It is shown that every maximal monotone operator on a real Banach space with relatively compact range is of type NI. Moreover, if the space has a separable dual space then every maximally monotone operator $T$ can be approximated by a sequence of maximal monotone operators of type NI, which converge to $T$ in a reasonable sense (in the sense of Kuratowski-Painleve convergence).
Some observations concerning McShane type integrals are collected. In particular, a simple construction of continuous major/minor functions for a McShane integrand in Rn is given.
The system of zero-pressure gas dynamics conservation laws describes the dynamics of free particles sticking under collision while mass and momentum are conserved. The existence of such solutions was established some time ago. Here we report a uniqueness result that uses the Oleinik entropy condition and a cohesion condition. Both of these conditions are automatically satisfied by solutions obtained in previous existence results. Important tools in the proof of uniqueness are regularizations, generalized characteristics and flow maps. The solutions may contain vacuum states as well as singular measures.
Standard properties of ϕ-divergences of probability measures are widely applied in various areas of information processing. Among the desirable supplementary properties facilitating employment of mathematical methods is the metricity of ϕ-divergences, or the metricity of their powers. This paper extends the previously known family of ϕ-divergences with these properties. The extension consists of a continuum of ϕ-divergences which are squared metric distances and which are mostly new but include also some classical cases like e. g. the Le Cam squared distance. The paper establishes also basic properties of the ϕ-divergences from the extended class including the range of values and the upper and lower bounds attained under fixed total variation.
In this article we introduce the notion of strongly ${\rm KC}$-spaces, that is, those spaces in which countably compact subsets are closed. We find they have good properties. We prove that a space $(X, \tau )$ is maximal countably compact if and only if it is minimal strongly ${\rm KC}$, and apply this result to study some properties of minimal strongly ${\rm KC}$-spaces, some of which are not possessed by minimal ${\rm KC}$-spaces. We also give a positive answer to a question proposed by O. T. Alas and R. G. Wilson, who asked whether every countably compact ${\rm KC}$-space of cardinality less than $c$ has the ${\rm FDS }$-property. Using this we obtain a characterization of Katětov strongly ${\rm KC}$-spaces and finally, we generalize one result of Alas and Wilson on Katětov-${\rm KC}$ spaces.
Biomechanical simulation activities are seen to undergo considerable growth in volume and scope. More complex and more complete models are now being generated. Biomechanical simulations are considered and extended well into the fields of transport vehicle occupant safety, biomedicine and virtual surgery, ergonomics and into the fields of leisure and sports article manufacture.
For an impact application like a car to pedestrian impact, correct modeling of a knee joint is important for description of the global response and dynamics after the impact. It is also useful for description of possible injuries. Based on the large research of available sources done in [3] in order to create an adequate knee joint, a simple articulated rigid body knee model is introduced. The model is based on the nonlinear joint accommodating flexion-extension and lateral rotation and translation. Joint characteristics are based on public experimental data. Dynamical validation of the new model is provided. The model is implemented into existing human articulated rigid body model ROBBY2 [2] and the frontal impact of a van versus a pedestrian is simulated including comparison to experiment.
The pre-crash activity of the human body is also essential from the point of influencing the global body motion. Hence, the influence of active muscles on the impact kinematics is investigated and comparison to passive model is provided. and Obsahuje seznam literatury