We prove higher integrability of the spatial gradient weak solutions to parabolic systems with $\phi$-growth, where $\varphi=\varphi(t)$ is a general Orlicz function. The need be neither degenerate nor singular. Our result generalized version one J. Kinnunen and Lewis [Duke Math. 102 (2000), no. 2, 253--271] for $p$-Laplace systems.

The aim of this paper is to present some results about the space $L^{\varPhi }(\nu ),$ where $\nu$ a vector measure on compact (not necessarily abelian) group and $\varPhi$ Young function. We show that under natural conditions, )$ becomes an $L^{1}(G)$ -module with respect usual convolution functions. also define one more structure ).$

In this short paper, we study sums of the shape $$\sum _{n\leqslant x}{f([x/n])}/{[x/n]},$$ where f is Euler totient function $$\varphi $$ , Dedekind $$\Psi sum-of-divisors $$\sigma or alternating $$\beta .$$ We improve previous results when $$f=\varphi and derive new estimates $$f=\Psi f=\sigma $$f=\beta

Abstract This article is dedicated to the study of singular codimension-one foliations ℱ {\mathcal{F}} on a simplicial complete toric variety X and their pullbacks by dominant rational maps φ : ℙ n ⇢ ...

finite affine groups are given by groups of translations and di-lations on finite cyclic groups. for cyclic groups of prime orderwe develop a time-scale (wavelet) analysis and show that for alarge class of non-zero window signals/vectors, the generatedfull cyclic wavelet system constitutes a frame whose canonicaldual is a cyclic wavelet frame.

Abstract Motivated by the well known fact that any nonzero solution of fundamental Cauchy functional equation may arbitrarily be prescribed on a Hamel basis, we deal with following problem: given $$\begin{aligned} E_1(\varphi ) = E_2(\varphi \end{aligned}$$ E <mml:mn...

Let $ mathcal{H}(mathbb{D}) $ denote the space of analytic functions on the open unit disc $mathbb{D}$. For a weight $mu$ and a nonnegative integer $n$, the $n$'th weighted type space $ mathcal{W}_mu ^{(n)} $ is the space of all $fin mathcal{H}(mathbb{D}) $ such that $sup_{zin mathbb{D}}mu(z)left|f^{(n)}(z)right|begin{align*}left|f right|_{mathcal{W}_...

Relative energies of the ground state isomers of 1,4-diphenyl-1,3-butadiene (DPB) are determined from the temperature dependence of equilibrium isomer compositions obtained with the use of diphenyl diselenide as catalyst. Temperature and concentration effects on photostationary states and isomerization quantum yields with biacetyl or fluorenone as triplet sensitizers with or without the presenc...

We consider trilayer ${\mathrm{F}}_{1}{\mathrm{F}}_{2}{\mathrm{F}}_{3}$ Josephson junctions that are finite in two dimensions and have arbitrary magnetizations each ferromagnet ${\mathrm{F}}_{i}\phantom{\rule{0.28em}{0ex}}(i=1,2,3)$. The trilayers sandwiched between $s$-wave superconductors with a macroscopic phase difference $\mathrm{\ensuremath{\Delta}}\ensuremath{\varphi}$. Our results revea...

Let G be a finite group and $$\varphi (G)=|\{a\in \mid o(a)=\exp (G)\}|$$ , where o(a) denotes the order of in $$\exp (G)$$ exponent G. Under natural hypothesis, this note we determine groups such that $$\forall \, H,K\le G$$ $$H\subseteq K$$ implies (H)\mid \varphi (K)$$ . This partially answers Problem 5.4 [6].