scholarly journals Some Aspects of Hankel Matrices in Coding Theory and Combinatorics

10.37236/1595 ◽  
2001 ◽  
Vol 8 (1) ◽  
Author(s):  
Ulrich Tamm
Keyword(s):  
Orthogonal Polynomials ◽  
Coding Theory ◽  
Catalan Numbers ◽  
Binomial Coefficients ◽  
Hankel Matrices ◽  
Alternating Sign Matrices ◽  
Determinant Formula ◽  
Plane Partitions ◽  
The Family ◽  
Definition Of

Hankel matrices consisting of Catalan numbers have been analyzed by various authors. Desainte-Catherine and Viennot found their determinant to be $\prod_{1 \leq i \leq j \leq k} {{i+j+2n}\over {i+j}}$ and related them to the Bender - Knuth conjecture. The similar determinant formula $\prod_{1 \leq i \leq j \leq k} {{i+j-1+2n}\over {i+j-1}}$ can be shown to hold for Hankel matrices whose entries are successive middle binomial coefficients ${{2m+1} \choose m}$. Generalizing the Catalan numbers in a different direction, it can be shown that determinants of Hankel matrices consisting of numbers ${{1}\over {3m+1}} {{3m+1} \choose m}$ yield an alternate expression of two Mills – Robbins – Rumsey determinants important in the enumeration of plane partitions and alternating sign matrices. Hankel matrices with determinant 1 were studied by Aigner in the definition of Catalan – like numbers. The well - known relation of Hankel matrices to orthogonal polynomials further yields a combinatorial application of the famous Berlekamp – Massey algorithm in Coding Theory, which can be applied in order to calculate the coefficients in the three – term recurrence of the family of orthogonal polynomials related to the sequence of Hankel matrices.

REGULATION OF MARRIAGE RELATIONS IN THE TURKESTAN REGION

2019 ◽  
Vol 22 (2) ◽  
pp. 27-32
Author(s):  
Khurshida Tillahodjaeva ◽  
Keyword(s):  
The Family ◽  
Role Of Women ◽  
Family And Marriage ◽  
Material Conditions ◽  
Definition Of

In this article we will talk about the scale of family and marriage relations in the early XX century in the Turkestan region, their regulation, legislation. Clearly reveals the role of women and men in the family, the definition of which is based on the material conditions of society, equality of rights and freedoms and its features.

scholarly journals Hexokinase 2 in Cancer: A Prima Donna Playing Multiple Characters

2021 ◽  
Vol 22 (9) ◽  
pp. 4716
Author(s):  
Francesco Ciscato ◽  
Lavinia Ferrone ◽  
Ionica Masgras ◽  
Claudio Laquatra ◽  
Andrea Rasola
Keyword(s):  
Endoplasmic Reticulum ◽  
Aerobic Glycolysis ◽  
Neoplastic Progression ◽  
Malignant Growth ◽  
Hexokinase 2 ◽  
Genetic Ablation ◽  
Contact Points ◽  
Survival Pathways ◽  
The Family ◽  
Definition Of

Hexokinases are a family of ubiquitous exose-phosphorylating enzymes that prime glucose for intracellular utilization. Hexokinase 2 (HK2) is the most active isozyme of the family, mainly expressed in insulin-sensitive tissues. HK2 induction in most neoplastic cells contributes to their metabolic rewiring towards aerobic glycolysis, and its genetic ablation inhibits malignant growth in mouse models. HK2 can dock to mitochondria, where it performs additional functions in autophagy regulation and cell death inhibition that are independent of its enzymatic activity. The recent definition of HK2 localization to contact points between mitochondria and endoplasmic reticulum called Mitochondria Associated Membranes (MAMs) has unveiled a novel HK2 role in regulating intracellular Ca2+ fluxes. Here, we propose that HK2 localization in MAMs of tumor cells is key in sustaining neoplastic progression, as it acts as an intersection node between metabolic and survival pathways. Disrupting these functions by targeting HK2 subcellular localization can constitute a promising anti-tumor strategy.

Innovative promotional strategies and diversification of flavoured mass merchandise cigar products: a case study of Swedish match

2021 ◽  
pp. tobaccocontrol-2020-056145 ◽  
Author(s):  
Ollie Ganz ◽  
Mary Hrywna ◽  
Kevin R J Schroth ◽  
Cristine D Delnevo
Keyword(s):  
Regulatory Authority ◽  
Business Practice ◽  
Smoking Prevention ◽  
Tobacco Products ◽  
The Family ◽  
Promotional Efforts ◽  
Promotional Strategies ◽  
Definition Of ◽  
The U.S

