Congruence Research Articles

On ideals of Sheffer stroke UP-algebras

The goal of the study is to introduce SUP-ideals on Sheffer Stroke UP-algebras (briefly, SUP-algebra) and its properties. We define SUP-ideals of SUP-algebras and then prove some properties. By describing a congruence relation on a SUP-algebra by the SUP-ideal, it is shown that the quotient set defined by the congruence relation is a SUP-algebra. Finally, SUP-homomorphisms on SUP-algebras are determined and the relationships between SUP-ideals of SUP-algebras are examined by means of the SUP-homomorphisms.

On The Algebraic Properties of l-Congruencies in Groups

This paper is dedicated to defining and studying the concept of congruencies in l-groups, where we prove the following main results: 1) If θ is a congruence relation on l-group G, then is l-group. 2) If is l-group, then for holds if and only if are equivalent. Also, we illustrate many examples to clarify the validity of our work.

Permutabitity of principal $ MS $-algebras

<abstract><p>In this paper, we continue to introduce new properties of principal $ MS $-algebras deal with congruence relations via $ MS $-congruence pairs. Necessary and sufficient conditions for a pair of congruences $ (\theta_{1}, \theta_{2})\in Con(L^{\circ\circ})\times Con_{lat}(D(L)) $ to become an $ MS $-congruence pair of a principal $ MS $-algebra (principal Stone algebra) $ L $ are obtained. We describe the lattice of all $ MS $-congruence pairs of a principal $ MS $-algebra $ L $ which induced by the Boolean elements of $ L $. We introduce certain special congruence $ \Psi $ on a principal $ MS $-algebra and its related properties which are useful for the topic of this paper. A characterization of $ 2 $-permutable congruences using $ MS $-congruence pairs of principal $ MS $-algebras is established. Finally, a characterization of $ n $-permutability of congruences of principal $ MS $-algebras is given, which is a generalization of the characterization of $ 2 $-permutability of congruences of such algebras.</p></abstract>

CRYPTANALYSIS USING LAPLACE TRANSFORM OF ERROR FUNCTION

This paper presents a new cryptographic scheme for encryption and decryption by introducing the Laplace transform of error function. Here we have used the concept of congruence relation and modular arithmetic to nd symmetric key, cipher text and Decryption process. The implementation has been done using Matlab.

Apéry-like numbers for non-commutative harmonic oscillators and automorphic integrals

The purpose of the present paper is to study the number theoretic properties of the special values of the spectral zeta functions of the non-commutative harmonic oscillator (NcHO), especially in relation to modular forms and elliptic curves from the viewpoint of Fuchsian differential equations, and deepen the understanding of the spectrum of the NcHO. We study first the general expression of special values of the spectral zeta function $\zeta\_Q(s)$ of the NcHO at $s=n$ $(n=2,3,\dots)$ and then the generating and meta-generating functions for Apéry-like numbers defined through the analysis of special values $\zeta\_Q(n)$. Actually, we show that the generating function $w\_{2n}$ of such Apéry-like numbers appearing (as the “first anomaly”) in $\zeta\_Q(2n)$ for $n=2$ gives an example of automorphic integral with rational period functions in the sense of Knopp, but still a better explanation remains to be clarified explicitly for $n>2$. This is a generalization of our earlier result on showing that $w\_2$ is interpreted as a $\Gamma(2)$-modular form of weight $1$. Moreover, certain congruence relations over primes for “normalized” Apéry-like numbers are also proven. In order to describe $w\_{2n}$ in a similar manner as $w\_2$, we introduce a differential Eisenstein series by using analytic continuation of a classical generalized Eisenstein series due to Berndt. The differential Eisenstein series is actually a typical example of the automorphic integral of negative weight. We then have an explicit expression of $w\_4$ in terms of the differential Eisenstein series. We discuss also shortly the Hecke operators acting on such automorphic integrals and relating Eichler’s cohomology group.

