We consider the decomposition of a maximal monotone operator into the sum of an antisymmetric operator and the subdifferential of a proper lower semicontinuous convex function. This is a variant of the well-known decomposition of a matrix into its symmetric and antisymmetric part. We analyze in detail the case when the graph of the operator is a linear subspace. Equivalent conditions of monotonicity are also provided. We obtain several new results on auto-conjugate representations including an explicit formula that is built upon the proximal average of the associated Fitzpatrick function and its Fenchel conjugate. These results are new and they both extend and complement recent work by Penot, Simons and Zălinescu. A nonlinear example shows the importance of the linearity assumption. Finally, we consider the problem of computing the Fitzpatrick function of the sum, generalizing a recent result by Bauschke, Borwein and Wang on matrices to linear relations.

In this thesis, the geometric margin is used for the first time as the robustness indicator of an uncoupled cellular neural network implementing a given Boolean function. First, robust template design for uncoupled cellular neural networks implementing linearly separable Boolean functions by support vector machines is proposed. A fast sequential minimal optimization algorithm is presented to find maximal margin classifiers, which in turn determine the robust templates. Some general properties of robust templates are investigated. An improved CFC algorithm implementing an arbitrarily given Boolean function is proposed. Two illustrative examples are provided to demonstrate the validity of the proposed method.

In this study, our aim is to determine the locations of bottle banks used in collecting recycled glass. The collection of recycled glass is done by a fleet of vehicles that visit some predetermined collection points, like restaurants and hospitals. The location of bottle banks depends on the closeness of the banks to the population zones where the recycled class is generated, and to the closeness of the banks to the predetermined collection points. A mathematical model, which combines the maximal covering problem in the presence of partial coverage and vehicle routing problem with profits, is presented. Heuristic procedures are proposed for the solution of the problem. Computational results based on generated test problems are provided. We also discuss a case study, where bottle banks are located in Yenimahalle, a district of Ankara

In this study, we propose a bi-objective facility location model that considers both partial coverage and service to uncovered demands. In this model, it is assumed that the demand nodes within the predefined distance of opened facilities are fully covered and after that distance the coverage level linearly decreases. The objectives are the maximization of the sum of full and partial coverage the minimization of the maximum distance between uncovered demand nodes and their closest opened facilities. We apply two existing Multi Objective Genetic Algorithms (MOGAs), NSGA-II and SPEA-II to the problem. We determine the drawbacks of these MOGAs and develop a new MOGA called modified SPEA-II (mSPEA-II) to avoid the drawbacks. In this method, the fitness function of SPEA-II is modified and the crowding distance calculation of NSGA-II is used. The performance of mSPEA-II is tested on randomly generated problems of different sizes. The results are compared with the solutions resulting from NSGA-II and SPEA-II. Our experiments show that mSPEA-II outperforms both NSGA-II and SPEA-II.

In this study, a metaheuristic procedure, particularly a variable neighborhood search procedure, is proposed to solve the combined location and selective traveling salesman problem in glass recycling. The collection of used glass is done by a collecting vehicle that visits a number of predefined collection centers, like restaurants and hospitals that are going to be referred to as compulsory points. Meanwhile, it is desired to locate a predetermined number of bottle banks to residential areas. The aim is to determine the location of these bottle banks and the route of the collecting vehicle so that all compulsory points and all bottle banks are visited and the maximum profit is obtained. Population zones are defined in residential areas and it is assumed that the people in a particular population zone will recycle their used glass to the closest bottle bank that fully or partially covers their zone. A Variable Neighborhood Search algorithm and its variant have been utilized for the solution of the problem. Computational experiments have been made on small and medium scale test problems, randomly generated and adapted from the literature.

Stochastic differential inclusions can be considered as a generalisation of stochastic differential equations. In particular a multivalued mapping describes the set of equations, in which a solution has to be found. This paper presents an existence result for a special parabolic stochastic inclusion. The proof is based on the method of upper and lower solutions. In the deterministic case this method was effectively introduced by S. Carl.

