For all 0 < q +? the Privalov class ?q consists of analytic functions f in a unit disk such that sup 0?r<1 1/2? ??,-? (ln+ |f(rei?)|)q d?< +?. In this paper we solve multiple interpolation problem for 1. Namely, find sufficient conditions explicit construction function solves class. addition, discuss necessity these conditions.

In this paper, we deal with soft lattice implication algebras based on fuzzy sets. Using the concepts of fuzzy (implicative) filters, (∈,∈∨q)fuzzy (implicative) filters and (∈,∈∨q)-fuzzy (implicative) filters, some characterizations for ∈-soft sets and q-soft sets to be (implicative) filteristic soft lattice implication algebras are established.

The Esfordi phosphate concentrate mainly contains fluorapatite, monazite, and xenotime as rare earth element (REE) minerals, accounting for 1.5% of rare earth metals. The monazite and xenotime minerals are refractory and their decomposition is only possible at high temperatures. Thus mechanical activation was used in the present work for this purpose. After 90 minutes of mechanical activation, ...

For an integer n ≥ 2 we denote by P (n) the largest prime factor of n. We obtain several upper bounds on the number of solutions of congruences of the form n! + 2 − 1 ≡ 0 (mod q) and use these bounds to show that lim sup n→∞ P (n! + 2 − 1)/n ≥ (2π + 3)/18.

We study the well-posedness and regularity of the generalized Navier-Stokes equations with initial data in a new critical space Q α;∞ (R ) = ∇ · (Qα(R )), β ∈ ( 1 2 , 1) which is larger than some known critical homogeneous Besov spaces. Here Qα(R ) is a space defined as the set of all measurable functions with sup(l(I)) Z

Some multiplicity results are obtained for periodic solutions of the nonautonomous superquadratic second-order discrete Hamiltonian systems Duðt 1Þ þ rF ðt; uðtÞÞ 1⁄4 0 8t 2 Z 0096-3 doi:10. q Sup Outsta * Co E-m Plea Com by using critical point theory, especially, a three critical points theorem proposed by Brezis and Nirenberg. 2007 Elsevier Inc. All rights reserved.

Let An be an n by n random matrix whose entries are independent real random variables with mean zero and variance one. We show that the logarithm of | detAn| satisfies a central limit theorem. More precisely, sup x∈R ̨̨̨ P ` log(| detAn|)− 12 log(n− 1)! q 1 2 logn ≤ x ́ − Φ(x) ̨̨̨ ≤ log 1 3+o(1) n.

This article concerns the existence of multiple non-radial positive solutions L<sup>2</sup>-constrained problem $$\displaylines{-\Delta{u}-Q(\varepsilon x)|u|^{p-2}u=\lambda{u},\quad \text{in }\mathbb{R}^N, \\ \int_{\mathbb{R}^N}|u|^2dx=1,}$$ where \(Q(x)\) is a radially symmetric function, ε>0 small parameter, \(N\geq 2\), and \(p \in (2, 2+4/N)\) assumed to be m...

Recent developments in the context of minimum residual finite element methods are paving way for designing quasi-optimal discretization non-standard function spaces, such as q -type Sobolev spaces. For ? 1, these have demonstrated huge potential avoiding notorious Gibbs phenomena, i.e. , occurrence spurious non-physical oscillations near thin layers and jump discontinuities. In this work we pro...