we give a new proof of the well known wedderburn's little theorem (1905) that a finite‎ ‎division ring is commutative‎. ‎we apply the concept of frobenius kernel in frobenius representation theorem in finite group‎ ‎theory to build a proof‎.

In this work, we extend a variable-length source coding theorem for discrete memoryless sources to ergodic time-invariant Markov sources of arbitrary order. To accomplish this extension, we establish a formula for the R enyi entropy rate limn!1 H(n)=n. The main tool used to obtain the R enyi entropy rate result is Perron-Frobenius theory. We also examine the expression of the R enyi en-tropy ra...

In this work, we extend a variable-length source coding theorem for discrete memoryless sources to ergodic time-invariant Markov sources of arbitrary order. To accomplish this extension, we establish a formula for the R enyi entropy rate lim n!1 H (n)=n. The main tool used to obtain the R enyi entropy rate result is Perron-Frobenius theory. We also examine the expression of the R enyi entropy r...

Consider a set of elements which we want to rate using information about their bilateral relationships. For instance sports teams and the outcomes of their games, journals and their mutual citations, web sites and their link structure, or social alternatives and the tournament derived from the voters’ preferences. A wide variety of scoring methods have been proposed to deal with this problem. I...

We prove comparison theorems for norms of iteration matrices in splittings of matrices in the setting of proper cones in a finite dimensional real space by considering cone linear absolute norms and cone max norms. Subject to mild additional hypotheses, we show that these comparison theorems can hold only for such norms within the class of cone absolute norms. Finally, in a Banach algebra setti...

This paper deals with homogeneous cooperative sys-terns, a class of positive systems. It is shown that they admit a fairly simple asymptotic behavior, thereby generalizing the well-known Perron-Frobenius theorem from linear to homogeneous systems. As a corollary a simple criterion for global asymptotic stability is established. Then these systems are subject to constant inputs and we prove that...

Abstract We prove a random Ruelle–Perron–Frobenius theorem and the existence of relative equilibrium states for class open closed interval maps, without imposing transitivity requirements, such as mixing covering conditions, which are prevalent in literature. This provides uniqueness conformal invariant measures with exponential decay correlations, allows us to expand examples (random) dynamica...

We establish an original result for the thermodynamic formalism in context of expanding circle transformations with indifferent fixed point. For observable whose modulus continuity is linked to dynamics near such a point, by identifying appropriate linear space evaluate action transfer operator, we show that there strictly positive eigenfunction associated maximal eigenvalue given as exponentia...

We show that for every “locally finite” unit-preserving completely positive map P acting on a C∗-algebra, there is a corresponding ∗-automorphism α of another unital C∗-algebra such that the two sequences P, P , P , . . . and α,α, α, . . . have the same asymptotic behavior. The automorphism α is uniquely determined by P up to conjugacy. Similar results hold for normal completely positive maps o...

We study positive linear Volterra integro-differential systems with infinitely many delays. Positivity is characterized in terms of the system entries. A generalized version of the Perron-Frobenius Theorem is shown; this may be interesting in its own right but is exploited here for stability results: explicit spectral criteria for L-stability and exponential asymptotic stability. Also the conce...