Tomáš Roubíček

Relaxation in optimization theory and variational calculus

Background generalities: order and topology linear and convex analysis optimization theory functions and measure spaces means of continuous functions some differential and integral equations non-cooperative game theory. Theory of convex compactifications: convex compactifications canonical form of convex compactifications approximation of convex compactifications extension of mappings. Young measures and their generalizations: classical Young measures various generalizations approximation theory extensions of Nemytskii mappings. Relaxation in optimization theory: abstract optimization problems optimization problems on Lebesgue spaces example - optimal control of dynamical systems example - elliptic optimal control problems example - parabolic optimal control problems example - optimal control of integral equations. relaxation in variational calculus I: convex compactifications of Sobolev spaces relaxation of variational problems - p > 1 optimality conditions for relaxed problems relaxation of variational problems - p = 1 convex approximation of relaxed problems. relaxation in variational calculus II: prerequisites around quasiconvexity gradient generalized Young functionals relaxation scheme and its FEM-approximation further approximation - an inner case further approximation - an outer case double-well problem - sample calculations. Relaxation in game theory: abstract game-theoretical problems games on Lebesgue spaces example - games with dynamical systems example - elliptic games bibliography list of symbols. (Part contents).

Renal artery revascularization improves heart failure control in patients with atherosclerotic renal artery stenosis

BACKGROUND Renal artery stenosis (RAS) impacts the pathogenesis and control of heart failure (HF) and may further contribute to increased cardiovascular morbidity and mortality in HF patients. However, the long-term effects of renal artery revascularization on cardiovascular outcomes in HF patients are not well studied. METHODS The prevalence of HF and its effects on all-cause mortality were studied in 163 consecutive patients with systemic hypertension and chronic kidney disease (serum creatinine >2 mg/dL) who underwent percutaneous transluminal renal angioplasty (PTRA) with stenting for atherosclerotic RAS. In addition, in 100 patients with RAS and coexistent HF, we compared the impact of medical treatment (n = 50) versus PTRA (n = 50) on clinical outcomes. RESULTS HF (predominantly normal ejection fraction) was present in 50/163 (31%) patients with systemic hypertension and chronic kidney disease (serum creatinine >2 mg/ dL) undergoing PTRA for RAS and represented the major predictor of all-cause mortality in these patients. When compared with sex-matched RAS and HF patients treated medically, PTRA with stenting was associated with a significant decrease in the New York Heart Association Functional Class (1.9 +/- 0.8 versus 2.6 +/- 1.0, P < 0.04) and a 5-fold reduction in the number of hospitalizations. However, renal artery revascularization did not impact mortality. CONCLUSION HF was present in one-third of patients with renal dysfunction and atherosclerotic RAS who were referred for PTRA. The presence of HF was associated with a significantly increased risk of death after PTRA with stenting. Renal artery revascularization resulted in improved HF control and a reduction in HF hospitalizations.

A rate-independent approach to the delamination problem

We study delamination processes for elastic bodies glued together by an adhesive as an activated, rate-independent process. The adhesive is assumed to absorb a specific amount of energy during the delami-nation process. A solution is defined by energetic principles of stability and balance of stored and dissipated energies with the work of external loading, realized here through displacement on parts of the boundary. Starting from a time discretization, we construct solutions via a rigorous limiting analysis. Moreover, we provide computer simulations for some model problems using a further finite-element spatial discretization.

Increased serum concentrations of macrophage inhibitory cytokine-1 in patients with obesity and type 2 diabetes mellitus: the influence of very low calorie diet

