This paper addresses the problems caused by an inappropriate selection of sliding surface parameters in fuzzy sliding mode controllers via an optimization approach. In particular, the proposed method employs the parallel distributed compensator scheme to design the state feedback based control law. The controller gains are determined in offline mode via a linear quadratic regular. The particle ...

We consider a system of nonlinear spinor and scalar fields with minimal coupling in general relativity. The nonlinearity in the spinor field Lagrangian is given by an arbitrary function of the invariants generated from the bilinear spinor forms S = ψ̄ψ and P = iψ̄γ5ψ; the scalar Lagrangian is chosen as an arbitrary function of the scalar invariant Υ = φ,αφ ,α, that becomes linear at Υ → 0. The sp...

The Casimir energy of a massless scalar field is semiclassically given by contributions due to classical periodic rays. The required subtractions in the spectral density are determined explicitly. The so defined semiclassical Casimir energy coincides with that obtained using zeta function regularization in the cases studied. Poles in the analytic continuation of zeta function regularization are...

An implicit function is defined to be the zero set of a scalar function F over space. Further, for points not on the implicit function, the sign of this scalar function tells us whether the point lies inside or outside the implicit function. The choice of whether positive values are inside or outside is arbitrary, since we may multiply an implicit function by −1 and change the notion of inside ...

We consider a nonlinear periodic problem driven by a nonhomogeneous differential operator, which includes as a particular case the scalar p-Laplacian. We assume that the reaction is a Carathéodory function which admits time-dependent zeros of constant sign. No growth control near ±∞ is imposed on the reaction. Using variational methods coupled with suitable truncation and comparison techniques,...

 Casimir entropy is an important aspect of casimir effect and at the nanoscale is visible. In this paper, we employ the path integral method to ‎obtain a‎ ‎general‎ relation for casimir entropy and ‎i‎nternal energy of arbitrary shaped objects in the presence of two, three and four dimension scalar fields and ‎the‎ electromagnetic field. For this purpose, using Lagrangian and based on a perturb...

Behaviour of a weekly self-interacting scalar eld with a small mass in the de Sitter background is investigated using the stochastic approach (including the case of a double-well interaction potential). Existence of the de Sitter invariant equilibrium quantum state of the scalar eld in the presence of interaction is shown for any sign of the mass term. The stochastic approach is further develop...

We prove that weak limits of entropy solutions to a one-dimensional scalar conservation law are entropy solutions as well. We consider a scalar conservation law ut + f(u)x = 0, (t, x) ∈ Π = (0, +∞)× R. (1) The flux function f(u) is supposed to be only continuous: f(u) ∈ C(R). Recall the notion of an entropy solution of (1) in the sense of Kruzhkov [6]. Definition 1. A bounded measurable functio...

We describe the qualitative properties of the solutions of the second order scalar equation ẍ + q(t)g(x) = 0, where q is a changing sign function, and consider the problem of existence and multiplicity of solutions which satisfy various different boundary conditions. In particular we outline some difficulties which arise in the use of the shooting approach.