Structural Evaluation by Generalized Integral Property

In this paper, we show structural cryptanalyses against two popular networks, i.e., the Feistel Network and the Substitute-Permutation Network (SPN). Our cryptanalyses are distinguishing attacks by an improved integral distinguisher. The integral distinguisher is one of the most powerful attacks against block ciphers, and it is usually constructed by evaluating the propagation characteristic of integral properties, e.g., the ALL or BALANCE property. However, the integral property does not derive useful distinguishers against block ciphers with non-bijective functions and bit-oriented structures. Moreover, since the integral property does not clearly exploit the algebraic degree of block ciphers, it tends not to construct useful distinguishers against block ciphers with low-degree functions. In this paper, we propose a new property called {\it the division property}, which is the generalization of the integral property. It can effectively construct the integral distinguisher even if the block cipher has non-bijective functions, bit-oriented structures, and low-degree functions. From viewpoints of the attackable number of rounds or chosen plaintexts, the division property can construct better distinguishers than previous methods. Although our attack is a generic attack, it can improve several integral distinguishers against specific cryptographic primitives. For instance, it can reduce the required number of chosen plaintexts for the 10-round distinguisher on Keccak-f from $2^{1025}$ to $2^{515}$. For the Feistel cipher, it theoretically proves that Simon 32, 48, 64, 96, and 128 have 9-, 11-, 11-, 13-, and 13-round integral distinguishers, respectively

A Study on Green Economy Indicators and Modeling: Russian Context

This article aims to assess and forecast the dynamics of a regional green economy. The research relevance is determined by the need to develop theoretical and methodological basis of the green economy for the transition period and to identify criteria basis for assessing the state and regional level of it. The authors applied the modern methods, which allowed to model criteria considering data uncertainty and both static and dynamic criteria. The research process involved the methods of scientific analysis, comparison and synthesis, the theory of fuzzy sets, and fuzzy modeling. The main principles and methodology of the criteria evaluation for a regional green economy are proposed. The principal methodological approach in this research combines the current state and dynamics of the green economy in evaluating and forecasting the conditions of data uncertainty. The research results form a theoretical, methodological, and practical basis for assessing the current state and level of a regional green economy development, determining the effectiveness of environmental and economic programs, optimizing financial management, conducting environmental monitoring, and developing state plans.The research was funded by the grant of the Ministry of Education and Science of the Russian Federation to Perm National Research Polytechnic University # 26.6884.2017/8.9 "Sustainable development of urban areas and the improvement of the human environment.

A Study on Green Economy Indicators and Modeling: Russian Context

This article aims to assess and forecast the dynamics of a regional green economy. The research relevance is determined by the need to develop theoretical and methodological basis of the green economy for the transition period and to identify criteria basis for assessing the state and regional level of it. The authors applied the modern methods, which allowed to model criteria considering data uncertainty and both static and dynamic criteria. The research process involved the methods of scientific analysis, comparison and synthesis, the theory of fuzzy sets, and fuzzy modeling. The main principles and methodology of the criteria evaluation for a regional green economy are proposed. The principal methodological approach in this research combines the current state and dynamics of the green economy in evaluating and forecasting the conditions of data uncertainty. The research results form a theoretical, methodological, and practical basis for assessing the current state and level of a regional green economy development, determining the effectiveness of environmental and economic programs, optimizing financial management, conducting environmental monitoring, and developing state plans.The research was funded by the grant of the Ministry of Education and Science of the Russian Federation to Perm National Research Polytechnic University # 26.6884.2017/8.9 "Sustainable development of urban areas and the improvement of the human environment.

Wiener-Hopf solution for impenetrable wedges at skew incidence

A new Wiener-Hopf approach for the solution of impenetrable wedges at skew incidence is presented. Mathematical aspects are described in a unified and consistent theory for angular region problems. Solutions are obtained using analytical and numerical-analytical approaches. Several numerical tests from the scientific literature validate the new technique, and new solutions for anisotropic surface impedance wedges are solved at skew incidence. The solutions are presented considering the geometrical and uniform theory of diffraction coefficients, total fields, and possible surface wave contribution

Asymptotic and structural properties of special cases of the Wright function arising in probability theory

This analysis paper presents previously unknown properties of some special cases of the Wright function whose consideration is necessitated by our work on probability theory and the theory of stochastic processes. Specifically, we establish new asymptotic properties of the particular Wright function 1Ψ1(ρ, k; ρ, 0; x) = X∞ n=0 Γ(k + ρn) Γ(ρn) x n n! (|x| <∞) when the parameter ρ ∈ (−1, 0)∪(0, ∞) and the argument x is real. In the probability theory applications, which are focused on studies of the Poisson-Tweedie mixtures, the parameter k is a non-negative integer. Several representations involving well-known special functions are given for certain particular values of ρ. The asymptotics of 1Ψ1(ρ, k; ρ, 0; x) are obtained under numerous assumptions on the behavior of the arguments k and x when the parameter ρ is both positive and negative. We also provide some integral representations and structural properties involving the ‘reduced’ Wright function 0Ψ1(−−; ρ, 0; x) with ρ ∈ (−1, 0) ∪ (0, ∞), which might be useful for the derivation of new properties of members of the power-variance family of distributions. Some of these imply a reflection principle that connects the functions 0Ψ1(−−;±ρ, 0; ·) and certain Bessel functions. Several asymptotic relationships for both particular cases of this function are also given. A few of these follow under additional constraints from probability theory results which, although previously available, were unknown to analysts

Perturbative Construction of Models of Algebraic Quantum Field Theory

We review the construction of models of algebraic quantum field theory by renormalized perturbation theory.Comment: 38 page

The evolution of vibrational excitations in glassy systems

The equations of the mode-coupling theory (MCT) for ideal liquid-glass transitions are used for a discussion of the evolution of the density-fluctuation spectra of glass-forming systems for frequencies within the dynamical window between the band of high-frequency motion and the band of low-frequency-structural-relaxation processes. It is shown that the strong interaction between density fluctuations with microscopic wave length and the arrested glass structure causes an anomalous-oscillation peak, which exhibits the properties of the so-called boson peak. It produces an elastic modulus which governs the hybridization of density fluctuations of mesoscopic wave length with the boson-peak oscillations. This leads to the existence of high-frequency sound with properties as found by X-ray-scattering spectroscopy of glasses and glassy liquids. The results of the theory are demonstrated for a model of the hard-sphere system. It is also derived that certain schematic MCT models, whose spectra for the stiff-glass states can be expressed by elementary formulas, provide reasonable approximations for the solutions of the general MCT equations.Comment: 50 pages, 17 postscript files including 18 figures, to be published in Phys. Rev.