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.     

Sensitivity Analysis to the Value of p of the ℓ p Distance Weber Problem

In this paper we analyze the sensitivity of the _p distance Weber problem to the value of p. We consider each power p to be in a range and not necessarily the same for each demand point. We find the set of possible optimal locations when p is in a given range. We also find the location that minimizes the expected cost, and find the Expected Value of Perfect Information. Computational results are presented.     

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.     

Construction of singular solutions to the p-harmonic equation and its limit equation for p=∞

Here, all solutions of the form u=r^kf() to the p-harmonic equation, div(|u|^p–2u)=0, (p>2) in the plane are determined. One main result is a representation formula for such solutions. Further, solutions with an isolated singularity at the origin are constructed (Theorem 1). Graphical illustrations are given at the end of the paper. Finally, all solutions u=r^kf() of the limit equation for p=, u _x ² u_xx+2u_xu_yu_xy+u _y ² u_yy=2, are constructed, some of which have a strong singularity at the origin (Theorem 2).     

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).     

Global $$W^{1,p}$$ estimates for solutions to the linearized Monge–Ampère equations

In this paper, we investigate regularity for solutions to the linearized Monge–Ampère equations when the nonhomogeneous term has low integrability. We establish global \(W^{1,p}\) estimates for all \(p<\frac{nq}{n-q}\) for solutions to the equations with right-hand side in \(L^q\) where \(n/2<q\le n\). These estimates hold under natural assumptions on the domain, Monge–Ampère measures, and boundary data. Our estimates are affine invariant analogues of the global \(W^{1,p}\) estimates of N. Winter for fully nonlinear, uniformly elliptic equations.     

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

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

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.     

Convergence of the reweighted ℓ 1 minimization algorithm for ℓ 2–ℓ p minimization

The iteratively reweighted ? ₁ minimization algorithm (IRL1) has been widely used for variable selection, signal reconstruction and image processing. In this paper, we show that any sequence generated by the IRL1 is bounded and any accumulation point is a stationary point of the ? ₂–? _p minimization problem with 0<p<1. Moreover, the stationary point is a global minimizer and the convergence rate is approximately linear under certain conditions. We derive posteriori error bounds which can be used to construct practical stopping rules for the algorithm.     

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     

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   

On the global convergence of a generalized iterative procedure for the minisum location problem with ℓ p distances for p > 2

This paper presents a procedure to solve the classical location median problem where the distances are measured with ? _p -norms with p > 2. In order to do that we consider an approximated problem. The global convergence of the sequence generated by this iterative scheme is proved. Therefore, this paper closes the still open question of giving a modification of the Weiszfeld algorithm that converges to an optimal solution of the median problem with ? _p norms and ${p \in (2, \infty)}$ . The paper ends with a computational analysis of the different provided iterative schemes.     

Bellman function for the estimates of Littlewood–Paley type and asymptotic estimates in the p−1 problem

We utilize the method of Bellman functions to derive new $L^p$-estimates of Littlewood–Paley type involving $p?1$. Among the applications to singular integrals we improve the $2(p?1)$ bounds for the Ahlfors–Beurling operator on $L^p(\mathbb{C})$ when $p\to \infty$. In addition, dimensionless estimates of Riesz transforms in the classical as well as in the Ornstein–Uhlenbeck setting are attained. To cite this article: O. Dragi?evi?, A. Volberg, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

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 the structural properties of the weight space L p(x),ω for 0 < p(x) < 1

The main purpose of this paper is to study the weight space L _p(x),ω for 0 < p(x) < 1 as well as the topology of this space. Embeddings between different Lebesgue spaces with variable exponent of summability are established. In particular, it is proved that the set of all linear continuous functionals over L _p(x),ω for 0 < p(x) < 1 consists only of the zero functional.