We consider a hierarchical maximal covering location problem to locate p health centers and q hospitals in such a way that maximum demand is covered, where health centers and hospitals have successively inclusive hierarchy. Demands are 3 types: demand requiring low-level service only, demand requiring high-level service only, and demand requiring both levels of service at the same time. All types of requirements of a demand point should be either covered by hospital providing both levels of service or referred to hospital via health center since a demand point is not covered unless all levels of requirements are satisfied. Thus, a health center cannot be opened unless it is suitable to refer its covered demand to a hospital. Referral is defined as coverage of health centers by hospitals. We also added partial coverage to this complex hierarchic structure, that is, a demand point is fully covered up to the minimum critical distance, non-covered after the maximum critical distance and covered with a decreasing quality while increasing distance to the facility between minimum and maximum critical distances. We developed an MIP formulation to solve the Hierarchical Maximal Covering Location Problem with referral in the presence of partial coverage. We solved small-size problems optimally using GAMS. For large-size problems we developed a Genetic Algorithm that gives near-optimal results quickly. We tested our Genetic Algorithm on randomly generated problems of sizes up to 1000 nodes.

In this study, a bi-objective capacitated facility location problem is presented which includes partial coverage concept and relocation of facility nodes. In partial coverage, a predefined distance between a demand node and a facility node is assumed to be fully covered. After the predefined distance, the service level commences to decay linearly. The problem is designed to consider the existence of already functioning facility nodes. It is allowed to close these existing facilities and open new facilities in potential sites. However, existing facility nodes are strongly favored against new facility nodes. The objectives are the maximization of the weighted total coverage and the minimization of number of facility nodes. A novel interactive multi-objective evolutionary algorithm is proposed to solve this problem, I-TREA. I-TREA is originated from NSGA-II and designed for interactive methods benefiting from quality infeasible solutions. The performance of I-TREA is benchmarked with a modified version of NSGA-II on randomly generated problems with various sizes and utility functions.

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The aim of this thesis is to analyze the kinematic and dynamic characteristics of a high-speed bearing system. The examined kinematic characteristics will include the maximal speed, fatigue life and stiffness of a bearing system. The stability and transmission force of a bearing system as well as the vibration of its shaft were the studied dynamic characteristics. These analyses were based on the kinemitics of bearing systems, rotor dynamics and elastohydrodynamic lubrication theory. According to these analyses, the interaction and consequence among these characteristics and the parameters of a bearing system will be explained. After these analyses, preliminary and simple design trends about a high-speed bearing system are going to be proposed.

We give a systematic study of the Hardy spaces of functions with values in the non-commutative Lp-spaces associated with a semifinite von Neumann algebra M. This is motivated by matrix valued harmonic analysis (operator weighted norm inequalities, operator Hilbert transform), as well as by the recent development of non-commutative martingale inequalities. Our non-commutative Hardy spaces are defined by non-commutative Lusin integral functions. It is proved in this dissertation that they are equivalent to those defined by the non-commutative Littlewood-Paley G-functions. We also study the Lp boundedness of operator valued dyadic paraproducts and prove that their Lq boundedness implies their Lp boundedness for all 1 < q < p < ∞.

The aim of this work is to present several new results concerning duality in scalar convex optimization, the formulation of sequential optimality conditions and some applications of the duality to the theory of maximal monotone operators. After recalling some properties of the classical generalized interiority notions which exist in the literature, we give some properties of the quasi interior and quasi-relative interior, respectively. By means of these notions we introduce several generalized interior-point regularity conditions which guarantee Fenchel duality. By using an approach due to Magnanti, we derive corresponding regularity conditions expressed via the quasi interior and quasi-relative interior which ensure Lagrange duality. These conditions have the advantage to be applicable in situations when other classical regularity conditions fail. Moreover, we notice that several duality results given in the literature on this topic have either superfluous or contradictory assumptions, the investigations we make offering in this sense an alternative. Necessary and sufficient sequential optimality conditions for a general convex optimization problem are established via perturbation theory. These results are applicable even in the absence of regularity conditions. In particular, we show that several results from the literature dealing with sequential optimality conditions are rediscovered and even improved. The second part of the thesis is devoted to applications of the duality theory to enlargements of maximal monotone operators in Banach spaces. After establishing a necessary and sufficient condition for a bivariate infimal convolution formula, by employing it we equivalently characterize the $\varepsilon$-enlargement of the sum of two maximal monotone operators. We generalize in this way a classical result concerning the formula for the $\varepsilon$-subdifferential of the sum of two proper, convex and lower semicontinuous functions. A characterization of fully enlargeable monotone operators is also provided, offering an answer to an open problem stated in the literature. Further, we give a regularity condition for the weak$^*$-closedness of the sum of the images of enlargements of two maximal monotone operators. The last part of this work deals with enlargements of positive sets in SSD spaces. It is shown that many results from the literature concerning enlargements of maximal monotone operators can be generalized to the setting of Banach SSD spaces.

