Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
62,792
result(s) for
"Sums"
Sort by:
Fortune and the cursed
Innovation-making is a classic theme in anthropology that reveals how people fine-tune their ontologies, live in the world and conceive of it as they do. This ethnographic study is an entrance into the world of Buryat Mongol divination, where a group of cursed shamans undertake the 'race against time' to produce innovative remedies that will improve their fallen fortunes at an unconventional pace. Drawing on parallels between social anthropology and chaos theory, the author gives an in-depth account of how Buryat shamans and their notion of fortune operate as 'strange attractors' who propagate the ongoing process of innovation-making. With its view into this long-term 'cursing war' between two shamanic factions in a rural Mongolian district, and the comparative findings on cursing in rural China, this book is a needed resource for anyone with an interest in the anthropology of religion, shamanism, witchcraft and genealogical change.
eBook
Hypergeometric functions over finite fields
Building on the developments of many people including Evans, Greene, Katz, McCarthy, Ono, Roberts, and Rodriguez-Villegas, we
consider period functions for hypergeometric type algebraic varieties over finite fields and consequently study hypergeometric functions
over finite fields in a manner that is parallel to that of the classical hypergeometric functions. Using a comparison between the
classical gamma function and its finite field analogue the Gauss sum, we give a systematic way to obtain certain types of hypergeometric
transformation and evaluation formulas over finite fields and interpret them geometrically using a Galois representation perspective. As
an application, we obtain a few finite field analogues of algebraic hypergeometric identities, quadratic and higher transformation
formulas, and evaluation formulas. We further apply these finite field formulas to compute the number of rational points of certain
hypergeometric varieties.
eBook
Group Constant-Sum Spectrum of Nearly Regular Graphs
For an undirected graph G, a zero-sum flow is an assignment of nonzero integer weights to the edges such that each vertex has a zero-sum, namely the sum of all incident edge weights with each vertex is zero. This concept is an undirected analog of nowhere-zero flows for directed graphs. We study a more general one, namely constant-sum A-flows, which gives edge weights using nonzero elements of an additive Abelian group A and requires each vertex to have a constant-sum instead. In particular, we focus on two special cases: A=Zk, the finite cyclic group of integer congruence modulo k, and A=Z, the infinite cyclic group of integers. The constant sum under a constant-sum A-flow is called an index of G for short, and the set of all possible constant sums (indices) of G is called the constant sum spectrum. It is denoted by Ik(G) and I(G) for A=Zk and A=Z, respectively. The zero-sum flows and constant-sum group flows for regular graphs regarding cases Z and Zk have been studied extensively in the literature over the years. In this article, we study the constant sum spectrum of nearly regular graphs such as wheel graphs Wn and fan graphs Fn in particular. We completely determine the constant-sum spectrum of fan graphs and wheel graphs concerning Zk and Z, respectively. Some open problems will be mentioned in the concluding remarks.
Journal Article
tg-Radical Supplemented Modules
In this work, we define tg-radical supplemented modules and cofinitely tg-radical supplemented modules. We investigate some properties of these modules. In addition, we present examples separating the tg-radical supplemented modules, g-supplemented modules, and ⊕-g-Rad-supplemented modules and also show the equality of these modules for projective and finitely generated modules. We give a characterization of cofinitely tg-radical supplemented modules. Furthermore, for any ring R, we show that any finite direct sum of tg-radical supplemented R-modules is tg-radical supplemented and that any direct sum of cofinitely tg-radical supplemented R-modules is a cofinitely tg-radical supplemented module.
Journal Article
Some Binomial Sums of \\(\\)-Jacobsthal and \\(\\)-Jacobsthal-Lucas Numbers
In this paper, we formulate some crucial identities containing \\(\\kappa\\)-Jacobsthal and \\(\\kappa\\)-Jacobsthal-Lucas numbers and use these identities to establish some binomial sums of \\(\\kappa\\)-Jacobsthal and \\(\\kappa\\)-Jacobsthal-Lucas numbers.
Journal Article
SUMS OF DISTINCT INTEGRAL SQUARES IN $\\mathbb {Q}(\\sqrt {2})$, $\\mathbb {Q}(\\sqrt {3})$ AND $\\mathbb {Q}(\\sqrt {6})
In this article, we determine all the totally positive integers of $\\mathbb {Q}(\\sqrt {m})$ which can be represented as sums of distinct integral squares, where m=2, 3, 6.
Journal Article
Parameterized Finite Binomial Sums
We offer intriguing new insights into parameterized finite binomial sums, revealing elegant identities such as ∑k=0,k≠nm+n(−1)kn−km+nk=(−1)nm+nn(Hm−Hn), where n,m are non-negative integers and Hn is the harmonic number. These formulas beautifully capture the intricate relationship between harmonic numbers and binomial coefficients, providing a fresh and captivating perspective on combinatorial sums.
Journal Article
Positive Gaussian Kernels also Have Gaussian Minimizers
We study lower bounds on multilinear operators with Gaussian kernels acting on Lebesgue spaces, with exponents below one. We put
forward natural conditions when the optimal constant can be computed by inspecting centered Gaussian functions only, and we give
necessary and sufficient conditions for this constant to be positive. Our work provides a counterpart to Lieb’s results on maximizers of
multilinear operators with real Gaussian kernels, also known as the multidimensional Brascamp-Lieb inequality. It unifies and extends
several inverse inequalities.
eBook