On the gibson barrier for the pólya problem

We study lower bounds on the number of nonzero entries in (0, 1) matrices such that the permanent is always convertible to the determinant by placing?±?signs on matrix entries.     

Fejér's theorem for the classesV p

La successione di elementi di una serie di Fourier derivata di una funzione appartenente alla classe di WienerV _p,p>1 (rispettivamente alla classe di Waterman {n ^β}B V o à quella di ChanturiyaV [n ^β] per qualsiasi 0<β<1) è sommabile verso (f(x+0)?f(x?0))/π mediante i metodi di Cèsaro di ordine α>1?1/p (α>β).     

Parameter Estimation for the NEAR（p） Model

As to the acronym NEAR(p), it means "New Exponential Autoregressive Process of order p". The NEAR(p) model is denned by where α0,α1,α2… are non-negative and sum to unity, and the residual sequence{εt} is defined as where q1, q2, … , qp+1 are non-negative and sum to unity, and {Et} is an independent and identically distributed (i.i.d.) sequence of standard exponential variants. Chan showed necessary and sufficient conditions for the existence of a stationary and ergodic NEAR(p) model.     

L p -Estimates for the Navier–Stokes Equations for Steady Compressible Flow

We consider the Navier–Stokes equations for compressible isentropic flow in the steady three-dimensional case. The pressure and the kinetic energy are estimated uniformly in L^q with being the density. This is an improvement of known estimates in the case Mathematics Subject Classification (2000): 35Q30, 76N10     

Estimates of the levy constant for\sqrt p and class number one criterion for ℚ(\sqrt p )

Let p ≡ = 3 (mod 4) be a prime, let ?( $\sqrt p $ ) be the length of the period of the expansion of $\sqrt p $ into a continued fraction, and let h(4p) be the class number of the field ?( $\sqrt p $ ). Our main result is as follows. For p > 91, h(4p)=1 if and only if ?( $\sqrt p $ ) > 0.56 $\sqrt p $ L_4p(1), where L_4p(1) is the corresponding Dirichlet series. The proof is based on studying linear relations between convergents of the expansion of $\sqrt p $ into a continued fraction. Bibliography: 13 titles.     

On some properties of generalized solutions of the wave equation in the classes L p and W p 1 for p ≥ 1

For each p ≥ 1, in closed analytic form, we establish the existence of a unique generalized solution in L _p of the mixed problem for the wave equation in the rectangle [0 ≤ x ≤ 1] × [0 ≤ t ≤ T] with zero initial conditions and with boundary conditions of the first kind, one of which is homogeneous. Next, we derive necessary conditions for this solution to belong to W _p ¹ . We present examples showing that these necessary conditions are not sufficient for any p ≥ 1.     

Necessary and sufficient conditions for a generalized solution to the initial-boundary value problem for the wave equation to belong to W p 1 with p ≥ 1

We establish necessary and sufficient conditions on the boundary function under which a generalized solution to the initial-boundary value problem for the wave equation with boundary conditions of the first kind belongs to W _p ¹ .     

L p -error estimates for positive linear operators using the second-order τ-modulus

ПустьМ[а, b] — множество вещественных функци йf, измеримых и ограниче нных на отрезке [а, b], иL: M[a, b] → M[a, b] — лин ейный положительный оператор. В статье пол учены оценки погрешностей аппроксимации вL _p -нор ме, выраженные в термина х так называемого усредненного локаль ного модуля гладкост и, илиτ-модуля. ПустьL облад ает свойствами: (e _i ,i(t):=t ⁱ дляi=0,1,2)Le ₀ =e ₀ ,Le ₁ =e ₁ ,Le ₂ (х)=х ² +β(х), x∈[a,b] и i)A ≦ min (1, (b-a)²/4) для 1 <p<∞, ii)A ≦ min (e ^?1 , (b — a)²) дляр=1 приA:=∥β∥_t8. Тогда выполнены оцен ки: $$\begin{gathered} \left\| {f - Lf} \right\|_p \leqq C\frac{p}{{p - 1}}\tau _2 (f;\sqrt A )_p 1< p< \infty \hfill \\ \left\| {f - Lf} \right\|_1 \leqq C\tau _2 \left( {f;\sqrt {A\ln \frac{1}{A}} } \right)_1 , \hfill \\ \end{gathered} $$ где положительные по стоянныеС не завися т от оператораL, функцииfи параметрар.     

