Functions Fi Research Articles

Нелинейно-регрессионный алгоритм обработки сигналов полупроводниковых химических сенсоров, обеспечивающий селективное детектирование примесей в искусственном воздухе

New method is developed for proceeding a conductance change response Δσ,μS of a temperature (T) modulated chemical sensor. The method provides reliable substance identification and measurement of its trace concentrations for such impurities in arti-ficial air as ammonia, acetone, hexane, propane, toluene, turpentine etc. Due to this method the response of the ΔσY for a substance Y in actual concentration C range is interpolated with a completely nonlinear regression via discriminant modelling func-tions Fi(z=103/T,Ai, bi,ci,..),i=1-4 or 5. For principal parameters the plots AiY(C) are built which compose the selectivity/gauge portrait of Y in the air. In case when the analogous parameters of unknown substance X fit this portrait the substance is iden-tified as Y. And the common abscissa of corresponding crossing points of AiX with the curves AiY(C) indicates the value of the X concentration in units been used for Y.

Arithmetic constraints of polynomial maps through discrete logarithms

Let q be a prime power, let Fq be the finite field with q elements and let θ be a generator of the cyclic group Fq⁎. For each a∈Fq⁎, let logθ⁡a be the unique integer i∈{1,…,q−1} such that a=θi. Given polynomials P1,…,Pk∈Fq[x] and divisors 1<d1,…,dk of q−1, we discuss the distribution of the functionsFi:y↦logθ⁡Pi(y)(moddi), over the set Fq∖∪i=1k{y∈Fq|Pi(y)=0}. Our main result entails that, under a natural multiplicative condition on the pairs (di,Pi), the functions Fi are asymptotically independent. We also provide some applications that, in particular, relates to past work.

Improved KASUMI block cipher for GSM-based mobile networks

ABSTRACT KASUMI is an eight-round Feistel network that produces 64-bit output from 64-bit input by using 128-bit key. Three functions FL, FO and FI are involved in each round and each function has its respective keys KL, KO and KI . In this work, modifications in the existing KASUMI are proposed to reduce the encryption time. In proposed KASUMI, the single FL function is divided into two functions such as FLleft and FLright. The FLleft function is constructed with two Rijndael’s 32-bit S -boxes. The FLright function is constructed with four stages where third and fourth stages are performing XOR and shift operations before final concatenation of two 16-bit data of FL function. The simulation results are provided in terms of encryption time taken versus number of iteration and encryption speed versus number of iteration to show that the proposed KASUMI block cipher design outperforms the conventional KASUMI block cipher.

Some properties of multivalued positive Boolean dependencies in the database model of block form

Objectives: The article proposed a new type of dependency on blocks and slices. Then found and proved the properties of this new dependency. Method: Logical inference methods were used. Findings: A new type of data relationship has been proposed: Multivalued positive Boolean dependencies on block and slice in the database model of block form. From this new concept, the article stated and demonstrated the equivalence of the three types of deduction, namely: m-deduction by logic, m-deduction by block, m-deduction by block has no more than two elements. Next are the necessary and sufficient criteria of the tight m-expression for the set of multivalued positive Boolean dependencies on block and slice, the sufficient properties for a set of functions fI;^;_g. The properties related to this new concept when the block degenerated into relation. Novelty: The proposed new dependency with their properties on the block and on the slice are completely new. Keywords: Multivalued positive Boolean dependencies; block; Boolean dependencies; block schemes

One Approach to the Solution of Problems in Plasma Dynamics

A system of equations for the motion of an ionized ideal gas is considered. An algorithm for the reduction of this system of nonlinear partial differential equations (PDEs) to systems of ordinary differential equations (ODEs) is presented. It is shown that the independent variable ψ in the systems of ODEs is determined from the relation ψ = t + xf1(ψ) + yf2(ψ) + zf3(ψ) after choosing (setting or finding) the functions fi(ψ), i = 1, 2, 3. These functions are either found from the conditions of the problem posed for the original system of PDEs or are given arbitrarily to obtain a specific system of ODEs. For the problem on the motion of an ionized gas near a body, we write a system of ODEs and discuss the issue of instability, which is observed in a number of cases. We also consider a problem of the motion of flows (particles) in a given direction, which is of significant interest in some areas of physics. We find the functions fi(ψ), i = 1, 2, 3, that provide the motion of a flow of the ionized gas in a given direction and reduce the system of PDEs to a system of ODEs.

