Search results for "value"

Complex powers and non-compact manifolds

2002

We study the complex powers $A^{z}$ of an elliptic, strictly positive pseudodifferential operator $A$ using an axiomatic method that combines the approaches of Guillemin and Seeley. In particular, we introduce a class of algebras, ``extended Weyl algebras,'' whose definition was inspired by Guillemin's paper on the subject. An extended Weyl algebra can be thought of as an algebra of ``abstract pseudodifferential operators.'' Many algebras of pseudodifferential operators are extended Weyl algebras. Several results typical for algebras of pseudodifferential operators (asymptotic completeness, construction of Sobolev spaces, boundedness between apropriate Sobolev spaces, >...) generalize to…

Functional Type Error Control for Stabilised Space-Time IgA Approximations to Parabolic Problems

2018

The paper is concerned with reliable space-time IgA schemes for parabolic initial-boundary value problems. We deduce a posteriori error estimates and investigate their applicability to space-time IgA approximations. Since the derivation is based on purely functional arguments, the estimates do not contain mesh dependent constants and are valid for any approximation from the admissible (energy) class. In particular, they imply estimates for discrete norms associated with stabilised space-time IgA approximations. Finally, we illustrate the reliability and efficiency of presented error estimates for the approximate solutions recovered with IgA techniques on a model example.

Systematisation of Systems Solving Physics Boundary Value Problems

2020

A general conservation law that defines a class of physical field theories is constructed. First, the notion of a general field is introduced as a formal sum of differential forms on a Minkowski manifold. By the action principle the conservation law is defined for such a general field. By construction, particular field notions of physics, e.g., magnetic flux, electric field strength, stress, strain etc. become instances of the general field. Hence, the differential equations that constitute physical field theories become also instances of the general conservation law. The general field and the general conservation law together correspond to a large class of relativistic hyperbolic physical …

Integrability of the one dimensional Schrödinger equation

2018

We present a definition of integrability for the one dimensional Schroedinger equation, which encompasses all known integrable systems, i.e. systems for which the spectrum can be explicitly computed. For this, we introduce the class of rigid functions, built as Liouvillian functions, but containing all solutions of rigid differential operators in the sense of Katz, and a notion of natural boundary conditions. We then make a complete classification of rational integrable potentials. Many new integrable cases are found, some of them physically interesting.

Approximating hidden chaotic attractors via parameter switching.

2018

In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical …

Solutions of nonlinear PDEs in the sense of averages

2012

Abstract We characterize p-harmonic functions including p = 1 and p = ∞ by using mean value properties extending classical results of Privaloff from the linear case p = 2 to all pʼs. We describe a class of random tug-of-war games whose value functions approach p-harmonic functions as the step goes to zero for the full range 1 p ∞ .

A delay time bound for distributed parameter circuits with bipolar transistors

1990

We prove here a stability theorem concerning a parabolic system of equations with non-linear boundary conditions that governs the behaviour of a class of networks in which the bipolar transistors operating under large-signal conditions are interconnected with reg-lines modelled by telegraph equations

A Mountain Pass Theorem for a Suitable Class of Functions

2009

On the zeros of Jacobi polynomials

1994

On the limits to the long-period method in classical economics. A note

2001

On a first reading of Theory of Production, Kurz & Salvadori (1995) appear to confine the empirical domain of the long-period models of the classical theory of value and distribution to stationary economies with non-constant returns to scale and to growing economies with constant returns to scale. Such a reading is shown to be untenable since it merges the two levels of exploring the extension of a model and of testing a theoretical hypothesis. Conversely, the way Kurz & Salvadori tackle the problems of price dynamics and returns to scale in growing economies is shown to be compatible with what appears to be Sraffa's (implicit) strategy of research.