Characterizing and Generating Bivariate Empirical Rank Distributions Satisfying Certain Positive Dependence Concepts

Abstract

This article introduces an approach for characterizing the classes of empirical distributions that satisfy certain positive dependence notions. Mathematically, this can be expressed as studying certain subsets of the class S_N of permutations of 1, …, N, where each subset corresponds to some positive dependence notions. Explicit techniques for it-eratively characterizing subsets of S_N that satisfy certain positive dependence concepts are obtained and various counting formulas are given. Based on these techniques, graph-theoretic methods are used to introduce new and more efficient algorithms for constructively generating and enumerating the elements of various of these subsets of S_N. For example, the class of positively quadrant dependent permutations in S_N is characterized in this fashion.     

Modules over cluster-tilted algebras that do not lie on local slices

We characterize the indecomposable transjective modules over an arbitrary cluster-tilted algebra that do not lie on a local slice, and we provide a sharp upper bound for the number of (isoclasses of) these modules.     

Mean square convergent three points finite difference scheme for random partial differential equations

In this paper, the random finite difference method with three points is used in solving random partial differential equations problems mainly: random parabolic, elliptic and hyperbolic partial differential equations. The conditions of the mean square convergence of the numerical solutions are studied. The numerical solutions are computed through some numerical case studies.     

A thermal-shock problem in magneto-thermoelasticity with thermal relaxation

The one-dimensional problem of distribution of thermal stresses and temperature is considered in a generalized thermoelastic electrically conducting half-space permeated by a primary uniform magnetic field when the bounding plane is suddenly heated to a constant temperature.The Laplace transform technique is used to solve the problem. Inverse transforms are obtained in an approximate manner using asymptotic expansions valid for small values of time.Nurnerical computations for two particular cases are carried out.     

Histidine-epoxy-activated sepharose beads embedded poly (2-hydroxyethyl methacrylate) cryogels for pseudobiospecific adsorption of human immunoglobulin G

The use of highly purified immunoglobulin became among the most powerful adopted strategies in therapeutic trials nowadays. Their role as immunomodulatory and anti-inflammatory agents has widened their scope of use. A novel continuous supermacroporous monolithic cryogels embedded with histidine-epoxy-activated-sepharose beads were synthetized as a new monolithic adsorbents for the separation of immunoglobulin G from human serum. The histidine-epoxy-activated-sepharose beads were embedded into the 2-hydroxyethyl methacrylate (HEMA) cryogels present in frozen aqueous solution inside a plastic syringe. The microstructure morphology of the cryogels was characterized by swelling measurement and scanning electron microscopy. The adsorption of human IgG on the histidine-epoxy-activated-sepharose beads pHEMA cryogels appeared to follow the Langmuir–Freundlich adsorption isotherm model. The maximum IgG adsorption was observed at 4°C and pH 7.4 and was found to be 26.95 mg/g of cryogel which is close to that obtained experimentally (24.49 mg/g). The cryogels were used for several adsorption-desorption cycles without any negligible decrease in their adsorption capacity.     

Theory of fractional order in generalized thermoelectric MHD

A new mathematical model of thermoelectric MHD theory has been constructed in the context of a new consideration of heat conduction with fractional orders. This model is applied to Stokes’ first problem for a conducting fluid with heat sources. Laplace transforms and state-space techniques [1] will be used to obtain the general solution for any set of boundary conditions. According to the numerical results and its graphs, conclusion about the new theory has been constructed. Some comparisons have been shown in figures to estimate the effects of the fractional order parameters on all the studied fields.     

A Molecular Electron Density Theory Study of the [3+2] Cycloaddition Reaction of an Azomethine Ylide with an Electrophilic Ethylene Linked to Triazole and Ferrocene Units

The [3+2] cycloaddition (32CA) reaction of an azomethine ylide (AY) with an electrophilic ethylene linked to triazole and ferrocene units has been studied within the Molecular Electron Density Theory (MEDT) at the ωB97X-D/6-311G(d,p) level. The topology of the electron localization function (ELF) of this AY allows classifying it as a pseudo(mono)radical species characterized by the presence of two monosynaptic basins, integrating a total of 0.76 e, at the C1 carbon. While the ferrocene ethylene has a strong electrophilic character, the AY is a supernucleophile, suggesting that the corresponding 32CA reaction has a high polar character and a low activation energy. The most favorable ortho/endo reaction path presents an activation enthalpy of 8.7 kcal·mol⁻¹, with the 32CA reaction being exergonic by −42.1 kcal·mol⁻¹. This reaction presents a total endo stereoselectivity and a total ortho regioselectivity. Analysis of the global electron density transfer (GEDT) at the most favorable TS-on (0.23 e) accounts for the high polar character of this 32CA reaction, classified as forward electron density flux (FEDF). The formation of two intermolecular hydrogen bonds between the two interacting frameworks at the most favorable TS-on accounts for the unexpected ortho regioselectivity experimentally observed.     

Fractional order theory in thermoelastic solid with three-phase lag heat transfer

In this work, the field equations of the linear theory of thermoelasticity have been constructed in the context of a new consideration of Fourier law of heat conduction with time-fractional order and three-phase lag. A uniqueness and reciprocity theorems are proved. One-dimensional application for a half-space of elastic material in the presence of heat sources has been solved using Laplace transform and state space techniques Ezzat (Canad J Phys Rev 86:1241–1250, 2008). According to the numerical results and its graphs, conclusion about the new theory has been established.     

State space approach to magnetohydrodynamic flow of perfectly conducting micropolar fluid with stretch

In this work we introduce a model of the boundary layer equations for a perfect conducting micropolar fluid with stretch, bounded by an infinite vertical flat plane surface of a constant temperature. This model is applied to study the effects of free convection currents on the flow of the fluid in the presence of a constant magnetic field. The state space technique is adopted for the solution of a one‐dimensional problem for any set of boundary conditions. The resulting formulation together with the Laplace transform techniques are applied to a thermal shock problem. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results are given and illustrated graphically for the problem. Copyright © 2011 John Wiley & Sons, Ltd.     

Non-linear analysis of creeping flow on the inclined permeable substrate plane subjected to an electric field

The effect of an externally applied electric field on the stability of a thin fluid film over an inclined porous plane is analyzed using linear and non-linear stability analysis in the long wave limit. The principle aim of this study is to illustrate the influence of electric field on the non-linear stability of a thin liquid layer flow down incline substrate when the plane is porous. The driving force for the instability under an electric field is an electrostatic force exerted on the free charges accumulated at the dividing interface. The coupled non-linear evolution equations for the local film thickness and the interfacial charge for two-dimensional disturbances are derived to analyze the effect of long-wave instabilities. The method of multiple scales is applied to obtain approximate solutions and analyze the stability criteria. Numerical simulations of this system of non-linear evolution equations are performed. It is found that the permeability parameter as well as the inclination of the plane plays a destabilizing role in the stability criteria, while the damping influence is observed for increasing of the electrical conductivity in both linear and non-linear behavior.