A necessary and sufficient condition for the well-posedness of some weakly hyperbolic cauchy problems

1983 ◽  
Vol 8 (7) ◽  
pp. 735-771 ◽  
Author(s):  
Takeshi Mandai
Keyword(s):  
Well Posedness ◽  
Sufficient Condition ◽  
Cauchy Problems ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

Accuracy estimates of regularization methods and conditional well-posedness of nonlinear optimization problems

2018 ◽  
Vol 26 (6) ◽  
pp. 789-797
Author(s):  
Mikhail Y. Kokurin
Keyword(s):  
Optimization Problems ◽  
Lower Semicontinuous ◽  
Well Posedness ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Closed Set ◽  
Nonlinear Minimization ◽  
Convex Closed Set ◽  
Ill Posed ◽  
Necessary And Sufficient

Abstract We investigate the nonlinear minimization problem on a convex closed set in a Hilbert space. It is shown that the uniform conditional well-posedness of a class of problems with weakly lower semicontinuous functionals is the necessary and sufficient condition for existence of regularization procedures with accuracy estimates uniform on this class. We also establish a necessary and sufficient condition for the existence of regularizing operators which do not use information on the error level in input data. Similar results were previously known for regularization procedures of solving ill-posed inverse problems.

scholarly journals A necessary and sufficient condition for the existence of a unique solution of a discrete boundary value problem

2003 ◽  
Vol 2003 (39) ◽  
pp. 2455-2463 ◽  
Author(s):  
Raghib Abu-Saris ◽  
Wajdi Ahmad
Keyword(s):  
Boundary Value Problem ◽  
Unique Solution ◽  
Boundary Value ◽  
Linear Difference Equation ◽  
Fundamental Question ◽  
Well Posedness ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Constant Coefficients ◽  
Necessary And Sufficient

Akth-order linear difference equation with constant coefficients subject to boundary conditions is considered. A necessary and sufficient condition for the existence of a unique solution for such a boundary value problem is established. The condition established answers a fundamental question for well-posedness and can be easily applied using a simple and computationally tractable algorithm that does not require finding the roots of the associated characteristic equation.

scholarly journals Multidimensional Tauberian theorems for vector-valued distributions

2014 ◽  
Vol 95 (109) ◽  
pp. 1-28 ◽  
Author(s):  
Stevan Pilipovic ◽  
Jasson Vindas
Keyword(s):  
Asymptotic Stability ◽  
Integral Transform ◽  
Tauberian Theorems ◽  
Sufficient Condition ◽  
Cauchy Problems ◽  
Necessary And Sufficient Condition ◽  
The Laplace Transform ◽  
Distribution Spaces ◽  
Necessary And Sufficient ◽  
Vector Valued

We prove several Tauberian theorems for regularizing transforms of vector-valued distributions. The regularizing transform of f is given by the integral transform Mf?(x,y) = (f*?y)(x), (x,y) ? Rn ? R+, with kernel ?y(t) = y?n?(t/y). We apply our results to the analysis of asymptotic stability for a class of Cauchy problems, Tauberian theorems for the Laplace transform, the comparison of quasiasymptotics in distribution spaces, and we give a necessary and sufficient condition for the existence of the trace of a distribution on {x0}?Rm. In addition, we present a new proof of Littlewood?s Tauberian theorem.

A Proposed Framework Emphasizing Auditor Reliability over Auditor Independence

2003 ◽  
Vol 17 (3) ◽  
pp. 257-266 ◽  
Author(s):  
Mark H. Taylor ◽  
F. Todd DeZoort ◽  
Edward Munn ◽  
Martha Wetterhall Thomas
Keyword(s):  
Public Interest ◽  
Auditor Independence ◽  
Public Confidence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Accounting Profession ◽  
The Public ◽  
Necessary And Sufficient

This paper introduces an auditor reliability framework that repositions the role of auditor independence in the accounting profession. The framework is motivated in part by widespread confusion about independence and the auditing profession's continuing problems with managing independence and inspiring public confidence. We use philosophical, theoretical, and professional arguments to argue that the public interest will be best served by reprioritizing professional and ethical objectives to establish reliability in fact and appearance as the cornerstone of the profession, rather than relationship-based independence in fact and appearance. This revised framework requires three foundation elements to control subjectivity in auditors' judgments and decisions: independence, integrity, and expertise. Each element is a necessary but not sufficient condition for maximizing objectivity. Objectivity, in turn, is a necessary and sufficient condition for achieving and maintaining reliability in fact and appearance.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

scholarly journals Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

Physics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 352-366
Author(s):  
Thomas Berry ◽  
Matt Visser
Keyword(s):  
Point Of View ◽  
Sufficient Condition ◽  
Use Of Self ◽  
Necessary And Sufficient Condition ◽  
Wigner Rotation ◽  
Inertial Frames ◽  
Explicit Formulae ◽  
Specific Implementation ◽  
Necessary And Sufficient ◽  
Lorentz Boosts

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary 4×4 Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae.

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