Thin points for Brownian motion

Let Θ(x,r) denote the occupation measure of the ball of radius r centered at x for Brownian motion {W_t}_0≤t≤1 in . We prove that for any analytic set E in [0,1], we have

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, where dim_P(E) is the packing dimension of E. We deduce that for any a≥1, the Hausdorff dimension of the set of “thin points” x for which

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, is almost surely 2−2/a; this is the correct scaling to obtain a nondegenerate “multifractal spectrum” for the “thin” part of Brownian occupation measure. The methods of this paper differ considerably from those of our work on Brownian thick points, due to the high degree of correlation in the present case. To prove our results, we establish general criteria for determining which deterministic sets are hit by random fractals of ‘limsup type' in the presence of long-range correlations. The hitting criteria then yield lower bounds on Hausdorff dimension. This refines previous work of Khoshnevisan, Xiao and the second author, that required decay of correlations.     

Simple Analytical Model of the Anodic Streamer

In this work, an analytical model is used to study the formation of the anodic streamer in high pressure electrical discharge. This model enabled us to see the space variations of the characteristics of the streamer such as the electric field and the propagation velocity of streamer. The validity of the analytic approach is demonstrated by comparing the model results to the data from the literature. A qualitative concord was found. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crystallization and stereocomplexation behavior of poly(D‐ and L‐lactide)‐b‐poly(N,N‐dimethylamino‐2‐ethyl methacrylate) block copolymers

The thermal properties, crystallization, and morphology of amphiphilic poly(D ‐lactide)‐b‐poly(N,N‐dimethylamino‐2‐ethyl methacrylate) (PDLA‐b‐PDMAEMA) and poly (L ‐lactide)‐b‐poly(N,N‐dimethylamino‐2‐ethyl methacrylate) (PLLA‐b‐PDMAEMA) copolymers were studied and compared to those of the corresponding poly(lactide) homopolymers. Additionally, stereocomplexation of these copolymers was studied. The crystallization kinetics of the PLA blocks was retarded by the presence of the PDMAEMA block. The studied copolymers were found to be miscible in the melt and the glassy state. The Avrami theory was able to predict the entire crystallization range of the PLA isothermal overall crystallization. The melting points of PLDA/PLLA and PLA/PLA‐b‐PDMAEMA stereocomplexes were higher than those formed by copolymer mixtures. This indicates that the PDMAEMA block is influencing the stability of the stereocomplex structures. For the low molecular weight samples, the stereocomplexes particles exhibited a conventional disk‐shape structure and, for high molecular weight samples, the particles displayed unusual star‐like shape morphology. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1397–1409, 2011     

Curvilinear smoothed particle hydrodynamics

We suggest a new set of equations to employ smoothed particle hydrodynamics (SPH) in a curvilinear space, and we refer to it as curvSPH. In classical SPH, the horizontal and vertical resolution of discretization is supposed to be equal for fluid particles. However, curvSPH makes the horizontal and vertical resolutions independent from each other. This is performed by transformation of physical space into an appropriate computational space with a different scale in horizontal and vertical directions. Solving a problem using SPH in a curvilinear space also provides capability to model curved boundaries as straight lines. In classical SPH, special care is needed to reach a uniform mass distribution along curved boundaries; however, producing uniform mass distribution along a line using curvSPH is straight forward. Different simulations, including simulation of a flip bucket are performed to demonstrate the applicability of the proposed method. Good agreement of results with experimental data and classical SPH confirms the capabilities of curvSPH. Copyright © 2016 John Wiley & Sons, Ltd.     

An effective ant colony optimization algorithm (ACO) for multi-objective resource allocation problem (MORAP)

The multi-objective resource allocation problem (MORAP) addresses the important issue which seeks to find the expected objectives by allocating the limited amount of resource to various activates. Resources may be manpower, assets, raw material or anything else in limited supply which can be used to accomplish the goals. The goals may be objectives (i.e., minimizing costs, or maximizing efficiency) usually driven by specific future needs. In this paper, in order to obtain a set of Pareto solution efficiently, we proposed a modified version of ant colony optimization (ACO), in this algorithm we try to increase the efficiency of algorithm by increasing the learning of ants. Effectiveness and efficiency of proposed algorithm was validated by comparing the result of ACO with hybrid genetic algorithm (hGA) which was applied to MORAP later.     

Duality in robust optimization: Primal worst equals dual best

We study the dual problems associated with the robust counterparts of uncertain convex programs. We show that while the primal robust problem corresponds to a decision maker operating under the worst possible data, the dual problem corresponds to a decision maker operating under the best possible data.     

The inhibitory effect of dissolved carbaryl in dioxane on physically adsorbed acetylcholinesterase

Acetylcholinesterase was immobilized by means of physical adsorption. The aim of this work is to describe the kinetic characterization of the immobilized acetylcholinesterase. Here we report the effects of immobilization, carbaryl and its solvent dioxane on the kinetic properties of acetylcholinesterase. The immobilized product has significant storage stability. Dioxane could decrease the acetylcholinesterase activity and increase the inhibitory effect of carbaryl. Immobilization could change acetylcholinesterase activity cooperatively. The inhibitory mechanism is hyperbolic noncompetitive. Carbaryl and dioxane could eliminate the substrate inhibition by a competitive mechanism and by changing the native conformation of acetylcholinesterase.     

Kinetics of the thermal isomerization of cis-methylcyclopropane carboxylic acid

The gas-phase thermal decomposition of cis-2-methylcyclopropane carboxylic acid was investigated in the temperature range 692–753 K and pressure between 10 and 70 Torr. Arrhenius parameters were determined for homogeneous, unimolecular formation of the isomeric products and for the overall loss-rate of the reactant. The determined values are in accordance with the Arrhenius parameters that were reported previously for the thermal unimolecular reactions of cyclopropane and other substituted cyclopropanes. The formation of isomeric products and the observed Arrhenius parameters are consistent with a biradical mechanism. The effect of surface on the reaction was studied at 732 K using the packed reaction vessel. It was observed that the rate of production of all isomeric products and the total loss of cis-2-methylcyclopropane carboxylic acid were not affected by increasing surface to volume ratio.     

Determination of Biogenic Amines in Cheese Using Simultaneous Derivatization and Microextraction Method Followed by Gas Chromatography–Mass Spectrometry

Microwave-assisted extraction and dispersive liquid–liquid microextraction followed by gas chromatography–mass spectrometry as a sensitive and efficient method was applied to extract and determine four biogenic amines (BAs) in Iranian Lighvan cheese samples. Carrez solutions were used for the sedimentation of proteins. Effective factors on the performance of microextraction were studied and optimized. The proposed method showed good linear ranges from 5 to 500 ng mL^?1, with the coefficients of determination higher than 0.9929. Average recoveries were between 97 and 103%. Limits of detection for all analyzed BAs ranged from 5.9 to 14.0 ng g^?1, and limits of quantitation ranged between 19.7 and 46.2 ng g^?1. Compared with previous methods, the proposed method is simple, fast, accurate, and precise and gives low detection limits for investigating trace amounts of BAs in Iranian Lighvan cheese samples. The levels of four BAs were determined in five Lighvan cheese samples. Cadaverine was found as prevailing amine in the cheese samples. Putrescine, tyramine, and histamine were present at the second, third, and fourth highest levels, respectively.