The multifractal theory of turbulence uses a saddle-point evaluation in determining the power-law behaviour of structure functions. Without suitable precautions, this could lead to the presence of logarithmic corrections, thereby violating known exact relations such as the four-fifths law. Using the theory of large deviations applied to the random multiplicative model of turbulence and calculat...

we define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital banach algebra a and show that the δ-approximate spectrum σ_δ (a) of a is compact. the relation between the δ-approximate spectrum and the usual spectrum is investigated. also an analogue of the classical gleason-kahane-zelazko theorem is established: for each ε>0, there is δ>0 such that if ϕ is...

For a graph $G$ with edge set $E(G)$, the multiplicative sum Zagreb index of $G$ is defined as$Pi^*(G)=Pi_{uvin E(G)}[d_G(u)+d_G(v)]$, where $d_G(v)$ is the degree of vertex $v$ in $G$.In this paper, we first introduce some graph transformations that decreasethis index. In application, we identify the fourteen class of trees, with the first through fourteenth smallest multiplicative sum Zagreb ...

We review how tools from multiplicative ergodic theory and the theory of positive operators are used in the analysis of exponential stability of the optimal nonlinear filter. Particularly, in the case of finite state, we relate the filter sensitivity to perturbations in its initial data to the Lyapunov spectral gap associated with the filtering equation, and, in a general setting, use Hilbert’s...

SUMMARY A preconditioning theory for Schwarz methods is presented. The theory establishes suucient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive deenite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition...

Given a theory T̃ of a polynomially bounded expansion R̃ of R̄ with the field of exponents Q, we introduce a theory T whose models are comprised of a dense pair of models of T̃ and a discrete multiplicative group. We will then prove that T is complete and admits quantifier elimination when predicates are added for certain existential formulas. In particular if T̃ = RCF then T axiomatises 〈R̄,Ralg, 2Z...

Coding theory is useful for real world applications. A notable example is digital television. Basically, coding theory is to study a way of detecting and/or correcting data that may be true or false. Moreover coding theory is an area of mathematics, in which there is an interplay between many branches of mathematics, e.g., abstract algebra, combinatorics, discrete geometry, information theory, ...

We consider the problem of minimal (multiplicative) complexity of polynomial multiplication and multiplication in finite extensions of fields. For infinite fields minimal complexities are known [Winograd, S. (1977) Math. Syst. Theory 10, 169-180]. We prove lower and upper bounds on minimal complexities over finite fields, both linear in the number of inputs, using the relationship with linear c...

We define and study equivariant analytic and local cyclic homology for smooth actions of totally disconnected groups on bornological algebras. Our approach contains equivariant entire cyclic cohomology in the sense of Klimek, Kondracki and Lesniewski as a special case and provides an equivariant extension of the local cyclic theory developped by Puschnigg. As a main result we construct a multip...

A preconditioning theory for Schwarz methods is presented. The theory establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition and ...