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...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.展开更多
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 ...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.展开更多
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.
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 com...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.展开更多
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)-...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.展开更多
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 ...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.展开更多
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...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.展开更多
Let <em>p</em> be an odd prime, the harmonic congruence such as <img alt="" src="Edit_843b278d-d88a-45d3-a136-c30e6becf142.bmp" />, and many different variations and generalizatio...Let <em>p</em> be an odd prime, the harmonic congruence such as <img alt="" src="Edit_843b278d-d88a-45d3-a136-c30e6becf142.bmp" />, and many different variations and generalizations have been studied intensively. In this note, we consider the congruences involving the combination of alternating harmonic sums, <img alt="" src="Edit_e97d0c64-3683-4a75-9d26-4b371c2be41e.bmp" /> where P<em><sub>P </sub></em>denotes the set of positive integers which are prime to <em>p</em>. And we establish the combinational congruences involving alternating harmonic sums for positive integer <em>n</em>=3,4,5.展开更多
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 ...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.展开更多
Let S(P) be a P-inversive semigroup. In this paper we describe the strong P-congruences on S(P) in terms of their P-kernel normal systems. We prove that any strong P-congruence on S(P) can present a P-kernel normal sy...Let S(P) be a P-inversive semigroup. In this paper we describe the strong P-congruences on S(P) in terms of their P-kernel normal systems. We prove that any strong P-congruence on S(P) can present a P-kernel normal system; conversely any P-kernel normal system of S(P) can determine a strong P-congruence.展开更多
Let S be an orthodox semigroup and γ the least inverse congruence on S. 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 c...Let S be an orthodox semigroup and γ the least inverse congruence on S. 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 p on S can be uniquely determined by the admissible triple induced by p, and there exists a lattice isomomorphism between C(S) and Ca(S).展开更多
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'recomm...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.展开更多
文摘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.
基金The NSF(ZR2010AL004)of Shandong Province of China
文摘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.
基金Supported by the National Natural Science Foundation of China（10961014,11101354） Supported by the Natural Science Foundation of Jiangxi Province（0611051） Supported by the Science Foundation of the Education Department of Jiangxi Province（GJ 09459）
文摘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.
基金National Natural Science Foundation of China(No.11671056)General Science Foundation of Shanghai Normal University,China(No.KF201840)。
文摘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.
基金Supported by National Natural Science Foundation of China（11201107）
文摘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.
文摘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.
文摘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.
文摘Let <em>p</em> be an odd prime, the harmonic congruence such as <img alt="" src="Edit_843b278d-d88a-45d3-a136-c30e6becf142.bmp" />, and many different variations and generalizations have been studied intensively. In this note, we consider the congruences involving the combination of alternating harmonic sums, <img alt="" src="Edit_e97d0c64-3683-4a75-9d26-4b371c2be41e.bmp" /> where P<em><sub>P </sub></em>denotes the set of positive integers which are prime to <em>p</em>. And we establish the combinational congruences involving alternating harmonic sums for positive integer <em>n</em>=3,4,5.
文摘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.
文摘Let S(P) be a P-inversive semigroup. In this paper we describe the strong P-congruences on S(P) in terms of their P-kernel normal systems. We prove that any strong P-congruence on S(P) can present a P-kernel normal system; conversely any P-kernel normal system of S(P) can determine a strong P-congruence.
基金The NNSF (19970128) of China and the NSF ((011438), (021073), (Z02017)) of Guangdong Province.
文摘Let S be an orthodox semigroup and γ the least inverse congruence on S. 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 p on S can be uniquely determined by the admissible triple induced by p, and there exists a lattice isomomorphism between C(S) and Ca(S).
基金supported by the National Natural Science Foundation of China(Nos.71971153,72231004,72022012,and 71871155)the Shandong Industrial Internet Innovation and Entrepreneurship Community.
文摘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.
