Syntheses and characterization of Sr(OH)2 and SrCO3 nanostructures by ultrasonic method

The Sr(OH)₂ and SrCO₃ nanostructures were synthesized by reaction of strontium(II) acetate and sodium hydroxide or tetramethylammonium hydroxide (TMAH) via ultrasonic method. Reaction conditions, such as the concentration of the Sr²⁺ ion, aging time, power of the ultrasonic device and alkali salts show important roles in the size, morphology and growth process of the final products. The pure crystalline SrCO₃ were obtained by heating of product at 400 °C. The Sr(OH)₂ and SrCO₃ nanostructures were characterized by scanning electron microscopy (SEM), X-ray powder diffraction (XRD), thermal gravimetric (TG), differential thermal analyses (DTA) and the infrared spectroscopy (IR).     

A spectral heuristic for bisecting random graphs

The minimum bisection problem is to partition the vertices of a graph into two classes of equal size so as to minimize the number of crossing edges. Computing a minimum bisection is NP‐hard in the worst case. In this paper we study a spectral heuristic for bisecting random graphs G_n(p,p′) with a planted bisection obtained as follows: partition n vertices into two classes of equal size randomly, and then insert edges inside the two classes with probability p′ and edges crossing the partition with probability p independently. If , where c₀ is a suitable constant, then with probability 1 ? o(1) the heuristic finds a minimum bisection of G_n(p,p′) along with a certificate of optimality. Furthermore, we show that the structure of the set of all minimum bisections of G_n(p,p′) undergoes a phase transition as . The spectral heuristic solves instances in the subcritical, the critical, and the supercritical phases of the phase transition optimally with probability 1 ? o(1). These results extend previous work of Boppana 5 . © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

Exact Solutions of the Klein-Gordon Equation for the Scarf-Type Potential via Nikiforov-Uvarov Method

In this paper we present the exact solutions of the one-dimensional Klein-Gordon equation for the Scarf-type potential with equal scalar and vector potentials. Exact solutions and corresponding energy eigenvalues equation are obtained using Nikiforov-Uvarov mathematical method for the s-wave bound state. The PT-symmetry and Hermiticity for this potential are also considered. It will be shown that the obtained results of the Scarf-type potential are reduced to the results of the well-known potentials in the special cases.     

Bi-criteria optimization problems for decision rules

We consider bi-criteria optimization problems for decision rules and rule systems relative to length and coverage. We study decision tables with many-valued decisions in which each row is associated with a set of decisions as well as single-valued decisions where each row has a single decision. Short rules are more understandable; rules covering more rows are more general. Both of these problems—minimization of length and maximization of coverage of rules are NP-hard. We create dynamic programming algorithms which can find the minimum length and the maximum coverage of rules, and can construct the set of Pareto optimal points for the corresponding bi-criteria optimization problem. This approach is applicable for medium-sized decision tables. However, the considered approach allows us to evaluate the quality of various heuristics for decision rule construction which are applicable for relatively big datasets. We can evaluate these heuristics from the point of view of (i) single-criterion—we can compare the length or coverage of rules constructed by heuristics; and (ii) bi-criteria—we can measure the distance of a point (length, coverage) corresponding to a heuristic from the set of Pareto optimal points. The presented results show that the best heuristics from the point of view of bi-criteria optimization are not always the best ones from the point of view of single-criterion optimization.     

A generalization of Eagon–Reiner’s theorem and a characterization of bi-CMt bipartite and chordal graphs

We give a generalization of Eagon-Reiner’s theorem relating Betti numbers of the Stanley-Reisner ideal of a simplicial complex and the CM_t property of its Alexander dual. Then we characterize bi-CM_t bipartite graphs and bi-CM_t chordal graphs. These are generalizations of recent results due to Herzog and Rahimi.     

First principles versus artificial neural network modelling of a solar desalination system with experimental validation

ABSTRACT

The present study mainly focuses on enhancing the performance of solar still unit using solar energy through cylindrical parabolic collector and solar panels. A 300 W solar panel is used to heat saline water by thermal elements outside the solar still unit. Solar panels are cooled during the hot hours of the day; thus, reducing their temperature may lead to an increase in solar panel efficiency followed by an increase in the efficiency of the solar still unit. The maximum amount of freshwater used in the experiment was 2.132 kg/day. The experiments were modelled using ANNs. Based on neural network simulation results, there is a significant correlation between experimental data and neural network modelling. This paper compares experimental data with data obtained from mathematical modelling and ANNs. As a conclusion, the artificial neural network prediction has been more accurate than the simplified first principles model presented.     

A neural network to solve quadratic programming problems with fuzzy parameters

In this paper, a representation of a recurrent neural network to solve quadratic programming problems with fuzzy parameters (FQP) is given. The motivation of the paper is to design a new effective one-layer structure neural network model for solving the FQP. As far as we know, there is not a study for the neural network on the FQP. Here, we change the FQP to a bi-objective problem. Furthermore, the bi-objective problem is reduced to a weighting problem and then the Lagrangian dual is constructed. In addition, we consider a neural network model to solve the FQP. Finally, some illustrative examples are given to show the effectiveness of our proposed approach.     

Solutions for the double Sine‐Gordon equation by Exp‐function,Tanh, and extended Tanh methods

In this work, we implement some analytical techniques such as the Exp‐function, Tanh, and extended Tanh methods for solving nonlinear partial differential equation, which contains sine terms, its name Double Sine‐Gordon equation. These methods obtain exact solutions of different types of differential equations in engineering mathematics. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010