Isomorphism Continuum Stored Energy Functional for Finite Thermoelastic Deformation

Continuum mechanics for isotropic finite thermoelastic deformations have been reviewed. Thermal effects on mechanical responses of rubbers have been captured by the isomorphism continuum stored energy (CSE) functional with the multiplicative decomposition of deformation gradient while preserving the structure of symmetry for finite structural deformation. The CSE finite thermoelastic model fits and predicts experimental data of SR and NR-C60 rubbers at different external temperatures. For internal temperature effects of both NR and NR-SIC rubbers, the CSE finite thermoelastic model of stored energy and entropy, along with the newly developed CTE and CI models, fits both nominal stress-stretch and temperature change-stretch experimental data in uniaxial extension tests.

ISOMORPHISMS AND DERIVATIONS IN C*-ALGEBRAS

In this article, we prove the Hyers-Ulam-Rassias stability of the following Cauchy-Jensen functional inequality：‖f （x） ＋ f （y） ＋ 2f （z） ＋ 2f （w）‖ ≤‖ 2f x ＋ y2 ＋ z ＋ w ‖（0.1）This is applied to investigate isomorphisms between C＊-algebras, Lie C＊-algebras and JC＊-algebras, and derivations on C＊-algebras, Lie C＊-algebras and JC＊-algebras, associated with the Cauchy-Jensen functional equation 2f （x ＋ y/2 ＋ z ＋ w） = f（x） ＋ f（y） ＋ 2f（z） ＋ 2f（w）.

The Homomorphism and Isomorphism on Hypergroup

Basing on the papers from [1] to [4], this paper gives some further research,mainly solves the following problems:(1) It proved that several theorems of subgroup which have been raised to the hypergroup are still true.(2) It proved that the isomorphous relationship of the bottomgroups which guid to the hypergroup can still keep such relationship.(3) It proved that the basic isomorphous Theorem and the homogenous Theorem of the bottomgroup which raise to the hypergroup are still true.(4) It point out that when the isomorphous bottomgroups have been raised to the hypergroup,the conditions which form the isomorphism should be lessened.

Simulated annealing algorithm for detecting graph isomorphism

Evolutionary computation techniques have mostly been used to solve various optimization problems, and it is well known that graph isomorphism problem （GIP） is a nondeterministic polynomial problem. A simulated annealing （SA） algorithm for detecting graph isomorphism is proposed, and the proposed SA algorithm is well suited to deal with random graphs with large size. To verify the validity of the proposed SA algorithm, simulations are performed on three pairs of small graphs and four pairs of large random graphs with edge densities 0.5, 0.1, and 0.01, respectively. The simulation results show that the proposed SA algorithm can detect graph isomorphism with a high probability.

SMALL INTO ISOMORPHISM FROM(c_0)INTO C(Ω)TYPE

If T is an isomorphism of （c0） into C（Ω） （where Ω is a sequentially compact and paracompact space, or a compact metric space in particular）, which satisfies the condition ｜｜T｜｜·｜｜T^-1｜｜ ≤ 1 ＋ε for some ε ∈ （0,1/5）, then T/｜｜T｜｜ is close to an isometry with an error less than 9ε. The proof of this article is simple without using the dual space or adjoint operator.

GPU acceleration of subgraph isomorphism search in large scale graph

A novel framework for parallel subgraph isomorphism on GPUs is proposed, named GPUSI, which consists of GPU region exploration and GPU subgraph matching. The GPUSI iteratively enumerates subgraph instances and solves the subgraph isomorphism in a divide-and-conquer fashion. The framework completely relies on the graph traversal, and avoids the explicit join operation. Moreover, in order to improve its performance, a task-queue based method and the virtual-CSR graph structure are used to balance the workload among warps, and warp-centric programming model is used to balance the workload among threads in a warp. The prototype of GPUSI is implemented, and comprehensive experiments of various graph isomorphism operations are carried on diverse large graphs. The experiments clearly demonstrate that GPUSI has good scalability and can achieve speed-up of 1.4–2.6 compared to the state-of-the-art solutions.

