Congruence Research Articles

An efficient PODI method for real-time simulation of indenter contact problems using RBF interpolation and contact domain decomposition

This paper proposes an efficient proper orthogonal decomposition with interpolation (PODI) method for real-time simulation of indenter contact problems. In the offline stage, POD models are constructed from displacement and von-Mises stress snapshots of full-order finite element solutions of indenter contact problems with training contact locations and indentation depths. Indentation depth and contact location are respectively used to interpolate POD basis vectors and POD coefficients by Lagrange interpolation with a congruence transformation and radial basis function (RBF) interpolation. In the online stage, displacements and von-Mises stress of solids under a new indentation loading are obtained very quickly by using the interpolated POD matrix and POD coefficients. A clustering-based contact domain decomposition (CDD) scheme is proposed to further improve the computational performance of the present PODI–RBF​ method. Numerical results show that the PODI–RBF method using the CDD scheme can be used to obtain finite element solutions of indenter contact problems at 400 ∼900 Hz on a personal computer for finite element models with 8000 ∼16000 nodes, which is promising to real-time simulation of indenter contact problems.

Congruences for critical values of higher derivatives of twisted Hasse–Weil L-functions, III

AbstractLetAbe an abelian variety defined over a number fieldk, letpbe an odd prime number and let$F/k$be a cyclic extension ofp-power degree. Under not-too-stringent hypotheses we give an interpretation of thep-component of the relevant case of the equivariant Tamagawa number conjecture in terms of integral congruence relations involving the evaluation on appropriate points ofAof the${\rm Gal}(F/k)$-valued height pairing of Mazur and Tate. We then discuss the numerical computation of this pairing, and in particular obtain the first numerical verifications of this conjecture in situations in which thep-completion of the Mordell–Weil group ofAoverFis not a projective Galois module.

Pseudo-valuations on commutative BE-algebras

In this paper, we study pseudo-valuations on commutative BE-algebrasand obtain some related results. Using the pseudo-metrics induced by pseudovaluations we introduce a congruence relation on BE-algebras

Norms over intuitionistic fuzzy congruence relations on rings

In this paper, by using norms, we define the concept of intuitionistic fuzzy equivalence relations and intuitionistic fuzzy congruence relations on ring R and we investigate some assertions. Also we define intuitionistic fuzzy ideals of ring R under norms and compare this with fuzzy equivalence relation and fuzzy congruence relation on ring R such that we define new introduced ring.

Algebraic properties of intuitionistic $$L-$$fuzzy multiset finite automata

Algebraic properties and structures of intuitionistic \(L-\)fuzzy multiset finite automata (ILFMA) are discussed through congruences on a semigroup in this paper. Firstly, we put forward the notion of the intuitionistic \(L-\)fuzzy compatible relation, the compatible monoid associated with the intuitionistic \(L-\)fuzzy compatible relation can be effectively constructed, and we construct two finite monoids through two different congruence relations on a given ILFMA, then we prove that they are isomorphic. Furthermore, using the quotient structure of ILFMA, algebraic properties of intuitionistic \(L-\)fuzzy multiset transformation semigroup are discussed. According to intuitionistic \(L-\)admissible relation and homomorphism of ILFMA, we show that there is a bijective correspondence between an ILFMA and the quotient structure of another ILFMA.

Assessment of Psychological Distress and Peer Relations among Trans Adolescents-An Examination of the Use of Gender Norms and Parent-Child Congruence of the YSR-R/CBCL-R among a Treatment-Seeking Sample.

Among trans adolescents, increased psychological distress is reported in the literature. The goal of this study was to examine psychological distress, associated peer relations and parent report congruence among the treatment-seeking sample of the Gender Identity Special Consultation (GISC) for youth at the Charité Berlin. Further, differences between the instruments’ binary gender norms were investigated. Retrospectively, we analyzed clinical data derived from the GISC. By initial interviews and using the Youth Self-Report and Child Behavior Checklist, n = 50 trans adolescents aged 12–18 years (M = 15.5) were examined for psychological problems and peer relations. Congruence between self and parent report was analyzed by correlations. Half of the sample reported suicidality, self-harm and bullying. Trans adolescents showed significantly higher internalizing and total problems than the German norm population. The congruence between self and parent report proved to be moderate to high. The level of congruence and poor peer relations were identified as predictors of internalizing problems. Significant differences between the female vs. male gender norms emerged regarding mean scores and the number of clinically significant cases. Data provide valuable implications for intervention on a peer and family level. There are limitations to the suitability of questionnaires that use binary gender norms, and further research on adequate instruments and assessment is needed.

