scholarly journals Necessary Conditions for Schur-Maximality

10.37236/7524 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Foster Tom ◽  
Stephanie Van Willigenburg
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
The Difference ◽  
A Chain ◽  
Schur Positive

McNamara and Pylyavskyy conjectured precisely which connected skew shapes are maximal in the Schur-positivity order, which says that $B\leq _s A$ if $s_A-s_B$ is Schur-positive. Towards this, McNamara and van Willigenburg proved that it suffices to study equitable ribbons, namely ribbons whose row lengths are all of length $a$ or $(a+1)$ for $a\geq 2$. In this paper we confirm the  conjecture of McNamara and Pylyavskyy in all cases where the comparable equitable ribbons form a chain. We also confirm a conjecture of McNamara and van Willigenburg regarding which equitable ribbons in general are minimal. Additionally, we establish two sufficient conditions for the difference of two ribbons to be Schur-positive, which manifest as diagrammatic operations on ribbons. We also deduce two necessary conditions for the difference of two equitable ribbons to be Schur-positive that rely on rows of length $a$ being at the end, or on rows of length $(a+1)$ being evenly distributed.

scholarly journals Stochastic Comparisons of Some Distances between Random Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 981
Author(s):  
Patricia Ortega-Jiménez ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
Financial Risk ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Stochastic Ordering ◽  
Random Variable ◽  
Distribution Functions ◽  
Stochastic Comparisons ◽  
Stochastic Orderings ◽  
Absolute Value ◽  
The Difference

The aim of this paper is twofold. First, we show that the expectation of the absolute value of the difference between two copies, not necessarily independent, of a random variable is a measure of its variability in the sense of Bickel and Lehmann (1979). Moreover, if the two copies are negatively dependent through stochastic ordering, this measure is subadditive. The second purpose of this paper is to provide sufficient conditions for comparing several distances between pairs of random variables (with possibly different distribution functions) in terms of various stochastic orderings. Applications in actuarial and financial risk management are given.

scholarly journals Noetherian properties in composite generalized power series rings

2020 ◽  
Vol 18 (1) ◽  
pp. 1540-1551
Author(s):  
Jung Wook Lim ◽  
Dong Yeol Oh
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Commutative Rings ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generalized Power Series ◽  
Ordered Monoid ◽  
Power Series Rings ◽  
Necessary And Sufficient ◽  
Equivalent Conditions

Abstract Let ({\mathrm{\Gamma}},\le ) be a strictly ordered monoid, and let {{\mathrm{\Gamma}}}^{\ast }\left={\mathrm{\Gamma}}\backslash \{0\} . Let D\subseteq E be an extension of commutative rings with identity, and let I be a nonzero proper ideal of D. Set \begin{array}{l}D+[\kern-2pt[ {E}^{{{\mathrm{\Gamma}}}^{\ast },\le }]\kern-2pt] := \left\{f\in [\kern-2pt[ {E}^{{\mathrm{\Gamma}},\le }]\kern-2pt] \hspace{0.15em}|\hspace{0.2em}f(0)\in D\right\}\hspace{.5em}\text{and}\\ \hspace{0.2em}D+[\kern-2pt[ {I}^{{\Gamma }^{\ast },\le }]\kern-2pt] := \left\{f\in [\kern-2pt[ {D}^{{\mathrm{\Gamma}},\le }]\kern-2pt] \hspace{0.15em}|\hspace{0.2em}f(\alpha )\in I,\hspace{.5em}\text{for}\hspace{.25em}\text{all}\hspace{.5em}\alpha \in {{\mathrm{\Gamma}}}^{\ast }\right\}.\end{array} In this paper, we give necessary conditions for the rings D+[\kern-2pt[ {E}^{{{\mathrm{\Gamma}}}^{\ast },\le }]\kern-2pt] to be Noetherian when ({\mathrm{\Gamma}},\le ) is positively ordered, and sufficient conditions for the rings D+[\kern-2pt[ {E}^{{{\mathrm{\Gamma}}}^{\ast },\le }]\kern-2pt] to be Noetherian when ({\mathrm{\Gamma}},\le ) is positively totally ordered. Moreover, we give a necessary and sufficient condition for the ring D+[\kern-2pt[ {I}^{{\Gamma }^{\ast },\le }]\kern-2pt] to be Noetherian when ({\mathrm{\Gamma}},\le ) is positively totally ordered. As corollaries, we give equivalent conditions for the rings D+({X}_{1},\ldots ,{X}_{n})E{[}{X}_{1},\ldots ,{X}_{n}] and D+({X}_{1},\ldots ,{X}_{n})I{[}{X}_{1},\ldots ,{X}_{n}] to be Noetherian.