Background: The need to find the underlying causes to handball injuries and to develop injury prevention programs is great. In other sports a relationship between maximal oxygen uptake (VO2 max) and injury have been seen. Purpose: To examine the relationship between VO2 max and/or lactate threshold and injuries in elite handball players. Methods: A prospective, non experimental correlational study was conducted. Thirty elite handball players and handball high school players were included. Injuries and test results for VO2-max, lactate threshold and potential confounders ( re-injury of the previous injury, re- injury of previous injury of the lower limb, age, BMI and legs and core strength for the high school players) were registered during the season 2014-2015. A bivariate analysis using Spearman's rank correlation calculation was conducted. Twenty-six respectively 11 of the players had data on VO2-max, respectively lactate threshold. Confounders that showed connection with injuries or injuries in the lower extremity were analyzed for the bivariate correlation with VO2-max and lactate threshold. Results: No significant correlation was found between VO2-max respectively lactate threshold and injury. Significant correlations were seen between previous injury respectively previous injury to the lower extremity and to get a re-injury. A significant correlation were seen between re-injury of a previous injury in the lower limb and VO2-max. Conclusions: Significant associations were seen between re- injury of earlier injury and between re-injury of the lower extremity and VO2-max and should therefore be considered in the clinical practice. Larger studies are needed to clarify the relationship between VO2-max and lactate threshold and injuries. / Bakgrund: Behovet att hitta bakomliggande orsaker till handbollsskador för att kunna utforma skadepreventiva åtgärder är stort. I andra idrotter har ett samband mellan maximal syreupptagningsförmåga (VO2-max) och skador kunnat ses. Syfte: Att undersöka samband mellan VO2-max och/eller laktattröskelvärde och skador hos elithandbollspelare. Metod: En prospektiv icke experimentell sambandsstudie utfördes. Trettio elithandbollsspelare och handbollsgymnasiespelare inkluderades. Skador och testresultat för VO2-max och laktattröskel samt tänkbara konfounders (återskada av tidigare generell skada, återskada av tidigare skada i nedre extremitet, ålder, BMI och ben och bålstyrka för gymnasiespelarna) registrerades under matchsäsongen 2014-2015. En bivariat analys med Spearmans rangkorrelationsberäkning utfördes. Tjugosex respektive 11 av spelarna hade data på VO2-max respektive laktattröskelvärde. Konfounders som visade samband med generella skador eller skador i nedre extremiteten analyserades bivariat för samband med VO2-max och laktattröskelvärde. Resultat: Inga signifikanta samband fanns mellan VO2-max respektive laktattröskelvärde och skador. Signifikanta samband fanns för tidigare generella skador respektive tidigare skada i nedre extremiteten och att återfå densamma samt mellan återskada av tidigare skada i nedre extremiteten och VO2-max. Konklusion: Signifikanta samband fanns för återskada av tidigare skada samt mellan återskada i nedre extremiteten och VO2-max vilket bör beaktas i den kliniska vardagen. Större studier behövs för att klargöra det sambandet mellan VO2-max respektive laktattröskel och skador.

