we consider the fundamental relation  on a semihypergroup  to interpret the lower and upper approximations as subsets of the fundamental semigroup  and we give some results in this connection. also, we introduce the notion of a bi-hyperideal to study the relationship between approximations and bi-hyperideals.

utilization of non-food-grade organic solvents and high shear forces in conventional liposome formation techniques has limited their applications as carriers of nutrecuticals in food industry. the objective of this research is the production of gamma-oryzanol bearing nanoliposome by using modified thermal method. nanoliposomes were produced by a suitable concentration of lecithin and gamma-oryz...

Total saponin of heat-processed ginseng (TSHG) stimulated the production of nitric oxide (NO) in interferon-gamma (IFN-gamma)-primed macrophages through the increased expression of inducible nitric oxide synthase (iNOS). However, TSHG by itself had a very weak effect on the NO synthesis without IFN-gamma priming. The saponins of white ginseng inhibited the NO production in lipopolysaccharide (L...

Selective visual attention is subserved by selective neuronal synchronization, entailing precise orchestration among excitatory and inhibitory cells. We tentatively identified these as broad (BS) and narrow spiking (NS) cells and analyzed their synchronization to the local field potential in two macaque monkeys performing a selective visual attention task. Across cells, gamma phases scattered w...

Experimental studies of nuclear matrix elements (NMEs) for neutrinoless double-$\ensuremath{\beta}$ decays (DBDs) and astro-neutrino $(\ensuremath{\nu})$ inverse $\ensuremath{\beta}$ (IBDs) are crucial $\ensuremath{\nu}$ beyond the standard model astro-$\ensuremath{\nu}$ since accurate theoretical calculations NMEs hard due to high sensitivity models parameters used models. Some important elect...

We study the weak radiative decays of ${\bf B}_b \to {\bf B}_n \gamma$ with B}_{b(n)} $ anti-triplet-bottom (octet) baryons in light front quark model. obtain that ${\cal B}(\Lambda_b \Lambda \gamma)= (7.1 \pm 0.3 )\times 10 ^{-6}$, which agrees well current experimental value $(7.1 1.7 ^{-6}$. predict B}(\Xi_b^0 \Xi^0 (1.0 0.1 ^{-5}$ and B}(\Xi_b^- \Xi^- \gamma) = (1.1 0.1) \times 10^{-5}$, ar...

We study oscillator chains of the form phi; (k) = omega(k) +K[Gamma( phi(k-1) - phi(k) )+Gamma( phi(k+1) - phi(k) )], where phi(k) epsilon[0,2pi) is the phase of oscillator k. In the thermodynamic limit where the number of oscillators goes to infinity, for suitable choices of Gamma(x), we prove that there is a critical coupling strength K(c), above which a stable frequency-entrained state exist...

We consider a family of weights which permit to generalize the Leray procedure obtain weak suitable solutions 3D incompressible Navier–Stokes equations with initial data in weighted $$L^2$$ spaces. Our principal result concerns existence regular global when velocity is an axisymmetric vector field without swirl such that both and its vorticity belong $$L^2 ( (1+ r^2)^{-\frac{\gamma }{2}} dx ) $...

Consider a rowwise independent triangular array of gamma random variables with varying parameters. Under several different conditions on the shape parameter, we show that the sequence of row-maximums converges weakly after linear or power transformation. Depending on the parameter combinations, we obtain both Gumbel and non-Gumbel limits. The weak limits for maximum of the coordinates of certai...