THE GEOMETRICAL PROPERTIES OF BERRY’S PHASE

Using the spectral decomposition of the Hamiltonian, we clarify the relationship of Berry’s effect with the parallel transport in the parameter space of this Hamiltonian. We derive the necessary and sufficient conditions under which this parallel transport is described by a natural, Riemannian connection. The considerations are illustrated by several examples.

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Some Generalized Theorems on Connectivity

Canadian Journal of Mathematics ◽

10.4153/cjm-1960-048-9 ◽

1960 ◽

Vol 12 ◽

pp. 546-554 ◽

Cited By ~ 1

Author(s):

R. E. Nettleton

Keyword(s):

Chromatic Number ◽

Connected Graph ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Dense Subgraphs ◽

Special Cases ◽

Necessary And Sufficient ◽

Relationship Of ◽

The Relationship

The “k-dense” subgraphs of a connected graph G are connected and contain neighbours of all but at most k-1 points. We consider necessary and sufficient conditions that a point be in Γk, the union of the minimal k-dense subgraphs. It is shown that Γk contains all the [m, k]-isthmuses” and [m, k]-articulators“— minimal subgraphs which disconnect the graph into at least k + 1 disjoint graphs—and that an [m, k]-isthmus or [m, k]-articulator of Γk disconnects G. We define “central points,” “degree” of a point, and “chromatic number” and examine the relationship of these concepts to connectivity. Many theorems contain theorems previously proved (1) as special cases.

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On cryptographic properties of (n + 1)-bit S-boxes constructed by known n-bit S-boxes

Journal of Mathematical Cryptology ◽

10.1515/jmc-2020-0004 ◽

2020 ◽

Vol 15 (1) ◽

pp. 258-265

Author(s):

Yu Zhou ◽

Daoguang Mu ◽

Xinfeng Dong

Keyword(s):

Sufficient Conditions ◽

Sum Of Squares ◽

Basic Component ◽

Necessary And Sufficient Conditions ◽

Autocorrelation Functions ◽

Walsh Spectrum ◽

Cryptographic Algorithms ◽

Necessary And Sufficient ◽

Relationship Of

AbstractS-box is the basic component of symmetric cryptographic algorithms, and its cryptographic properties play a key role in security of the algorithms. In this paper we give the distributions of Walsh spectrum and the distributions of autocorrelation functions for (n + 1)-bit S-boxes in [12]. We obtain the nonlinearity of (n + 1)-bit S-boxes, and one necessary and sufficient conditions of (n + 1)-bit S-boxes satisfying m-order resilient. Meanwhile, we also give one characterization of (n + 1)-bit S-boxes satisfying t-order propagation criterion. Finally, we give one relationship of the sum-of-squares indicators between an n-bit S-box S0 and the (n + 1)-bit S-box S (which is constructed by S0).

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Insensitivity and reversed Markov processes

Advances in Applied Probability ◽

10.2307/1427322 ◽

1983 ◽

Vol 15 (4) ◽

pp. 752-768 ◽

Cited By ~ 18

Author(s):

W. Henderson

Keyword(s):

Markov Processes ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Necessary And Sufficient ◽

The Relationship

This paper is concerned with the relationship between insensitivity in a certain class of Markov processes and properties of that process when time is reversed. Necessary and sufficient conditions for insensitivity are established and linked to already proved results. A number of examples of insensitive systems are given.

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Semicritical Rings and the Quotient Problem

Canadian Mathematical Bulletin ◽

10.4153/cmb-1984-025-7 ◽

1984 ◽

Vol 27 (2) ◽

pp. 160-170

Author(s):

Karl A. Kosler

Keyword(s):

Quotient Ring ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Prime Ideals ◽

Regular Elements ◽

The Right ◽

Minimal Prime ◽

Necessary And Sufficient ◽

Quotient Rings ◽

The Relationship

AbstractThe purpose of this paper is to examine the relationship between the quotient problem for right noetherian nonsingular rings and the quotient problem for semicritical rings. It is shown that a right noetherian nonsingular ring R has an artinian classical quotient ring iff certain semicritical factor rings R/Ki, i = 1,…,n, possess artinian classical quotient rings and regular elements in R/Ki lift to regular elements of R for all i. If R is a two sided noetherian nonsingular ring, then the existence of an artinian classical quotient ring is equivalent to each R/Ki possessing an artinian classical quotient ring and the right Krull primes of R consisting of minimal prime ideals. If R is also weakly right ideal invariant, then the former condition is redundant. Necessary and sufficient conditions are found for a nonsingular semicritical ring to have an artinian classical quotient ring.

