We present a finite difference method for discretizing a Heaviside function H(u(~x)), where u is a level set function u : Rn 7→ R that is positive on a bounded region Ω ⊂ R. There are two variants of our algorithm, both of which are adapted from finite difference methods that we proposed for discretizing delta functions in [13–15]. We consider our approximate Heaviside functions as they are use...

Crocin, a component of saffron, showed hypotensive which is perhaps due to vascular smooth muscle relaxant effect. The relaxant effects of saffron on tracheal smooth muscle also could be due to its constituent, crocin. In the present study, the relaxant effects of crocin and its possible mechanisms on rat tracheal smooth muscle were investigated. The relaxant effects of three cumulative concent...

In this paper, we show first that if a solution u of the equation i*2(l, x, u, Du, D)u = f{t, x,u, Du), where Pi{t, x,u, Du, D) is a second order strictly hyperbolic quasilinear operator, is conormal with respect to a single characteristic hypersurface S of Pi in the past and S is smooth in the past, then S is smooth and u is conormal with respect to S for all time. Second, let So arjd Si be ch...

In this paper, we attempt to investigate a class of constrained nonsmooth convex optimization problems, that is, piecewise C2 convex objectives with smooth convex inequality constraints. By using the Moreau-Yosida regularization, we convert these problems into unconstrained smooth convex programs. Then, we investigate the second-order properties of the Moreau-Yosida regularization η. By introdu...

We describe the fundamentals of algorithms for minimizing a smooth nonlinear function, and extensions of these methods to the sum of a smooth function and a convex nonsmooth function. Such objective functions are ubiquitous in data analysis applications, as we illustrate using several examples. We discuss methods that make use of gradient (first-order) information about the smooth part of the f...

In this article, we study the classical solution of mixed problem in a quarter plane for one-dimensional wave equation. On bottom boundary, Cauchy conditions are specified, and second them has discontinuity first kind at point. The smooth boundary condition is set side boundary. built using method characteristics an explicit analytical form. uniqueness proved, under which piecewise-smooth exist...

‎In this paper‎, ‎we introduce the structure of a groupoid associated to a vector field‎ ‎on a smooth manifold‎. ‎We show that in the case of the $1$-dimensional manifolds‎, ‎our‎ ‎groupoid has a‎ ‎smooth structure such that makes it into a Lie groupoid‎. ‎Using this approach‎, ‎we associated to‎ ‎every vector field an equivalence‎ ‎relation on the Lie algebra of all vector fields on the smooth...

By combining the field-weakening control principle of a new axial flux-switching permanent-magnet motor (AFFSSPM) with the space vector pulse width modulation (SVPWM) and maximum torque per voltage (MTPV) control principle, a novel field-weakening control strategy for AFFSSPM is proposed in this paper. In the first stage of the field-weakening, the difference between the reference voltage updat...

In this note we study whether specific elements in the second homology of simply connected closed $4$-manifolds can be represented by smooth or topologically flat embedded spheres.