The Deformation Analysis of the 3D Alignment Control Network Based on the Multiple Congruence Models

In the construction and maintenance of particle accelerators,all the accelerator elements should be installed in the same coordinate system,only in this way could the devices in the actual world be consistent with the design drawings.However,with the occurrence of the movements of the reinforced concrete cover plates at short notice or building deformations in the long term,the control points upon the engineering structure will be displaced,and the fitness between the subnetwork and the global control network may be irresponsible.Therefore,it is necessary to evaluate the deformations of the 3D alignment control network.Different from the extant investigations,in this paper,to characterize the deformations of the control network,all of the congruent models between the points measured in different epochs have been identified,and the congruence model with the most control points is considered as the primary or fundamental model,the remaining models are recognized as the additional ones.Furthermore,the discrepancies between the primary S-transformation parameters and the additional S-transformation parameters can reflect the relative movements of the additional congruence models.Both the iterative GCT method and the iterative combinatorial theory are proposed to detect multiple congruence models in the control network.Considering the actual work of the alignment,it is essential to identify the competitive models in the monitoring network,which can provide us a hint that,even the fitness between the subnetwork and the global control network is good,there are still deformations which may be ignored.The numerical experiments show that the suggested approaches can describe the deformation of the 3D alignment control network roundly.

Architectures and Algorithms of Generalized Congruence Neural Networks

In this paper a novel class of neural networks called generalized congruence neural networks (GCNN) is proposed. All neurons in the neural networks are activated in the form of congruence. The architectures, learning rules and two algorithms are presented. Simulation results indicate that such network has satisfactory generalization properties near the sample points. Since this kind of neural nets can be easily operated and implemented, it is appropriate to make further research concerning the theory and applications of GCNN.

A SPECIAL KIND OF PRINCIPAL CONGRUENCES ON MS-ALGEBRAS

In this article, for any a in the MS-algebra L, the author considers the con- gruence of the form defined by （x,y） ∈θa→←x∧a°° = y ∧a° and x ∨ a°° = y ∨ a°°. A characterization of subdirectly irreducible MS-algebras is given and it is also proved that the union of two principal congruences having this form is a principal congruence if and only if L ∈ K2 ∨ K3.

ON SYMMETRIC EXTENDED MS-ALGEBRAS WHOSE CONGRUENCES ARE PERMUTABLE

Algebras whose congruences are permutable were investigated by a number of authors in the literature. In this paper, we study the symmetric extended MS-algebras whose congruences are permutable. Some results obtained by Jie Fang on symmetric extended De Morgan algebras are generalized.

P-congruence-free Epigroups

Let P denote the equivalence relation on an epigroup in which any of its classes consists precisely of those elements owning the same pseudo-inverse. The purpose of the paper is to characterize epigroups on which any congruence either contains P or its join with P is the identity relation on epigroups. As a special subclass of epigroups, completely 0-simple semigroups having the same property are also described.

COBORDISM AND ROKHLIN CONGRUENCES

In this paper, we give a cobordism proof of the higher dimensional Rokhlin congruences established in [8].

Rectangular Ring Congruences on an E-inversive Semiring

In this paper, we discussed the property of rectangular band semiring congruence and ring congruence on a semiring and gave some characterizations and structure of rectangular ring congruence on an E-inversive semiring.

One Class of the Least Congruences on Completely Regular Semigroups

Congruence is a very important aspect in the study of the semigroup theory.In general,the Kernel-trace characterizations,Green's relations and subvarieties are main tools in the consideration of congruences on completely regular semigroups.In this paper,we give one class of congruences on completely regular semigroups with the representation of wreath product of translational hulls on completely simple semigroups.By this new way,the least Clifford semigroup congruences on completely regular semigroups are generalized.

On the Error Term for the Number of Solutions of Certain Congruences

Let f(x) be an irreducible polynomial of degree m ≥ 2 with integer coefficients,and let r(n) denote the number of solutions x of the congruence f(x) ≡ 0(mod n) satisfying0 ≤ x < n. Define ?(x) =Σ 1≤n≤x r(n)-αx, where α is the residue of the Dedekind zeta function ζ(s, K) at its simple pole s = 1. In this paper it is shown that ∫_1~X?~2(x)dx? ε{X^(3-6/m+3+ε)if m ≥ 3,X^(2+ε) if m = 2,for any non-Abelian polynomial f(x) and any ε > 0. This result constitutes an improvement upon that of Lü for the error terms on average.

Fibonacci Congruences and Applications

When we study a congruence T(x) ≡ ax modulo m as pseudo random number generator, there are several means of ensuring the independence of two successive numbers. In this report, we show that the dependence depends on the continued fraction expansion of m/a. We deduce that the congruences such that m and a are two successive elements of Fibonacci sequences are those having the weakest dependence. We will use this result to obtain truly random number sequences xn. For that purpose, we will use non-deterministic sequences yn. They are transformed using Fibonacci congruences and we will get by this way sequences xn. These sequences xn admit the IID model for correct model.