ADJACENT MARTIX METHOD OF IDENTIFYING ISOMORPHISM TO PLANAR KINEMATIC CHAIN WITH MULTIPLE JOINTS AND HIGHER PAIRS

The adjacent matrix method for identifying isomorphism to planar kinematic chain with multiple joints and higher pairs is presented. The topological invariants of the planar kinematic chain can be calculated and compared by adjacent matrix. The quantity of calculation can be reduced effectively using the several divisions of bars and the reconfiguration of the adjacent matrix. As two structural characteristics of adjacent matrix, the number of division and division code are presented. It can be identified that two kinematic chains are isomorphic or not by comparing the structural characteristics of their adjacent matrixes using a method called matching row-to-row. This method may be applied to the planar linkage chain too. So, the methods of identifying isomorphism are unified in the planar kinematic chain that has or hasn＇t higher pairs with or without multiple joints. And it has some characters such as visual, simple and convenient for processing by computer, and so on.

Similar Vertices and Isomorphism Detection for Planar Kinematic Chains Based on Ameliorated Multi-Order Adjacent Vertex Assignment Sequence

Isomorphism detection is fundamental to the synthesis and innovative design of kinematic chains(KCs).The detection can be performed accurately by using the similarity of KCs.However,there are very few works on isomorphism detection based on the properties of similar vertices.In this paper,an ameliorated multi-order adjacent vertex assignment sequence(AMAVS)method is proposed to seek out similar vertices and identify the isomorphism of the planar KCs.First,the specific definition of AMAVS is described.Through the calculation of the AMAVS,the adjacent vertex value sequence reflecting the uniqueness of the topology features is established.Based on the value sequence,all possible similar vertices,corresponding relations,and isomorphism discrimination can be realized.By checking the topological graph of KCs with a different number of links,the effectiveness and efficiency of the proposed method are verified.Finally,the method is employed to implement the similar vertices and isomorphism detection of all the 9-link 2-D0F(degree of freedom)planar KCs.

ISOMORPHISMS OF VARIABLE HARDY SPACES ASSOCIATED WITH SCHRÖDINGER OPERATORS

Let L:=-△+V be the Schrodinger operator on R^(n)with n≥3,where V is a non-negative potential satisfying△^(-1)(V)∈L^(∞)(R^(n)).Let w be an L-harmonic function,determined by V,satisfying that there exists a positive constantδsuch that,for any x∈Rn,0<δ≤w(x)≤1.Assume that p(·):R^(n)→(0,1]is a variable exponent satisfying the globally log-Hölder continuous condition.In this article,the authors show that the mappings HL^(p)(·))(R^(n))■f■wf∈H^(p)(·)(R^(n))and HL^(p(·))(R^(n))■f■(-△)^(1/2)L^(-1/2)(f)∈H^(p(·))(R^(n))are isomorphisms between the variable Hardy spaces HL^(p(·))(R^(n)),associated with L,and the variable Hardy spaces H^(p(·))(R^(n)).

ISOMORPHISMS OF CIRCULANT DIGRAPHS OF DEGREE 3

In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine theisomorphic classes of circulant digraphs of degree 3. In particular, we characterizethose circulant digraphs of degree 3 which don't satisfy Adam's conjecture.

ON THE ISOMETRIC ISOMORPHISM OF PROBABILISTIC METRIC SPACES

There are two kinds of isometric isomorphism in probabilistic metric space theory. The first is that a PM space (E, F) is isometrically isomorphic to another PM space (E', F'), and the second is that a PM space (E, F) is isometrically isomorphic to a generating space of quasi-metric family (E', d(r), r is an element of (0, 1)). This paper establishes the connection between the two kinds of isometric isomorphism.

The Isomorphism Theorem of Regular Bisimple ω2-semigroups

In this paper we study the isomorphisms of two regular bisimple ω2- semigroups and obtain a criterion for two such semigroups to be isomorphic.

