Some results on Riccati equations,Floquet theory and applications

In this paper, we present two new results to the classical Floquet theory, which provides the Floquet multipliers for two classes of the planar periodic system. One of these results provides the Floquet multipliers independently of the solution of system. To demonstrate the application of these analytical results, we consider a cholera epidemic model with phage dynamics and seasonality incorporated.     

New results in the theory of multivalued mappings. II. Analysis and applications

This is the second part of a survey by Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkins, and V. V. Obukhovskii on new results in the field of analysis of multivalued mappings and their applications during the 1980's.Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 29, pp. 107–159, 1991.     

New additive results on Drazin inverse and its applications

In this paper, the Drazin inverse of certain sums and block triangular matrices are presented.     

New and old results in resultant theory

Resultants play an increasingly important role in modern theoretical physics: they appear whenever we have nonlinear (polynomial) equations, nonquadratic forms, or non-Gaussian integrals. Being a research subject for more than three hundred years, resultants are already quite well studied, and many explicit formulas, interesting properties, and unexpected relations are known. We present a brief overview of these results, from classical ones to those obtained relatively recently. We emphasize explicit formulas that could bring practical benefit in future physical research.     

Recent results in the theory and applications of CARMA processes

Just as ARMA processes play a central role in the representation of stationary time series with discrete time parameter, \((Y_n)_{n\in \mathbb {Z}}\) , CARMA processes play an analogous role in the representation of stationary time series with continuous time parameter, \((Y(t))_{t\in \mathbb {R}}\) . Lévy-driven CARMA processes permit the modelling of heavy-tailed and asymmetric time series and incorporate both distributional and sample-path information. In this article we provide a review of the basic theory and applications, emphasizing developments which have occurred since the earlier review in Brockwell (2001a, In D. N. Shanbhag and C. R. Rao (Eds.), Handbook of Statistics 19; Stochastic Processes: Theory and Methods (pp. 249–276), Amsterdam: Elsevier).     

New results and applications for multi-secret sharing schemes

In a multi-secret sharing scheme (MSSS), \(\ell \) different secrets are distributed among the players in some set \(\mathcal{P }=\{P_1,\ldots ,P_n\}\) , each one according to an access structure. The trivial solution to this problem is to run \(\ell \) independent instances of a standard secret sharing scheme, one for each secret. In this solution, the length of the secret share to be stored by each player grows linearly with \(\ell \) (when keeping all other parameters fixed). Multi-secret sharing schemes have been studied by the cryptographic community mostly from a theoretical perspective: different models and definitions have been proposed, for both unconditional (information-theoretic) and computational security. In the case of unconditional security, there are two different definitions. It has been proved that, for some particular cases of access structures that include the threshold case, a MSSS with the strongest level of unconditional security must have shares with length linear in \(\ell \) . Therefore, the optimal solution in this case is equivalent to the trivial one. In this work we prove that, even for a more relaxed notion of unconditional security, and for some kinds of access structures (in particular, threshold ones), we have the same efficiency problem: the length of each secret share must grow linearly with \(\ell \) . Since we want more efficient solutions, we move to the scenario of MSSSs with computational security. We propose a new MSSS, where each secret share has constant length (just one element), and we formally prove its computational security in the random oracle model. To the best of our knowledge, this is the first formal analysis on the computational security of a MSSS. We show the utility of the new MSSS by using it as a key ingredient in the design of two schemes for two new functionalities: multi-policy signatures and multi-policy decryption. We prove the security of these two new multi-policy cryptosystems in a formal security model. The two new primitives provide similar functionalities as attribute-based cryptosystems, with some advantages and some drawbacks that we discuss at the end of this work.     

New approach for weighted pseudo-almost periodic functions under the light of measure theory,basic results and applications

The aim of this work is to present new approach to study weighted pseudo almost periodic functions using the measure theory. We present a new concept of weighted ergodic functions which is more general than the classical one. Then we establish many interesting results on the functional space of such functions like completeness and composition theorems. The theory of this work generalizes the classical results on weighted pseudo almost periodic functions. For illustration, we provide some applications for evolution equations which include reaction diffusion systems and partial functional differential equations.     

New global distributions in number theory and their applications

Consideration of an example corresponding to the partition of integers results in revision of certain physical concepts. A substantial term is added to the Bose–Einstein distribution. The notion of “fractional dimension” is introduced. Some effects considered earlier as pure quantum effects are explained from the classical standpoint. A distribution depending on three fixed points is given.     

