in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...

λ-Scale is an enrichment of lambda calculus which is adapted to emergent algebras. It can be used therefore in metric spaces with dilations.

We present a set-theoretic version of some basic dilation results operator theory. The we have considered are Wold decomposition, Halmos dilation, Sz. Nagy inter-twining lifting, commuting and non-commuting dilations, BCL theorem, etc. point out natural generalizations variations.

In our case, we present a case of an 80-year-old male who was referred to the gastroenterologist for evaluation suspicious mass. CT imaging at time had shown intrahepatic and extrahepatic biliary dilations, patient thought have pancreatic or common bile duct A mass biopsy showed no malignancy, further warranted. The found elevated IgG4 levels diagnosed with IgG4-sclerosing cholangitis (IgG4-SC)...

Abstract Using probabilistic tools, we prove that any weak* continuous semigroup $(T_t)_{t \geqslant 0}$ of self-adjoint unital completely positive measurable Schur multipliers acting on the space $\mathrm {B}({\mathrm {L}}^2(X))$ bounded operators Hilbert ${\mathrm {L}}^2(X)$ , where X is a suitable measure space, can be dilated by group Markov $*$ -automorphisms bigger von Neumann algebra. We...

The gap junction channel protein connexin40 (Cx40) is crucial in vascular and renal physiology, because Cx40-deficient mice exhibit impaired conduction of endothelium-dependent dilations and pronounced hypertension. The latter precludes mechanistic insights into the role of endothelial Cx40, because long-lasting hypertension itself may affect conduction and Cx expression. We aimed to identify e...

We hypothesized that hydrogen peroxide (H2O2) has a role in the local regulation of skeletal muscle blood flow, thus significantly affecting the myogenic tone of arterioles. In our study, we investigated the effects of exogenous H2O2 on the diameter of isolated, pressurized (at 80 mmHg) rat gracilis skeletal muscle arterioles (diameter of approximately 150 microm). Lower concentrations of H2O2 ...