On isotopisms and strong isotopisms of commutative presemifields

In this paper we prove that the $P(q,\ell)$ ($q$ odd prime power and $\ell>1$ odd) commutative semifields constructed by Bierbrauer in \cite{BierbrauerSub} are isotopic to some commutative presemifields constructed by Budaghyan and Helleseth in \cite{BuHe2008}. Also, we show that they are strongly isotopic if and only if $q\equiv 1(mod\,4)$. Consequently, for each $q\equiv -1(mod\,4)$ there exist isotopic commutative presemifields of order $q^{2\ell}$ ($\ell>1$ odd) defining CCZ--inequivalent planar DO polynomials.Comment: References updated, pag. 5 corrected Multiplication of commutative LMPTB semifield

A Carlitz type result for linearized polynomials

For an arbitrary $q$-polynomial $f$ over $\mathbb{F}_{q^n}$ we study the problem of finding those $q$-polynomials $g$ over $\mathbb{F}_{q^n}$ for which the image sets of $f(x)/x$ and $g(x)/x$ coincide. For $n\leq 5$ we provide sufficient and necessary conditions and then apply our result to study maximum scattered linear sets of $\mathrm{PG}(1,q^5)$

control algorithm design for degradation mitigation and lifetime improvement of polymer electrolyte membrane fuel cells

Abstract The improvement of reliability, durability and availability of fuel cell systems represents a key factor for their mass-market deployment in several application areas. The development of advanced algorithms oriented towards fuel cell system monitoring, diagnostics, prognostics and control can significantly reduce the incidence of degradation mechanisms and faulty events on fuel cell performance and durability. Therefore, a valuable increase in system efficiency and lifetime can be achieved by proper design of such algorithms, especially for applications working under highly variable load profiles. The present work deals with the design of a model-based control algorithm aimed at mitigating degradation effects on a Polymer Electrolyte Membrane Fuel Cell (PEMFC) system. Such an algorithm embeds cell degradation models, describing Ostwald ripening and Platinum dissolution mechanisms, which affects the cell Electrochemical Surface Area. The control algorithm is developed aiming at PEMFC durability improvement, while ensuring user power request, and its performance is evaluated in simulated environment addressing stationary power generation applications with variable load profile and comparing the cell degradation decay under different control strategies

Small Minimal Blocking Sets inPG(2, q3)

AbstractWe extend the results of Polverino (1999, Discrete Math., 208/209, 469–476; 2000, Des. Codes Cryptogr., 20, 319–324) on small minimal blocking sets in PG(2,p3 ), p prime, p≥ 7, to small minimal blocking sets inPG (2, q3), q=ph, p prime, p≥ 7, with exponent e≥h. We characterize these blocking sets completely as being blocking sets of Rédei-type

On the nuclei of a finite semifield

In this paper we collect and improve the techniques for calculating the nuclei of a semifield and we use these tools to determine the order of the nuclei and of the center of some commutative presemifields of odd characteristic recently constructed

Author's response to 'CAP and HCAP are different? An unresolved question

Dear Editor, We thank the authors for the interest in our recent publication and for their useful comments. Unfortunately we consider the comparison with the publication from Giannella et al1 poorly appropriate in many aspects. The main strength of our work is the multicentre prospective case–control study design (match by age, gender and period of hospitalisation). Although severity scores were not used for matching, we considered this design the most appropriate to describe healthcare-associated pneumonia (HCAP) features. In fact, the Giannella group performed an observational prospective study only on patients admitted to internal medicine departments: these elements (study design and patients) could justify a different population composition and, consequently, different microbiological and clinical findings. In fact, in comparison..