel
Keyword(s):  
Product Formula ◽  
Combinatorial Proof ◽  
Rook Theory ◽  
Special Cases ◽  
Ferrers Board ◽  
General Product ◽  
Product Formulas

There are a number of so-called factorization theorems for rook polynomials that have appeared in the literature. For example, Goldman, Joichi and White showed that for any Ferrers board $B = F(b_1, b_2, \ldots, b_n)$, $$\prod_{i=1}^n (x+b_i-(i-1)) = \sum_{k=0}^n r_k(B) (x)\downarrow_{n-k}$$ where $r_k(B)$ is the $k$-th rook number of $B$ and $(x)\downarrow_k = x(x-1) \cdots (x-(k-1))$ is the usual falling factorial polynomial. Similar formulas where $r_k(B)$ is replaced by some appropriate generalization of the $k$-th rook number and $(x)\downarrow_k$ is replaced by polynomials like $(x)\uparrow_{k,j} = x(x+j) \cdots (x+j(k-1))$ or $(x)\downarrow_{k,j} = x(x-j) \cdots (x-j(k-1))$ can be found in the work of Goldman and Haglund, Remmel and Wachs, Haglund and Remmel, and Briggs and Remmel. We shall refer to such formulas as product formulas. The main goal of this paper is to develop a new rook theory setting in which we can give a uniform combinatorial proof of a general product formula that includes, as special cases, essentially all the product formulas referred to above. We shall also prove $q$-analogues and $(p,q)$-analogues of our general product formula.

scholarly journals General Product Formula of Multiple Integrals of Lévy Process

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Nishant Agrawal ◽  
Yaozhong Hu ◽  
Neha Sharma
Keyword(s):  
Lévy Process ◽  
Product Formula ◽  
Levy Process ◽  
Multiple Integrals ◽  
General Product

Factor Influencing Consumers on Beguiling Craze of Online Shopping: A Study of Attitude in Nagpur City of Maharashtra (India)

2019 ◽  
Vol 118 (11) ◽  
pp. 137-145
Author(s):  
Sohail Imran Khan ◽  
Rohat Zada
Keyword(s):  
Online Shopping ◽  
Young Generation ◽  
Web Based ◽  
High Significance ◽  
Online Fraud ◽  
Return Policy ◽  
Large State ◽  
Evolution Of Technology ◽  
Center City ◽  
General Product

Evolution of technology has completely revolutionaries’ day to day life of common man. Technology has penetrated in our life like anything. These days everybody is using technology for their benefit’s and marketers are no an exception to it. They are using technology to reach to the customers. Days are far gone when people used to line up in stores to purchase the general product. These days, more and more individuals lean toward online shopping, which is presently a pattern of style and fashion. Nagpur, the center city of the country and world-famous for its oranges is advancing towards computerized explosion that makes high significance on the assessment of the present acknowledgment level of online shopping by the youngsters. In this way, understanding the by and a large state of customer's attitude towards web-based shopping is significant for the Nagpurians. In this study, 143 respondents took part in the survey. Respondents were selected through simple random technique. Data was analyzed using SPSS Version 22. This study found that online shopping is very common in this young generation of Nagpur. Major reason for Nagpurains to do online shopping is that it saves a lot of time. However, consumer those who do not shop online is only because of online fraud, lack of personal touch and no return policy. Nagpur consumers do prescribe online shopping as an elective path for shopping.

Complex group algebras of the direct product of non-isomorphic Suzuki groups

2019 ◽  
Vol 19 (02) ◽  
pp. 2050036
Author(s):  
Morteza Baniasad Azad ◽  
Behrooz Khosravi
Keyword(s):  
Direct Product ◽  
Group Algebra ◽  
Irreducible Character ◽  
Prime Numbers ◽  
Product Formula ◽  
Character Degrees ◽  
Group Algebras ◽  
Complex Group ◽  
Complex Group Algebra ◽  
Suzuki Groups

In this paper, we prove that the direct product [Formula: see text], where [Formula: see text] are distinct numbers, is uniquely determined by its complex group algebra. Particularly, we show that the direct product [Formula: see text], where [Formula: see text]’s are distinct odd prime numbers, is uniquely determined by its order and three irreducible character degrees.

