lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  ulrich hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. using hohle's idea, we show that for a (universal) algebra $a$, th...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  Ulrich Hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. Many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. Using Hohle's idea, we show that for a (universal) algebra $A$, th...

A semigroup is a set of elements to which is related an operation usually called multiplication and an equivalence relation, such that the set is closed and associative relative to the operation. We shall discuss, briefly, finite semigroups which are uniquely factorable in the same sense as the multiplicative semigroup of all nonzero integers. Clifford' defined an arithmetic in such a way as to...

We describe the second (generalized) Feng-Rao distance for elements in an Arf numerical semigroup that are greater than or equal to the conductor of the semigroup. This provides a lower bound for the second Hamming weight for one point AG codes. In particular, we can obtain the second Feng-Rao distance for the codes defined by asymptotically good towers of function fields whose Weierstrass semi...

We show that the multiplication operator associated to a fractional power of a Gamma random variable, with parameter q > 0, maps the convex cone of the 1-invariant functions for a self-similar semigroup into the convex cone of the q-invariant functions for the associated Ornstein-Uhlenbeck (for short OU) semigroup. We also describe the harmonic functions for some other generalizations of the OU...

The algebraic structure ([0,∞), +, ≤), together with Lebesgue measure (and the usual topology), is the standard representation of time for a variety of probabilistic models. These include reliability theory and the aging of lifetime distributions, renewal processes, and Markov processes, to name just a few. The purpose of this monograph is to study probability models in which the standard repre...

We consider another class of generalized Lipschitzian type mappings and utilize the same to prove fixed point theorems for asymptotically regular and uniformly generalized Lipschitzian one-parameter semigroups of self-mappings defined on bounded metric spaces equipped with uniform normal structure which yield corresponding results in respect of semigroup of iterates of a self-mapping as corolla...

Here, we extend the weak KAM and Aubry-Mather theories to optimal switching problems. We consider three issues: the analysis of the calculus of variations problem, the study of a generalized weak KAM theorem for solutions of weakly coupled systems of Hamilton-Jacobi equations, and the long-time behavior of time-dependent systems. We prove the existence and regularity of action minimizers, obtai...

Using concepts of generalized asymptotic and logarithmic densities based on weighted arithmetic means over an arithmetical semigroup G we prove that under some additional technical assumptions on the weighted counting function of its elements, a subset of G exists with all four generalized densities (upper and lower asymptotic and logarithmic) prescribed subject to the natural condition 0 ≤ d(A...