Efficient Expressive Attribute-Based Encryption with Keyword Search over Prime-Order Groups

Attribute-based encryption with keyword search(ABEKS)is a novel cryptographic paradigm that can be used to implementfine-grained access control and retrieve ciphertexts without disclosing the sensitive information.It is a perfect combination of attribute-based encryption(ABE)and public key encryption with keyword search(PEKS).Nevertheless,most of the existing ABEKS schemes have limited search capabilities and only support single or simple conjunctive keyword search.Due to the weak search capability and inaccurate search results,it is difficult to apply these schemes to practical applications.In this paper,an effi-cient expressive ABEKS(EABEKS)scheme supporting unbounded keyword uni-verse over prime-order groups is designed,which supplies the expressive keyword search function supporting the logical connectives of“AND”and“OR”.The proposed scheme not only leads to low computation and communica-tion costs,but also supports unbounded keyword universe.In the standard model,the scheme is proven to be secure under the chosen keyword attack and the cho-sen plaintext attack.The comparison analysis and experimental results show that it has better performance than the existing EABEKS schemes in the storage,com-putation and communication costs.

About Upper and Lower Strong Fractional Weighted Mean Convergence by Moduli for Triple Sequences

In article, I present a study on upper and lower statistical convergence, and upper and lower strong fractional weighted mean convergence by moduli for triple sequences. One of the generalizations of the discrete operator Cesàro, was weighted mean operators, which are linear operators, too. Given a modulus function f, I established that a triple sequence that is f-upper or lower strong fractional weighted mean convergent, in some supplementary conditions, is also f-lower or upper statistically convergent. The results of this paper adapt the results obtained in [1] and [2] to upper and lower strong fractional weighted mean convergence and to triple sequence concept. Furthermore, new concepts can be applied to the approximation theory, topology, Fourier analysis, analysis interdisciplinary with applications electrical engineering, robotics and other domains.

Unb ounded Motions in Asymmetric Oscillators Dep ending on Derivatives

In this paper, we consider the unboundedness of solutions for the asymmetric equation x00＋ax＋？bx？＋？（x）ψ（x0）＋f（x）＋g（x0）=p（t）, where x＋ = max{x, 0}, x？ = max{？x, 0}, a and b are two different positive constants, f （x） is locally Lipschitz continuous and bounded,？（x）, ψ（x）, g（x） and p（t） are continuous functions, p（t） is a 2π-periodic function. We discuss the existence of unbounded solutions under two classes of conditions： the resonance case √1a＋ √1b ∈Q and the nonresonance case√1a ＋ √1b /∈Q.

Approximate Kepler’s Elliptic Orbits with the Relativistic Effects

Beginning with a Lagrangian, we derived an approximate relativistic orbit equation which describes relativistic corrections to Keplerian orbits. The critical angular moment to guarantee the existence of periodic orbits is determined. An approximate relativistic Kepler’s elliptic orbit is illustrated by numerical simulation via a second-order perturbation method of averaging.

Data Secure Storage Mechanism of Sensor Networks Based on Blockchain

As the number of sensor network application scenarios continues to grow,the security problems inherent in this approach have become obstacles that hinder its wide application.However,it has attracted increasing attention from industry and academia.The blockchain is based on a distributed network and has the characteristics of non-tampering and traceability of block data.It is thus naturally able to solve the security problems of the sensor networks.Accordingly,this paper first analyzes the security risks associated with data storage in the sensor networks,then proposes using blockchain technology to ensure that data storage in the sensor networks is secure.In the traditional blockchain,the data layer uses a Merkle hash tree to store data;however,the Merkle hash tree cannot provide non-member proof,which makes it unable to resist the attacks of malicious nodes in networks.To solve this problem,this paper utilizes a cryptographic accumulator rather than a Merkle hash tree to provide both member proof and non-member proof.Moreover,the number of elements in the existing accumulator is limited and unable to meet the blockchain’s expansion requirements.This paper therefore proposes a new type of unbounded accumulator and provides its definition and security model.Finally,this paper constructs an unbounded accumulator scheme using bilinear pairs and analyzes its performance.

BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS FOR THE GENERALIZED DODD-BULLOUGH-MIKHAILOV EQUATION

In this paper, the generalized Dodd-Bullough-Mikhailov equation is studied. The existence of periodic wave and unbounded wave solutions is proved by using the method of bifurcation theory of dynamical systems. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given.Some exact explicit parametric representations of the above travelling solutions are obtained.

Random Attractors for Stochastic Reaction-Diffusion Equations with Distribution Derivatives on Unbounded Domains

In this paper, we prove the existence of random attractors for a stochastic reaction-diffusion equation with distribution derivatives on unbounded domains. The nonlinearity is dissipative for large values of the state and the stochastic nature of the equation appears spatially distributed temporal white noise. The stochastic reaction-diffusion equation is recast as a continuous random dynamical system and asymptotic compactness for this demonstrated by using uniform estimates far-field values of solutions. The results are new and appear to be optimal.

Homotopy Method for Non-convex Programming in Unbonded Set

In the past few years, much and much attention has been paid to the method for solving non-convex programming. Many convergence results are obtained for bounded sets. In this paper, we get global convergence results for non-convex programming in unbounded sets under suitable conditions.