Asymptotics for some polynomial patterns in the primes

AbstractWe prove asymptotic formulae for sums of the form $$\sum\limits_{n\in {\open z}^d\cap K} {\prod\limits_{i = 1}^t {F_i} } (\psi _i(n)),$$where K is a convex body, each Fi is either the von Mangoldt function or the representation function of a quadratic form, and Ψ = (ψ1, …, ψt) is a system of linear forms of finite complexity. When all the functions Fi are equal to the von Mangoldt function, we recover a result of Green and Tao, while when they are all representation functions of quadratic forms, we recover a result of Matthiesen. Our formulae imply asymptotics for some polynomial patterns in the primes. For instance, they describe the asymptotic behaviour of the number of k-term arithmetic progressions of primes whose common difference is a sum of two squares.The paper combines ingredients from the work of Green and Tao on linear equations in primes and that of Matthiesen on linear correlations amongst integers represented by a quadratic form. To make the von Mangoldt function compatible with the representation function of a quadratic form, we provide a new pseudorandom majorant for both – an average of the known majorants for each of the functions – and prove that it has the required pseudorandomness properties.

Common belief in approximate rationality

This paper substitutes the standard rationality assumption with approximate rationality in normal form games. We assume that players believe that their opponents might be ε-rational, i.e. willing to settle for a suboptimal choice, and so give up an amount ε of expected utility, in response to the belief they hold. For every player i and every opponents’ degree of rationality ε, we require player i to attach at least probability Fi(ε) to his opponent being ε-rational, where the functions Fi are assumed to be common knowledge amongst the players. We refer to this event as belief in F-rationality. The notion of Common Belief in F-Rationality (CBFR) is then introduced as an approximate rationality counterpart of the established Common Belief in Rationality. Finally, a corresponding recursive procedure is designed that characterizes those beliefs players can hold under CBFR.

On a question of A. Kameyama concerning self-similar metrics

A. Kameyama introduced the concept of self-similar topological system and asked the following fundamental question: given a topological self-similar system (K,(fi)i∈{1,2,...,N}), does there exist a metric on K comparable to the topology such that all the functions fi are contractions? We modify Kameyama's question (which has a negative answer for an arbitrary topological self-similar system) by weakening the requirement that the functions in the topological self-similar system be contractions to requiring that they be φ-contractions. More precisely we give an affirmative answer to the following question: given a topological self-similar system (K,(fi)i∈{1,2,...,N}) does there exist a metric δ on K which is compatible with the original topology and a comparison function φ:[0,∞)→[0,∞) such that all the functions fi:(K,δ)→(K,δ) are φ-contractions? Consequently the iterated function system ((K,d),(fi)i∈{1,2,...,N}), where d is a metric on K compatible with the original topology on K, is φ-hyperbolic.

Exponential energy decay and blow-up of solutions for a system of nonlinear viscoelastic wave equations with strong damping

Abstract In this paper, we consider the system of nonlinear viscoelastic equations u t t - Δ u + ∫ 0 t g 1 ( t - τ ) Δ u ( τ ) d τ - Δ u t = f 1 ( u , v ) , ( x , t ) ∈ Ω × ( 0 , T ) , v t t - Δ v + ∫ 0 t g 2 ( t - τ ) Δ v ( τ ) d τ - Δ v t = f 2 ( u , v ) , ( x , t ) ∈ Ω × ( 0 , T ) with initial and Dirichlet boundary conditions. We prove that, under suitable assumptions on the functions g i , f i (i = 1, 2) and certain initial data in the stable set, the decay rate of the solution energy is exponential. Conversely, for certain initial data in the unstable set, there are solutions with positive initial energy that blow up in finite time. 2000 Mathematics Subject Classifications: 35L05; 35L55; 35L70.

