Symmetries and correlation inequalities for classicaln-vector models

We describe a new class of single spin measures on then-dimensional sphereS _r ⁿ of radiusr (n 4) for which Lebowitz-type [J. Lebowitz,J. Stat. Phys. 16:463 (1977)] inequalities hold. This is achieved by an appropriate parametrization ofS _r ⁿ . The above class includes the uniform measures onxs Rⁿ ¦x¦ r for any 0 p r. The second topic of this paper is an abstract formulation of the first Griffiths inequality [R. B. Griffiths,J. Math. Phys. 8:478 (1967)] and the underlying symmetry property.     

再论Pedoe不等式的高维推广及应用

本文对欧氏空间E~n中的两个n维单形,给出了著名的Pedoe不等式的一个实质性推广,并讨论了它的应用.     

Inequalities for linear combinations of monomials in p-Newton sequences

The partial order on monomials that corresponds to domination when evaluated at positive Newton sequences is fully understood. Here we take up the corresponding partial order on linear combinations of monomials. In part using analysis based upon the cone structure of the exponents in p-Newton sequences, an array of conditions is given for this new partial order. It appears that a characterization in general will be difficult. Within the case in which all coefficients are 1, the situation in which, for general sequence length, there are two monomials, each of length two and nonnegative integer exponents, the partial order is fully characterized. The characterization is combinatorial, in terms of indices in the monomials, and, already here there is much more than term-wise domination.     

Kinematics of layered reinforced-concrete planar beam finite elements with embedded transversal cracking

In this work crack formation and development is addressed and implemented in a planar layered reinforced-concrete beam element. The crack initiation and growth is described using the strength criterion in conjunction with exact kinematics of the interlayer connection. In this way a novel embedded-discontinuity beam finite element is derived in which the tensile stresses in concrete at the crack position reaching the tensile strength will trigger a crack to open. Since the element is multi-layered, in this way the crack is allowed to propagate through the depth of the beam. The cracked layer(s) will involve discontinuity in the cross-sectional rotation equal to the crack-profile angle, as well as a discontinuity in the position vector of the layer’s reference line. A bond–slip relationship is superimposed onto this model in a kinematically consistent manner with reinforcement being treated as an additional layer of zero thickness with its own material parameters and a constitutive law implemented in the multi-layered beam element.     

Harnack's inequality for parabolic nonlocal equations

The main result of this paper is a nonlocal version of Harnack's inequality for a class of parabolic nonlocal equations. We additionally establish a weak Harnack inequality as well as local boundedness of solutions. None of the results require the solution to be globally positive.     

An efficient iterative method for finding common fixed point and variational inequalities in Hilbert spaces

ABSTRACT

In this paper, we investigate the problem of finding a common solution to a fixed point problem involving demi-contractive operator and a variational inequality with monotone and Lipschitz continuous mapping in real Hilbert spaces. Inspired by the projection and contraction method and the hybrid descent approximation method, a new and efficient iterative method for solving the problem is introduced. Strong convergence theorem of the proposed method is established under standard and mild conditions. Our scheme generalizes and extends some of the existing results in the literature, and moreover, its computational effort is less per each iteration compared with related works.     

Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation.     

On the Discrete Criteria and JØ rgensen Inequalities for SL(m,F((t)))

In this paper, the author gives the discrete criteria and J\o rgensen inequalities of subgroups for the special linear group on $\overline{\mathrm{F}}((t))$ in two and higher dimensions.