Importance of Darcy–Forchheimer porous medium in 3D convective flow of carbon nanotubes

This article explores Darcy–Forchheimer 3D flow of water-based carbon nanomaterial (CNTs). A bi-directional linear stretchable surface has been used to create the flow. Flow in porous space is represented by Darcy–Forchheimer expression. Heat transfer mechanism is explored through convective heating. Results for single-wall (SWCNTs) and multi-wall (MWCNTs) carbon nanotubes have been presented and compared. The reduction of partial differential system into nonlinear ordinary differential system is made through suitable variables. Optimal homotopic scheme is used for solutions development of governing flow problem. Optimal homotopic solution expressions for velocities and temperature are studied through graphs by considering various estimations of physical variables. Skin friction coefficients and local Nusselt number are analyzed through plots. Our findings show that the skin friction coefficients and local Nusselt number are enhanced for larger values of nanoparticles volume fraction.     

Franck–Condon Factors and r‐Centroids for the B–, C–, F–, and G–X Band Systems of YF Molecule

The Franck–Condon factors and r‐centroids, which are very closely related to relative transition probabilities, have been evaluated by a more reliable numerical integration procedure for the B¹π–X¹Σ⁺, C¹Σ⁺–X¹Σ⁺, F¹Σ⁺–X¹Σ⁺, and G¹π–X¹Σ⁺ band systems of the YF molecule, using suitable potentials.     

Dirac Quantization of t’Hooft-Polyakov Monopole Field: Axial Hamiltonization

In this article, we carry out the Hamiltonization in the axial gauge,of the t’Hooft-Polyakov monopole field outside the localized region, which represents the monopole’s core. One feature of the treatment here, is using the Higgs vacuum condition as both strong and weak equation instead of using it in the degree of freedom reduction.     

One-body and Two-body Fractional Parentage Coefficients for Spinor Bose-Einstein Condensation

A very effective tool, namely, the analytical expression of the fractional parentage coefficients (FPC), is introduced in this paper to deal with the total spin states of N-body spinor bosonic systems, where N is supposed to be large and the spin of each boson is one. In particular, the analytical forms of the one-body and two-body FPC for the total spin states with {N} and {N−1,1} permutation symmetries have been derived. These coefficients facilitate greatly the calculation of related matrix elements, and they can be used even in the case of N→∞. They appear as a powerful tool for the establishment of an improved theory of spinor Bose-Einstein condensation, where the eigenstates have the total spin S and its Z-component being both conserved.     

Kinetic market models with single commodity having price fluctuations

We study here numerically the behavior of an ideal gas like model of markets having only one non-consumable commodity. We investigate the behavior of the steady-state distributions of money, commodity and total wealth, as the dynamics of trading or exchange of money and commodity proceeds, with local (in time) fluctuations in the price of the commodity. These distributions are studied in markets with agents having uniform and random saving factors. The self-organizing features in money distribution are similar to the cases without any commodity (or with consumable commodities), while the commodity distribution shows an exponential decay. The wealth distribution shows interesting behavior: gamma like distribution for uniform saving propensity and has the same power-law tail, as that of the money distribution, for a market with agents having random saving propensity.     

Coherent quantum transport in two-dimensional electron gas/superconductor double junctions with Rashba spin-orbit coupling

Based on the extended Blonder-Tinkham-Klapwijk (BTK) approach, we have investigated the coherent quantum transport in two-dimensional electron gas/superconductor (2DEG/SC) double tunneling junctions in the presence of the Rashba spin-orbit coupling (RSOC). It is found that all the reflection coefficients in BTK theory as well as conductance spectra oscillate with the external voltage and energy. The oscillation feature of conductance can be tuned largely by the RSOC for low insulating barriers, while for high insulating barriers it is almost independent of the RSOC. These phenomena are essentially different from those found in ferromagnet/superconductor double tunneling junctions.     

Complex-scaling treatment for high-lying doubly excited resonances for screened Coulomb helium atom

This work presents an investigation on the doubly excited ¹S ^e autoionizing states of screened helium atom lying below the n = 4 threshold of the He⁺ ion. The potential generated in this system is represented by a Yukawa type potential. We have employed complex-coordinate rotation method, as it is a powerful scheme to study high lying resonances. Hylleraas type wave function is used to consider the correlation effect between all the charged particles. Our resonance parameters for the resonances lying below the He⁺ (n = 2) threshold agree well with those of the existing calculations by using the stabilization method. Resonances associated with higher thresholds are new calculations. All the present results are well converged with basis length N = 444.     

Almost sure comparison of birth and death processes with application to M/M/s queueing systems

Given conditions, which concern the infinitesimal parameters of two birth and death processes, the processes are constructed on the same probability space such that one process is almost surely larger than the other. Application is made to M/M/s queueing systems. Stochastic comparisons of queue length and virtual waiting time in two M/M/s systems are obtained.     

A competitive (dual) simplex method for the assignment problem

Where there is abundance of mystery and confusion in every direction, the truth seldom remains hidden for long. It's a matter of having plenty of angles to go at it from. Only the utterly simple crimes - the simplex crimes, you may say - have the trick of remaining baffling. - Sir John (from Michael Innes,The Open House (A Sir John Appleby Mystery), Penguin Books, 1974).A dual simplex method for the assignment problem leaves open to choice the activity (i,j) of rowi and columnj that is to be dropped in pivoting so long asx _ij < 0. A choice (i,j) over columnsj having at least 3 basic activities that minimizesx _ij is shown to converge in at most ( ₂ ^n-1 ) pivots, and at most O(n ³) time, and it is argued that on average the number of pivots is at mostn logn. Dedicated with affection to George B. Dantzig on the occasion of his seventieth birthday.     

线性回归在林区生产决策中的应用

在黑龙江省伊春林区 ,以 16个林业局调查的数据为依据 ,并由木材年采伐量与剩余物密切相关这一特点 ,应用数理统计知识 ,建立了回归分析方程 ,从而对木材采伐量和剩余物做出预测和控制 ,为保护森林生态环境及林区工业生产的宏观决策 ,提供了重要的参考数据