In this thesis, we investigate various problems in the representation theory of finite groups of Lie type. In Chapter 2, we hope to make sense of the last statement - we will introduce some background and notation that will be useful for the remainder of the thesis. In Chapter 3, we find bounds for the largest irreducible representation degree of a finite unitary group. In Chapter 4, we describe the block distribution and Brauer characters in cross characteristic for Sp₆(2ᵃ) in terms of the irreducible ordinary characters. This will be useful in Chapter 5 and Chapter 7, which focus primarily on the group Sp₆(2ᵃ) and contain the main results of this thesis, which we now summarize. Given a subgroup H ≤ G and a representation V for G, we obtain the restriction V|H of V to H by viewing V as an FH-module. However, even if V is an irreducible representation of G, the restriction V|H may (and usually does) fail to remain irreducible as a representation of H. In Chapter 5, we classify all pairs (V, H), where H is a proper subgroup of G = Sp₆(q) or Sp₄(q) with q even, and V is an l-modular representation of G for l ≠ 2 which is absolutely irreducible as a representation of H. This problem is motivated by the Aschbacher-Scott program on classifying maximal subgroups of finite classical groups. The local-global philosophy plays an important role in many areas of mathematics. In the representation theory of finite groups, the so-called "local-global" conjectures would relate the representation theory of G to that of certain proper subgroups, such as the normalizer of a Sylow subgroup. One might hope that these conjectures could be proven by showing that they are true for all simple groups. Though this turns out not quite to be the case, some of these conjectures have been reduced to showing that a finite set of stronger conditions hold for all finite simple groups. In Chapter 7, we show that Sp₆(q) and Sp₄(q), q even, are "good" for these reductions.

Subject of the study. Aerobic capacity and cardiac structure and function of healthy young males. Background. Data regarding the relationship between the parameters of aerobic capacity (such as maximal oxygen uptake or anaerobic threshold) and cardiac structure as well as function remain sparse and controversial. Aim. To determine how the parameters of aerobic capacity are correlated with those of cardiac structure and function. Objectives: 1. To determine the correlation between anaerobic thresholds and myocardial structure. 2. To determine how strongly the maximal oxygen uptake and cardiac structure are correlated. 3. To determine the correlation of indices of aerobic capacity to the parameters of myocardial function at rest. Hypothesis. Cardiac structure and function of healthy young men is directly linked not only to maximal oxygen uptake but anaerobic thresholds as well. Conclusions. The direct correlation of the parameters of concentric cardiac hypertrophy with aerobic capacity (anaerobic thresholds as well as maximal oxygen uptake) indices was detected. However, we failed to detect a significant correlation between indices of eccentric cardiac hypertrophy or myocardial function and aerobic capacity.

This study examined whether a high-intensity interval (IT) or a continuous steady-state (CT) exercise training program had the greatest effect on fat oxidation rates and fat mass loss in a population of untrained overweight and obese females. Thirteen female subjects (VO2peak 30.6 ± 1.29 ml.kg.min-1, BMI 29 ± 0.79, fat mass [FM] 33.3 ± 2.09 kg) were randomly assigned to either a CT (exercise at the relative intensity that elicits the maximal fat oxidation rate [FATmax] ) or an IT (intervals alternating 5 minutes at 40% and 85% VO2peak) training group that exercised approximately 1 hour, 3 days.week-1 for 10 weeks. Body composition assessments, peak oxygen uptake (VO2peak), FATmax and plasma free fatty acid (FFA) concentrations were examined pre- and post-training using dual-energy X-ray absorptiometry (DEXA), ParvoMedics gas analysis system and FFA half micro tests (Roche Diagnostics). No significant differences were found post-training in body weight (kg), body fat (%), fat-free mass, or fat mass (P>0.05). The relative exercise intensity that elicited FATmax was significantly increased from 35.3 ± 2.55% to 44.7 ± 3.56% in the IT group post-training (P <0.05). The maximal fat oxidation rate was determined at a higher relative exercise intensity after 10 weeks of a IT program compared with a CT program, which resulted in longer durations of fat oxidation during submaximal exercise bouts. These data suggest that an IT program induces a greater increase in the relative exercise intensity that elicits maximal fat oxidation after 10 weeks of training compared to a CT program in this population. Although body composition and FATmax were not altered, it is possible that through training induced metabolic adaptations from the IT program, intramuscular triacylglyceride (IMTG) contributions to fat oxidation at a given steady-state work rate could be increased post-training.