In 2009, the Family Smoking Prevention and Tobacco Control Act (TCA) granted the U.S. Food and Drug Administration (FDA) regulatory authority over tobacco products, although initially this only included cigarettes, smokeless tobacco and roll-your-own tobacco. In 2016, the deeming rule extended regulatory authority to include all tobacco products, including cigars. The deeming rule prohibited the introduction of new tobacco products into the marketplace without proper marketing authorisation and laid out pathways for tobacco companies to follow. The deeming rule should have frozen the cigar marketplace in 2016. In this paper, we describe how the cigarillo marketplace, nevertheless, continues to diversify with new brands, flavors, styles and packaging sizes entering the market regularly. As an example, we highlight recent promotional efforts by Swedish Match North America (Swedish Match) for their popular cigarillo brands, including White Owl, Night Owl and Garcia y Vega’s Game brand. We argue that ambiguities in the TCA make it unclear whether Swedish Match’s seemingly new cigarillos fit the definition of new tobacco products and, if so, whether they are on the market legally. Swedish Match and other cigarillo companies may be taking advantage of these ambiguities to promote a variety of cigarillo flavors and styles in innovative ways. Given that cigars are combustible tobacco products that pose many of the same risks as cigarettes, this business practice raises significant concerns regarding the protection of public health, particularly among young people.

Elementary Notes on Simple Summations and Summations of Products

1936 ◽  
Vol 15 (1) ◽  
pp. 141-176
Author(s):  
Duncan C. Fraser
Keyword(s):  
Orthogonal Polynomials ◽  
Least Squares ◽  
Divided Differences ◽  
Binomial Coefficients ◽  
Special Point

SynopsisThe paper is intended as an elementary introduction and companion to the paper on “Orthogonal Polynomials,” by G. J. Lidstone, J.I.A., vol. briv., p. 128, and the paper on the “Sum and Integral of the Product of Two Functions,” by A. W. Joseph, J.I.A., vol. lxiv., p. 329; and also to Dr. Aitken's paper on the “Graduation of Data by the Orthogonal Polynomials of Least Squares,” Proc. Roy. Soc. Edin., vol. liii., p. 54.Following Dr. Aitken Σux is defined for the immediate purpose to be u0+…+ux−1.The scheme of successive summations is set out in the form of a difference diagram and is extended to negative arguments. The special point to which attention is drawn is the existence of a wedge of zeros between the sums for positive arguments and those for negative arguments.The rest of the paper is for the greater part a study of the table of binomial coefficients for positive and for negative arguments. The Tchebychef polynomials are simple functions of the binomial coefficients, and after a description of a particular example and of its properties general methods are given of forming the polynomials by means of tables of differences. These tables furnish examples of simple, differences, of divided differences, of adjusted differences, and of a system of special adjusted differences which gives a very easy scheme for the formation of the Tchebychef polynomials.

The limits of the family Evaniidae (Insecta: Hymenoptera) and a new genus from Lebanese Amberamber

2002 ◽  
Vol 33 (1) ◽  
pp. 23-34 ◽  
Author(s):  
Hasan H. Basibuyuk ◽  
Mike G. Fitton ◽  
Alexandr P. Rasnitsyn ◽  
Donald L.J. Quicke
Keyword(s):  
Fore Wing ◽  
New Genus ◽  
Cladistic Analysis ◽  
Wing Venation ◽  
New Genus And Species ◽  
Ground Plan ◽  
The Family ◽  
Definition Of

AbstractThe definition of the family Evaniidae is revised and Cretevaniidae are synonymised with Evaniidae based on evidence derived from recently described Mesozoic taxa and a new genus and species, Lebanevania azari, described here from Lebanese amber. A fore leg with a long trochanter and a 12-segmented antenna are autapomorphies of the new genus. A large, high and wide head and a high and short mesosoma are derived characters shared with other Evaniidae. The new genus also has complete fore wing venation and lacks a tubular petiole, which are ground plan features of the Evanioidea. A cladistic analysis of fossil and extant members of the superfamily Evanioidea and notes on fossil taxa are presented.

XV.—The Placoderm Fish Rhachiosteus pterygiatus Gross and its Relationships

1966 ◽  
Vol 66 (15) ◽  
pp. 377-392 ◽  
Author(s):  
Roger S. Miles
Keyword(s):  
Sensory System ◽  
System A ◽  
The Family ◽  
Definition Of

SynopsisThe holotype and only known specimen of Rhachiosteus pterygiatus Gross is partially redescribed and new restorations are given. Attention is drawn to important points in its osteology and the possible development of a cutaneous sensory system. A definition of the family Rhachiosteidsæ Stensiö is given. This family differs from all other described groups of euarthrodires in the lack of posterior lateral and posterior dorsolateral flank plates. Rhachiosteus is a pachyosteomorph brachythoracid, as defined in the text, and may be fairly closely related in some way to the (coccosteomorph) family Coccosteidsæ. There is no indication that it is closely related to any other known pachyosteomorph, or to other groups of arthrodires, such as the Rhenanida and Ptyctodontida, in which there are no posterior flank plates.

scholarly journals ON DIVISIBILITY OF BINOMIAL COEFFICIENTS

2012 ◽  
Vol 93 (1-2) ◽  
pp. 189-201 ◽  
Author(s):  
ZHI-WEI SUN
Keyword(s):  
Higher Order ◽  
Catalan Numbers ◽  
Binomial Coefficients

AbstractIn this paper, motivated by Catalan numbers and higher-order Catalan numbers, we study factors of products of at most two binomial coefficients.

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