L‐fuzzy congruence classes in universal algebras

In this paper, we study fuzzy congruence relations and their classes; so-called fuzzy congruence classes in universal algebras whose truth values are in a complete lattice satisfying the infinite meet distributive law. Fuzzy congruence relations generated by a fuzzy relation are fully characterized in different ways. The main result in this paper is that, we give several Mal'cev-type characterizations for a fuzzy subset of an algebra A in a given variety to be a class of some fuzzy congruence on A. Some equivalent conditions are also given for a variety of algebras to possess fuzzy congruence classes which are also fuzzy subuniverses. Special fuzzy congruence classes called fuzzy congruence kernels are characterized in a more general context in universal algebras.

Some Properties of Rough Pythagorean Fuzzy Sets

Pythagorean fuzzy sets are advancements of the intuitionistic fuzzy sets and overcome their limitations. In this paper, we exploit the concept of full congruence relation of Pythagorean fuzzy sets and define the lower and upper approximations of Pythagorean fuzzy set. Using the concept of approximations of Pythagorean fuzzy set we introduce the concept of rough Pythagorean fuzzy set.

Congruence relations for p-adic hypergeometric functions $$\widehat{{\mathscr {F}}}_{a,...,a}^{(\sigma )}(t)$$ and its transformation formula

We introduce new kinds of p-adic hypergeometric functions. We show these functions satisfy congruence relations similar to Dwork’s p-adic hypergeometric functions, so they are convergent functions. We also show that there is a transformation formula between our new p-adic hypergeometric functions and p-adic hypergeometric functions of logarithmic type defined in Asakura (New p-adic hypergeometric functions and syntomic regulators. arXiv:1811.03770) in a particular case.

Preideals in EQ-algebras

EQ-algebras were introduced by Novak (2006) as an algebraic structure of truth values for fuzzy-type theory (FFT). Novák and De Baets (2009) introduced various kinds of EQ-algebras such as good, residuated, and IEQ-algebras. In this paper, we define the notion of (pre)ideal in bounded EQ-algebras (BEQ-algebras) and investigate some properties. Then, we introduce a congruence relation on good BEQ-algebras by using ideals, and then, we solve an open problem in Paad (2019). Moreover, we show that in IEQ-algebras, there is a one-to-one correspondence between congruence relations and the set of ideals. In the following, we characterize the generated preideal in BEQ-algebras, and by using this, we prove that the family of all preideals of a BEQ-algebra is a complete lattice. Then, we show that the family of all preideals of a prelinear IEQ-algebras is a distributive lattice and becomes a Heyting algebra. Finally, we show that we can construct an MV-algebra from the family of all preideals of a prelinear IEQ-algebra.

Reversible data hiding in encrypted images based on homomorphism and block-based congruence transformation

Reversible data hiding in encrypted images based on homomorphism and block-based congruence transformation

Hybrid Structures on EQ-Algebras

In this paper, the notion of hybrid structures on EQ-algebras is introduced, and some related properties are provided. Moreover, the concept of hybrid (pre)filters in EQ-algebras is provided and some related results are given. In the following, the quotient EQ-algebras with respect to a hybrid filter of an EQ-algebra are studied and it is shown that this quotient structure is a separated EQ-algebra for any hybrid filter. Moreover, the concept of strong relative congruence relation is introduced and some related properties are characterized. Finally, it is proved that there is a one-to-one correspondence between the set of all relative congruence relation and the set of all hybrid filters with a few additional conditions.

Congruence properties of indices of triangular numbers multiple of other triangular numbers

For any non-square integer multiplier \(k\), there is an infinity of triangular numbers multiple of other triangular numbers. We analyze the congruence properties of indices \(\xi\) of triangular numbers multiple of triangular numbers. Remainders in congruence relations \(\xi\) modulo \(k\) come always in pairs whose sum always equal \((k-1)\), always include 0 and \((k-1)\), and only 0 and \((k-1)\) if \(k\) is prime, or an odd power of a prime, or an even square plus one or an odd square minus one or minus two. If the multiplier \(k\) is twice the triangular number of \(n\), the set of remainders includes also \(n\) and \((n^{2}-1)\) and if \(k\) has integer factors, the set of remainders include multiples of a factor following certain rules. Algebraic expressions are found for remainders in function of \(k\) and its factors, with several exceptions. This approach eliminates those \(\xi\) values not providing solutions.