An Echelon Form of Weakly Infeasible Semidefinite Programs and Bad Projections of the psd Cone

A weakly infeasible semidefinite program (SDP) has no feasible solution, but it has approximate solutions whose constraint violation is arbitrarily small. These SDPs are ill-posed and numerically often unsolvable. They are also closely related to “bad” linear projections that map the cone of positive semidefinite matrices to a nonclosed set. We describe a simple echelon form of weakly infeasible SDPs with the following properties: (i) it is obtained by elementary row operations and congruence transformations, (ii) it makes weak infeasibility evident, and (iii) it permits us to construct any weakly infeasible SDP or bad linear projection by an elementary combinatorial algorithm. Based on our echelon form, we generate a library of computationally very difficult SDPs. Finally, we show that some SDPs in the literature are in our echelon form, for example, the SDP from the sum-of-squares relaxation of minimizing Motzkin’s famous polynomial.

The extension of L-algebras and states

In this paper, we introduce EL-algebra, a new algebraic structure extended from L-algebras, where the top element is not assumed and each EL-algebra contains an L-algebra. First, we study the dual atom and the branch on EL-algebras, from which we find that the implication of any two elements in an EL-algebra is always in branch V(1), which is an L-algebra. Based on this result, some relationships among EL-algebras, L-algebras, BCK-algebras, and l-groups are presented. Moreover, we introduce and investigate prime EL-algebras, ideals and congruence relations on EL-algebras. Then, the notions of Bosbach state and state-morphism on EL-algebras are presented, and some of their properties are investigated. Finally, using two different kinds of orthogonal relations on EL-algebras, ⊤ and ⊥, we define two classes of Riečan states on EL-algebras. In addition, some relationships between the Bosbach state and these two Riečan states are studied.

Quotient Pseudo Hyper GR-algebras

A pseudo hyper GR-algebra is an algebraic structure involving two distinct hyperoperations. Properties of this hyper algebra have been studied and given illustrations. This paper focuses on the quotient structure of pseudo hyper GR-algebras. From an equivalence relation on a pseudo hyper GR-algebra H, we can define a congruence relation on H that is used in the constructionof the quotient structure H/I, where I is the congruence class of 0 under the congruence relation. Moreover, some isomorphism theorems of pseudo hyper GR-algebras are included in this paper.

Inferring probable distributional gaps and climate change impacts on the medically important viper Echis leucogaster in the western Sahara-Sahel: An ecological niche modeling approach

Abstract. Bouam I, Khelfaoui F, Saoudi M. 2022. Inferring probable distributional gaps and climate change impacts on the medically important viper Echis leucogaster in the western Sahara-Sahel: An ecological niche modeling approach. Biodiversitas 23: 5175-5183. Knowledge of biodiversity distribution and how climate change may affect species across the Sahara-Sahel is scarce despite it harboring both high biodiversity and a high rate of endemism. As ectotherms, snakes are particularly vulnerable to climate change and susceptible to range shifts and demographic changes driven by climate change. Ecological niche models are a common method for predicting the probability of the occurrence of species and future range shifts induced by climate change. This study examines the probable gaps in the distribution of the white-bellied saw-scaled viper, Echis leucogaster, and the potential influence of climate change on its future geographic range in the western Sahara-Sahel. The currently predicted environmentally suitable areas fitted well with the known geographical range of the species showed relative congruence with the Sahara-Sahel ecoregion delineations and identified areas without known occurrences. In the future, the environmental conditions for the occurrence of E. leucogaster are predicted to increase, as the environmentally suitable areas will potentially experience an increase in their proportion. Future projections also showed that the potentially suitable areas might undergo moderate southward shifts during the late twenty-first century. The results of the present study significantly expand our knowledge on the potential distribution of E. leucogaster and provide valuable insights to guide future sampling efforts and conservation planning for the species.

Characterisation of the lattice operations on positive operators with respect to the spectral order

Kubo and Ando [10] defined a family of operations on positive operators that are now referred to as Kubo-Ando means. These operations are monotone with respect to the usual order and they satisfy the so called transformer inequality, a property which relates the operations to the usual order and congruence transformations. In this paper, we derive a spectral order analogue of the transformer inequality, and we prove that, essentially, the only operations on positive operators which are monotone with respect to the spectral order and satisfy this new transformer inequality are the join and the meet operations with respect to the spectral order.

