Narrow Results

We consider a mean-field model to describe the dynamics of $N_1$ bosons of species one and $N_2$ bosons of species two in the limit as $N_1$ and $N_2$ go to infinity. We embed this model into Fock space and use it to describe the time evolution of coherent states which represent two-component condensates. Following this approach, we obtain a microscopic quantum description for the dynamics of such systems, determined by the Schrödinger equation. Associated to the solution to the Schrödinger equation, we have a reduced density operator for one particle in the first component of the condensate and one particle in the second component. In this paper, we estimate the difference between this operator and the projection onto the tensor product of two functions that are solutions of a system of equations of Hartree type. Our results show that this difference goes to zero as $N_1$ and $N_2$ go to infinity.

We study a confined mixture of Rb and K atoms in a one dimensional optical lattice, at low temperature, in the quanta1 degeneracy regime. This mixture exhibits an attractive boson-fermion interaction, and thus above certain values of the number of particles the mixture collapses. We investigate, in the mean-field approximation, the curve for which this phenomenon occurs, in the space of number of particles of both species. This is done for different types of optical lattices.

In this paper, we analyze a mixture of Lognormal and Log-Logistic distribution. We estimate the parameters of the introduced distribution by using the expectation-maximization (EM) algorithm. Various phenomena in the field of medicine and economy could be modeled by this mixture. In this paper, it is used to construct new mortality model for determining the unisex premium rates in life insurance. The application of the model is illustrated in the case of Serbian population and its advantages are presented in the context of life insurance premium calculation.

Experimental studies of the Raman scattering of the band of C = O vibrations of acetone (1710 cm^–1) showed that the parallel and perpendicular polarized components have a large half-width (respectively, 11.6 and 18 cm^–1) and also the bands' maxima of these components are shifted by ~5 cm^–1. In the neutral solvent (heptane), the difference of the maxima position of the bands decreases. Calculations showed that the molecules of acetone can aggregate to form a dimer with the energy gain of 10.1 kJ/mole. In the dimer several hydrogen bonds are formed between the oxygen atom of one molecule and the hydrogen atoms of CH₃-group of another molecule. In an aqueous mixture of acetone, according to calculations, there is a possibility for formation of dimers and closed trimer aggregates with the energy gain, respectively, 19.1 and 45.8 kJ/mole. Calculation showed that symmetric and antisymmetric O–H vibrations of water are displaced in the interaction with acetone to lower frequencies, respectively, to 3808.4 and to 3931.8 ^–1.

In this paper large deviations for mixture of large deviation systems are investigated. Some general results are presented, with conditions either less restrictive or more practical for verification. Applications are illustrated in a concrete case-mixture of products of probability measures (homogeneous or inhomogeneous). We also discussed potential applications to problems of statistic inference for hidden Markov models.

A computational fluid dynamics (CFD) simulation of laminar convection of Al₂O₃–water bio-nanofluids in a circular tube under constant wall temperature conditions was conducted, employing a single-phase model and three different two-phase models (volume of fluid (VOF), mixture and Eulerian). The steady-state, three-dimensional flow conservation equations were discretised using the finite volume method (FVM). Several parameters such as temperature, flow field, skin friction and heat transfer coefficient were computed. The computations showed that CFD predictions with the three different two-phase models are essentially the same. The CFD simulations also demonstrated that single-phase and two-phase models yield the same results for fluid flow but different results for thermal fields. The two-phase models, however, achieved better correlation with experimental measurements. The simulations further showed that heat transfer coefficient distinctly increases with increasing nanofluid particle concentration. The physical properties of the base fluid were considered to be temperature-dependent, while those of the solid particles were constant. Grid independence tests were also included. The simulations have applications in novel biomedical flow processing systems.

Clustering is a major tool for microarray gene expression data analysis. The existing clustering methods fall mainly into two categories: parametric and nonparametric. The parametric methods generally assume a mixture of parametric subdistributions. When the mixture distribution approximately fits the true data generating mechanism, the parametric methods perform well, but not so when there is nonnegligible deviation between them. On the other hand, the nonparametric methods, which usually do not make distributional assumptions, are robust but pay the price for efficiency loss. In an attempt to utilize the known mixture form to increase efficiency, and to free assumptions about the unknown subdistributions to enhance robustness, we propose a semiparametric method for clustering. The proposed approach possesses the form of parametric mixture, with no assumptions to the subdistributions. The subdistributions are estimated nonparametrically, with constraints just being imposed on the modes. An expectation-maximization (EM) algorithm along with a classification step is invoked to cluster the data, and a modified Bayesian information criterion (BIC) is employed to guide the determination of the optimal number of clusters. Simulation studies are conducted to assess the performance and the robustness of the proposed method. The results show that the proposed method yields reasonable partition of the data. As an illustration, the proposed method is applied to a real microarray data set to cluster genes.