scholarly journals On the equivalence of three-dimensional differential systems

2020 ◽  
Vol 18 (1) ◽  
pp. 1164-1172
Author(s):  
Jian Zhou ◽  
Shiyin Zhao
Keyword(s):  
Periodic Solutions ◽  
Differential System ◽  
Necessary Conditions ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Periodic Systems ◽  
Structural Form ◽  
Differential Systems

Abstract In this paper, firstly, we study the structural form of reflective integral for a given system. Then the sufficient conditions are obtained to ensure there exists the reflective integral with these structured form for such system. Secondly, we discuss the necessary conditions for the equivalence of such systems and a general three-dimensional differential system. And then, we apply the obtained results to the study of the behavior of their periodic solutions when such systems are periodic systems in t.

A Direct Rotatability Criterion for Spherical Four-Bar Linkages

1995 ◽  
Vol 117 (4) ◽  
pp. 597-600 ◽  
Author(s):  
K. C. Gupta ◽  
R. Ma
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Absolute Value ◽  
The Difference ◽  
Necessary And Sufficient ◽  
Four Bar Linkage

The necessary and sufficient conditions for the full input rotatability in a spherical four-bar linkage are proved. The direct criterion is: for all twist angles α in the range [0, π], the excess (deficit) of the sum of the frame and input twist angles over (from) π should, in absolute value, be greater than that for the coupler and follower twist angles; the difference between the follower and input twist angles, in absolute value, should be greater than that for the coupler and follower twist angles. Application of the direct criterion to full rotatability of other links are discussed and some variations in the form of the criterion are developed.

scholarly journals XXIII.—On the Disruptive Discharge of Electricity: An Experimental Thesis for the Degree of Doctor of Science, Department A

1878 ◽  
Vol 28 (2) ◽  
pp. 633-671 ◽  
Author(s):  
Alexander Macfarlane
Keyword(s):  
Copper Wire ◽  
Late Summer ◽  
The Other ◽  
Straight Line ◽  
Summer Session ◽  
The Difference ◽  
A Chain ◽  
The One ◽  
Metallic Parts ◽  
The University

The experiments to which I shall refer were carried out in the physical laboratory of the University during the late summer session. I was ably assisted in conducting the experiments by three students of the laboratory,—Messrs H. A. Salvesen, G. M. Connor, and D. E. Stewart. The method which was used of measuring the difference of potential required to produce a disruptive discharge of electricity under given conditions, is that described in a paper communicated to the Royal Society of Edinburgh in 1876 in the names of Mr J. A. Paton, M. A., and myself, and was suggested to me by Professor Tait as a means of attacking the experimental problems mentioned below.The above sketch which I took of the apparatus in situ may facilitate tha description of the method. The receiver of an air-pump, having a rod capable of being moved air-tight up and down through the neck, was attached to one of the conductors of a Holtz machine in such a manner that the conductor of the machine and the rod formed one conducting system. Projecting from the bottom of the receiver was a short metallic rod, forming one conductor with the metallic parts of the air-pump, and by means of a chain with the uninsulated conductor of the Holtz machine. Brass balls and discs of various sizes were made to order, capable of being screwed on to the ends of the rods. On the table, and at a distance of about six feet from the receiver, was a stand supporting two insulated brass balls, the one fixed, the other having one degree of freedom, viz., of moving in a straight line in the plane of the table. The fixed insulated ball A was made one conductor with the insulated conductor of the Holtz and the rod of the receiver, by means of a copper wire insulated with gutta percha, having one end stuck firmly into a hole in the collar of the receiver, and having the other fitted in between the glass stem and the hollow in the ball, by which it fitted on to the stem tightly. A thin wire similarly fitted in between the ball B and its insulating stem connected the ball with the insulated half ring of a divided ring reflecting electrometer.

