Characters, Weil sums and cc-differential uniformity with an application to the perturbed Gold function

Building upon the observation that the newly defined~\cite{EFRST20} concept of $c$-differential uniformity is not invariant under EA or CCZ-equivalence~\cite{SPRS20}, we showed in~\cite{SG20} that adding some appropriate linearized monomials increases the $c$-differential uniformity of the inverse function, significantly, for some~$c$. We continue that investigation here. First, by analyzing the involved equations, we find bounds for the uniformity of the Gold function perturbed by a single monomial, exhibiting the discrepancy we previously observed on the inverse function. Secondly, to treat the general case of perturbations via any linearized polynomial, we use characters in the finite field to express all entries in the $c$-Differential Distribution Table (DDT) of an $(n,n)$-function on the finite field \F_{p^n}, and further, we use that method to find explicit expressions for all entries of the $c$-DDT of the perturbed Gold function (via an arbitrary linearized polynomial).Comment: 22 page

CC-differential bent functions and perfect nonlinearity

Drawing inspiration from Nyberg's paper~\cite{Nyb91} on perfect nonlinearity and the $c$-differential notion we defined in~\cite{EFRST20}, in this paper we introduce the concept of $c$-differential bent functions in two different ways (thus extending Kumar et al.~\cite{Ku85} classical definition). We further extend the notion of perfect $c$-nonlinear introduced in~\cite{EFRST20}, also in two different ways, and show that, in both cases, the concepts of $c$-differential bent and perfect $c$-nonlinear are equivalent (under some natural restriction of the parameters). Some constructions of functions with these properties are also provided; one such construction provides a large class of PcN functions with respect to all $c$ in some subfield of the field under consideration. We also show that both our classes of $0$-differential bents are supersets of permutation polynomials, and that Maiorana-McFarland bent functions are not differential bent (of the first kind).Comment: 24 page

C -differential bent functions and perfect nonlinearity

17 USC 105 interim-entered record; under review.The article of record as published may be found at https://doi.org/10.1016/j.dam.2021.10.010Drawing inspiration from Nyberg’s paper (Nyberg, 1991) on perfect nonlinearity and the c-differential notion we defined in Ellingsen et al. (2020), in this paper we introduce the concept of c-differential bent functions in two different ways (thus extending Kumar et al. (1985) classical definition). We further extend the notion of perfect c-nonlinear introduced in Ellingsen et al. (2020), also in two different ways, and show that, in both cases, the concepts of c-differential bent and perfect c-nonlinear are equivalent (under some natural restriction of the parameters). Some constructions of functions with these properties are also provided; one such construction provides a large class of PcN functions with respect to all c in some subfield of the field under consideration. We also show that both our classes of 0-differential bents are supersets of permutation polynomials, and that Maiorana–McFarland bent functions are not differential bent (of the first kind).Pantelimon Stănică acknowledges the sabbatical support from Naval Postgraduate School from September 2020 to July 2021

A quantum algorithm to estimate the Gowers U2U_2 norm and linearity testing of Boolean functions

We propose a quantum algorithm to estimate the Gowers $U_2$ norm of a Boolean function, and extend it into a second algorithm to distinguish between linear Boolean functions and Boolean functions that are $\epsilon$-far from the set of linear Boolean functions, which seems to perform better than the classical BLR algorithm. Finally, we outline an algorithm to estimate Gowers $U_3$ norms of Boolean functions

Analysis of the Influence of Wind Turbines on the Power Line Protection Operation

In the article an experimental power system consisting of Russian equipment, as well as 220 kV power line distance protection, are simulated in the RTDS Simulator. The settings were calculated and the polygonal characteristics of distance protection were constructed. A sequential installation of wind turbines into various nodes of the power system was carried out and the correct operation of the protection was verified. As a result of the study, the influence of wind turbines on the distance protection when they are connected between the protection installation site and the point of the short circuit is revealed. The analysis of this influence is made. Possible ways to solve the identified problems are proposed, such as the use of adaptive distance protection, as well as numerous studies of the behavior of wind turbines in various operating modes for further analysis and possible adjustment of guidelines for relay protection using new algorithms for calculating and configuring of distance protection. The results of this work can be used to improve and clarify the recommendations for tuning, produced by manufacturers of relay protection devices, which currently do not take into account the influence of wind turbines

