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

Loss of largest and oldest individuals of the Montpellier snake correlates with recent warming in the southeastern Iberian Peninsula

The effects of climate change on organisms are now being extensively studied in many different taxa. However, the variation in body size, usually shrinkage in response to increasing temperature, has received little attention regarding to reptiles. During past periods of global warming, many organisms shrank in size, and current evidence and experiments manipulating temperature have shown a biomass decrease in some organisms with increasing temperatures. Here we test whether the body size of the Montpellier snake Malpolon monspessulanus from the southeastern Iberian Peninsula is changing and correlated with the increasing temperature in this region during a 39year period (1976–2014). We measured the snout–vent length (SVL) of vouchers in scientific collections to check for trends in adult body size at the population level in relation with temperature, while controlling for the age of the individuals (estimated by skeletochronology, n¼141). Given the great ontogenetic variation in body size of the study species, we categorized age in 3 classes: “young adults” (under 5 years old), “intermediate adults” (from 5 to 7 years old), and “old adults” (from 8 to 14 years old). By means of linear mixed models, we found a negative relationship between SVL of “old adults” and average annual temperature in the region during the lifetime of each individual. Our results indicate that largest and oldest individuals of the Montpellier Snake, that is, males because of strong sexual size dimorphism in this species, disappeared from the study population, and suggest that it occurred in response to rising environmental temperature.Junta de Andalucía RNM-25

Quantum Neural Networks for Forecasting Inflation Dynamics

103–106Inflation is a key indicator in the economy that measures the average level of prices of goods and services, being an important ratio in public and private decision-making, so predicting it with precision has always been a concern of economists. This paper makes inflation predictions with different time horizons applying quantum theory through Quantum Neural Networks. The results obtained teach that Quantum Neural Networks overcome the predictive power of the existing models in the previous literature and yields a low-level of errors when predicting any change in the direction of the forecast trend

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

Neural networks for estimating Macro Asset Pricing model in football clubs

The recent crisis caused by COVID-19 directly affected consumption habits and thestability sof financial markets. In particular, the football industry has been hit hard bythis pandemic and therefore has more volatile stock prices. Given this new scenario,further research is needed to accurately estimate the value of the shares of footballclubs. In this paper, we estimate an asset pricing model in football clubs with differentcompositions of risk nature using non-linear techniques of artificial neural networks.Usually, asset pricing models have been estimated with linear methods such as ordi-nary least squares (...