A Direct Rotatability Criterion for Spherical Four-Bar Linkages

1994 ◽  
Author(s):  
R. Ma ◽  
K. C. Gupta
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Absolute Value ◽  
The Difference ◽  
Necessary And Sufficient ◽  
Four Bar Linkage

Abstract The necessary and sufficient conditions for the full input rotatability in a spherical four bar linkage are proved. The direct criterion is: for all twist angles α in the range [0, π], the excess (deficit) of the sum of the frame and input twist angles over (from) π should, in absolute value, be greater than that for the coupler and follower twist angles; the difference between the follower and input twist angles, in absolute value, should be greater than that for the coupler and follower twist angles. Application of the direct criterion to full rotatability of other links are discussed and some variations in the form of the criterion are developed.

scholarly journals Iodination of insulin in aqueous and organic solvents

1969 ◽  
Vol 115 (1) ◽  
pp. 11-18 ◽  
Author(s):  
A. Massaglia ◽  
U. Rosa ◽  
G. Rialdi ◽  
C. A. Rossi
Keyword(s):  
Ethylene Glycol ◽  
Organic Solvents ◽  
Molecular Conformation ◽  
Aqueous Media ◽  
Native Structure ◽  
Experimental Conditions ◽  
Polar Environment ◽  
Polar Area ◽  
The Difference ◽  
A Chain

1. The iodination of insulin was studied under various experimental conditions in aqueous media and in some organic solvents, by measuring separately the uptake of iodine by the four tyrosyl groups and the relative amounts of monoiodotyrosine and di-iodotyrosine that are formed. In aqueous media from pH1 to pH9 the iodination occurs predominantly on the tyrosyl groups of the A chain. Some organic solvents increase the iodine uptake of the B-chain tyrosyl groups. Their efficacy in promoting iodination of Tyr-B-16 and Tyr-B-26 is in the order: ethylene glycol and propylene glycol≃methanol and ethanol>dioxan>8m-urea. 2. It is suggested that each of the four tyrosyl groups in insulin has a different environment: Tyr-A-14 is fully exposed to the solvent; Tyr-A-19 is sterically influenced by the environmental structure, possibly by the vicinity of a disulphide interchain bond; Tyr-B-16 is embedded into a non-polar area whose stability is virtually independent of the molecular conformation; Tyr-B-26 is probably in a situation similar to Tyr-B-16 with the difference that its non-polar environment depends on the preservation of the native structure.

scholarly journals On the numerical solution for nonlinear elliptic equations with variable weight coefficients in an integral boundary conditions

2021 ◽  
Vol 26 (4) ◽  
pp. 738-758
Author(s):  
Regimantas Čiupaila ◽  
Kristina Pupalaigė ◽  
Mifodijus Sapagovas
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Nonlinear Elliptic Equations ◽  
Integral Boundary ◽  
Nonlinear Elliptic ◽  
Variable Weight ◽  
The Difference ◽  
Convergence Of Iterative Method

In the paper the two-dimensional elliptic equation with integral boundary conditions is solved by finite difference method. The main aim of the paper is to investigate the conditions for the convergence of the iterative methods for the solution of system of nonlinear difference equations. With this purpose, we investigated the structure of the spectrum of the difference eigenvalue problem. Some sufficient conditions are proposed such that the real parts of all eigenvalues of the corresponding difference eigenvalue problem are positive. The proof of convergence of iterative method is based on the properties of the M-matrices not requiring the symmetry or diagonal dominance of the matrices. The theoretical statements are supported by the results of the numerical experiment.

scholarly journals New Results on Degree Sequences of Uniform Hypergraphs

10.37236/3414 ◽  
2013 ◽  
Vol 20 (4) ◽  
Author(s):  
Sarah Behrens ◽  
Catherine Erbes ◽  
Michael Ferrara ◽  
Stephen G. Hartke ◽  
Benjamin Reiniger ◽  
...  
Keyword(s):  
Efficient Algorithm ◽  
Necessary Conditions ◽  
Degree Sequence ◽  
Sufficient Conditions ◽  
Degree Sequences ◽  
Uniform Hypergraph ◽  
Graphic Sequence ◽  
Uniform Hypergraphs ◽  
Open Question

A sequence of nonnegative integers is $k$-graphic if it is the degree sequence of a $k$-uniform hypergraph. The only known characterization of $k$-graphic sequences is due to Dewdney in 1975. As this characterization does not yield an efficient algorithm, it is a fundamental open question to determine a more practical characterization. While several necessary conditions appear in the literature, there are few conditions that imply a sequence is $k$-graphic. In light of this, we present sharp sufficient conditions for $k$-graphicality based on a sequence's length and degree sum.Kocay and Li gave a family of edge exchanges (an extension of 2-switches) that could be used to transform one realization of a 3-graphic sequence into any other realization. We extend their result to $k$-graphic sequences for all $k \geq 3$. Finally we give several applications of edge exchanges in hypergraphs, including generalizing a result of Busch et al. on packing graphic sequences.

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