We introduce index systems, a tool for studying isolated invariant sets of dynamical systems that are not necessarily hyperbolic. The mapping of the index systems mimics the expansion and contraction of hyperbolic maps on the tangent space, and they may be used like Markov partitions to generate symbolic dynamics. Every continuous dynamical system satisfying a weak form of expansiveness possess...

We consider a flow of incompressible Newtonian fluid through a pipe with helical shape. We suppose that the flow is governed by the prescribed pressure drop between pipe’s ends. Such model has relevance to some important engineering applications. Under small data assumption, we prove the existence and uniqueness of the weak solution to the corresponding Navier-Stokes system with pressure bounda...

We construct geodesics in the Wasserstein space of probability measures along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show that a local Poincaré inequality and the measure contraction property follow from the Ricci curvature bounds defined by Sturm. We also show for a large class o...

We develop both phenomenological and molecular-statistical theory of smectic- A -smectic- C phase transition with anomalously weak smectic layer contraction. Using a general mean-field molecular model, we demonstrate that a relatively simple interaction potential suffices to describe the transition both in conventional and de Vries type smectics. The theoretical results are in excellent agreeme...

We prove L1{contraction principle and uniqueness of solutions for quasilinear elliptic{parabolic equations of the form @t[b(u)] div[a(ru; b(u))] + f(b(u)) = 0 in (0; T ) ; where b is monotone nondecreasing and continuous. We only assume that u is a weak solution of nite energy (see [1]). In particular, we do not suppose that the distributional derivative @t[b(u)] is a bounded Borel measure or a...

(b) Present Condition, July 1929.? (1) The left leg and arm are spastic and rigid. Atrophy or loss of nutrition are not very noticeable. The grip is, however, weak. (2) The left knee-jerk and ankle clonus are markedly exaggerated, Babinsk's sign present. Upper limb jerks exaggerated. No loss of epicritic or protopathic sensation. (3) Slight paresis of right face, unequal contraction of pupils, ...

We present some fixed point results for mappings which satisfy Hardy–Rogers rational type, quasicontraction type, weak contraction type and generalized fψ type cyclic conditions in 0-complete partial metric spaces. Presented results generalize or improve many existing fixed point theorems in the literature. To demonstrate our results, we give throughout the paper some examples. One of the possi...

metabolic alkalosis is characterized by high hco3- as it is seen in chronic respiratory acidosis, but ph differentiates the two disorders. there is no characteristic symptom or sign. orthostatic hypotension may be encountered. weakness and hyporeflexia occur if serum k+ is markerdly low. tetany and neuromuscular irritability occur rarely. we report the results of retrospective data analysis of ...

Choice functions on tournaments always select the maximal element (Condorcet winner), provided they exist, but this property does not hold in the more general case of weak tournaments. In this paper we analyze the relationship between the usual choice functions and the set of maximal elements in weak tournaments. We introduce choice functions selecting maximal elements, whenever they exist. Mor...

Introduction: It was shown in a previous study, that MCPIP, a cilostamide derivative, increased atrial contraction force without changing contraction rate. To improve this property, two new derivatives of cilostamide were synthesized and their effects on PDE3 activity and isolated rat atria contraction were investigated. Methods: The inhibitory effect of each compound on PDE3 enzyme was dete...