L-Fuzzy Congruences and L-Fuzzy Kernel Ideals in Ockham Algebras

In this paper, we study fuzzy congruence relations and kernel fuzzy ideals of an Ockham algebraA,f, whose truth values are in a complete lattice satisfying the infinite meet distributive law. Some equivalent conditions are derived for a fuzzy ideal of an Ockham algebraAto become a fuzzy kernel ideal. We also obtain the smallest (respectively, the largest) fuzzy congruence onAhaving a given fuzzy ideal as its kernel.

Tense Operators on BL-algebras and Their Applications

In this paper, the notions of tense operators and tense filters in \(BL\)-algebras are introduced and several characterizations of them are obtained. Also, the relation among tense \(BL\)-algebras, tense \(MV\)-algebras and tense Boolean algebras are investigated. Moreover, it is shown that the set of all tense filters of a \(BL\)-algebra is complete sublattice of \(F(L)\) of all filters of \(BL\)-algebra \(L\). Also, maximal tense filters and simple tense \(BL\)-algebras and the relation between them are studied. Finally, the notions of tense congruence relations in tense \(BL\)-algebras and strict tense \(BL\)-algebras are introduced and an one-to-one correspondence between tense filters and tense congruences relations induced by tense filters are provided.

Integer-valued polynomials satisfying the Lucas property

The classical theorem of Lucas states that the binomial polynomials, which form a basis for integer-valued polynomials, satisfy a congruence relation related to their integer parameters. We consider here three problems connected with this result in the setting of discrete valued structures. The first problem asks for the shapes of Lagrange-type interpolation polynomials which constitute a basis for integer-valued polynomials and satisfy the Lucas property; the result so obtained extends a 2001 result of Boulanger and Chabert. For the second problem, we show that the Carlitz polynomials, which form a basis for integer-valued polynomials in a function field, satisfy the Lucas property, and derive criteria guaranteeing that Carlitz-like polynomials, which constitute a basis for integer-valued polynomials, enjoy the Lucas property. The third problem is to find conditions on general polynomials which form a basis for integer-valued polynomials ensuring that they satisfy the Lucas property.

Synchronization Control for Discrete-Time-Delayed Dynamical Networks With Switching Topology Under Actuator Saturations.

This article is concerned with the synchronization control problem for a class of discrete-time dynamical networks with mixed delays and switching topology. The saturation phenomenon of physical actuators is specifically considered in designing feedback controllers. By exploring the mixed-delay-dependent sector conditions in combination with the piecewise Lyapunov-like functional and the average-dwell-time switching, a sufficient condition is first established under which all trajectories of the error dynamics are bounded for admissible initial conditions and nonzero external disturbances, while the l2 - l∞ performance constraint is satisfied. Furthermore, the exponential stability of the error dynamics is ensured for admissible initial conditions in the absence of disturbances. Second, by using some congruence transformations, the explicit condition guaranteeing the existence of desired controller gains is obtained in terms of the feasibility of a set of linear matrix inequalities. Then, three convex optimization problems are formulated regarding the disturbance tolerance, the l2 - l∞ performance, and the initial condition set, respectively. Finally, two simulation examples are given to show the effectiveness and merits of the proposed results.

Strong Relations Of Fuzzy Automata

Strong diminution and strong dependability relation of fuzzy automata are introduced and prove that strong dependability relation is an equivalence relation and congruence relation.

Construction of (n-Fold) EQ-Algebras by Using Fuzzy n-Fold Filters

In this paper, the concept of fuzzy [Formula: see text]-fold (positive implicative, implicative, fantastic) filters in [Formula: see text]-algebras is defined and several results and relation among them are investigated. Then [Formula: see text]-fold (implicative) positive implicative [Formula: see text]-algebras are constructed by using [Formula: see text]-fold fuzzy positive (implicative) filters and suitable congruence relations on [Formula: see text]-algebras.

Isomorphism Theorems on Intuitionistic Fuzzy Abstract Algebras

The concept of abstract algebra on intuitionistic fuzzy sets were introduced and some basic theorems were proved by authors in 2017. In this study, homomorphism between intuitionistic fuzzy abstract algebras is defined, intuitionistic fuzzy function is examined and then intuitionistic fuzzy congruence relations are defined on intuitionistic fuzzy abstract algebra. First and third isomorphism theorems on intuitionistic abstract algebras are introduced.