Weak Isomorphism of Finite Group

On the basis of the quasi-isomorphism of finite groups, a new mapping, weak isomorphism, from a finite group to another finite group is defined. Let G and H be two finite groups and G be weak-isomorphic to H. Then G≌H if G satisfies one of the following conditions. 1） G is a finite Abelian group. 2） The order of G is p^3. 3 ） The order of G is p^n＋1 and G has a cyclic normal subgroup N = 〈a〉 of order p^n. 4） G is a nilpotent group and if p^││G│, then for any P ∈ Sylp （G）, P has a cyclic maximal subgroup, where p is a prime; 5） G is a maximal class group of order p4（p〉3）.

Characterizations of Isomorphisms by Multiplicative Maps on Operator Algebras

In this paper, we discuss some multiplicative preservers and give some characterizations of isomorphisms or conjugate isomorphisms on β(X), where β(X) denotes the algebra of all bounded linear operators on a Banach space X.

Subgraph Isomorphism Based Intrinsic Function Reduction in Decompilation

Program comprehension is one of the most important applications in decompilation. The more abstract the decompilation result the better it is understood. Intrinsic function is introduced by a compiler to reduce the overhead of a function call and is inlined in the code where it is called. When analyzing the decompiled code with lots of inlined intrinsic functions, reverse engineers may be confused by these detailed and repeated operations and lose the goal. In this paper, we propose a method based graph isomorphism to detect intrinsic function on the CFG (Control Flow Graph) of the target function first. Then we identify the boundary of the intrinsic function, determine the parameter and return value and reduce the intrinsic function to a single function call in the disassembled program. Experimental results show that our method is more efficient at reducing intrinsic functions than the state-of-art decompilers such as Hex-Rays, REC and RD (Retargetable Decompiler).

ISOMETRIC ISOMORPHISMS OF TRIANGULAR BANACH ALGEBRAS

Let A and B be Banach algebras.Let M be a Banach A,B module with bounded 1.Then T=AM 0B is a Banach algebra with the usual operations and the norm AM 0B=‖A‖+‖M‖+‖B‖.Such an algebra is called a triangular Banach algebra.In this paper the isometric isomorphisms of triangular Banach algebras are characterized.

STUDY ON ISOMORPHISM OF PLANAR KINEMATIC CHAINS

The isomorphism of planar kinematic chains is studied. The original methods for de- tecting isomorphism is discussed. A new matrix, the link -link path matrix, is presented to show the structures of planar kinematic chains. It is simple and reliable to detect isomorphism of planar kinematic chains by using the link-link path matrix.

Eventually homological isomorphisms and Gorenstein projective modules

We prove that a certain eventually homological isomorphism between module categories induces triangle equivalences between their singularity categories,Gorenstein defect categories and stable categories of Gorenstein projective modules.Furthermore,we show that the Auslander-Reiten conjecture and the Gorenstein symmetry conjecture can be reduced by eventually homological isomorphisms.Applying these results to arrow removal and vertex removal,we describe the Gorenstein projective modules over some non-monomial algebras and verify the Auslander-Reiten conjecture for certain algebras.

On the Proof of the Contradiction of Set Theory

The article is devoted to proving the inconsistency of set theory arising from the existence of strange trees. All steps of the proof rely on common informal set-theoretic reasoning, but they take into account the prohibitions that were introduced into axiomatic set theories in order to overcome the difficulties encountered by the naive Cantor set theory. Therefore, in fact, the article is about proving the inconsistency of existing axiomatic set theories, in particular, the ZFC theory.

Isomorphisms of Cubic Cayley Graphs on Dihedral Groups and Sparse Circulant Matrices

We show that,up to isomorphism,there is a unique non-CI connected cubic Cayley graph on the dihedral group of order 2n for each even number n≥4.This answers in the negative the question of Li whether all connected cubic Cayley graphs are CI-graphs(Discrete Math.,256,301-334(2002)).As an application,a formula is derived for the number of isomorphism classes of connected cubic Cayley graphs on dihedral groups,which generalises the earlier formula of Huang et al.dealing with the particular case when n is a prime(Acta Math.Sin.,Engl.Ser.,33,996-1011(2017)).As another application,a short proof is also given for a result on sparse circulant matrices obtained by Wiedemann and Zieve(arXiv preprint,(2007)).