New results on value functions and applications to MaxSup and MaxInf problems

In this paper, in the setting of sequential spaces, we consider the value functions v_S and v_I defined by v_S(x)=sup_y∈K(x)f(x,y) and v_I(x)=inf_y∈K(x)f(x,y), and we introduce sufficient conditions on the value functions and on the data, weaker than upper semicontinuity, which guarantee the existence of maximum for such functions. Various examples illustrate the results and the connections with previous results.     

New comparison results for impulsive integro-differential equations and applications

We prove some new maximum principles for ordinary integro-differential equations. This allows us to introduce a new definition of lower and upper solutions which leads to the development of the monotone iterative technique for a periodic boundary value problem related to a nonlinear first-order impulsive integro-differential equation.     

New results on applications of Nevanlinna methods to value sharing problems

Let $\mathbb{K}$ be a complete algebraically closed p-adic field of characteristic zero. We give a new Nevanlinna-type theorem that lets us obtain results of uniqueness for two meromrphic functions inside a disk, sharing 4 bounded functions CM. Let P be a polynomial of uniqueness for meromorphic functions in $\mathbb{K}$ or in an open disk, let f, g be two transcendental meromorphic functions in the whole field $\mathbb{K}$ or meromorphic functions in an open disk of $\mathbb{K}$ that are not quotients of bounded analytic functions and let α be a small meromorphic function with respect to f and g. We apply results in algebraic geometry and a new Nevanlinna theorem for p-adic meromorphic functions in order to prove a result of uniqueness for functions: we show that if f′P′(f) and g′P′(g) share α counting multiplicity, then f = g, provided that the multiplicity order of zeros of P′ satisfy certain inequalities. A breakthrough in this paper consists of replacing inequalities n ≥ k + 2 or n ≥ k + 3 used in previous papers by a new Hypothesis (G). Another consists of using the new Nevanlinna-type Theorem.     

Application of averaging techniques to traffic flow theory

Real traffic data are very versatile and are hard to explain with the so‐called standard fundamental diagram. A simple microscopic model can show that the heterogeneity of traffic results in a reduced mean flow and that the reduction is proportional to the density variance. Standard averaging techniques allow us to evaluate this reduction without having to describe the complex microscopic interactions. Using a second equation for the variance results in a two‐dimensional hyperbolic system that can be put in conservative form. The Riemann problem is completely solved in the case of a parabolic fundamental diagram, and the solutions are compared with the famous second‐order Aw–Rascle–Zhang model in a simulation of lane reduction. Adding a diffusion term results in entropy production, and the diffusive model is studied as well. Finally, a numerical scheme is used and converges to the analytical solution. Copyright © 2016 John Wiley & Sons, Ltd.     

Measure theory and pseudo almost automorphic functions: New developments and applications

In this work, we establish a new concept of weighted pseudo almost automorphic functions using the measure theory. We present new results on weighted ergodic functions like completeness and composition theorems. The theory of this work generalizes the classical results on weighted pseudo almost periodic and automorphic functions. For illustration, we provide some applications for evolution equations which include reaction-diffusion systems and partial functional differential equations.     

New results in subdifferential calculus with applications to convex optimization

Chain and addition rules of subdifferential calculus are revisited in the paper and new proofs, providing local necessary and sufficient conditions for their validity, are presented. A new product rule pertaining to the composition of a convex functional and a Young function is also established and applied to obtain a proof of Kuhn-Tucker conditions in convex optimization under minimal assumptions on the data. Applications to plasticity theory are briefly outlined in the concluding remarks.The financial support of the Italian Ministry for University and Scientific and Technological Research is gratefully acknowledged.     

Overview of some new results concerning the theory and applications of the Rayleigh special function

The author’s previous work provided a detailed overview of the results concerning the theory and applications of the Rayleigh special function starting from its appearance in science until recent years. Its numerous applications in various areas of mathematics, physics, and other fields were described, and an extensive bibliography was presented. This work overviews the studies not covered in the previous one and addresses new results published in many monographs and journals. Additionally, results concerning the estimation of zeros of some special polynomials and functions closely related to the Rayleigh function are described. The overview embraces the issues addressed in the scientific literature up to the last years. Dedicated to the memory of Academician A.A. Samarskii, my teacher and friend. The text was submitted by the author in English.