Let F be a totally real field and p rational prime unramified in F. We prove partial classicality theorem for overconvergent Hilbert modular forms: when the slope is small compared to subset of weights, an form partially classical. use method analytic continuation.

We prove the partial Hölder continuity for minimizers of quasiconvex functionals \begin{equation*} \mathcal{F}({\bf u}) \colon =\int_{\Omega} f(x,{\bf u},D{\bf u})\,\textrm{d} x, \end{equation*} where $f$ satisfies a uniform VMO condition with respect to $x$ -variable and is continuous ${\bf u}$ . The growth gradient variable assumed general one.

Antivenoms have been used successfully for more than a century and up to now constitute the only effective treatment for snakebites .The production of antivenin started long time ago when the calmette was prepared the antivenom in 1894.The method currently used to prepare antivenom by most of the manufacturers are originated from the method of Pope which was develop in 1938. Several new approac...

Let $\Omega\subset\mathbb{C}$ be a bounded domain. In this note, we use complex variable methods to study the number of critical points function $v=v_\Omega$ that solves elliptic problem $\Delta v = -2$ in $\Omega,$ with boundary values $v=0$ on $\partial\Omega.$ This has classical flavor but is especially motivated by recent studies localization eigenfunctions. We provide an upper bound $v$ wh...

For simplicity, we adopt the following convention: x, x0, y, y0, r are real numbers, z, z0 are elements of R2, f , f1, f2 are partial functions from R2 to R, R is a rest, and L is a linear function. Let us note that every rest is total. Let f be a partial function from R2 to R and let z be an element of R2. The functor pdiff1(f, z) yielding a function from R2 into R is defined as follows: (Def....

The in v itro incorporation o f 14C-leucine by rat liver microsomes is studied under four different physiological states: 1. Normal liver o f adult rats (NL), 2. irradiated (4 000 rads) liver (IL), 3. liver after partial hepatectomy (RL) and 4. regenerating liver in preirradiated rats (IRL) 2, 5, 12, and 24 hours after treatment. Both irradiation and partial hepatectomy, when applied separately...

Alten proved in [4] that the FEP holds for commutative residuated lattices that satisfy any knotted rule. A class of algebras K is said to have the FEP, if for every algebra A in K and every finite partial subalgebra B of A, there exists a finite algebra D in K such that B embeds into D. B is a finite partial subalgebra of A, if B is a finite subset of A and each n−ary operation f on A induces ...

Let F be a field of characteristic 2. The aim this paper is to give complete proof the norm theorem for singular F-quadratic forms which are not totally singular, i.e., we necessary and sufficient conditions normed irreducible polynomial F[x1,…,xn] becomes such quadratic form over rational function F(x1,…,xn). This completes partial results proved on question in [8]. Combining present work with...