In this note, we study the n×n random Euclidean matrix whose entry (i, j) is equal to f(‖Xi−Xj‖) for some function f and the Xi’s are i.i.d. isotropic vectors inR. In the regime where n and p both grow to infinity and are proportional, we give some sufficient conditions for the empirical distribution of the eigenvalues to converge weakly. We illustrate our result on log-concave random vectors.

In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.

The purpose of the present paper is to introduce a class $D_{Sigma ;delta }^{n}C_{0}(alpha )$ of bi-concave functions defined by Al-Oboudi differential operator. We find estimates on the Taylor-Maclaurin coefficients $leftvert a_{2}rightvert $ and $leftvert a_{3}rightvert$ for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.

Studies of optimal growth in a multisector framework are generally addressed in reduced form models. These are defined by an indirect utility function which summarizes the consumers’ preferences and the technologies. Weak concavity assumptions of the indirect utility function allow one to prove differentiability of optimal solutions and stability of steady state. This paper shows that if the co...

We have fabricated spherical and cylindrical concave micro-mirrors in silicon with dimensions from 20 microm to 100 microm. The fabrication process involves standard photolithography followed by large area ion beam irradiation and electrochemical anodisation in a HF electrolyte. After thermal oxidation the silicon surface roughness is less than 2 nm. We also present a multilayer porous silicon ...

Zeldes (1989), Carroll (1992; 1993), and others have shown that optimal consumption behavior for consumers facing income uncertainty can be remarkably di erent from the certainty-equivalent case. Carroll (1992; 1993) observes that many of the di erences can be attributed to the concavity of the consumption function under uncertainty, but he does not describe the conditions under which the consu...

In German, the course of phrase-final rising intonation can be modelled by an interpolation between three points in the pitch contour, giving a more appropriate description than current approaches to German intonation that only include the alignment of rises and their pitch range. Within this 3-point model, the parameter range proportion produces different contour shapes: concave and convex. Th...

Carroll and Kimball (1996) show that the consumption function for an agent with time-separable, isoelastic preferences is concave in the presence of income uncertainty. In this paper I show that concavity breaks down if we abandon time-separability. Namely, if an agent maximizing an isoelastic recursive utility has preferences for early resolution of uncertainty, there always exists a distribut...

US Patent 6,284,563 (Joseph Fjelstad) describes a method of making compliant microelectronic assemblies. This technique introduces a compliant layer (140) with a number of concave areas on top of a microelectronic element. Conductive flexible bond ribbons (175) are plated in these concave areas and extend to the periphery of the device. Electrical contacts can be formed with precision by placin...