Universality of Operator Ordering in Kinetic Energy Operator for Particles Moving on two Dimensional Surfaces

When the motion of a particle is constrained on the two-dimensional surface, excess terms exist in usual kinetic energy 1/(2m)∑ pi2 with hermitian form of Cartesian momentum pi (i = 1,2,3), and the operator ordering should be taken into account in the kinetic energy which turns out to be 1/(2m)∑ (1/fi)pifipi where the functions fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. The existence of non-trivial fi shows the universality of this constraint induced operator ordering in quantum kinetic energy operator for the constraint systems.

Quantum Motion on 2D Surfaces of Spherical Topology

When the motion of a particle is constrained on the two-dimensional surface, excess terms exist in usual kinetic energy 1/(2μ) ∑ pi2 with hermitian form of Cartesian momentum pi (i = 1,2,3), and the operator ordering should be taken into account in the kinetic energy which turns out to be 1/(2μ) ∑ (1/fi)pifipi where the functions fi are dummy factors in classical mechanics and nontrivial in quantum mechanics. In this article, the explicit forms of the dummy functions fi for quantum motion on some 2D surfaces of revolution of spherical topology are given.

The Existence and Uniqueness of Nash Equilibrium Point in an m-player Game “Shoot Later, Shoot First!”

We consider the following "silent duel" of m players with a possible economic interpretation. Each player has one "bullet", which she can shoot at any time during the time interval (0,1). The probability that the i-th player hits the "target" at moment t is given by an increasing accuracy function fi(t) .T he winner is the player who hits the target first. Under natural assumptions on the functions fi(t) we prove the existence and uniqueness of a Nash equilibrium point in this game, and we provide an explicit construction of this equilibrium. Thisconstructionallowsustoobtainexactsolutionsformanyspecificexamples. Some of them are presented.

Finite parametrization of solutions of equations in a free monoid. II

In the preceding paper of the author parametrizing functions Fi, Th, Ro were introduced depending on word variables, positive-integer variables, and variables whose values are finite sequences of positive-integer variables. With the help of the parametrizing functions Fi, Th, Ro finite formulae are written out for the family of solutions of every equation of the form , where and are arbitrary words in the alphabet , , in a free monoid.

REDUCTION OF DISCRETE DYNAMICAL SYSTEMS OVER GRAPHS

In this paper we study phase space relations in a certain class of discrete dynamical systems over graphs. The systems we investigate are called Sequential Dynamical Systems (SDSs), which are a class of dynamical systems that provide a framework for analyzing computer simulations. Specifically, an SDS consists of (i) a finite undirected graph Y with vertex set {1,2,…,n} where each vertex has associated a binary state, (ii) a collection of Y-local functions (Fi,Y)i∈ v [Y] with [Formula: see text] and (iii) a permutation π of the vertices of Y. The SDS induced by (i)–(iii) is the map [Formula: see text] The paper is motivated by a general reduction theorem for SDSs which guarantees the existence of a phase space embedding induced by a covering map between the base graphs of two SDSs. We use this theorem to obtain information about phase spaces of certain SDSs over binary hypercubes from the dynamics of SDSs over complete graphs. We also investigate covering maps over binary hypercubes, [Formula: see text], and circular graphs, Circ n. In particular we show that there exists a covering map [Formula: see text] if and only if 2n≡0 mod n+1. Furthermore, we provide an interpretation of a class of invertible SDSs over circle graphs as right-shifts of length n-2 over {0,1}2n-2. The paper concludes with a brief discussion of how we can extend a given covering map to a covering map over certain extended graphs.

Finite parametrization of solutions of equations in a free monoid. I

Complete solutions of all primitively parametrizable basis equations in a free monoid are written out. Parametrizing functions Fi, Th, Ro are introduced depending on word variables, positive integer variables, and variables whose values are finite sequences of positive-integer variables. Finite formulae for the family of solutions of all Fi-, Th-, Ro-parametrizable basis equations of the form in a free monoid are written out with the help of the parametrizing functions.