Necessary and sufficient conditions for the lipschitzian invertibility of nonlinear difference operators in the spacesl p (ℤ, ℝ) with 1≤p≤∞with 1≤p≤∞

Necessary and sufficient conditions for the Lipschitzian invertibility of the difference map

On the global wellposedness for the nonlinear Schrödinger equations with L p -large initial data

We consider the Cauchy problem for the nonlinear Schrödinger equations $ \begin{array}{l} iu_t + \triangle u \pm |u|^{p-1}u =0, \qquad x \in \mathbb{R}^d, \quad t \in \mathbb{R} \\ u(x,0)= u_0(x), \qquad x \in \mathbb{R}^d \end{array} $ for 1 < p < 1 + 4/d and prove that there is a ${\rho (p ,d) \in (1,2)}We consider the Cauchy problem for the nonlinear Schr?dinger equations

l iut + \triangle u ±|u|p-1u = 0,        x ? \mathbbRd,     t ? \mathbbR u(x,0) = u0(x),        x ? \mathbbRd \begin{array}{l} iu_t + \triangle u \pm |u|^{p-1}u =0, \qquad x \in \mathbb{R}^d, \quad t \in \mathbb{R} \\ u(x,0)= u_0(x), \qquad x \in \mathbb{R}^d \end{array}      17. A Jackson Type Estimate for Shepard Operators in L p Spaces for p≧ 1      Wei Xiao  Songping Zhou 《Acta Mathematica Hungarica》2002,95(3):217-224 This paper considers the approximation of the Kantorovich–Shepard operators in spaces for . For the Kantorovich–Shepard operators are defined by (1.1). Then where is a positive number depending only on and , and $$ \varepsilon_{n} =\cases{ n^{-1}, & if \ 2$$ " align="middle" border="0"> ; \cr\nosm n^{-1}\log n, & if \ ; \cr\nosm n^{1-\lambda}, & if \ . \cr} $$      18. Temporal asymptotics for the p’th power Newtonian fluid in one space dimension      Stephen J. Watson  Marta Lewicka 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,125(5):633-651 The balance laws of mass, momentum and energy are considered for a pth power Newtonian fluid undergoing one dimensional longitudinal motions. For initial-boundary value problems involving fixed endpoints held at a prescribed temperature or insulated, we prove exponential convergence of solutions to equilibria for generic initial data. The estimates for different boundary conditions are presented in a unified manner by utilising the thermodynamic concept of availability.      19. On the Global Pinching Theorem for the Minimal Submanifolds in the Unit Spheres S~(n+p)(1)      林峻岷 《数学进展》1990,(2) J.Simons proved that if a minimal submanifold,M~n in the unit sphere S~(n+p)(1)satisfies,|B|~2相似文献    20. Interior W^2,1／／p,∞ Estimates for Generalized Solutions of the Parabo      陈丽  王柔怀 《东北数学》2000,16(4):387-390

A Jackson Type Estimate for Shepard Operators in L p Spaces for p≧ 1

This paper considers the approximation of the Kantorovich–Shepard operators in spaces for . For the Kantorovich–Shepard operators are defined by (1.1). Then

Temporal asymptotics for the p’th power Newtonian fluid in one space dimension

The balance laws of mass, momentum and energy are considered for a pth power Newtonian fluid undergoing one dimensional longitudinal motions. For initial-boundary value problems involving fixed endpoints held at a prescribed temperature or insulated, we prove exponential convergence of solutions to equilibria for generic initial data. The estimates for different boundary conditions are presented in a unified manner by utilising the thermodynamic concept of availability.     

On the Global Pinching Theorem for the Minimal Submanifolds in the Unit Spheres S~(n+p)(1)

J.Simons proved that if a minimal submanifold,M~n in the unit sphere S~(n+p)(1)satisfies,|B|~2相似文献