Search results for "Bounded"

Algebras with intermediate growth of the codimensions

2006

AbstractLet F be a field of characteristic zero and let A be an F-algebra. The polynomial identities satisfied by A can be measured through the asymptotic behavior of the sequence of codimensions and the sequence of colengths of A. For finite dimensional algebras we show that the colength sequence of A is polynomially bounded and the codimension sequence cannot have intermediate growth. We then prove that for general nonassociative algebras intermediate growth of the codimensions is allowed. In fact, for any real number 0<β<1, we construct an algebra A whose sequence of codimensions grows like nnβ.

Varieties of Algebras with Superinvolution of Almost Polynomial Growth

2015

Let A be an associative algebra with superinvolution ∗ over a field of characteristic zero and let $c_{n}^{\ast }(A)$ be its sequence of corresponding ∗-codimensions. In case A is finite dimensional, we prove that such sequence is polynomially bounded if and only if the variety generated by A does not contain three explicitly described algebras with superinvolution. As a consequence we find out that no intermediate growth of the ∗-codimensions between polynomial and exponential is allowed.

A generalized porous medium equation related to some singular quasilinear problems

2014

Abstract In this paper we study the existence and nonexistence of solutions for a Dirichlet boundary value problem whose model is { − ∑ m = 1 ∞ a m Δ u m = f in  Ω u = 0 on  ∂ Ω , where Ω is a bounded domain of R N , a m is a sequence of nonnegative real numbers, and f is in L q ( Ω ) , q > N 2 .

The norm of the characteristic function of a set in the John‐Nirenberg space of exponent p

2020

Derived length and character degrees of solvable groups

2003

We prove that the derived length of a solvable group is bounded in terms of certain invariants associated to the set of character degrees and improve some of the known bounds. We also bound the derived length of a Sylow p-subgroup of a solvable group by the number of different p-parts of the character degrees of the whole group.

A Hierarchy of Twofold Resource Allocation Automata Supporting Optimal Sampling

2009

We consider the problem of allocating limited sampling resources in a "real-time" manner with the purpose of estimating multiple binomial proportions. More specifically, the user is presented with `n ' sets of data points, S 1 , S 2 , ..., S n , where the set S i has N i points drawn from two classes {*** 1 , *** 2 }. A random sample in set S i belongs to *** 1 with probability u i and to *** 2 with probability 1 *** u i , with {u i }. i = 1, 2, ...n , being the quantities to be learnt. The problem is both interesting and non-trivial because while both n and each N i are large, the number of samples that can be drawn is bounded by a constant, c . We solve the problem by first modelling it a…

Nonlocal Minimal Surfaces and Nonlocal Curvature

2019

Recall that if a set E has minimal local perimeter in a bounded set Ω, then it has zero mean curvature at each point of ∂E ∩ Ω (see [51]), and the equation that says that the curvature is equal to zero is the Euler–Lagrange equation associated to the minimization of the perimeter of a set.

Two-Sided Estimates of the Solution Set for the Reaction–Diffusion Problem with Uncertain Data

2009

We consider linear reaction–diffusion problems with mixed Dirichlet–Neumann–Robin conditions. The diffusion matrix, reaction coefficient, and the coefficient in the Robin boundary condition are defined with an uncertainty which allow bounded variations around some given mean values. A solution to such a problem cannot be exactly determined (it is a function in the set of “possible solutions” formed by generalized solutions related to possible data). The problem is to find parameters of this set. In this paper, we show that computable lower and upper bounds of the diameter (or radius) of the set can be expressed throughout problem data and parameters that regulate the indeterminacy range. Ou…

PARAMETER BOUNDED ESTIMATION FOR QUASISPECIES MODELS OF MOLECULAR EVOLUTION

2006

Abstract The Quasispecies models identification for Evolutionary Dynamics is considered in a worst-case deterministic setting. These models analyze the DNA and RNA evolution or describe the population dynamics of viruses and bacteria. In this paper we identify the Fitness and the Replication Probability parameters of a genetic sequences, subject to a set of stringent constraints to have physical meaning and to guarantee positiveness. The conditional central estimate and the Uncertainty Intervals are determined. The effectiveness of the proposed procedure has been illustrated by means of simulation experiments while tests on real data are under concern.

A Reinforcement Learning Approach for User Preference-aware Energy Sharing Systems

2021

Energy Sharing Systems (ESS) are envisioned to be the future of power systems. In these systems, consumers equipped with renewable energy generation capabilities are able to participate in an energy market to sell their energy. This paper proposes an ESS that, differently from previous works, takes into account the consumers’ preference, engagement, and bounded rationality. The problem of maximizing the energy exchange while considering such user modeling is formulated and shown to be NP-Hard. To learn the user behavior, two heuristics are proposed: 1) a Reinforcement Learning-based algorithm, which provides a bounded regret and 2) a more computationally efficient heuristic, named BPT- ${K}…