The Maximum Principle for a Hyperbolic Grid System and Its Applications

The extremum principle for one hyperbolic equation [namely, system (1) with n = 1] under some constraints on the coefficients and the solution class [1] was proved for the first time in [1]. The maximum principle for the absolute value |U(ξ, η)| = ( ∑n i=1 ui(ξ, η) 2) was studied in [2–4] for system (1) in some special cases. Important new extremal properties of solutions of system (1) were obtained in [5, 6]. In the present paper, we prove the maximum principle for the grid analog of system (1) and use it to prove the existence and uniqueness of the solution of the finite-difference counterpart of the Darboux problem. The finite-difference method was earlier used for the approximate solution of boundary value problems in [7–10]. To construct the grid domain, we split the interval AB into N = 2N1 equal parts and draw characteristics of system (1) through the partition points. We obtain a grid of square cells with mesh width h. The set of grid points belonging to ∆ (respectively, ∆) will be denoted by ∆h (respectively, ∆h). We number the points of ∆h as follows: first, we number the points lying on AC in ascending order of η : (0, 0), (0, 1), (0, 2), . . . , (0, N); then we number the points lying on the line ξ = h in the same order: (1, 1), (1, 2), . . . , (1, N), and so on. Throughout the following, we assume that the coefficients of system (1) and the functions fi are continuous in ∆. The value of a function at a grid point (k,m) is understood as the value at the point with coordinates (kh,mh). System (1) can be approximated at a grid point (k,m) ∈ ∆h by the system of finite-difference equations RiU(k,m) ≡ [(1 + aih+ bih) ui(k,m)− (1 + aih) ui(k − 1,m) − (1 + bih) ui(k,m− 1) + ui(k − 1,m− 1)]/h

On Acyclic Orientations and Sequential Dynamical Systems

We study a class of discrete dynamical systems that consists of the following data: (a) a finite (labeled) graph Y with vertex set {1,…,n}, where each vertex has a binary state, (b) a vertex labeled multi-set of functions (Fi,Y: F2n→F2n)i, and (c) a permutation π∈Sn. The function Fi,Y updates the binary state of vertex i as a function of the states of vertex i and its Y-neighbors and leaves the states of all other vertices fixed. The permutation π represents a Y-vertex ordering according to which the functions Fi,Y are applied. By composing the functions Fi,Y in the order given by π we obtain the sequential dynamical system (SDS):[FY,π]=Fπ(n),Y∘⋯∘Fπ(1),Y: F2n→F2n.In this paper we first establish a sharp, combinatorial upper bound on the number of non-equivalent SDSs for fixed graph Y and multi-set of functions (Fi,Y). Second, we analyze the structure of a certain class of fixed-point-free SDSs.

Elastic theory of 1D-quasiperiodic stacking of 2D crystals

A general solution of the elastic fields in 1D hexagonal quasicrystals withpoint groups 6mm, 62h2h, 6̅m2h and6/mhmm is given in terms of four `harmonic' functions Fi(i = 1,2,3,4). Then we consider the problem of a circular crack embedded in aninfinite 1D hexagonal quasicrystal of point group 6mm. The results obtainedin this paper automatically reduce to those in the classical elasticity theorywhen the phason field is absent.

Harmonic sums and mellin transforms

The finite and infinite harmonic sums form the general basis for the Mellin transforms of all individual functions fi(x) describing inclusive quantities such as coefficient and splitting functions which emerge in massless field theories. We discuss the mathematical structure of these quantities.

General solutions for coupled equations for piezoelectric media

Three general solutions are obtained for the coupled dynamic equations for a transversely isotropic piezoelectric medium. These solutions are expressed in terms of the two functions ψ and F, where ψ satisfies a second-degree partial differential equation and F a sixth-degree partial differential equation, respectively. If the terms concerning the derivatives of time are removed, the results become three general solutions for the corresponding equilibrium equations, in which the function F can be represented by functions Fi (i = 1, 2, 3), each of which satisfies a second-degree partial differential equation by utilizing a generalized Almansi theorem; and the solution Wang and Zheng [Int. J. Solids Structures32, 105–115 (1995)] obtained is proved to be consistent with one case of one of the three general solutions. When the constants e15 = e31 = e33 = 0 the piezo-electric coupling is absent; then, two of the solutions reduce to the elasticity general solutions for a transversely isotropie medium, one of which is the result Hu [Acta Scientia Sin.2(2), 145–151 (1953)] obtained; the other one has not been published. Last, the solution in the limiting explicit form for the problem for a half-space with concentrated loads at the boundary is obtained by utilizing the general solutions.