THE ONE-SIDED HANDAMARD PRINCIPAL VALUE FOR SINGULAR-INTEGRALS OF HIGH ORDER AND ITS APPLICATIONS

0 IntroductionLet L = ab be a non-closed smooth arc oriented from a to b, t∈ L, t≠a,b, be the fixed point, andf(t) ∈H. (L) . The usual Hadamard principal value is defined asAbout properties and applications of singular integals of high order were investigated by many authors([1],[2],[3] etc. ) In 1987, the concepts of Hadamard principal value at one-side for singular integralsof high order and the rules of their differentiation are introduced [4]. In this paper we established the rulesof substitution of variable for one-sided Hadamard principal value of singular integrals of high order, andthen, we gave some applications in evaluation of real definite integrals.

ATTRACTORS FOR THE GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN

By the interpolating inequality and a priori estimates in the weighted space,the existence of the global solutions for the Ginzburg-Landau equation coupled with the BBM equation in an unbounded domain is considered, and the existence of the maximal attractor is obtained.

INFINITE ELEMENT METHOD FOR PROBLEMS ON UNBOUNDED AND MULTIPLY CONNECTED DOMAINS

The author studies the infinite element method for the boundary value problems of second order elliptic equations on unbounded and multiply connected domains. The author makes a partition of the domain into infinite number of elements. Without dividing the domain, as usual, into a bounded one and an exterior one, he derives an initial value problem of an ordinary differential equation for the combined stiffness matrix, then obtains the approximate solution with a small amount of computer work. Numerical examples are given.

Global Topological Linearization with Unbounded Nonlinear Term

In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, the above result was generalized to global under the condition that f(x) is a bounded function. In this paper, we delete the condition that f(x) is a bounded function, and prove that if f(x) has suitable structure, then x′=Ax+f(x) can be linearized.

ON SOLUTIONS OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS,WITH UNBOUNDED STOPPING TIMES AS TERMINAL AND WITH NON-LIPSCHITZ COEFFICIENTS,AND PROBABILISTIC INTERPRETATION OF QUASI-LINEAR ELLIPTIC TYPE INTEGRO-DIFFERENTIAL EQUATIO

The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of solutions and the continuous dependence of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi_linear elliptic type integro_differential equations is obtained.

Homotopy Continuous Method for Weak Efficient Solution of Multiobjective Optimization Problem with Feasible Set Unbounded Condition

In this paper, we propose a homotopy continuous method (HCM) for solving a weak efficient solution of multiobjective optimization problem (MOP) with feasible set unbounded condition, which is arising in Economical Distributions, Engineering Decisions, Resource Allocations and other field of mathematical economics and engineering problems. Under the suitable assumption, it is proved to globally converge to a weak efficient solution of (MOP), if its x-branch has no weak infinite solution.

Issues in the Influence of Ito-type Noise on the Oscillation of Solutions of Delay Differential Pantograph Equations

In this paper, a deterministic delay differential pantograph equation （DDPE） with an unbounded memory is stochastically perturbed by an Ito-type noise. The contribution of white noise to the oscillatory behaviour of the new stochastic delay differential pantograph equation （SDDPE） is investigated. It is established that under certain conditions and with a highly positive probability, the new stochastic delay differential pantograph equation has an oscillatory solution influenced by the presence of the noise. This is not possible with the original deterministic system which has a non-oscillatory solution due to the absence of noise.

On the Stable Method Computing Values of Unbounded Operators

Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a family of bounded operators to rough approximate data that do not necessarily lie within the domain of unbounded operator. In this paper we shall be concerned with the stable method of computing values of unbounded operators having perturbations and the stability is established for this method.

On the Method of Multiplier-enlargement and Approximation of Unbounded Continuous Functions

By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.

Error Analysis of ERM Algorithm with Unbounded and Non-Identical Sampling

A standard assumption in the literature of learning theory is the samples which are drawn independently from an identical distribution with a uniform bounded output. This excludes the common case with Gaussian distribution. In this paper we extend these assumptions to a general case. To be precise, samples are drawn from a sequence of unbounded and non-identical probability distributions. By drift error analysis and Bennett inequality for the unbounded random variables, we derive a satisfactory learning rate for the ERM algorithm.

THE EXISTENCE OF INFINITELY MANY SO UTIONS OF QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS IN UNBOUNDED DOMAINS

In this paper, we use the concentration-compactness principle together with the Mountain Pass Lemma to get the existence of nontrivial solutions and the existence of infinitely many solutions of the problem need not be compact operators from E to R~1.

BOUNDARY VALUE PROBLEMS FOR FULLY NONLINEAR UNIFORMLY ELLIPTIC EQUATIONS OF SECOND IN UNBOUNDED DOMAINS

We consider fully nonlinear equations of the formF（z,u,Du,D2u） = F（x,y,u,uz,uy,uzz,uzy,uyy） = 0 （1）in unbounded open subset G = R2\Ωof the plane R2,where F is a real continuous function on U = G×R×R2×R3 and Ω= Ωi,Ωi is a simply connected region （i=1,2,"",N） . We assume the function F hascontinuous partial der ivatives Fuzz, Fuzy, Fuyy. on U.For a real function r C（ G） a real function u（x,y） is called a solution of （1） satisfyingu = r on G,（2）if there exists a constant P0】2 such that u C1 （ ） W2.pLoc0 （G） satisfies （1） almost everywhere and （2）in the common sense.The method for treating the above exterior Dirichlet problem in a given unbounded region is as fol-