scholarly journals On a large class of non-linear coding methods based on Boolean invertible matrices

2008 ◽  
Vol 21 (3) ◽  
pp. 365-372
Author(s):  
Costas Karanikas ◽  
Nikolaos Atreas
Keyword(s):  
Large Class ◽  
Natural Numbers ◽  
Riesz Product ◽  
Random Generator ◽  
Main Target ◽  
Non Linear ◽  
Class Of Matrices ◽  
Invertible Matrices

The main target of this work is to construct a large enumerated class of non- linear coding methods, based on a discrete invertible transform called Riesz Product, which is associated to a class of Boolean invertible matrices of order m ? m. The particular class of matrices is uniquely determined by a couple of permutations of the first m natural numbers {1, 2, ..., m}, so for any m = 1, 2, 3, ..., we get at least (m!)2 different non-linear coding methods. The resulting encoding/decoding method is very fast and requires low memory. It can be used both as a new encryption tool or as a Boolean random generator. .

scholarly journals Perturbative linearization of super-Yang-Mills theories in general gauges

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Hannes Malcha ◽  
Hermann Nicolai
Keyword(s):  
Large Class ◽  
Fourth Order ◽  
Landau Gauge ◽  
Third Order ◽  
Yang Mills ◽  
Free Theory ◽  
Non Linear ◽  
Functional Measure ◽  
Non Local ◽  
Jacobi Determinant

Abstract Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant of the transformation equals the product of the fermionic determinants obtained by integrating out the gauginos and ghosts at least on the gauge hypersurface. While this transformation has been known so far only for the Landau gauge and to third order in the Yang-Mills coupling, we here extend the construction to a large class of (possibly non-linear and non-local) gauges, and exhibit the conditions for all statements to remain valid off the gauge hypersurface. Finally, we present explicit results to second order in the axial gauge and to fourth order in the Landau gauge.

scholarly journals RG flows of integrable σ-models and the twist function

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
François Delduc ◽  
Sylvain Lacroix ◽  
Konstantinos Sfetsos ◽  
Konstantinos Siampos
Keyword(s):  
Renormalization Group ◽  
Large Class ◽  
Rational Function ◽  
Integrable Model ◽  
Renormalization Group Flow ◽  
Flow Equations ◽  
Non Linear ◽  
Group Flow

Abstract In the study of integrable non-linear σ-models which are assemblies and/or deformations of principal chiral models and/or WZW models, a rational function called the twist function plays a central rôle. For a large class of such models, we show that they are one-loop renormalizable, and that the renormalization group flow equations can be written directly in terms of the twist function in a remarkably simple way. The resulting equation appears to have a universal character when the integrable model is characterized by a twist function.

scholarly journals On the structure of least common multiple matrices from some class of matrices

2018 ◽  
Vol 10 (1) ◽  
pp. 179-184
Author(s):  
A.M. Romaniv
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Smith Normal Form ◽  
Least Common Multiple ◽  
The Matrix ◽  
Singular Matrices ◽  
Class Of Matrices ◽  
Smith Normal Forms ◽  
Invertible Matrices ◽  
Principal Ideal Domains

For non-singular matrices with some restrictions, we establish the relationships between Smith normal forms and transforming matrices (a invertible matrices that transform the matrix to its Smith normal form) of two matrices with corresponding matrices of their least common right multiple over a commutative principal ideal domains. Thus, for such a class of matrices, given answer to the well-known task of M. Newman. Moreover, for such matrices, received a new method for finding their least common right multiple which is based on the search for its Smith normal form and transforming matrices.

Spherical gravitational waves

1959 ◽  
Vol 251 (994) ◽  
pp. 233-271 ◽  
Keyword(s):  
General Relativity ◽  
Gravitational Waves ◽  
Large Class ◽  
Linear Approximation ◽  
Gravitational Radiation ◽  
Gravitational Mass ◽  
Field Equations ◽  
Spherical Waves ◽  
Non Linear ◽  
External Forces

The field of gravitational radiation emitted from two moving particles is investigated by means of general relativity. A method of approximation is used, and in the linear approximation retarded potentials corresponding to spherical gravitational waves are introduced. As is already known, the theory in this approximation predicts that energy is lost by the system. The field equations in the second, non-linear, approximation are then considered, and it is shown that the system loses an amount of gravitational mass precisely equal to the energy carried away by the spherical waves of the linear approximation. The result is established for a large class of particle motions, but it has not been possible to determine whether energy is lost in free gravitational motion under no external forces. The main conclusion of this work is that, contrary to opinions frequently expressed, gravitational radiation has a real physical existence, and in particular, carries energy away from the sources.

Recursion theory on orderings. II

1980 ◽  
Vol 45 (2) ◽  
pp. 317-333 ◽  
Author(s):  
J. B. Remmel
Keyword(s):  
Large Class ◽  
General Model ◽  
Recursion Theory ◽  
Second Order ◽  
Splitting Theorem ◽  
Natural Numbers ◽  
Partial Orderings

In [6], G. Metakides and the author introduced a general model theoretic setting in which to study the lattice of r.e. substructures of a large class of recursively presented models . Examples included , the natural numbers with equality, 〈 Q, ≤ 〉, the rationals under the usual ordering, and a large class of n-dimensional partial orderings. In this setting, we were able to generalize many of the constructions of classical recursion theory so that the constructions yield the classical results when we specialize to the case of and new results when we specialize to other models. Constructions to generalize Myhill's Theorem on creative sets [8], Friedberg's Theorem on the existence of maximal sets [3], Dekker's Theorem on the degrees of hypersimple sets [2], and Martin's Theorem on the degrees of maximal sets [5] were produced in [6]. In this paper, we give constructions to generalize the Morley-Soare Splitting Theorem [7] and Lachlan's characterization of hyperhypersimple sets [4] in §2, constructions to generalize Lachlan's theorems on the existence of major subsets and r-maximal sets contained in maximal sets [4] in §3, and constructions to generalize Robinson's construction of r-maximal sets that are not contained in any maximal sets [11] and second-order maximal sets [12] in §4.In §1 of this paper, we give the precise definitions of our model theoretic setting and deal with other preliminaries. Also in §1, we define the notions of “uniformly nonrecursive”, “uniformly maximal”, etc. which are the key notions involved in the generalizations of the various theorems that occur in §§2, 3 and 4.