Hasse–Witt matrices, unit roots and period integrals

Motivated by the work of Candelas et al. (Calabi–Yau manifolds over finite fields, I. arXiv:hep-th/0012233, 2000) on counting points for quintic family over finite fields, we study the relations among Hasse–Witt matrices, unit-root part of zeta functions and period integrals of Calabi–Yau hypersurfaces in both toric varieties and flag varieties. We prove a conjecture by Vlasenko (Higher Hasse–Witt matrices. Indag Math 29(5):1411–1424, 2018) on unit-root F-crystals for toric hypersurfaces following Katz’s local expansion method (1984, 1985) in logarithmic setting. The Frobenius matrices of unit-root F-crystals also have close relation with period integrals. The proof gives a way to pass from Katz’s congruence relations in terms of expansion coefficients (1985) to Dwork’s congruence relations (1969) about periods.

QUOTIENT SEMINEAR-RINGS OF THE ENDOMORPHISM OF SEMINEAR-RINGS

A seminear-ring is a generalization of ring. In ring theory, if is a ring with the multiplicative identity, then the endomorphism module is isomorphic to . Let be a seminear-ring. Here, we can construct the set of endomorphism from to itself denoted by . We show that if is a seminear-ring, then is also a seminear-ring over addition and composition function. We will apply the congruence relation to get the quotient seminear-ring endomorphism. Furthermore, we show the relation between c-ideal and congruence relations. So, we can construct the quotient seminear-ring endomorphism with a c-ideal.

H ∞ filtering of discrete-time Markovian jump singular systems via bounded real lemma and supermartingale-liked approach

This paper addresses the filtering for discrete-time Markovian jump singular systems (MJSSs). While the existing researches have only given the sufficient conditions, in this paper a sufficient and necessary condition is established to guarantee that the filtering error system is regular, causal, stochastically stable and performance in light of supermartingale-liked approach and property of conditional expectation as well as – bounded real lemma. For obtaining the filter, an equivalent matrix inequality to the obtained one in nonlinear form is provided in terms of congruence transformation. Thus the desired filter can be developed by choosing matrix variables with certain structures. Finally, two simulations are provided to show the effectiveness of the proposed techniques in this paper.

New types of rough Pythagorean fuzzy UP-filters of UP-algebras

The aim of this paper is to introduce nine types of rough Pythagorean fuzzy sets in UP-algebras and nine types of rough sets in UP-algebras. Then we study relation of these rough Pythagorean fuzzy sets and new types of Pythagorean fuzzy UP-filter under equivalence (congruence) relation. Moreover, we will also discuss \(t\)-level subsets of rough Pythagorean fuzzy sets in UP-algebras to study the relationships between rough Pythagorean fuzzy sets and rough sets in UP-algebras which we defined them above. Finally, we discuss the concept of homomorphisms between IUP-algebras and also study the direct and inverse images of four special subsets.

Stability analysis and robust controller design for systems with mixed time-delays and stochastic nonlinearity via cone complementarity linearization

The stochastic Takagi-Sugeno (T-S) fuzzy discrete dynamic output feedback control is investigated for a class of stochastic T-S fuzzy discrete networked control systems. Firstly, the T-S fuzzy model and stochastic Bernoulli theory are employed to approximate the discrete system plant. Secondly, the T-S fuzzy model and stochastic Bernoulli theory are employed to design the stochastic T-S fuzzy discrete dynamic output feedback controller. Thirdly, the stochastic Bernoulli theory is employed to describe the characteristics of random occurrence for multipath packet dropouts. The delay-dependent discrete Lyapunov functional and Schur complement are employed, the closed-loop system is stochastically finite-time bounded stable subject to (c1,c2,ω¯,N,R). The Schur complement and congruence transformation matrix are introduced to determine controller gain matrices. The cone complementarity linearization is applied to convert controller design into nonlinear minimization constraints for solving the nonconvex problem caused by fuzzy-basis-dependent LMIs. Simulations are given to show the effectiveness of proposed methods.

