In this paper, we show that a linear unbounded operator associated with an Euler–Bernoulli beam equation under shear boundary feedback generates a C0-semigroup in the underlying state Hilbert space. This provides an answer to a long time unsolved problem due to the lack of dissipativity for the operator. The main steps are a careful estimation of the Green’s function and the verification of the...

The main purpose of this paper is to establish some new results onthe superstability and stability via a fixed point approach forthe Pexiderized exponential equation, i.e.,$$|f(x+y)-g(x)h(y)|leq psi(x,y),$$where $f$, $g$ and $h$ are three functions from an arbitrarycommutative semigroup $S$ to an arbitrary unitary complex Banachalgebra and also $psi: S^{2}rightarrow [0,infty)$ is afunction. Fur...

The Brauer semigroup Bn of partitions of a 2n-element set into two-element subsets, can be generalized in various ways. For example we may consider arbitrary partitions to obtain the semigroup Cn. The visualization of elements of these semigroups as chips leads us to the Temperley-Lieb semigroup TLn and its analogue TLCn. We study combinatorial properties of these four semigroups. For example, ...

The numerical semigroup generated by relatively prime positive integers a1, . . . , an is the set S of all linear combinations of a1, . . . , an with nonnegative integral coefficients. The largest integer which is not an element of S is called the Frobenius number of S. Recently, J. M. Maŕın, J. L. Ramı́rez Alfonśın, and M. P. Revuelta determined the Frobenius number of a Fibonacci semigroup, th...

Clifford and Preston (1961) showed several important characterizations of right groups. It was shown in Roy and So (1998) that, among topological semigroups, compact right simple or left cancellative semigroups are in fact right groups, and the closure of a right simple subsemigroup of a compact semigroup is always a right subgroup. In this paper, it is shown that such results can be generalize...

Let $S$ be a semitopological semigroup. The $wap-$ compactification of semigroup S, is a compact semitopological semigroup with certain universal properties relative to the original semigroup, and the $Lmc-$ compactification of semigroup $S$ is a universal semigroup compactification of $S$, which are denoted by $S^{wap}$ and $S^{Lmc}$ respectively. In this paper, an internal construction of ...

This paper concerns the structure of strongly continuous one parameter semigroups of completely positive contractions of B(H) = B(K⊗L(0,∞)) which are intertwined by translation. These are called CP -flows over K. Using Bhat’s dilation result each unital CP -flow over K dilates to an Eo-semigroup of B(H1) where H1 can be considered to contain B(K⊗L(0,∞)). Every spatial Eo-semigroup is cocycle co...