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The Q0-matrix completion problem

Arab Journal of Mathematical Sciences ◽

10.1016/j.ajmsc.2019.08.001 ◽

2020 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Kalyan Sinha

Keyword(s):

Matrix Completion ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Completion Problem ◽

Matrix Completion Problem ◽

Necessary And Sufficient ◽

The Relationship

A matrix is a Q0-matrix if for every k∈{1,2,…,n}, the sum of all k×k principal minors is nonnegative. In this paper, we study some necessary and sufficient conditions for a digraph to have Q0-completion. Later on we discuss the relationship between Q and Q0-matrix completion problem. Finally, a classification of the digraphs of order up to four is done based on Q0-completion.

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Insensitivity and reversed Markov processes

Advances in Applied Probability ◽

10.1017/s0001867800021595 ◽

1983 ◽

Vol 15 (04) ◽

pp. 752-768 ◽

Cited By ~ 9

Author(s):

W. Henderson

Keyword(s):

Markov Processes ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Necessary And Sufficient ◽

The Relationship

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Process tree-based analysis method of DECLARE relation constraints in acyclic bridge-less well-structured workflow nets

ECTI Transactions on Computer and Information Technology (ECTI-CIT) ◽

10.37936/ecti-cit.2019132.203107 ◽

2019 ◽

Vol 13 (2) ◽

pp. 104-111

Author(s):

Shingo Yamaguchi ◽

Mohd Anuaruddin Bin Ahmadon

Keyword(s):

Polynomial Time ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Analysis Method ◽

Declarative Language ◽

Tree Representation ◽

Workflow Nets ◽

Necessary And Sufficient ◽

The Relationship ◽

Process Tree

In this paper, we proposed a method to analyze workflows’ constraints whose templates are defined in a declarative language called DECLARE. Checking such constraints is important but known to be intractable in general. Our results show three things. First, utilizing a tree representation of workflow process called {\it process tree}, we provided necessary and sufficient conditions on the constraints. Second, those conditions enable us to not only check a given constraint in polynomial time but also find a clue for improving the net if it violates the constraint. Third, we revealed the relationship among the constraint templates.

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On the representation of analytic functions by infinite series

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences ◽

10.1098/rsta.1953.0003 ◽

1953 ◽

Vol 245 (900) ◽

pp. 429-468 ◽

Cited By ~ 24

Keyword(s):

General Theory ◽

Infinite Series ◽

Analytic Functions ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Topological Methods ◽

Basic Series ◽

Necessary And Sufficient ◽

The Relationship ◽

Product Sets

Given a set of functions {p k {z)}, necessary and sufficient conditions are known under which the basic series ∑ (k=0) ∞ II k f (0)p k (z) will represent all functions f ( z ) in certain classes. The various cases are included in a general theory given in part II. Questions of uniqueness are discussed, and an attempt is made to initiate a theory of representation by series of the form ∑ (k=0) ∞ α k p k (z) which are not necessarily basic. Topological methods are used, and part I is devoted largely to preliminaries. In part III is discussed the relationship between given sets and various associated sets such as the inverse and product sets.

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Demand functions and demand manifolds

Economic Theory Bulletin ◽

10.1007/s40505-021-00203-1 ◽

2021 ◽

Author(s):

Alan Beggs

Keyword(s):

Demand Function ◽

Firm Behavior ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Static Properties ◽

Demand Functions ◽

Necessary And Sufficient ◽

The Relationship

AbstractMrázová and Neary (2017) introduce the notion of the Demand Manifold which expresses the relationship between the elasticity and curvature of a demand function. They argue that this determines many important comparative static properties of firm behavior. This paper gives necessary and sufficient conditions for two demand functions to have the same demand manifold and so to have similar comparative static properties.

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Certain Types of Interval-Valued Fuzzy Graphs

Journal of Applied Mathematics ◽

10.1155/2013/857070 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 4

Author(s):

Muhammad Akram ◽

Noura Omair Alshehri ◽

Wieslaw A. Dudek

Keyword(s):

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Intuitionistic Fuzzy ◽

Fuzzy Graphs ◽

Irregular Interval ◽

Intuitionistic Fuzzy Graphs ◽

Necessary And Sufficient ◽

The Relationship ◽

Interval Valued

We propose certain types of interval-valued fuzzy graphs including balanced interval-valued fuzzy graphs, neighbourly irregular interval-valued fuzzy graphs, neighbourly total irregular interval-valued fuzzy graphs, highly irregular interval-valued fuzzy graphs, and highly total irregular interval-valued fuzzy graphs. Some interesting properties associated with these new interval-valued fuzzy graphs are investigated, and necessary and sufficient conditions under which neighbourly irregular and highly irregular interval-valued fuzzy graphs are equivalent are obtained. We also describe the relationship between intuitionistic fuzzy graphs and interval-valued fuzzy graphs.

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