We consider the initial value Cauchy problem for a class of evolution equations whose Hamiltonian is Weyl quantization homogeneous quadratic form with non-negative definite real part. The solution semigroup shown to be strongly continuous on several spaces: Shubin-Sobolev spaces, Schwartz space, tempered distributions, equal index Beurling type Gelfand-Shilov spaces and their dual ultradistribu...

We introduce a new invariant for C?-algebras of stable rank one that merges the Cuntz semigroup information together with K1-group information. This semigroup, termed Cu1-semigroup, is constructed as equivalence classes pairs consisting positive element in stabilization given C?-algebra unitary unitization hereditary subalgebra generated by element. show Cu1-semigroup well-defined continuous fu...

Let B be a σ–unital C–algebra. We show that every strongly continuous E0–semigroup on the algebra of adjointable operators on a full Hilbert B–module E gives rise to a full continuous product system of correspondences over B. We show that every full continuous product system of correspondences over B arises in that way. If the product system is countably generated, then E can be chosen countabl...

Let {r(Z):Z>0} be a C0-semigroup on a Banach space X with generator A , and let x € X. If a (A) n ;'R is empty and t »-> T(t)x is uniformly continuous, then ||7"(Z)jc|| —> 0 as t —» oo . If the semigroup is sun-reflexive, o(A)CiiR is countable, Pa(A)DiS. is empty, and 1 >-> T(t)x is uniformly weakly continuous, then T(t)x —► 0 weakly as t —» oo . Questions of almost periodicity and of stabiliza...

In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinitedimensional Banach space that is very different from—and considerably shorter than—the one recently given by Bermúdez, Bonilla and Martinón. We also show the existence of a strongly dense family of topologically mixing operators on every separable infinite...

We consider the Moore-Gibson-Thompson equation which arises, e.g., as a linearization of a model for wave propagation in viscous thermally relaxing fluids. This third order in time equation displays, even in the linear version, a variety of dynamical behaviors for their solutions that depend on the physical parameters in the equation. These range from non-existence [3] and instability to expone...

An efficient synthesis route to 1,4-dihydropyrimidine derivatives from reaction of divergent aldehydes with ethylacetoacetate and urea under solvent-free conditions by ZnO nanoparticles as a relative in expansive, eco-friendly, easy available, non-volatile, non-explosion, thermally robust, recyclable and easy to handle catalyst at 90°C with excellent yields is described. Unenhanced reaction tim...

An efficient synthesis route to 1,4-dihydropyrimidine derivatives from reaction of divergent aldehydes with ethylacetoacetate and urea under solvent-free conditions by ZnO nanoparticles as a relative in expansive, eco-friendly, easy available, non-volatile, non-explosion, thermally robust, recyclable and easy to handle catalyst at 90°C with excellent yields is described. Unenhanced reaction tim...

Pyramid Image Coding is a natural coding scheme for applications where progressive transmission is desired. In this kind of coder, versions of the original image at several resolution levels are formed by successive filtering and subsampling. Then, beginning from the coarsest image, the image is used to produce an estimate for the next (higher resolution) level and the error is coded and transm...