On Times to Quasi-stationarity for Birth and Death Processes

The purpose of this paper is to present a probabilistic proof of the well-known result stating that the time needed by a continuous-time finite birth and death process for going from the left end to the right end of its state space is a sum of independent exponential variables whose parameters are the negatives of the eigenvalues of the underlying generator when the right end is treated as an absorbing state. The exponential variables appear as fastest strong quasi-stationary times for successive dual processes associated to the original absorbed process. As an aftermath, we get an interesting probabilistic representation of the time marginal laws of the process in terms of “local equilibria.”      

A strong inorganic acid‐initiated methacrylate polymerization strategy for room temperature preparation of monolithic columns for capillary electrochromatography

A facile strong inorganic acid‐initiated methacrylate polymerization strategy was developed for fabricating monolithic columns at room temperature. The prepared monoliths were characterized by FTIR spectrometry, mercury intrusion porosimeter and SEM, while their performance was evaluated by CEC for the separation of various types of compounds including alkyl benzenes, polycyclic aromatic hydrocarbons, nonsteroidal anti‐inflammatory drugs, anilines, and nitrophenol isomers. The column‐to‐column and batch‐to‐batch reproducibility for the prepared monoliths in terms of the RSD of EOF flow velocity, retention factor, and the minimum plate height of naphthalene ranged from 3.4 to 12.4%. The fabricated monoliths gave excellent performance for the separation of the test neutral compounds with the theoretical plates of 170 000–232 000 plates per meter for thiourea, and 77 400–112 300 plates per meter for naphthalene. The proposed strong inorganic acid‐initiated methacrylate polymerization strategy is a promising alternative for fabricating organic polymer‐based monoliths.     

An iterative approximation method for solving a general system of variational inequality problems and mixed equilibrium problems

In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a general system of variational inequalities for a cocoercive mapping in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets. Our results extend and improve the corresponding results of Ceng, Wang, and Yao [L.C. Ceng, C.Y. Wang, J.C. Yao, Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities, Math. Methods Oper. Res. 67 (2008) 375–390], Ceng and Yao [L.C. Ceng, J.C. Yao, A hybrid iterative scheme for mixed equilibrium problems and fixed point problems, J. Comput. Appl. Math. doi:10.1016/j.cam.2007.02.022], Takahashi and Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506–515] and many others.     

Asplund Spaces, Stegall Variational Principle and the RNP

Given a pair of Banach spaces X and Y such that one is the dual of the other, we study the relationships between generic Fréchet differentiability of convex continuous functions on Y (Asplund property), generic existence of linear perturbations for lower semicontinuous functions on X to have a strong minimum (Stegall variational principle), and dentability of bounded subsets of X (Radon-Nikodym Property).      

A generalization of the strong Fitzpatrick inequality

We present a generalization of the strong Fitzpatrick inequality in the context of reflexive Banach spaces, involving a twisted bigger conjugate function. We also introduce a related family of gap functions for maximal monotone inclusion problems.     

On Marcinkiewicz-Zygmund laws

Marcinkiewicz-Zygmund laws with convergence rates are established here for a class of strictly stationary ergodic sequences.     

Option pricing and hedge portfolios for poisson progresses

Price processes influenced by Poisson processes are considered and the value of a sum of European call options obtained. The novel feature of the paper is the use of analogues of strochastic flows to derive a martingale representation resut and the heding portfolio     

SINGULARLY PERTURBED NONLINEAR NEUMANN PROBLEMS ON SYMMETRIC DOMAINS

Abstract

This paper is concerned with global stability of strong rarefaction waves of the Jin–Xin relaxation model for the p-system. The proofs are given by an elementary energy method and the existence of a positively invariant region obtained by Serre [Serre, D. (2000). Relaxations semi-lineaire et cinetique des systemes de Lois de conservation. Ann. Inst. H. Poincare Anal. Non Lineaire 17(2):169–192] plays an important role in our analysis.     

Impacts of biomass-burning on aerosol properties of a severe haze event over Shanghai

Anthropogenic aerosols have significant impacts on the environment and human health in the Yangtze River Delta region, one of the most densely populated regions in the world. A biomass-burning plume swept across this area (Shanghai) in May 2009, leading to changes in the physical and optical properties of aerosols, which were investigated using ground-based remote sensing and in situ measurements via comparisons with dust pollution and background conditions. Experiments show that the biomass-burning plume led to an increase in the average aerosol optical depth (AOD) at 500 nm from 0.73 to 1.00 (37% higher), an absorption Angstrom exponent (AAE) of 1.48, and an increase in the Angstrom exponent (α) up to 1.53. Furthermore, local dust aerosols derived from road dust and/or construction dust also led to higher values of AOD (2.68) and AAE (2.16), and a daily average value of α of 1.05. For the biomass-burning plume, the aerosol particles exhibited significant variations in short-wavelength spectra. The single scattering albedo at 670 nm decreased remarkably under the influence of the biomass-burning plume, indicating the significant absorptive ability of the biomass-burning pollution and higher ratio of absorption aerosols within the plume. Under the effects of the biomass-burning, the volume concentration of fine-mode aerosols increased significantly and the PM-fine/PM-coarse volume concentration ratio reached 12.33. This relatively large change in fine-mode particles indicates that biomass-burning has a greater impact on fine-mode aerosols than on coarse-mode aerosols.