scholarly journals A new product formula involving Bessel functions

2021 ◽  
pp. 1-17
Author(s):  
Mohamed Amine Boubatra ◽  
Selma Negzaoui ◽  
Mohamed Sifi
Keyword(s):  
Bessel Functions ◽  
New Product ◽  
Product Formula

scholarly journals Design of Consumables in a Resource-Efficient Economy—A Literature Review

2021 ◽  
Vol 13 (3) ◽  
pp. 1036
Author(s):  
Siri Willskytt
Keyword(s):  
Life Cycle ◽  
Literature Review ◽  
Product Design ◽  
Circular Economy ◽  
Design Guidelines ◽  
The Novel ◽  
Specific Design ◽  
Design Considerations ◽  
Life Cycle Perspective ◽  
General Product

Consumable products have received less attention in the circular economy (CE), particularly in regard to the design of resource-efficient products. This literature review investigates the extent to which existing design guidelines for resource-efficient products are applicable to consumables. This analysis is divided into two parts. The first investigates the extent to which general product-design guidelines (i.e., applicable to both durables and consumables) are applicable to consumables. This analysis also scrutinizes the type of recommendations presented by the ecodesign and circular product design, to investigate the novel aspects of the CE in product design. The second analysis examines the type of design considerations the literature on product-type specific design guidelines recommends for specific consumables and whether such guidelines are transferable. The analysis of general guidelines showed that, although guidelines are intended to be general and applicable to many types of products, their applicability to consumable products is limited. Less than half of their recommendations can be applied to consumables. The analysis also identified several design considerations that are transferable between product-specific design guidelines. This paper shows the importance of the life-cycle perspective in product design, to maximize the opportunities to improve consumables.

scholarly journals Completely bounded bimodule maps and spectral synthesis

2017 ◽  
Vol 28 (10) ◽  
pp. 1750067 ◽  
Author(s):  
M. Alaghmandan ◽  
I. G. Todorov ◽  
L. Turowska
Keyword(s):  
Tensor Product ◽  
Compact Group ◽  
Closed Subset ◽  
Spectral Synthesis ◽  
Locally Compact Group ◽  
Product Formula ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Multiplication Algebra

We initiate the study of the completely bounded multipliers of the Haagerup tensor product [Formula: see text] of two copies of the Fourier algebra [Formula: see text] of a locally compact group [Formula: see text]. If [Formula: see text] is a closed subset of [Formula: see text] we let [Formula: see text] and show that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] then [Formula: see text] is a set of local spectral synthesis for [Formula: see text]. Conversely, we prove that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] and [Formula: see text] is a Moore group then [Formula: see text] is a set of spectral synthesis for [Formula: see text]. Using the natural identification of the space of all completely bounded weak* continuous [Formula: see text]-bimodule maps with the dual of [Formula: see text], we show that, in the case [Formula: see text] is weakly amenable, such a map leaves the multiplication algebra of [Formula: see text] invariant if and only if its support is contained in the antidiagonal of [Formula: see text].

scholarly journals The Trotter-Kato product formula for Gibbs semigroups

1990 ◽  
Vol 131 (2) ◽  
pp. 333-346 ◽  
Author(s):  
Hagen Neidhardt ◽  
Valentin A. Zagrebnov
Keyword(s):  
Product Formula

Zero correlation with lower-order terms for automorphic L-functions

2016 ◽  
Vol 12 (01) ◽  
pp. 27-55
Author(s):  
Timothy L. Gillespie ◽  
Yangbo Ye
Keyword(s):  
Lower Order ◽  
Product Formula ◽  
Cuspidal Representation ◽  
Zero Correlation ◽  
Lower Order Terms ◽  
Refined Version ◽  
Low Order

Let [Formula: see text] be a self-contragredient automorphic cuspidal representation of [Formula: see text] for [Formula: see text]. Using a refined version of the Selberg orthogonality, we recompute the [Formula: see text]-level correlation of high non-trivial zeros of the product [Formula: see text]. In the process, we are able to extract certain low-order terms which suggest the asymptotics of these statistics are not necessarily universal, but depend upon the conductors of the representations and hence the ramification properties of the local components coming from each [Formula: see text]. The computation of these lower-order terms is unconditional as long as all [Formula: see text].

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