Bilevel convex programming models

Bilevel convex models are studied after being cast into a parametric programming form. This form has a lexicographic inner-outer structure where the optimal value of the outer model is optimized on the set of optimal solutions of the inner model. Optimal solutions are characterized using a Lagrangian saddle-point approach and a marginal value formula is given for the outer model. These are used to formulate a general method for finding an optimal solution by input optimization.     

Minimum-norm fixed point of nonexpansive mappings with applications

The purpose of this paper is to present two new iterative algorithms to find the minimum norm fixed point of nonexpansive nonself-mappings in the framework of Hilbert spaces. The results presented in this paper improve and extend the corresponding ones announced by Yao and Xu [Yao Y, Xu HK. Iterative methods for finding minimum norm fixed point of mappings with applications. Optimization. 2011;60:645–658] and many others. Some applications to convex minimization and split feast problems(SFP) are also included.     

Models and Algorithms for Carsharing Systems and Related Problems

In a Carsharing System, a fleet of cars is distributed at specified stations in an urban area, users can take and return cars at any time and station. For operating such a system in a satisfactory way, the stations have to keep a good ratio between the total number of places and the number of cars in each station, in order to refuse as few customer requests as possible. In this work, we propose to model the resulting problem of balancing the load of the stations as a General Pickup and Delivery Problem. As problems of this type are known to be hard, we discuss possible heuristic approaches both for the static (offline) and the dynamic (online) version of the problem, and give approximation results for special cases.     

On the existence of positive solutions of the p‐Laplacian dynamic equations on time scales

In this paper, we investigate the existence of positive solutions for a nonlinear m‐point boundary value problem for the p‐Laplacian dynamic equations on time scales, by applying a Krasnosel'skii's fixed point theorem. As an application, an example is included to demonstrate the main results. Copyright © 2017 John Wiley & Sons, Ltd.     

Naturally derived green bio-additives

During the last few years, special attention has been paid by the lubricant industry towards vegetable oil-based lubricants due to their biodegradability, renewability and excellent tribological properties. But to maintain the biodegradability of the final lubricants, the additive in the lubricants must also be biodegradable. Hence, in our present work, multifunctional lubricating oil additive based on castor oil has been investigated as a less toxic, feasible alternative to traditional petroleum based additives. Homopolymer of castor oil and its copolymer with α-pinene were synthesized by a thermal method using azobisisobutyronitrile as a radical initiator. Characterization of the prepared polymers was performed by spectral analysis and gel permeation chromatography (GPC). Additive performances of each of the prepared polymers as viscosity index improvers/viscosity modifiers and pour point depressants were carefully evaluated. Photo micrographic image was used to study the effectiveness of the additives as pour point depressants. Thermogravimetric analysis (TGA) was conducted to investigate the thermal response of the additives at high temperature. Finally, biodegradability of all the polymers was tested against fungal pathogen by the disc diffusion method and soil burial test. The study illuminated excellent additive performances of the polymers and thus their potential for acting as entirely naturally derived green bio-additives for lube oil.     

Applying the combined integral method to one-dimensional ablation

In this paper the combined integral method is applied to a simple one-dimensional ablation problem. One of the drawbacks of heat balance integral methods is how to choose the approximating function. It is common to use a polynomial form but even then it is not clear what the power of the highest order term should be. Previous studies have determined exponents either from exact solutions or from expansions valid over short time scales; neither approach is satisfactory nor very accurate for larger times. We combine the heat balance and refined integral methods to determine this exponent as part of the solution process, and conclude that it is in fact time-dependent in the ablation stage. From comparing the approximate solutions with numerical and exact analytical solutions whenever possible, we show that this new method greatly improves the accuracy on standard methods, without overcomplicating the method.     

Critical temperatures of elements from their boiling points

A linear relation between critical temperature and boiling point is proposed for elements belonging to the same group in the periodic table. The validity of the relationship is demonstrated for the alkalies and the groups 16, 17 and 18. From this the critical temperature of tellurium is predicted as 2325?K and that for polonium as 2277?K.     

Two improved formulations for the minimum latency problem

In network problems, latency is associated with the metric used to evaluate the length of the path from a root vertex to each vertex in the network. In this work we are dealing with two applications or variations of the minimum latency problem known as the repairman problem and the deliveryman problem. We have developed two integer formulations for the minimum latency problem and compared them with other two formulations from the literature for the time-dependent traveling salesman problem. The present work highlights the similarities and differences between the different formulations. In addition, we discuss the convenience of including a set of constraints in order to reduce the computation time needed to reach the optimal solution. We have carried out extensive computational experimentation on asymmetrical instances, since they provide the characteristics of the deliveryman and repairman problems in a better way.     

Elastic behavior of composites containing multi-layer coated particles with imperfect interface bonding conditions and application to size effects and mismatch in these composites

This paper proposes a procedure to deal with n-layered inclusion based composites with imperfect interfaces (which conditions consist of displacement or stress vector jumps) respecting spherical symmetry. For that purpose, “discontinuity matrices” have been introduced. These matrices have been derived for several classical interface-models and an asymptotic method has been used to determine some of them. A self-consistent condition based on a strain-energy equivalence in the case of inclusion-matrix type composite materials is restated for n-layered inclusions with imperfect interfaces and applied to get estimates of such composites materials. The remarkable feature of the presently self consistent approach is that it does not need any tedious algebra providing the attached interface models respect the spherical symmetry. The present Generalized Self Consistent Model (GSCM) is then used to study size effects and mismatch in composites reinforced by coated inclusions.     

On tight 6-cycle decompositions of complete 3-uniform hypergraphs

The complete 3-uniform hypergraph of order v has a vertex set V of size v and the set of all 3-element subsets of V as its edge set. A tight 6-cycle is a hypergraph with vertex set $\{a,b,c,d,e,f\}$ and edge set $\{\{a,b,c\},\{b,c,d\},\{c,d,e\},\{d,e,f\},\{e,f,a\},\{f,a,b\}\}$. We show that there exists a decomposition of the complete 3-uniform hypergraph of order v into isomorphic copies of a tight 6-cycle if and only if $v\equiv 1$, 2, 10, 20, 28, or $29(\mathrm{mod}36)$.