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In this paper, by using the structure properties of algebras and the technique of matrix operation, we investigate the structure of local Lie triple derivations on triangular algebras. Under some mild conditions, we prove that each local Lie triple derivation of triangular algebras can be expressed as the sum of a derivation and a linear map from the triangular algebra to its center that vanishes at Lie triple products. Finally, we apply the main result to the problem of characterizing local Lie triple derivations on an upper triangular matrix algebra. [ABSTRACT FROM AUTHOR]

In this paper, we further study implicative derivations on FI-lattices and obtain some new results of them. In particular, we prove that the set of all implicative derivations on FI-lattice forms a monoid. Also, we generalize the implicative derivations by homomorphism, which is called generalized implicative derivation, on FI-lattices and obtain some important results of them. The results of this paper generalize the corresponding results of derivations on the logical algebras of t-norm based fuzzy logic. [ABSTRACT FROM AUTHOR]

In this paper, interior and closure operators on quasi-pseudo-BL algebras are introduced and investigated. First, we give the definitions of multiplicative interior operators (mi-operators, for short), weak mi-operators, wmi-operators and weak wmi-operators on a quasi-pseudo-BL algebra and discuss the relationship among them. Meanwhile, we study the related properties of these operators on a quasi-pseudo-BL algebra and discuss the operators on the quotient algebra with respect to a normal weak filter. Second, we introduce the concepts of additive closure operators (ac-operators, for short), weak ac-operators, sac-operators and weak sac-operators on a good quasi-pseudo-BL algebra. We study the relations among them and discuss the related properties. Moreover, we present the connections between (weak) wmi-operators and (weak) ac-operators on a good quasi-pseudo-BL algebra. Finally, we investigate the properties of the induced operators on some quasi-pseudo-MV algebras. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce the notion of quasi-Boolean algebras as a generalization of Boolean algebras. First we discuss some properties of quasi-Boolean algebras. Next we define ideals and filters of quasi-Boolean algebras and investigate the related properties. We also show that there is a one-to-one correspondence between the set of ideals and the set of ideal congruences on a quasi-Boolean algebra. Finally, we present the relationship between quasi-Boolean algebras and Boolean quasi-rings. [ABSTRACT FROM AUTHOR]

This paper discusses the Cholesky decomposition in the symmetrized max-plus algebra. By using a link between the conventional algebra and the symmetrized max-plus algebra, we show the existence of the Cholesky decomposition of a matrix over the symmetrized max-plus algebra. A matrix has the Cholesky decomposition if it is symmetric and has principal leading submatrices whose determinant are positive. The results can be used to determine the solution of linear balance systems. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce the concepts of implicative filters, positive implicative filters, fantastic filters and associative filters in a pseudo-quasi-MV algebra. The properties of these types of filters are investigated and the relationships between them are also discussed. [ABSTRACT FROM AUTHOR]

Such sections of algebra as the theory of finite fields and the theory of polynomials over finite fields have increasingly influence on the construction of various systems for protecting information, encoding and decoding information. In the last two decades, polynomials, especially irreducible polynomials, have played a significant role in computer cryptography. Using the properties of irreducible polynomials maximizes the efficient computer implementation of arithmetic in finite fields, which is of particular importance for cryptography and coding theory. The present paper is devoted to the study of irreducible polynomials of a special type. Namely, explicit root polynomial formulas for third-degree cyclic polynomials over a field of characteristic 2 are obtained. A review of known results on irreducible normal polynomials and sets of their root polynomials over arbitrary fields is also given. In addition, the problem of finding irreducible polynomials is considered. The results of the work can be used in cryptographic applications and coding theory. [ABSTRACT FROM AUTHOR]

Let G be a graph of order n. The incidence energy IE(G) of graph G, IE for short, is defined as the sum of all singular values of its incidence matrix. In this paper, we determine the maximal incidence energy IE(G) among all connected graphs with the connectivity κ and edge connectivity κ' and Kκ' ∨(K1∪Kn-κ'-1) has the maximal incidence energy. [ABSTRACT FROM AUTHOR]

Behavioral Hybrid Process Calculus (BHPC) is a formalism for Modeling and analysis of hybrid systems combining process algebras and the behavioral approach for Modeling of instantaneous changes and continuous evolution. BHPC is supported by Bhave toolset, containing a tool for a novel way of visualization of hybrid systems simulations msp-svg and a new version of hybrid simulator. In this paper, we present the latest developments of Bhave toolset and apply it for case studies of system control and electronic system design. [ABSTRACT FROM AUTHOR]

Compensating CSP (cCSP) is a language defined to model long running business transactions within the framework of standard CSP process algebra. In earlier work, we have defined both traces and operational semantics of the language. We have shown the consistency between the two semantic models by defining a relationship between them. Synchronization was missing from the earlier semantic definitions which is an important feature for any process algebra. In this paper, we address this issue by extending the syntax and semantics to support synchronization and define a relationship between the semantic models. Moreover, we improve the scalability of our proof technique by mechanically verifying the semantic relationship using theorem prover PVS. We show how to embed process algebra terms and semantics into PVS and to use these embeddings to prove the semantic relationship. [ABSTRACT FROM AUTHOR]

ACP hssrt is a hybrid process algebra obtained by extending a combination of two existing extensions of Algebra of Communicating Processes (ACP), namely the process algebra with continuous relative timing and the process algebra with propositional signals, for the formal specification and analysis of hybrid systems. In addition to equational axioms, this hybrid process algebra has rules to derive equations with the help of real analysis. ACPhssrt is also closely related to the theory of hybrid automata, so ACPhssrt can be reasonable easily translated to hybrid automata. This enables automatic verification of ACPhssrt specifications using existing hybrid automaton-based verification tools (e.g. PHAVer and HyTech). Since ACPhssrt is a well-developed algebraic theory from the field of hybrid process algebras with the above-mentioned features, it seems to allow rigorous the formal specification and analysis of digital/analog/mixed-signal circuits. In order to explore this fact, in this paper, we study a mixed-signal circuit: a half wave rectifier in ACPhssrt. Some basic properties of the half wave rectifier are analysed in a formal way and some correctness requirements are also proven to be satisfied. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of searching the maximum-weighted matching in Halin graphs. We give an O(∣V∣) algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we present an neural network approach to solve a set of nonlinear equations. A modified Hopfield network has been developed to optimize a energy function. This approach provides faster convergence and extremely accurate solutions for all solvable systems. We solved and discussed several illustrative examples in order to depict the powerfulness of the proposed method. [ABSTRACT FROM AUTHOR]

For positive integers k and l , the Ramsey number R(k,l) is the least positive integer n such that for every graph G of order n , either G contains kK as a subgraph or Ḡ contains Kl as a subgraph. In this paper it is shown that Ramsey numbers R(k,l) ≥ 2kl - 3k - 3l + 6 when ≤ 3 k ≤ l, and R(k,l) ≥ 2kl - 3k + 2l - 12 when ≤ 5 k ≤ l. [ABSTRACT FROM AUTHOR]