Zero Jordan product determined Banach algebras

A Banach algebra $A$ is said to be a zero Jordan product determined Banach algebra if every continuous bilinear map $\varphi\colon A\times A\to X$, where $X$ is an arbitrary Banach space, which satisfies $\varphi(a,b)=0$ whenever $a$, $b\in A$ are such that $ab+ba=0$, is of the form $\varphi(a,b)=\sigma(ab+ba)$ for some continuous linear map $\sigma$. We show that all $C^*$-algebras and all group algebras $L^1(G)$ of amenable locally compact groups have this property, and also discuss some applications

Maps preserving zeros of a polynomial

Let \A be an algebra and let $f(x_1,...,x_d)$ be a multilinear polynomial in noncommuting indeterminates $x_i$. We consider the problem of describing linear maps \phi:\A\to \A that preserve zeros of $f$. Under certain technical restrictions we solve the problem for general polynomials $f$ in the case where \A=M_n(F). We also consider quite general algebras \A, but only for specific polynomials $f$.Comment: 11 pages, accepted for publication in Linear Algebra App

The Kadison problem on a class of commutative Banach algebras with closed cone

summary:The main result of the paper characterizes continuous local derivations on a class of commutative Banach algebra $A$ that all of its squares are positive and satisfying the following property: Every continuous bilinear map $\Phi$ from $A\times A$ into an arbitrary Banach space $B$ such that $\Phi(a,b)=0$ whenever $ab=0$, satisfies the condition $\Phi (ab,c)=\Phi(a,bc)$ for all $a,b,c\in A$

Oscillating viscous flow past a streamwise linear array of circular cylinders

This paper addresses the viscous flow developing about an array of equally spaced identical circular cylinders aligned with an incompressible fluid stream whose velocity oscillates periodically in time. The focus of the analysis is on harmonically oscillating flows with stroke lengths that are comparable to or smaller than the cylinder radius, such that the flow remains two-dimensional, time-periodic and symmetric with respect to the centreline. Specific consideration is given to the limit of asymptotically small stroke lengths, in which the flow is harmonic at leading order, with the first-order corrections exhibiting a steady-streaming component, which is computed here along with the accompanying Stokes drift. As in the familiar case of oscillating flow over a single cylinder, for small stroke lengths, the associated time-averaged Lagrangian velocity field, given by the sum of the steady-streaming and Stokes-drift components, displays recirculating vortices, which are quantified for different values of the two relevant controlling parameters, namely, the Womersley number and the ratio of the inter-cylinder distance to the cylinder radius. Comparisons with results of direct numerical simulations indicate that the description of the Lagrangian mean flow for infinitesimally small values of the stroke length remains reasonably accurate even when the stroke length is comparable to the cylinder radius. The numerical integrations are also used to quantify the streamwise flow rate induced by the presence of the cylinder array in cases where the periodic surrounding motion is driven by an anharmonic pressure gradient, a problem of interest in connection with the oscillating flow of cerebrospinal fluid around the nerve roots located along the spinal canal.This work was supported by the National Institute of Neurological Disorders and Stroke through contract no. 1R01NS120343-01 and by the National Science Foundation through grant no. 1853954. The work of W.C. was partially supported by the Spanish MICINN through the coordinated project PID2020-115961RB

Predicting Systemic Banking Crises using Extreme Gradient Boosting

571-575Considering the great ability of decision trees techniques to extract useful information from large databases and to handle heterogeneous variables, this paper applies Extreme Gradient Boosting for the prediction of systemic banking crises. To this end, prediction models have been constructed for different regions and the whole world. The results obtained show that Extreme Gradient Boosting overcomes the predictive power of existing models in the previous literature and provides more explanatory information on the causes that produce systemic banking crises, being the demand for deposits, the level of domestic credit and banking assets some of the most significant variables

Emission taxes and feed-in subsidies in the regulation of a polluting monopoly

The paper studies the use of emission taxes and feed-in subsidies for the regulation of a monopoly that can produce the same good with a technology that employs a polluting input and a clean technology. In the first part of the paper, we show that the efficient solution can be implemented combining a tax on emissions and a subsidy on clean output. The tax is lower than the environmental damages, and the subsidy is equal to the difference between the price and the marginal revenue. In the second part of the paper, the second-best tax and subsidy are also calculated solving a two-stage policy game between the regulator and the monopoly with the regulator acting as the leader of the game. We find that the second-best tax rate can be the Pigouvian tax, but only if the marginal costs of the clean technology are constant. Using a linear–quadratic specification of the model, we show that the clean output is larger when a feed-in subsidy is used than when the tax is applied, but the dirty output can be larger or lower depending on the magnitude of marginal costs of the clean technology and marginal damages. The same occurs for the net social welfare, although we find that for low enough marginal costs of the clean technology, the net social welfare is larger when a feed-in subsidy is used to promote clean output regardless the importance of the marginal damages