On the Proof of Universality for Orthogonal and Symplectic Ensembles in Random Matrix Theory

We give a streamlined proof of a quantitative version of a result from P. Deift and D. Gioev, Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles. IMRP Int. Math. Res. Pap. (in press) which is crucial for the proof of universality in the bulk P. Deift and D. Gioev, Universality in Random Matrix Theory for Orthogonal and Symplectic Ensembles. IMRP Int. Math. Res. Pap. (in press) and also at the edge P. Deift and D. Gioev, {Universality at the edge of the spectrum for unitary, orthogonal and symplectic ensembles of random matrices. Comm. Pure Appl. Math. (in press) for orthogonal and symplectic ensembles of random matrices. As a byproduct, this result gives asymptotic information on a certain ratio of the β=1,2,4 partition functions for log gases.     

Correlation between pole location and asymptotic behavior for Painlevé I solutions

We extend the technique of asymptotic series matching to exponential asymptotics expansions (transseries) and show by using asymptotic information that the extension provides a method of finding singularities of solutions of nonlinear differential equations. This transasymptotic matching method is applied to Painlevé's first equation, P1. The solutions of P1 that are bounded in some direction towards infinity can be expressed as series of functions obtained by generalized Borel summation of formal transseries solutions; the series converge in a neighborhood of infinity. We prove (under certain restrictions) that the boundary of the region of convergence contains actual poles of the associated solution. As a consequence, the position of these exterior poles is derived from asymptotic data. In particular, we prove that the location of the outermost pole x_p(C) on ℝ⁺ of a solution is monotonic in a parameter C describing its asymptotics on anti‐Stokes lines and obtain rigorous bounds for x_p(C). We also derive the behavior of x_p(C) for large C ∈ ℂ. The appendix gives a detailed classical proof that the only singularities of solutions of P1 are poles. © 1999 John Wiley & Sons, Inc.     

Synthesis of Robust MOFs@COFs Porous Hybrid Materials via an Aza-Diels–Alder Reaction: Towards High-Performance Supercapacitor Materials

Metal–organic frameworks (MOFs) and covalent organic frameworks (COFs) have attracted enormous attention in recent years. Recently, MOF@COF are emerging as hybrid architectures combining the unique features of the individual components to enable the generation of materials displaying novel physicochemical properties. Herein we report an unprecedented use of aza-Diels–Alder cycloaddition reaction as post-synthetic modification of MOF@COF-LZU1, to generate aza-MOFs@COFs hybrid porous materials with extended π-delocalization. A a proof-of-concept, the obtained aza-MOFs@COFs is used as electrode in supercapacitors displaying specific capacitance of 20.35 μF cm⁻² and high volumetric energy density of 1.16 F cm⁻³. Our approach of post-synthetic modification of MOFs@COFs hybrids implement rational design for the synthesis of functional porous materials and expands the plethora of promising application of MOFs@COFs hybrid porous materials in energy storage applications.     

Stochastic optimization approach of car value depreciation

This paper presents a stochastic model for a car's value and its depreciation under random repairs modeled by a Poisson process; the usage functional is defined, and the optimal selling time is estimated. Exact or approximative formulas are provided where possible. The car's value is evaluated as an asset with negative return and paying random normally distributed dividends at stochastic times, which are Erlang distributed. Copyright © 2012 John Wiley & Sons, Ltd.     

Norm calculations of a class of integral operators

In this paper we calculate the norm of a special class of integral operators acting on Lp (Cn,dvs), where dvs is the Gaussian measure on Cn.