scholarly journals Two New Criteria for Comparison in the Bruhat Order

10.37236/1847 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Brian Drake ◽  
Sean Gerrish ◽  
Mark Skandera
Keyword(s):  
Schur Functions ◽  
Type A ◽  
Bruhat Order ◽  
The Other ◽  
Nonnegative Polynomials ◽  
New Criteria

We give two new criteria by which pairs of permutations may be compared in defining the Bruhat order (of type $A$). One criterion utilizes totally nonnegative polynomials and the other utilizes Schur functions.

scholarly journals Schubert Polynomials and $k$-Schur Functions

10.37236/4139 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Carolina Benedetti ◽  
Nantel Bergeron
Keyword(s):  
Finite Type ◽  
Schur Functions ◽  
Type A ◽  
Bruhat Order ◽  
Schur Function ◽  
Quasisymmetric Functions ◽  
Affine Grassmannian ◽  
Schubert Polynomial ◽  
Schubert Polynomials ◽  
General Program

The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type $A$ by a Schur function, which we refer to as Schubert vs. Schur problem, can be understood combinatorially from the multiplication in the space of dual $k$-Schur functions. Using earlier work by the second author, we encode both problems by means of quasisymmetric functions. On the Schubert vs. Schur side, we study the poset given by the Bergeron-Sottile's $r$-Bruhat order, along with certain operators associated to this order. Then, we connect this poset with a graph on dual $k$-Schur functions given by studying the affine grassmannian order of  Lam-Lapointe-Morse-Shimozono. Also, we define operators associated to the graph on dual $k$-Schur functions which are analogous to the ones given for the Schubert vs. Schur problem. This is the first step of our more general program of showing combinatorially  the positivity of the multiplication of a dual $k$-Schur function by a Schur function.

scholarly journals New oscillation criteria for second-order neutral differential equations with distributed deviating arguments

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Osama Moaaz ◽  
Choonkil Park ◽  
Elmetwally M. Elabbasy ◽  
Waed Muhsin
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
The Other ◽  
Riccati Transformation ◽  
Transformation Technique ◽  
Deviating Arguments ◽  
Neutral Differential Equations ◽  
Second Order Differential Equations ◽  
Continuous Delay ◽  
New Criteria

AbstractIn this work, we create new oscillation conditions for solutions of second-order differential equations with continuous delay. The new criteria were created based on Riccati transformation technique and comparison principles. Furthermore, we obtain iterative criteria that can be applied even when the other criteria fail. The results obtained in this paper improve and extend the relevant previous results as illustrated by examples.

Anatomie, histologie et affinités de l'appareil séricigène des Hersilia Sav. et Aud. (Araneae: Hersiliidae)

1984 ◽  
Vol 62 (1) ◽  
pp. 97-106 ◽  
Author(s):  
Jacqueline Kovoor
Keyword(s):  
Type A ◽  
The Other ◽  
Secretory Cells ◽  
Evolutionary Stage ◽  
Type B ◽  
Outer Coat ◽  
Silk Glands ◽  
Single Protein

Although hersiliid spiders do not spin any webs, their silk glands, which belong to six types, are large and complex. Two groups of ampullate glands, one opening on the anterior spinnerets and the other on the median spinnerets, secrete two proteins each. About 180 pyriform glands are clearly bipartite. Over 200 type A aciniform glands opening on the median and posterior spinnerets are made up of three categories of secretory cells. Silk from these glands consists of two proteins (core and outer coat) joined together by an intermediary layer of acidic glycoprotein. All the 160 type B aciniform glands opening on the posterior spinnerets secrete a single protein. Fifty tubuliform glands opening on the median and posterior spinnerets produce two proteins, one of which is coloured. As in Urocteinae, long posterior spinnerets and large, numerous aciniform and tubuliform glands are correlated with swathing of prey and egg-cocoon construction. In Lycosidae and Agelenidae, the ampullate glands show the same number and distribution according to the spinnerets. However, anatomical and histochemical features of hersiliid aciniform and ampullate glands are close to those of some Araneoidea. Apart from peculiar characteristics, silk glands of Hersilia might represent an intermediate evolutionary stage towards Araneoidea.