Analysis of the Influence of Wind Turbines on the Power Line Protection Operation

In the article an experimental power system consisting of Russian equipment, as well as 220 kV power line distance protection, are simulated in the RTDS Simulator. The settings were calculated and the polygonal characteristics of distance protection were constructed. A sequential installation of wind turbines into various nodes of the power system was carried out and the correct operation of the protection was verified. As a result of the study, the influence of wind turbines on the distance protection when they are connected between the protection installation site and the point of the short circuit is revealed. The analysis of this influence is made. Possible ways to solve the identified problems are proposed, such as the use of adaptive distance protection, as well as numerous studies of the behavior of wind turbines in various operating modes for further analysis and possible adjustment of guidelines for relay protection using new algorithms for calculating and configuring of distance protection. The results of this work can be used to improve and clarify the recommendations for tuning, produced by manufacturers of relay protection devices, which currently do not take into account the influence of wind turbines

Road monitoring system based on iot technology for SmartCity

This work is devoted to the problem of automatic road quality control, which can be used by both road repair services and common drivers. This paper provides a survey of different known techniques and algorithms of finding potholes on the road and describe our own method, using accelerometer. It will be shown our device for detecting potholes on the road, which can be used, as a part of the IoT system of SmartCity. It uses data from an accelerometer for finding road bumps

Circulating levels of Bcl-2 and its expression in the nasal mucosa of patients with chronic rhinosinusitis

Aim: To evaluate expression of anti-apoptotic Bcl-2 protein in the nasal tissue and its levels in blood serum of patients with chronic rhinosinusitis with (CRSwNP) and without nasal polyps (CRSsNP). Material and methods: Expression of Bcl-2 in the sinonasal tissue and its levels in blood serum of patients with CRSsNP and CRSwNP were evaluated immunohistochemically and using ELISA, respectively. Results: In patients with CRSsNP, Bcl-2 was overexpressed in nasal epithelial cells mainly in the atrophic regions. However, its upregulation was also observed in regions with epithelial cell proliferation. Immunostaining for Bcl-2 was stronger both in the stroma and epithelial lining compared with control subjects. The level of Bcl-2 in blood serum was elevated in both forms of chronic rhinosinusitis with a more pronounced increase in CRSwNP. Conclusion: CRSsNP and especially CRSwNP are associated with overexpression of anti-apoptotic Bcl-2 in nasal epithelial cells and in the lamina propria against the background of elevated circulating concentrations of Bcl-2

Investigation of the properties of magnetocaloric Mn1-xFexNiGe (0.05 ≤ x ≤ 0.30) films

MnNiGe-based solid solutions are currently positioned as “green” magnetocaloric materials, promising for use in magnetic refrigerators [1-3]. The magnetic behavior of the MnNiGe system is strongly dependent on doping, special heat treatment, pressure imposition, etc. One of the most important factors determining the magnetic behavior of the system is the state of the sample - film or massive. Твердые растворы на основе MnNiGe в настоящее время позиционируются как «зеленые» магнитокалорические материалы, перспективные для использования в магнитных холодильниках [1-3]. Магнитное поведение системы MnNiGe сильно зависит от легирования, специальной термообработки, давления и т. Д. Одним из наиболее важных факторов, определяющих магнитное поведение системы, является состояние образца - пленки или массива

Surface topography of the InSb-MnSb thin films

In that report we observe a semiconductor eutectic composite InSb-MnSb thin films, prepared by the "flash evaporation" method. The atomic force microscopy and the scanning electron microscopy were employed for investigation microstructure and surface relief of the InSb-MnSb thin films. В этом отчете мы наблюдаем за тонкими пленками полупроводникового электического композита InSb-MnSb, полученными методом «мгновенного испарения». С помощью атомно-силовой микроскопии и сканирующей электронной микроскопии исследованы микроструктура и рельеф поверхности тонких пленок InSb-MnSb