OBJECTIVE Macrophage inhibitory cytokine-1 (MIC-1) is a novel regulator of energy homeostasis. We explored whether alterations in MIC-1 levels contribute to metabolic disturbances in patients with obesity and/or obesity and type 2 diabetes mellitus (T2DM). DESIGN We measured serum MIC-1 levels and its mRNA expression in subcutaneous and visceral adipose tissue of 17 obese nondiabetic women, 14 obese women with T2DM and 23 healthy lean women. We also explored the relationship of MIC-1 with anthropometric and biochemical parameters and studied the influence of 2-week very low calorie diet (VLCD) on serum MIC-1 levels. METHODS Serum MIC-1 levels were measured by ELISA and its mRNA expression was determined by RT-PCR. RESULTS Both obese and T2DM group had significantly elevated serum MIC-1 levels relative to controls. T2DM group had significantly higher serum MIC-1 levels relative to obese group. Serum MIC-1 positively correlated with body weight, body fat, and serum levels of triglycerides, glucose, HbAlc, and C-reactive protein and it was inversely related to serum high-density lipoprotein cholesterol. Fat mRNA MIC-1 expression did not significantly differ between lean and obese women but it was significantly higher in subcutaneous than in visceral fat in both groups. VLCD significantly increased serum MIC-1 levels in obese but not T2DM group. CONCLUSION Elevated MIC-1 levels in patients with obesity are further increased by the presence of T2DM. We suggest that in contrast to patients with cancer cachexia, increased MIC-1 levels in obese patients and diabetic patients do not induce weight loss.

Increased production of proinflammatory cytokines in adipose tissue of patients with end-stage renal disease.

OBJECTIVE The number of patients with end-stage renal disease (ESRD) is rising and these patients are at higher risk of cardiovascular disease. We studied the role of hormonal production of adipose tissue in the development of chronic inflammation in patients with ESRD before kidney transplantation. METHODS Fifteen women with ESRD and 17 healthy women (control) underwent single blood drawing and visceral and subcutaneous adipose tissue sampling during surgery (kidney transplantation in the ESRD group or cholecystectomy in the control group). Serum concentrations of C-reactive protein, interleukin-6, tumor necrosis factor-alpha, leptin, adiponectin, resistin, monocyte chemoattractant protein-1 were measured. Messenger RNA expression of the same hormones, adiponectin receptors 1 and 2 and immunocompetent cell marker CD68 in subcutaneous and visceral samples were measured using real-time polymerase chain reaction. Adipose tissue was examined immunohistochemically for CD68-positive cells. RESULTS Serum concentrations of C-reactive protein, adiponectin, resistin, interleukin-6, tumor necrosis factor-alpha, and monocyte chemoattractant protein-1 were significantly higher in the ESRD versus control group. Subcutaneous and visceral mRNA expressions of tumor necrosis factor-alpha and CD68 were significantly increased in the ESRD versus control group. Adiponectin receptor-1 and monocyte chemoattractant protein-1 mRNA expressions were significantly higher in visceral but not in subcutaneous adipose tissue of the ESRD group. Messenger RNA expressions of resistin, leptin, adiponectin, interleukin-6, and adiponectin receptor-2 in both fat depots did not significantly differ between groups. Increased infiltration of subcutaneous and visceral adipose tissue with CD68-positive immunocompetent cells was found in the ESRD group by histologic examination. CONCLUSION Subcutaneous and visceral adipose tissues in ESRD express higher amounts of proinflammatory cytokines and may play a role in the development of systemic inflammation.

Adhesive Contact of Visco-elastic Bodies and Defect Measures Arising by Vanishing Viscosity

An adhesive unilateral contact of elastic bodies with a small viscosity in the linear Kelvin--Voigt rheology at small strains is scrutinized. The flow rule for debonding the adhesive is considered rate-independent and unidirectional. The asymptotics for the viscosity or for external loading speed approaching zero is proved in some special cases, in particular when inertia is neglected or when delamination is in Mode II (pure shear). The solutions thus obtained involve certain defect-like measures recording in some sense natural additional energy dissipated in the bulk due to (vanishing) viscosity. Reflecting also the conventional engineering concept, the delamination is thus driven by stress rather than energy. An explicit example leading to a nontrivial defect measure is given. (A correction is attached to the PDF.)

Quasi-Static Small-Strain Plasticity in the Limit of Vanishing Hardening and Its Numerical Approximation

The quasi-static rate-independent evolution of the Prager-Ziegler-type model of plasticity with hardening is shown to converge to the rate-independent evolution of the Prandtl-Reuss elastic/perfectly plastic model. Based on the concept of energetic solutions we study the convergence of the solutions in the limit for hardening coefficients converging to

Numerical approximation of Young measures in non-convex variational problems

0

Dissipative Evolution of Microstructure in Shape Memory Alloys

by using the abstract method of

Models of Microstructure Evolution in Shape Memory Alloys

\Gamma