scholarly journals Casselman’s Basis of Iwahori Vectors and the Bruhat Order

2011 ◽  
Vol 63 (6) ◽  
pp. 1238-1253 ◽  
Author(s):  
Daniel Bump ◽  
Maki Nakasuji
Keyword(s):  
Weyl Group ◽  
Bruhat Order ◽  
Group Element ◽  
The Other ◽  
Intertwining Operators ◽  
Transition Matrices ◽  
Natural Basis ◽  
Spherical Representation ◽  
Langlands Parameters ◽  
Combinatorial Condition

AbstractW. Casselman defined a basis fu of Iwahori fixed vectors of a spherical representation of a split semisimple p-adic group G over a nonarchimedean local field F by the condition that it be dual to the intertwining operators, indexed by elements u of the Weyl group W. On the other hand, there is a natural basis , and one seeks to find the transition matrices between the two bases. Thus, let and . Using the Iwahori–Hecke algebra we prove that if a combinatorial condition is satisfied, then , where z are the Langlands parameters for the representation and α runs through the set S(u, v) of positive coroots (the dual root systemof G) such that with rα the reflection corresponding to α. The condition is conjecturally always satisfied if G is simply-laced and the Kazhdan–Lusztig polynomial Pw0v,w0u = 1 with w0 the long Weyl group element. There is a similar formula for conjecturally satisfied if Pu,v = 1. This leads to various combinatorial conjectures.

The infrared spectrum of di-imide near 7.6 μm

1981 ◽  
Vol 59 (5) ◽  
pp. 663-672 ◽  
Author(s):  
K-E. J. Hallin ◽  
J. W. C. Johns ◽  
A. Trombetti
Keyword(s):  
Infrared Spectrum ◽  
Gas Phase ◽  
Type A ◽  
Phase Spectrum ◽  
The Other ◽  
Mode Analysis ◽  
Simultaneous Presence ◽  
Torsional Mode ◽  
Bending Mode ◽  
Type C

The gas phase spectrum of N2H2 has been investigated in the region of 7.6 μm at a resolution of about 0.06cm−1. Two bands have been identified; one, near 1288 cm−1, is a type C band and must correspond to ν4 (the hitherto unidentified Au torsional mode), and the other, near 1317 cm−1, is a type A–B hybrid and corresponds to ν6 (the Bu bending mode). Analysis of the spectrum is complicated by the simultaneous presence of strong A-type and B-type Coriolis interactions which couple the observed levels.

scholarly journals Symplectic Keys and Demazure Atoms in Type C

10.37236/9235 ◽  
2021 ◽  
Vol 28 (2) ◽  
Author(s):  
João Miguel Santos
Keyword(s):  
Type A ◽  
Bruhat Order ◽  
Young Tableaux ◽  
Hyperoctahedral Group ◽  
Similar Role ◽  
Type C ◽  
Left And Right ◽  
Demazure Atoms ◽  
The Right

We compute, mimicking the Lascoux-Schützenberger type A combinatorial procedure, left and right keys for a Kashiwara-Nakashima tableau in type C. These symplectic keys have a similar role as the keys for semistandard Young tableaux. More precisely, our symplectic keys give a tableau criterion for the Bruhat order on the hyperoctahedral group and cosets, and describe Demazure atoms and characters in type C. The right and the left symplectic keys are related through the Lusztig involution. A type C Schützenberger evacuation is defined to realize that involution.

Induced Representations and Invariants

1950 ◽  
Vol 2 ◽  
pp. 334-343 ◽  
Author(s):  
G. DE B. Robinson
Keyword(s):  
Representation Theory ◽  
Symmetric Group ◽  
Explicit Formula ◽  
Linear Group ◽  
Schur Functions ◽  
The Other ◽  
Induced Representations ◽  
Direct Sum ◽  
Invariant Matrices ◽  
The One

1. Introduction. The problem of the expression of an invariant matrix of an invariant matrix as a direct sum of invariant matrices is intimately associated with the representation theory of the full linear group on the one hand and with the representation theory of the symmetric group on the other. In a previous paper the author gave an explicit formula for this reduction in terms of characters of the symmetric group. Later J. A. Todd derived the same formula using Schur functions, i.e. characters of representations of the full linear group.

