where Xt= jBtjp and St = max 0 r t jBrjp. In the case p=1 the closed form for s 7! g (s) is found. This yields 1;q = (q(q+1)=2)( (1+(q+1)=q)) for all q > 0 . In the case p 6= 1 no closed form for s 7! g (s) seems to exist. The inequality above holds also in the case p = q+1 (Doob’s maximal inequality ). In this case the equation above (with K = p=2c ) admits g (s) = s as the maximal solution, a...

and Applied Analysis 3 By the boundary conditions, the previous second term vanishes. The second inequality in the Signorini boundary condition (2) 3 tells us that we have to require that σ belongs to the convex cone as follows: H + := H + (div, Ω, Γ S ) := {τ ∈ H (div, Ω) : γ^τ | ΓS ≥ 0} , (7) where “≥ 0” means that ⟨γ 0 󰜚, γ^τ⟩ ≥ 0 for any smooth function 󰜚 on Ω with 󰜚 = 0 on Γ D and 󰜚 ≥ 0 on...

The Republic of Ireland has been the fastest growing economy in the OECD over the latter half of the 1990’s, an expansion known as the Celtic Tiger. Some commentators have commented on the gains from the boom being concentrated amongst the top of the income distribution. In this paper we shall try to understand what has happened to inequality over the period 1987-2004 and to understand the dete...

Sharp extensions of Pitt’s inequality and bounds for Stein-Weiss fractional integrals are obtained that incorporate gradient forms and vector-valued operators. Such results include HardyRellich inequalities. Weighted inequalities provide quantitative information to characterize integrability for differential and integral operators and intrinsically are determined by their dilation character. In...

in this paper we will prove that if $l$ is a continuous symmetric n-linear form on a hilbert spaceand $widehat{l}$ is the associated continuous n-homogeneous polynomial, then $||l||=||widehat{l}||$.for the proof we are using a classical generalized  inequality due to s. bernstein for entire functions of exponential type. furthermore we study the case that if x is a banach space then we have tha...

The relationship between economic inequality and HIV infection among young Malawian women is estimated with multi-level logit models of the individual probability of being infected. Two community levels are considered: the immediate neighbourhood, and Malawi‟s districts. We find a strong positive association between communal inequality and the risk of HIV infection. The relationship between eco...

Let x : M → Sn+p be an n-dimensional submanifold in an (n + p)dimensional unit sphere Sn+p, x : M → Sn+p is called a Willmore submanifold if it is an extremal submanifold to the following Willmore functional: ∫ M (S − nH) 2 dv, where S = ∑ α,i,j (hij) 2 is the square of the length of the second fundamental form, H is the mean curvature of M . In [13], author proved an integral inequality of Sim...

The aim of this paper is to show that Jensen’s Inequality and an extension of Chebyshev’s Inequality complement one another, so that they both can be formulated in a pairing form, including a second inequality, that provides an estimate for the classical one. 1. Introduction The well known fact that the derivative and the integral are inverse each other has a lot of interesting consequences, on...

Second-order necessary conditions are developed for an abstract nonsmooth control problem with mixed state-control equality and inequality constraints as well as a constraint of the form G(x, u) e T, where T is a closed convex set of a Banach space with nonempty interior. The inequality constraints g{s, x, u) < 0 depend on a parameter 5 belonging to a compact metric space S. The equality constr...