scholarly journals Asymptotic set-point regulation for a large class of non-linear hydraulic networks

2017 ◽  
Vol 50 (1) ◽  
pp. 5355-5360
Author(s):  
Tom Nørgaard Jensen ◽  
Carsten Skovmose Kallesøe ◽  
Rafał Wisniewski
Keyword(s):  
Large Class ◽  
Set Point ◽  
Non Linear ◽  
Hydraulic Networks

VARIATIONS ON A THEME OF CASSELS FOR ADDITIVE BASES

2006 ◽  
Vol 02 (02) ◽  
pp. 249-265 ◽  
Author(s):  
G. GREKOS ◽  
L. HADDAD ◽  
C. HELOU ◽  
J. PIHKO
Keyword(s):  
Large Class ◽  
Natural Numbers ◽  
Average Order ◽  
Basic Properties ◽  
Additive Basis ◽  
Perfect Squares ◽  
Variations On A Theme

We introduce the notion of caliber, cal (A, B), of a strictly increasing sequence of natural numbers A with respect to another one B, as the limit inferior of the ratio of the nth term of A to that of B. We further consider the limit superior t(A) of the average order of the number of representations of an integer as a sum of two elements of A. We give some basic properties of each notion and we relate the two together, thus yielding a generalization, of the form t(A) ≤ t(B)/ cal (A, B), of a result of Cassels specific to the case where A is an additive basis of the natural numbers and B is the sequence of perfect squares. We also provide some formulas for the computation of t(A) in a large class of cases, and give some examples.

scholarly journals On a new generalization of Alzer's inequality

2000 ◽  
Vol 23 (12) ◽  
pp. 815-818 ◽  
Author(s):  
Feng Qi ◽  
Lokenath Debnath
Keyword(s):  
Lower Bound ◽  
Large Class ◽  
Mean Value ◽  
Mathematical Induction ◽  
Mean Value Theorem ◽  
Natural Numbers ◽  
Real Numbers ◽  
Positive Real

Let{an}n=1∞be an increasing sequence of positive real numbers. Under certain conditions of this sequence we use the mathematical induction and the Cauchy mean-value theorem to prove the following inequality:anan+m≤((1/n)∑i=1nair(1/(n+m))∑i=1n+mair)1/r, wherenandmare natural numbers andris a positive number. The lower bound is best possible. This inequality generalizes the Alzer's inequality (1993) in a new direction. It is shown that the above inequality holds for a large class of positive, increasing and logarithmically concave sequences.

scholarly journals ODE/IQFT correspondence for the generalized affine $$ \mathfrak{sl} $$(2) Gaudin model

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Gleb A. Kotousov ◽  
Sergei L. Lukyanov
Keyword(s):  
Sigma Models ◽  
Large Class ◽  
Integrable System ◽  
Condensed Matter ◽  
Gaudin Model ◽  
Kondo Model ◽  
Non Linear ◽  
Linear Sigma Models ◽  
Model Fits

Abstract An integrable system is introduced, which is a generalization of the $$ \mathfrak{sl} $$ sl (2) quantum affine Gaudin model. Among other things, the Hamiltonians are constructed and their spectrum is calculated using the ODE/IQFT approach. The model fits into the framework of Yang-Baxter integrability. This opens a way for the systematic quantization of a large class of integrable non-linear sigma models. There may also be some interest in terms of Condensed Matter applications, as the theory can be thought of as a multiparametric generalization of the Kondo model.

Fair enumeration combinators

2017 ◽  
Vol 27 ◽  
Author(s):  
MAX S. NEW ◽  
BURKE FETSCHER ◽  
ROBERT BRUCE FINDLER ◽  
JAY MCCARTHY
Keyword(s):  
Programming Language ◽  
Time Scales ◽  
Ad Hoc ◽  
The Other ◽  
Language Models ◽  
Natural Numbers ◽  
Random Generator ◽  
Long Time ◽  
Short Time ◽  
Better Than

AbstractEnumerations represented as bijections between the natural numbers and elements of some given type have recently garnered interest in property-based testing because of their efficiency and flexibility. There are, however, many ways of defining these bijections, some of which are better than others. This paper offers a new property of enumeration combinators called fairness that identifies enumeration combinators that are better suited to property-based testing. Intuitively, the result of a fair combinator indexes into its argument enumerations equally when constructing its result. For example, extracting the nth element from our enumeration of three-tuples indexes about $\sqrt[3]{n}$ elements into each of its components instead of, say, indexing $\sqrt[2]{n}$ into one and $\sqrt[4]{n}$ into the other two, as you would if a three-tuple were built out of nested pairs. Similarly, extracting the nth element from our enumeration of a three-way union returns an element that is $\frac{n}{3}$ into one of the argument enumerators. The paper presents a semantics of enumeration combinators, a theory of fairness, proofs establishing fairness of our new combinators and that some combinations of fair combinators are not fair. We also report on an evaluation of fairness for the purpose of finding bugs in programming-language models. We show that fair enumeration combinators have complementary strengths to an existing, well-tuned ad hoc random generator (better on short time scales and worse on long time scales) and that using unfair combinators is worse across the board.

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