A planar underactuated bipedal robot with an impulsive foot model is considered. The analysis extends previous work on a model with unactuated point feet of Westervelt et al. 1 to include the actuator model of Kuo . The impulsive actuator at each leg end is active only during the double support phase, which results in the model being identical to the model with unactuated point feet for the sin...

We demonstrate that solving the classical problems mentioned in the title on quadrature domains when the given boundary data is rational is as simple as the method of partial fractions. A by-product of our considerations will be a simple proof that the Dirichlet-to-Neumann map on a double quadrature domain sends rational functions on the boundary to rational functions on the boundary. The resul...

In this paper we study the ergodicity and the related semigroup property for a class of symmetric Markov jump processes associated with time changed symmetric α-stable processes. For this purpose, explicit and sharp criteria for Poincaré type inequalities (including Poincaré, super Poincaré and weak Poincaré inequalities) of the corresponding non-local Dirichlet forms are derived. Moreover, our...

We consider two new classes of twisted D=4 quantum Poincaré symmetries described as the dual pairs of noncocommutative Hopf algebras. Firstly we investigate the two-parameter class of twisted Poincaré algebras which provide the Liealgebraic noncommutativity of the translations. The corresponding star-products and new deformed Lie-algebraic Minkowski spaces are introduced. We discuss further the...

Whereas the rabbinic tradition attacks King Asa of Judah for trusting in himself rather than in G-d and, in particular, for drafting the sages, Josephus, the apologist, omits such details and, indeed, whitewashes Asa completely. He is praised particularly, in language reminiscent of Josephus' portraits of Saul and David, as well as of Thucydides' Pericles, for putting his nation in order. In pa...

The profession of occupational therapy promotes individuals to achieve health and wellness through engagement in meaningful occupations of daily living. This occupation-focused profession plays a critical role in health care in a multitude of settings with a wide range of clients. The paper highlights a global overview of the philosophies of occupational therapy, the current international pract...

The Poincaré-Bendixson theorem plays an important role in the study of the qualitative behavior of dynamical systems on the plane; it describes the structure of limit sets in such systems. We prove a version of the Poincaré-Bendixson Theorem for two dimensional hybrid dynamical systems and describe a method for computing the derivative of the Poincaré return map, a useful object for the stabili...

The choice of a closed regular neighborhood of a finite polyhedron embedded in a manifold enables one to write the ambient space as a union of two manifolds, the neighborhood and its complement, glued along a common boundary component. Poincaré duality embeddings are a homotopy theoretic version of this in which the manifolds are replaced by Poincaré spaces and the gluing is now done with respe...

We call Poincaré time the time associated to the Poincaré (or first return) map of a vector field. In this paper we prove the non-accumulation of isolated critical points of the Poincaré time T on hyperbolic polycycles of polynomial vector fields. The result is obtained by proving that the Poincaré time of a hyperbolic polycycle either has an unbounded principal part or is an almost regular fun...

We consider the inverse problem for the second order hyperbolic equation in a bounded domain in R n with lower order terms depending analytically on the time variable. We prove that the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the hyperbolic equation up to a diffeomorphism and a gauge transformation.