The goal of this study was to develop mixtures of peripherally halogenated boron subphthalocyanines (BsubPcs) to explore these macrocycles as mixed alloys for applications within the organic electronic space. These halogenated BsubPc mixtures were synthesized by reacting mixtures of commercially available phthalonitriles, namely 4,5-dichlorophthalonitrile (Cl₂-pn), 4,5-difluorophthalonitrile (F₂-pn), tetrachlorophthalonitrile (Cl₄-pn), and tetrafluorophthalonitrile (F₄-pn), with boron trichloride (BCl${}_3)$ to achieve mixed halogenation upon formation of the BsubPcs. More specifically, as named, Cl₂-pn + F₂-pn and Cl₄-pn + F₄-pn mixtures were used to form Cl-Cl${}_{2\mathrm{\text{n}}}$F${}_{2\mathrm{\text{m}}}$BsubPc and Cl-Cl${}_{4\mathrm{\text{n}}}$F${}_{4\mathrm{\text{m}}}$BsubPc, respectively. To establish a firm synthetic methodology, the reaction kinetics of forming the BsubPc mixtures from their respective phthalonitrile mixtures were compared to the kinetics of the standard procedures forming the individual BsubPcs, for example, Cl-Cl${}_{12}$BsubPc from Cl₄-pn. As we use BCl₃ to form the BsubPcs, the axial bond is in general chloride, but we observed again random fluoride axial exchange, and therefore moved to the second step to have complete axial fluorination. Crude mixed halogenated BsubPcs were sublimed at high purities to enable physical characterization, including a study of UV-Vis absorption spectra differentiation, and cyclic (CV) and differential pulse voltammograms (DPV) electrochemical differentiation. We also did density functional theory (DFT) calculations for points of physical properties comparison. The comparison points are together with fully peripherally chlorinated Cl${}_{\mathrm{\text{n}}}$BsubPcs and fluorinated F${}_{\mathrm{\text{n}}}$BsubPcs. Given the outcomes, we foresee in future studies the ability to tune different ratios of peripherally halogenated BsubPc mixtures via synthetic tools, to enable tuning of the HOMO LUMO energy levels, which could consequently tune their application and performance in organic electronics.

This paper presents reports on simulation and comparative analysis of single stage vapor compression refrigeration system and cascade systems using carbon dioxide, hydrocarbons (HCs) and CO₂/HCs mixture. Thermodynamic parameters of fluids are given using the software REFPROP 9.0. To select the most suitable HCs, three criteria have been fixed: T_c, T_t and T_b. It is found that the HCs chosen in low-stage are propane, propylene and ethane and those for the high-stage are propane, propylene and isobutane. The fraction mixture in the two loops has been varied and results are compared with single stage and cascade systems using CO₂ and R22. The fraction x${}_{\mathrm{\text{CO2}}}$ is varied in the two loops. Results are compared for single and cascade systems using CO₂ and R22. For the single stage system, we find for x_CO2 = 0.5, an improvement of COP of 14% for CO₂/propane mixture and 36% for the CO₂/propylene mixture. It is found that for x_CO2 = 0.3, cascade system using propane/CO₂ mixtures presents a COP lower than that of cascade system using pure CO₂. About of 70% of unfriendly fluids like CFCs and HCFCs can be replaced with CO₂, without affecting the performance of cascade refrigeration systems.

Due to the ozone depletion issue, R-502, which had long been used as the refrigerant of an ice cream refrigerator, has been replaced by R-404A. However, global warming potential (GWP) of R-404A is high, and thus, a replacement refrigerant is necessary in the long term. Natural refrigerants, such as R-290 or DME (dimethylether), could be a choice. In this study, an ice cream refrigerator cycle was optimized using R-290/DME mixture (mass fraction 65/35). The optimization was accomplished through a search for the proper refrigerant charge amount and the opening of the expansion valve. For the present ice cream refrigerator having 2.8L freezer volume, the optimum charge amount was 900g, and the optimum valve opening was $+$120${}^{\circ }$. At this configuration, the ice cream formation time was 3${}^{\prime }$ 6${}^{\prime \prime }$ and COP was 2.0. The ice cream formation time was much shorter than when R-404A was used, and the COP was increased by more than 100%. For actual usage of the refrigerant, however, the flammability issue of the R-290/DME mixture should be cleared.

Wind energy has been the focus of attention by governments over the past several decades because it is clean and renewable energy source that offers many advantages compared to others. This paper reports a particle swarm optimization based flowchart used to identify the most appropriate wind speed distribution function. In this procedure, the PSO algorithm modifies and estimates the parameters of the distribution functions examined. The distributions of Nakagami, Normal and Weibull are judged for right-skewed, non-skewed and left-skewed distributions, respectively. The outcomes showed that each function offers impressive performance compared to the others in its defined conditions. Despite the changes of one-component distribution’s parameters made by the PSO algorithm are not significant, the same changes will affect the function’s performance greatly. Because of the sufficient flexibility offered by the nominated functions, the proposed flowchart is applicable for all wind regimes.

We study a confined mixture of Rb and K atoms in a one dimensional optical lattice, at low temperature, in the quantal degeneracy regime. This mixture exhibits an attractive boson-fermion interaction, and thus above certain values of the number of particles the mixture collapses. We investigate, in the mean-field approximation, the curve for which this phenomenon occurs, in the space of number of particles of both species. This is done for different types of optical lattices.

The aim of this paper is to explain important but not popular properties related to gamma processes and show the applicability of these properties. We define subclasses (CME and its subclasses) of the class of infinitely divisible distributions, which are generated by mixtures and convolutions from gamma distributions, and study their properties. Then we apply the obtained results to the uni-modality of the distributions in the above classes, the boundedness in space-time parameters of transition densities of subordinators generated by CME distributions and the determination of the class of hitting time distributions of 1-dimensional generalized diffusion processes. Finally, we remark that some subclasses of the class CME and the class of selfdecomposable distributions are often used in mathematical finance.