A Study of the Effect of Standard Laboratory Processing on Speed and Resolution of Three Black and White Aerial Films

1983 ◽  
Vol 37 (1) ◽  
pp. 3-10
Author(s):  
E. A. Fleming ◽  
M. Landreville ◽  
E. Nagy
Keyword(s):  
Type A ◽  
The Other ◽  
Small Scale ◽  
High Contrast ◽  
Aerial Photo ◽  
Standard Laboratory ◽  
Average Gradient ◽  
Black And White ◽  
Contrast Range ◽  
Film Speed

Three aerial films were tested using standard aerial photo laboratory processing procedures for three different chemistries. Relationships were established with respect to average gradient, speed, base plus fog, graininess and resolution for low, medium and high contrast targets. The films compared were Kodak Double-X type 2405, Kodak Plus-X type 2402 and Kodak Panatomic-X 2412. The processing was done in a Kodak Versamat processor using Type A, 885 and Versaflo chemistry. The results indicated that processing in 885 chemistry enhanced film speed. The versatility of Double-X in terms of speed and contrast range was demonstrated, however the resolution of Panatomic-X greatly exceeded that of either of the other two films and shows promise for small scale mapping photography.

Delayed Choice with Correlated Photons

1988 ◽  
Vol 43 (2) ◽  
pp. 110-114
Author(s):  
O. E. Rössler
Keyword(s):  
Quantum Mechanics ◽  
Choice Experiment ◽  
Foundations Of Quantum Mechanics ◽  
Type A ◽  
The Other ◽  
Delayed Choice ◽  
Epr Experiment ◽  
The One

Abstract A new experiment in the foundations of quantum mechanics is proposed. The existence of correlated photons -first seen by Wheeler -can be taken as a hint to devise a ‘‘double-wing’’ delayed choice experiment in Wheeler’s sense. A path choice (polarization choice) measurement made on the one side should then block an interference type measurement made on the other side (‘‘distant choice’’). A precondition for the combined measurement to work in theory is that the correlated photons used are of the ‘‘prepolarized’’ (Selleri) rather than the ‘‘unpolarized’’ (Böhm) type. A first EPR experiment involving prepolarized photons was recently performed by Alley and Shih. It may be used as a partial experiment within the proposed experiment.

scholarly journals Pyranoanthocyanin Derived Pigments in Wine: Structure and Formation during Winemaking

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Ana Marquez ◽  
María P. Serratosa ◽  
Julieta Merida
Keyword(s):  
Pyruvic Acid ◽  
Formation Process ◽  
Second Generation ◽  
Type A ◽  
Enol Form ◽  
Hydroxycinnamic Acids ◽  
The Other ◽  
Yeast Fermentation ◽  
Type B ◽  
Initial Compound

In recent years many studies have been carried out on new pigments derived from anthocyanins that appear in wine during processing and aging. This paper aims to summarize the latest research on these compounds, focusing on the structure and the formation process. The main pyranoanthocyanins are formed from the reaction between the anthocyanins and some metabolites released during the yeast fermentation: carboxypyranoanthocyanins or type A vitisins, formed upon the reaction between the enol form of the pyruvic acid and the anthocyanins; type B vitisins, formed by the cycloaddition of an acetaldehyde molecule on an anthocyanin; methylpyranoanthocyanins, resulted from the reaction between acetone and anthocyanins; pinotins resulted from the covalent reaction between the hydroxycinnamic acids and anthocyanins; and finally flavanyl-pyranoanthocyanins. On the other hand, the second generation of compounds has also been reviewed, where the initial compound is a pyranoanthocyanin. This family includes oxovitisins, vinylpyranoanthocyanins, pyranoanthocyanins linked through a butadienylidene bridge, and pyranoanthocyanin dimers.

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