Size Reduction of Bulk Alumina for Mass Production of Fluorescent Nanoalumina by Fungus <Emphasis Type="Italic">Humicola</Emphasis> sp.

In recent years, nanomaterials have made their way into hundreds of biomedical, life-sciences and technological applications. One such nanomaterial of extreme importance is nanoalumina (Al₂O₃ nanoparticles). This nanomaterial is an epitome of diversity with applications exhibited in the fields of catalysis, cosmetics, theranostics, energy generation, biosensors, drug-delivery, tumor-regression, etc. However, problems persist in terms of biocompatibility, cost-effectiveness, reproducibility and mass-production of nanoalumina by the presently existent physical, chemical and biological methodologies. Herein, we for the first time are presenting a top-down biofabrication method by which size reduction of commercial bulk alumina/aluminum oxide (5 µm) into nanoalumina (5–25 nm) is carried out by a thermophilic fungus Humicola sp. within 96 h of reaction at just 50 °C. The so-formed nanoalumina is highly stable, water dispersible, fluorescent and natural protein capped; characterization engaged standard techniques. These nanoparticles exhibit anti-bacterial properties against Gram-positive Bacillus subtilis strain and may serve as broad spectrum bactericidal agents. We believe that our novel top-down approach may be extensively used in the facile, inexpensive, eco-friendly and reliable fabrication of abundant quantities of nanomaterials of different chemical compositions, sizes and shapes with better control and predictability over the properties as derived from their substrates. The mechanistic aspect of said protocol is underway.     

Super face d-antimagic labeling for disjoint union of toroidal fullerenes

The discovery of the fullerene molecules and related forms of carbon such as nanotubes has generated an explosion of activity in chemistry, physics, and materials science. Classical fullerene is an all-carbon molecule in which the atoms are arranged on a pseudospherical framework made up entirely of pentagons and hexagons. A toroidal fullerene (toroidal polyhex) is a cubic bipartite graph embedded on the torus such that each face is a hexagon. In this paper we examine the existence of entire labeling, where face-weights of all 6-sided faces of disjoint union of toroidal fullerenes form an arithmetic progression with common difference \(\hbox {d}\in \{1,2,3\}\).     

Rating players in test match cricket

In general, the evaluation of player performance in test cricket is based on measures such as batting and bowling averages. These measures have a number of limitations, among which is that they fail to take into account the context in which runs are made or conceded and wickets are taken or given away. Furthermore, batting and bowling averages do not allow the comparison of performances in these two disciplines; this is because batting and bowling performances are measured using different metrics. With these issues in mind, we develop a new player rating system for test cricket. We use multinomial logistic regression to model match outcome probabilities session by session. We then use these probabilities to measure the overall contribution of players to the match outcome based on their individual batting, bowling and fielding contributions during each session. Our measure of contribution has the potential for rating players over time and for determining the ‘best’ player in a match, a series or a calendar year. We use results from 104 matches (2010–2012) to illustrate the method.     

Solving mixed-integer robust optimization problems with interval uncertainty using Benders decomposition

Uncertainty and integer variables often exist together in economics and engineering design problems. The goal of robust optimization problems is to find an optimal solution that has acceptable sensitivity with respect to uncertain factors. Including integer variables with or without uncertainty can lead to formulations that are computationally expensive to solve. Previous approaches for robust optimization problems under interval uncertainty involve nested optimization or are not applicable to mixed-integer problems where the objective or constraint functions are neither quadratic, nor linear. The overall objective in this paper is to present an efficient robust optimization method that does not contain nested optimization and is applicable to mixed-integer problems with quasiconvex constraints (? type) and convex objective funtion. The proposed method is applied to a variety of numerical examples to test its applicability and numerical evidence is provided for convergence in general as well as some theoretical results for problems with linear constraints.     

Creeping flow analysis of slightly non-Newtonian fluid in a uniformly porous slit

This paper provides the analysis of the steady, creeping flow of a special class of slightly viscoelastic, incompressible fluid through a slit having porous walls with uniform porosity. The governing two dimensional flow equations along with non-homogeneous boundary conditions are non-dimensionalized. Recursive approach is used to solve the resulting equations. Expressions for stream function, velocity components, volumetric flow rate, pressure distribution, shear and normal stresses in general and on the walls of the slit, fractional absorption and leakage flux are derived. Points of maximum velocity components are also identified. A graphical study is carried out to show the effect of porosity and non-Newtonian parameter on above mentioned resulting expressions. It is observed that axial velocity of the fluid decreases with the increase in porosity and non-Newtonian parameter. The outcome of this theoretical study has significant importance both in industry and biosciences.     

Capacity switching options under rivalry and uncertainty

Deregulated infrastructure industries exhibit stiff competition for market share. Firms may be able to limit the effects of competition by launching new projects in stages. Using a two-stage real options model, we explore the value of such flexibility. We first demonstrate that the value of investing in a sequential manner for a monopolist is positive but decreases with uncertainty. Next, we find that a typical duopoly firm’s value relative to a monopolist’s decreases with uncertainty as long as the loss in market share is high. Intriguingly, this result is reversed for a low loss in market share. We finally show that this loss in value is reduced if a firm invests in a sequential manner and specify the conditions under which sequential capacity expansion is more valuable for a duopolist firm than for a monopolist.     

SOP: parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems

This paper presents a canonical dual approach for solving a nonconvex global optimization problem governed by a sum of 4th-order polynomial and a log-sum-exp function. Such a problem arises extensively in engineering and sciences. Based on the canonical duality–triality theory, this nonconvex problem is transformed to an equivalent dual problem, which can be solved easily under certain conditions. We proved that both global minimizer and the biggest local extrema of the primal problem can be obtained analytically from the canonical dual solutions. As two special cases, a quartic polynomial minimization and a minimax problem are discussed. Existence conditions are derived, which can be used to classify easy and relative hard instances. Applications are illustrated by several nonconvex and nonsmooth examples.     

Self-adjointness in unitary isotopes of JB*-algebras

We prove that x is in the norm closure of invertibles whenever x is self-adjoint in some unitary isotope of a JB*-algebra. In the sequel, we investigate certain links between the elements of the unit ball which are self-adjoint in some unitary isotope of a JB*-algebra and the elements which are average of two unitaries. Received: 9 September 2005     

粘滑混合边界条件下平面边界前的Stokes流动

对具有粘滑混合边界条件的平面边界,建立一个Stokes流动的一般性定理,利用双调和函数A与调和函数B,表示了3维Stokes流动的速度场和压力场.关于无滑动平面边界前Stokes流动的早期定理,成为该一般性定理的一个特例.进一步地,从一般性定理导出了一个推论,根据该Stokes流函数,给出了粘滑边界条件时刚性平面轴对称Stokes流动问题的解,得到了流体作用在边界上的牵引力和扭矩公式.给出了一个说明性的例子.