Search results for "Bounded function"

From Feynman–Kac formulae to numerical stochastic homogenization in electrical impedance tomography

2016

In this paper, we use the theory of symmetric Dirichlet forms to derive Feynman–Kac formulae for the forward problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities corresponding to different electrode models on bounded Lipschitz domains. Subsequently, we employ these Feynman–Kac formulae to rigorously justify stochastic homogenization in the case of a stochastic boundary value problem arising from an inverse anomaly detection problem. Motivated by this theoretical result, we prove an estimate for the speed of convergence of the projected mean-square displacement of the underlying process which may serve as the theoretical foundation for the de…

Stability Analysis of a Linear Parameter Varying Adaptive Output Feedback Control System

2021

Abstract Output feedback control systems often require an adaptive filter for properly shaping the loop transfer function, as certain system plant parameters may be uncertain or varying. This renders the overall closed loop to a linear parameter varying (LPV) system, for which the stability analysis is challenging due to non-trivial dynamics of the adaptation law. This paper develops a stability analysis technique of a feedback controlled oscillatory system. A polytopic overapproximation of the parameter set together with the feasibility of certain LMIs guarantees asymptotic stability of the closed loop. The varying filter parameter is only required to be lower and upper bounded, where the …

Towards an Agent-Based Model for the Analysis of Macroeconomic Signals

2020

This work introduces an agent-based model for the analysis of macroeconomic signals. The Bottom-up Adaptive Model (BAM) deploys a closed Walrasian economy where three types of agents (households, firms and banks) interact in three markets (goods, labor and credit) producing some signals of interest, e.g., unemployment rate, GDP, inflation, wealth distribution, etc. Agents are bounded rational, i.e., their behavior is defined in terms of simple rules finitely searching for the best salary, the best price, and the lowest interest rate in the corresponding markets, under incomplete information. The markets define fixed protocols of interaction adopted by the agents. The observed signals are em…

On monadic quantale algebras: basic properties and representation theorems

2010

Motivated by the concept of quantifier (in the sense of P. Halmos) on different algebraic structures (Boolean algebras, Heyting algebras, MV-algebras, orthomodular lattices, bounded distributive lattices) and the resulting notion of monadic algebra, the paper introduces the concept of a monadic quantale algebra, considers its properties and provides several representation theorems for the new structures.

Landau's theorem and the number of conjugacy classes of zeros of characters

2021

Abstract Motivated by a 2004 conjecture by the author and J. Sangroniz, Y. Yang has recently proved that if G is solvable then the index in G of the 8th term of the ascending Fitting series is bounded in terms of the largest number of zeros in a row in the character table of G. In this note, we prove this result for arbitrary finite groups and propose a stronger form of the 2004 conjecture. We conclude the paper showing some possible ways to prove this strengthened conjecture.

Continuous *-homomorphisms of Banach Partial *-algebras

2007

We continue the study of Banach partial *-algebras, in particular the question of the interplay between *-homomorphisms and biweights. Two special types of objects are introduced, namely, relatively bounded biweights and Banach partial *-algebras satisfying a certain Condition (S), which behave in a more regular way. We also present a systematic construction of Banach partial *-algebras of this type and exhibit several examples.

Representations of modules over a*-algebra and related seminorms

2008

Representations of a module X over a � -algebra A# are considered and some related seminorms are constructed and studied, with the aim of finding bounded � -representations of A #.

Banach elements and spectrum in Banach quasi *-algebras

2006

A normal Banach quasi -algebra (X;A_0) has a distinguished Banach - algebra X_b consisting of bounded elements of X. The latter -algebra is shown to coincide with the set of elements of X having fi nite spectral radius. If the family P(X) of bounded invariant positive sesquilinear forms on X contains suffi ciently many elements then the Banach -algebra of bounded elements can be characterized via a C -seminorm defi ned by the elements of P(X).

The Navier–Stokes equations in exterior Lipschitz domains: L -theory

2020

Abstract We show that the Stokes operator defined on L σ p ( Ω ) for an exterior Lipschitz domain Ω ⊂ R n ( n ≥ 3 ) admits maximal regularity provided that p satisfies | 1 / p − 1 / 2 | 1 / ( 2 n ) + e for some e > 0 . In particular, we prove that the negative of the Stokes operator generates a bounded analytic semigroup on L σ p ( Ω ) for such p. In addition, L p - L q -mapping properties of the Stokes semigroup and its gradient with optimal decay estimates are obtained. This enables us to prove the existence of mild solutions to the Navier–Stokes equations in the critical space L ∞ ( 0 , T ; L σ 3 ( Ω ) ) (locally in time and globally in time for small initial data).

2020

Abstract This paper shows global uniqueness in two inverse problems for a fractional conductivity equation: an unknown conductivity in a bounded domain is uniquely determined by measurements of solutions taken in arbitrary open, possibly disjoint subsets of the exterior. Both the cases of infinitely many measurements and a single measurement are addressed. The results are based on a reduction from the fractional conductivity equation to the fractional Schrodinger equation, and as such represent extensions of previous works. Moreover, a simple application is shown in which the fractional conductivity equation is put into relation with a long jump random walk with weights.