State operators on pseudo EQ-algebras

Pseudo EQ-algebras were introduced by X.L. Xin as possible algebraic semantics for fuzzy type theory. The main goal of this paper is to investigate pseudo EQ-algebras with internal states. To begin with, we introduce the notion of pseudo EQ-algebras with internal state(simplify, ISPEQ-algebra) and study its properties. Moreover, we discuss the relation between ISPEQ-algebras and states on pseudo EQ-algebras. In the following, we study state filters(simplify S-fliters) and state prefilters(simplify S-prefliters) of ISPEQ-algebras. We construct ISPEQ-algebras from S-fliters and derive congruence relation θ of ISPEQ-algebras. In the end, we give the generating formula of prefilters on residuated pseudo EQ-algebras and based on that we get the generating formula of S-prefilters on residuated pseudo EQ-algebras.

Compartmentalization as the norm: Exploring the bundling of (un-)sustainable practices in Germany

In the face of intensifying socio-ecological crisis phenomena, a public and academic discourse of urgency has developed with regard to the sustainable transformation of lifestyles. However, in reality, individuals prove resistant to normative calls for more sustainable consumption and consumption patterns often remain inconsistent across different domains of everyday life. A variety of relatively well-studied causes exist for this (e.g., behavioral lock-ins or motivational goal conflicts). Nevertheless, it remains crucial to empirically investigate questions such as: Between which everyday domains are relations of congruence or incongruence particularly pronounced? And how do these relations differ with sociodemographic variables?Starting from a practice theoretical perspective on everyday life, I present empirical findings on the clustering of (un-)sustainable everyday practices in the fields of energy, food, and mobility. Drawing on population representative survey data from the German cities of Muenster and Stuttgart (n = 2005), I identify six distinct clusters of (un-)sustainable practice patterns by combining a multiple correspondence analysis and a hierarchical cluster analysis. Furthermore, I show how these clusters relate to sociodemographic characteristics. My overall analysis reveals that compartmentalization rather than congruence of (un-)sustainable everyday practices is the empirical norm. However, two clusters represent uniformly (un-)sustainable performances of practices but each only account for less than 10% of the surveyed population.

Ramanujan-type systems of nonlinear ODEs for [formula omitted] and [formula omitted

This paper aims to introduce two systems of nonlinear ordinary differential equations whose solution components generate the graded algebra of quasi-modular forms on Hecke congruence subgroups Γ0(2) and Γ0(3). Using these systems, we provide the generated graded algebras with an sl2(ℂ)-module structure. As applications, we introduce Ramanujan-type tau functions for Γ0(2) and Γ0(3), and obtain some interesting and non-trivial recurrence and congruence relations.

An Efficient Approach to Approximate Fuzzy Ideals of Semirings Using Bipolar Techniques

The bipolar fuzzy (BF) set is an extension of the fuzzy set used to solve the uncertainty of having two poles, positive and negative. The rough set is a useful mathematical technique to handle vagueness and impreciseness. The major objective of this paper is to analyze the notion of approximation of BF ideals of semirings by combining the theories of the rough and BF sets. Then, the idea of rough approximation of BF subsemirings (ideals, bi-ideals and interior ideals) of semirings is developed. In addition, semirings are characterized by upper and lower rough approximations using BF ideals. Further, it is seen that congruence relations (CRs) and complete congruence relations (CCRs) play fundamental roles for rough approximations of bipolar fuzzy ideals. Therefore, their associated properties are investigated by means of CRs and CCRs.

Dynamic anti-windup design for linear systems with time-varying state delay and input saturations

This paper considers the dynamic anti-windup design problem for linear systems with time-varying state delay, input saturations and external disturbances. A dynamic anti-windup compensator is first designed that is dependent on the upper bound of the time-varying delay. Then, using an augmented Lyapunov–Krasovskii functional, a distributed-delay-dependent sector condition, some advanced inequalities and some congruence transformations, sufficient conditions are established under which the state trajectories of the closed-loop systems are bounded and meanwhile, the performance can be guaranteed. The anti-windup compensator gain can be explicitly solved by means of linear matrix inequalities. For the case of constant delay, the corresponding result is also presented. Finally, two numerical examples illustrate the effectiveness and advantages of the proposed results.