In this paper we propose a notion of weak bisimulation for a class of weighted automata with unobservable transitions where weights are taken from an idempotent semiring. In particular the (max/+), (min/+) or (max/min) dioid are considered. The proposed bisimulation is a natural extension of Milner’s well known weak bisimulation for untimed automata (i. e., weighted automata over the boolean se...

Finitely-hollow lifting and hollow-weak modules are two generalizations of hollow module which is a weaker version module. In this paper, we have defined another generalization hollow-lifting namely finitely-hollow-weak (f-hollow-weak lifting) Various properties been seen found that, it not closed under quotients summands in general, so sufficient conditions provided f-hollow-weak property inhe...

Max-algebra, where the classical arithmetic operations of addition and multiplication are replaced by a ⊕ b := max(a, b) and a ⊗ b := a + b offers an attractive way for modelling discrete event systems and optimization problems in production and transportation. Moreover, it shows a strong similarity to classical linear algebra: for instance, it allows a consideration of linear equation systems ...

The goal of this article is to introduce a new approach to model equilibrium in financial markets with an insider. We prove the existence and uniqueness in law of equilibrium for these markets. Our setting is weaker than Back’s one and it can be interpreted as a first theoretical step towards developing statistical test procedures. Additionally, it allows various forms of insider information to...

This paper considers the real-valued random variables X1, . . . , Xn with corresponding distributions F1, . . . , Fn, such that X1, . . . , Xn admit some dependence structure and n(F1 + · · · + Fn) belongs to the class dominatedly varying-tailed distributions. The weak equivalence relations between the quantities P(Sn > x), P(max{X1, . . . , Xn} > x), P(max{S1, . . . , Sn} > x) and ∑n k=1 Fk(x)...

Let (H,R) be a quasitriangular weak Hopf algebra, and A a quantum commutative weak H-module algebra. We establish the relationship of homological dimensions between weak smash product algebra A#H and A under some conditions. As an application, we consider the case of twisted weak Hopf algebra. Mathematics Subject Classification (2010): 16T05

Given a graph G, a subset M of V (G) is a module of G if for each v ∈ V (G) ∖M , v is adjacent to all the elements of M or adjacent to none of them. For instance, V (G), ∅ and {v} (v ∈ V (G)) are modules of G called trivial. Given a graph G, ωM(G) (respectively αM(G)) denotes the largest integer m such that there is a module M of G which is a clique (respectively a stable) set in G with ∣M ∣ = ...

This paper aims to unify and extend existing techniques for deriving upper bounds on the transient of max-plus matrix powers. To this aim, we introduce the concept of weak CSR expansions: A = CSR⊕B. We observe that most of the known bounds (implicitly) take the maximum of (i) a bound for the weak CSR expansion to hold, which does not depend on the values of the entries of the matrix but only on...

Detection of weak signals in a special v-mixing noise class is the signals are weak, asymptotic performance is of interest. considered. The detector structure is restricted to sums of memoryless nonlinear transformations of the observations, correlated with the data A common measure of asymptotic performance is the sequence and compared to a fixed threshold. Using the efficacy to measure effica...

Traditional Serial-Serial multiplier addresses the high data sampling rate. It is effectively considered as the entire partial product matrix with n data sampling cycle for n×n multiplication function instead of 2n cycles in the conventional multipliers. The existing Serial-Serial multiplier is the first bit serial structure. Newly developed serial-serial multiplier design is capable of process...