Suppose Y is a regular covering of a graph X with covering transformation group π = Z. This paper gives an explicit formula for the L zeta function of Y and computes examples. When π = Z, the L zeta function is an algebraic function. As a consequence it extends to a meromorphic function on a Riemann surface. The meromorphic extension provides a setting to generalize known properties of zeta fun...

In this paper, we introduce a suitable algebraic structure for efficient computation of the parametric normal form of Hopf singularity based on a notion of formal decompositions. Our parametric state and time spaces are respectively graded parametric Lie algebra and graded ring. As a consequence, the parametric state space is also a graded module. Parameter space is observed as an integral doma...

Based on a new demand — the commutativity of belief functions combination with refinement/coarsening of the frame of discernment — the role of the disjunctive rule of combination has increased. To compare the nature of this rule with a more frequent but also more controversional one, i.e. with Dempster’s rule, an algebraic analysis was used. The basic necessary definitions both from the Dempste...

Let $G = {rm Res}_{F/mathbb{Q}}(GL_n)$ where $F$ is a number field‎. ‎Let $S^G_{K_f}$ denote an ad`elic locally symmetric space for some level structure $K_f.$ Let ${mathcal M}_{mu,{mathbb C}}$ be an algebraic irreducible representation of $G({mathbb R})$ and we let $widetilde{mathcal{M}}_{mu,{mathbb C}}$ denote the associated sheaf on $S^G_{K_f}.$ The aim of this paper is to classify the data ...

Let H(B) denote the space of all holomorphic functions on the unit ball B Cn. We investigate the following integral operators: Tg( f )(z)= ∫ 1 0 f (tz) g(tz)(dt/t), Lg( f )(z)= ∫ 1 0 f (tz)g(tz)(dt/t), f H(B), z B, where g H(B), and h(z)= ∑n j=1 zj(∂h/∂zj)(z) is the radial derivative of h. The operator Tg can be considered as an extension of the Cesàro operator on the unit disk. The boundedness...

The theory of rough sets provides a widely used modern tool, and in particular, rough sets induced by quasiorders are in the focus of the current interest, because they are strongly interrelated with the applications of preference relations and intuitionistic logic. In this paper, a structural characterisation of rough sets induced by quasiorders is given. These rough sets form Nelson algebras ...

Let Y be a complex algebraic variety, G y Y an action of an algebraic group on Y , U ⊆ Y (C) a complex submanifold, Γ < G(C) a discrete, Zariski dense subgroup of G(C) which preserves U , and π : U → X(C) an analytic covering map of the complex algebraic variety X expressing X(C) as Γ\U . We note that the theory of elimination of imaginaries in differentially closed fields produces a generalize...

In this paper, we examine the relationship between the topology of a manifold M , specifically the finite dimensional representation theory of the fundamental group 7t, (M), and the Lie groups that can act on M. More precisely, let G be a connected semisimple Lie group of higher real rank, and suppose G acts continuously on a (topological) manifold M, preserving a finite measure. The main theme...

Suppose Y is a regular covering of a graph X with covering transformation group π = Z. This paper gives an explicit formula for the L2 zeta function of Y and computes examples. When π = Z, the L2 zeta function is an algebraic function. As a consequence it extends to a meromorphic function on a Riemann surface. The meromorphic extension provides a setting to generalize known properties of zeta f...

Weed detection is a key problem of spot spraying that could reduce the herbicide usage. Spectral information of plants is very useful to detect weeds in real-time for the fast response time. However, the cost of an imaging spectrograph-based weed detection system is too high. Therefore, the main objective of this study was to explore a method to classify crop and weed plants using the spectral ...