Convexity of chance constrained programming problems with respect to a new generalized concavity notion

In this paper, convexity of chance constrained problems have been investigated. A new generalization of convexity concept, named h-concavity, has been introduced and it has been shown that this new concept is the generalization of the ??-concavity. Then, using the new concept, some of the previous results obtained by Shapiro et al. [in Lecture Notes on Stochastic Programming Modeling and Theory, SIAM and MPS, 2009] on properties of ??-concave functions, have been extended. Next the convexity of chance constraints with independent random variables is investigated. It will be shown how concavity properties of the mapping related to the decision vector have to be combined with suitable properties of decrease or increase for the marginal densities in order to arrive at convexity of the feasible set for large enough probability levels and then sufficient conditions for convexity of chance constrained problems which has been introduced by Henrion and Strugarek [in Convexity of chance constraints with independent random variables. Comput. Optim. Appl. 41:263?C276, 2008] has been extended in this paper for a wider class of real functions.     

Solving nonlinear multi-objective optimization problems with fuzzy relation inequality constraints regarding Archimedean triangular norm compositions

We propose an approach to solve a nonlinear multi-objective problem subject to fuzzy relation inequalities with max-Archimedean-t-norm composition by a genetic algorithm. The additive generator of Archimedean t-norms is utilized to reform the existent genetic algorithm to solve the constrained nonlinear multi-objective optimization problems. We consider thoroughly the feasible set of the fuzzy relation inequality systems in three possible cases, namely “≤”, “≥” and the combination of them. In general, their feasible sets are nonconvex which are completely determined by one vector as their maximum solution and a finite number of minimal solutions. The maximum and minimal solutions are formulated by using the additive generator. Additionally, we present some conditions for each case under which the problem can be reduced. Finally, each reduced problem is solved by the genetic algorithm and the efficiency of the proposed method is shown by some numerical examples.     

Solving the sum-of-ratios problems by a harmony search algorithm

The sum-of-ratios problems have numerous applications in economy and engineering. The sum-of-ratios problems are considered to be difficult, as these functions are highly nonconvex and multimodal. In this study, we propose a harmony search algorithm for solving a sum-of-ratios problem. Numerical examples are also presented to demonstrate the effectiveness and robustness of the proposed method. In all cases, the solutions obtained using this method are superior to those obtained from other methods.     

Returns to scale in multiplicative models in data envelopment analysis

One class of models introduced in DEA is called multiplicative models, in which, as shown by Banker and Maindiratta (Manag. Sci. 32:126–135, 1986), the piecewise linear frontiers usually employed in DEA are replaced by a frontier that is piecewise Cobb-Douglas(=log  linear). Banker and Maindiratta (Manag. Sci. 32:126–135, 1986) introduced a model to identify the most productive scale size pattern, and Banker et al. (Eur. J. Oper. Res. 154:345–362, 2004) presented a two-stage method for the identification of returns to scale (RTS) in multiplicative models. In this paper it is shown that both the RTS situation and the MPSS pattern could be determined by a single model in one step. The new method is important in the computational point of view.     

Low-frequency Vibrational Modes in Small Polypeptides of Essential Amino Acids

Optics and Spectroscopy - The length-dependent low-frequency terahertz absorption spectrum of the essential amino acid chains has been investigated. Since this special type of amino acids cannot be...     

Nonlinear scalarization functions and polar cone in set optimization

In this paper, some new nonlinear scalarization functions are introduced and some of their properties are investigated. Using these functions and the polar cone, we characterize set optimal solutions of set optimization problems. Also, some relationships between the cone-convexity (resp. cone-quasiconvexity) of a set-valued map and the convexity (resp. quasiconvexity) of its scalarized versions are established.     

The Effects of Non-thermal Plasma on the Morphology of Ce-doped ZnO: Synthesis,Characterization and Photocatalytic Activity of Hierarchical Nanostructures

ZnO nanoparticles with and without 8 mol % Ce dopant were synthesized by precipitation method and the prepared samples were treated with various types of non-thermal plasma in order to study their effects on the morphology and photocatalytic activity of the samples. As-prepared Ce-doped ZnO has a hexagonal wurtzite structure and the crystal system was not changed by the plasma treatment. The morphology of Ce-doped ZnO was changed from spherical particle to flower and rod-like shapes by the plasma treatment. The particle size of the treated Ce-doped ZnO is smaller in comparison with that of untreated sample. The photodegradation of methylene blue by the plasma-treated Ce-doped ZnO in aqueous solution is higher than that of the untreated Ce-doped ZnO. The enhancement of the photocatalytic activity by the plasma-treated samples may come from the particle size reduction, enhancement in charge separation efficiency and increase of the surface area.     

Scalarization of Levitin–Polyak well-posed set optimization problems

The aim of this paper is to study Levitin–Polyak (LP in short) well-posedness for set optimization problems. We define the global notions of metrically well-setness and metrically LP well-setness and the pointwise notions of LP well-posedness, strongly DH-well-posedness and strongly B-well-posedness for set optimization problems. Using a scalarization function defined by means of the point-to-set distance, we characterize the LP well-posedness and the metrically well-setness of a set optimization problem through the LP well-posedness and the metrically well-setness of a scalar optimization problem, respectively.     

A modified algorithm for solving the proposed models by Ghodousian and Khorram and Khorram and Ghodousian

In this paper, we focus on the proposed algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max-prod composition that it has been proposed by Ghodousian and Khorram [A. Ghodousian, E. Khorram, An algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max-prod composition, Appl. Math. Comput. 178 (2006) 502–509]. Firstly, we show that the algorithm may not lead to the optimal solution in some cases. Secondly, we propose a new algorithm for solving the presented model by Ghodousian and Khorram (2006), as mentioned above. In fact, it modifies the presented algorithm in the Ghodousian and Khorram’s paper. Also, this algorithm is extended to the presented model by Khorram and Ghodousian [E. Khorram, A. Ghodousian, Linear objective function optimization with fuzzy relation equation constraints regarding max-av composition, Appl. Math. Comput. 173 (2006) 872–886.] with max-av composition. Finally, some numerical examples are given for illustrating the purposes.     

Electro-spray of high viscous liquids for producing mono-sized spherical alginate beads

Alginate beads, often used for controlled release of enzymes and drugs, are usually produced by spraying sodium alginate liquid into a gelling agent using mechanical vibration nozzle or air jet. In this work an alternative method of electro-spray was employed to form droplets with desired size from a highly viscous sodium alginate solution using constant DC voltage. The droplets were then cured in a calcium chloride solution. The main objective was to produce mono-sized beads from such a highly viscous and non-Newtonian liquid (1000-5000 mPa s). The effects of nozzle diameter, flow rate and concentration of liquid on the size of the beads were investigated. Among the parameters studied, voltage had a pronounced effect on the size of beads as compared to flow rate zzle diameter and concentration of alginate liquid. The size of beads was reduced to a minimum value with increasing the voltage in the range of 0-10 kV. At the early stages of voltage increase (I.e. Up to about 4 kV), the rate of size reduction was relatively low, while the dripping mode dominated. However, in the middle part of the range of applied voltage, where the rate of size reduction was high (I.e. About 4-7 kV), an unstable transition occurred between dripping and jetting. At the end part of the range (I.e. 7-10 kV) jet mode of spray was observed. Increasing the height of fall of the droplets was found to improve the sphericity of the beads, because of the increased time of flight for the droplets. This was especially identifiable at higher concentrations of the alginate liquid (I.e. 3 w/v%)