The purpose of this study was to investigate how maximal power output (P[subscript max]), as measured via the inertial load technique, changes throughout a collegiate soccer season in relation to training load completed. Furthermore, this study also aimed to describe the time course of recovery of [maximal power output] following two collegiate soccer matches in one weekend. The current investigation involved two experimental periods. The first took place throughout the 2010 Big XII soccer season. Nineteen Division I female collegiate soccer players (19.9 ± 1.2 yrs, 165.1 ± 6.6 cm, 61.0 ± 6.8 kg) from the same collegiate soccer team completed regular inertial load testing and perceptual fatigue questionnaires throughout this study period. These athletes' training was not altered in any way by the investigators throughout the 2010 season. During the second experimental period, two off-season matches were played in one weekend during the 2011 off-season. Training was prescribed by coaches, with the aim of simulating an in-season training week. [Maximal power output] and perceptual fatigue responses were monitored every day throughout the second study period. All training and matches throughout the study were monitored via the session RPE method. The results demonstrated that STARTERS experience much greater load throughout the season than NON-STARTERS (p<0.05, 2247 ± 176 AU and 1585 ± 174 AU), accounted for by increased load experienced during matches. This increased training load throughout the season lead to a decline in [maximal power output] in STARTERS (to 92.3 ± 6%, p<0.05) whilst [maximal power output] was maintained in NON-STARTERS (p>0.05) for the duration of the season. Furthermore, STARTERS experienced greater muscle soreness throughout the in-season period compared to NON-STARTERS. During the second experimental period [maximal power output] declined (p<0.05, 93.3 ± 7%) two days following matches played on the weekend and remained reduced for three days. Notably, two heavy training days in the middle of the training week appeared to have detrimental effects on both [maximal power output] and perceptual fatigue responses. The main finding of this study is that [maximal power output] declined throughout the middle and latter parts of the season in STARTERS, after experiencing significantly greater training loads than NON-STARTERS throughout the season. The current findings, combined with previous investigations, suggest that the inertial load technique may be useful in monitoring fatigue in team sport athletes. / text

We consider the decomposition of a maximal monotone operator into the sum of an antisymmetric operator and the subdifferential of a proper lower semicontinuous convex function. This is a variant of the well-known decomposition of a matrix into its symmetric and antisymmetric part. We analyze in detail the case when the graph of the operator is a linear subspace. Equivalent conditions of monotonicity are also provided. We obtain several new results on auto-conjugate representations including an explicit formula that is built upon the proximal average of the associated Fitzpatrick function and its Fenchel conjugate. These results are new and they both extend and complement recent work by Penot, Simons and Zălinescu. A nonlinear example shows the importance of the linearity assumption. Finally, we consider the problem of computing the Fitzpatrick function of the sum, generalizing a recent result by Bauschke, Borwein and Wang on matrices to linear relations.

Electrical stimulation has been widely used in the field of sport training or functional rehabilitation to enhance strength training and to assess voluntary muscle activation. Two superimposed techniques can be used: 1) the twitch interpolation technique, which consists of interjecting an electrical stimulus onto the muscle nerve; and 2) the percutaneous superimposed electrical stimulation technique, where the stimulation is applied to the muscle belly. These two superimposed techniques can be used to evaluate the ability to fully activate a muscle. Temperature is important for muscle function. Muscle contraction and relaxation becomes quicker, development of power increasing as the temperature of the body raises. Immoderate temperature of the muscle, as a result, can decrease physical efficiency. However it is unclear how muscle heating can affect superimposed pulse force, therefore our aim was to determine and compare variant temperature affect on additionally activated quadriceps femoris muscle during isometric load. The study was performed at Lithuanian Academy of Physical Education. The subjects were 10 healthy adult men (age 22,1 ± 2,3 years, weight 72,3 ± 4,9 kg, height 178 ± 5,7 cm) who were not actively going in for sports. The study was consisted of two stages. During the first stage subjects were tested under control conditions. During the second stage (was performed after two weeks) subjects were tested, when their muscles were heated. Quadriceps femoris... [to full text]

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