Analogous Systems Principles and Concepts of Traditional Chinese Medicine and Congruence Couple Therapy

This article explicates the analogous principles and concepts between traditional Chinese medicine(TCM)and congruence couple therapy(CCT).Although originating out of vastly different times and places,TCM and CCT share a view of health based on systems understanding to facilitate the interconnections of the parts of an organism rather than focusing on eliminating symptoms.Both approaches aim to release Qi(气)and vitality by removing blockages through adjusting the interactions,adaptation,and balance of multiple elements and Yin‑Yang energies.The goal is to liberate the Qi or life force through improved holistic balance and cooperation.While TCM focuses on interventions at the level of the body,CCT focuses on the attention,awareness,acknowledgement,and alignment of the four human dimensions consisting of the intrapsychic,interpersonal,intergenerational,and universal‑spiritual.In light of the current trend toward increasing mental,substance use,and neurological disorders,in particular among countries of middle and low income,dialogue to explore these compatibilities between TCM and CCT is conducive to the continuous evolution of TCM and Western therapies to address not only physical health but also the exigencies of contemporary addiction and mental health care within a mind–body relationship matrix.

Congruences on an Orthodox Semigroup

Let 5 be an orthodox semigroup and γ the least inverse congruence on 5. C(S) denotes the set of all congruences on S. In this paper we introduce the concept of admissible triples for S, where admissible triples are constructed by the congruences on S/γ , the equivalences on E(S)/L and E(S)/R. The notation Ca(S) denotes the set of all admissible triple for S. We prove that every congruence ρ on S can be uniquely determined by the admissible triple induced by ρ, and there exists a lattice isomomorphism between C(S) and Ca(S).

Super Congruences Involving Alternating Harmonic Sums

Let p be an odd prime, the harmonic congruence such as , and many different variations and generalizations have been studied intensively. In this note, we consider the congruences involving the combination of alternating harmonic sums, where PP denotes the set of positive integers which are prime to p. And we establish the combinational congruences involving alternating harmonic sums for positive integer n=3,4,5.

Digital Influencer's choice of product endorsement:A perspective of congruence

To infer product fitness information,consumers often consult digital influencers who exert effort to learn and evaluate product features and then propagate information to their followers.However,influencers'recommendations are not limited to products that exactly match their expertise,which may lead followers to unfollow them.This study investigates which product(high or low congruence)an influencer should endorse and how much endorsement effort should be exerted.Using a theoretical model,we obtain several interesting results.First,endorsing a low-congruence product can surprisingly benefit the influencer if the penalty per lost follower is moderate or if the influencer has sufficiently high efficiency in reducing the perception error of this product.Second,although the influencer has high expertise in the high-congruence product,she will lose more followers when endorsing it than when endorsing the low-congruence product if a particularly small or large proportion of her followers are potential consumers of the low-congruence product.Third,when the influencer endorses the low-congruence product,the number of new followers increases with the size of the influencer's follower base only when the follower base is small and a large proportion of followers are potential consumers of the low-congruence product.Interestingly,as the size of the follower base increases,the influencer always exerts more effort when endorsing the high-congruence product but will exert less effort in learning about the low-congruence product if a sufficiently small proportion of followers are potential consumers.Finally,after taking consumers'knowledge about product features into account,the main results still hold,and when considering the competition between influencers,we uncover the conditions under which both influencers will choose to endorse the high-congruence product.

Congruence浅议

本文在对congruence的涵义和理论发展脉络进行归纳和清理的基础上,从认知语言学的视角提出了三条判别一致式与非一致式的标准,即主语典型性标准,是否隐涵根隐喻的标准和是否体现人体活动的标准。在总结名词化的范围时,作者发现,名词化可以存在于六种不同的及物性过程中,而且不同的及物性过程均可通过名词化而以语法隐喻的形式实现对语义的编码,这样一来,不同过程间的相互隐喻和名词化隐喻间的非对称性被消解。

Representation of Congruences on Regular Semigroups with Inverse Transversals

For a regular semigroup with an inverse transversal, we have Saito’s structure W(I, S°, Λ, *, α,β). We represent congruences on this kind of semigroups by the so-called congruence assemblage which consist of congruences on the structure component parts I, S° and Λ. The structure of images of this type of semigroups is also presented.

Maximal and Minimal Congruences on Some Semigroups

In 2006, Sanwong and Sullivan described the maximal congruences on the semigroup N consisting of all non-negative integers under standard multiplication, and on the semigroup T（X） consisting of all total transformations of an infinite set X under composition. Here, we determine all maximal congruences on the semigroup Zn under multiplication modulo n. And, when Y lohtain in X, we do the same for the semigroup T（X, Y） consisting of all elements of T（X） whose range is contained in Y. We also characterise the minimal congruences on T（X. Y）.

Principal Congruence Subgroups of Hecke Groups H(q^(1/2))

Using the notion of quadratic reciprocity, we discuss the principal congruence subgroups of the Hecke groups H（√q）,q 〉 5 prime number.

Congruence Subgroups of Hecke Groups

Hecke groups are an important tool in subgroups of Hecke groups play an important rule investigating functional equations, and congruence in research of the solutions of the Dirichlet series. When q, m are two primes, congruence subgroups and the principal congruence subgroups of level m of the Hecke group H（√q） have been investigated in many papers. In this paper, we generalize these results to the case where q is a positive integer with q ≥ 5, √q ￠ Z and m is a power of an odd prime.

Congruence Pairs of Decomposable MS-Algebras

In this paper,the authors first introduce the concept of congruence pairs on the class of decomposable MS-algebras generalizing that for principal MS-algebras(see[13]).They show that every congruence relationθon a decomposable MS-algebra L can be uniquely determined by a congruence pair(θ_(1),θ_(2)),whereθ_(1)is a congruence on the de Morgan subalgebra L^(∞)of L andθ_(2)is a lattice congruence on the sublattice D(L)of L.They obtain certain congruence pairs of a decomposable MS-algebra L via central elements of L.Moreover,they characterize the permutability of congruences and the strong extensions of decomposable MS-algebras in terms of congruence pairs.