Anonymous and leakage resilient IBE and IPE

We construct identity-based encryption and inner product encryption schemes under the decision linear assumption. Their private user keys are leakage-resilient in several scenarios. In particular,

• In the bounded memory leakage model (Akavia et al., TCC, vol. 5444, pp. 474–495, 2009), our basic schemes reach the maximum-possible leakage rate \(1-o(1)\).
• In the continual memory leakage model (Brakerski et al., Overcoming the hole in the bucket: public-key cryptography resilient to continual memory leakage, 2010; Dodis et al., Cryptography against continuous memory attacks, 2010), variants of the above schemes enjoy leakage rate at least \(\frac{1}{2} -o(1)\). Among the results, we improve upon the work of Brakerski et al. by presenting adaptively secure IBE schemes.

In addition, we prove that our IBE schemes are anonymous under the DLIN assumption, so that ciphertexts leaks no information on the corresponding identities. Similarly, attributes in IPE are proved computationally hidden in the corresponding ciphertexts.

     

On the period function in a class of generalized Lotka-Volterra systems

In this note, motivated by the recent results of Wang et al. [Wang et al., Local bifurcations of critical periods in a generalized 2D LV system, Appl. Math. Comput. 214 (2009) 17-25], we study the behaviour of the period function of the center at the point (1,1) of the planar differential system

     

Growup of solutions for a semilinear heat equation with supercritical nonlinearity

We consider a Cauchy problem for a semilinear heat equation

(P)     

Multiple blowup of solutions for a semilinear heat equation II

The present paper is concerned with a Cauchy problem for a semilinear heat equation

(P)     

Various behaviors of solutions for a semilinear heat equation after blowup

The present paper is concerned with a Cauchy problem for a semilinear heat equation

(P)     

Dynamics of a stochastic Lotka-Volterra model perturbed by white noise

This paper continues the study of Mao et al. investigating two aspects of the equation

     

Blowup behavior of solutions for a semilinear heat equation with supercritical nonlinearity

This paper is concerned with blowup phenomena of solutions for the Cauchy and the Cauchy-Dirichlet problem of

(P)     

Nonoscillation and positivity of solutions to first order state-dependent differential equations with impulses in variable moments

The state-dependent delay differential equation

     

Composite structure of global unbounded solutions of nonlinear heat equations with critical Sobolev exponents

We describe special asymptotic structures of solutions of the semilinear heat equation

     

Semilinear reaction-diffusion systems of several components

The homogeneous Dirichlet boundary value problem

     

Nonexistence of type II blowup solution for a semilinear heat equation

A solution u of a Cauchy problem for a semilinear heat equation

     

Zeros of a Certain Class of Gauss Hypergeometric Polynomials

We prove that as n → ∞, the zeros of the polynomial

$$_2 F_1 \left[ {\begin{array}{*{20}c}{ - n,\alpha n + 1} \\{\alpha n + 2} \\\end{array} ;z} \right]$$

cluster on (a part of) a level curve of an explicit harmonic function. This generalizes previous results of Boggs, Driver, Duren et al. (1999–2001) to the case of a complex parameter α and partially proves a conjecture made by the authors in an earlier work.

     

A High-Order <Emphasis Type="Italic">B</Emphasis>-Spline Collocation Method for Solving Nonlinear Singular Boundary Value Problems Arising in Engineering and Applied Science

In this paper, a high-order B-spline collocation method on a uniform mesh is presented for solving nonlinear singular two-point boundary value problems with Neumann and Robin boundary conditions:

$$\begin{aligned} (p(x)y')'= & {} p(x)f(x,y), \quad 0<x\le 1, \\ y'(0)= & {} 0,\quad ay(1)+by'(1)=c, \end{aligned}$$

where \(p(x)=x^{\alpha }g(x),\alpha \ge 0\) is a general class of non-negative function. The error analysis for the quartic B-spline interpolation is discussed. To demonstrate the applicability and efficiency of our method we consider eight numerical examples, seven of which arise in various branches of applied science and engineering: (1) equilibrium of isothermal gas sphere; (2) thermal explosion; (3) thermal distribution in the human head; (4) oxygen diffusion in a spherical cell; (5) stress distribution on shallow membrane cap; (6) reaction diffusion process in a spherical permeable catalyst; (7) heat and mass transfer in a spherical catalyst. It is shown that our method has fourth-order convergence and is more accurate than finite difference methods (Chawla et al., in BIT 28:88–97, 1988; Pandey et al. in J Comput Appl Math 224:734–742, 2009) and B-spline collocation methods (Abukhaled et al. in Int J Numer Anal Model 8:353–363, 2011; Khuri and Sayfy in Int J Comput Methods 11(1):1350052, 2014).

     

Analytic mappings between noncommutative pencil balls

In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analytic functions) defined by power series in noncommuting variables and evaluate these functions on sets of matrices of all dimensions; we call such situations dimension-free. These types of functions have recently been used in the study of dimension-free linear system engineering problems (Helton et al. (2009) [10], de Oliviera et al. (2009) [8]). In the earlier paper (Helton et al. (2009) [9]) we characterized NC analytic maps that send dimension-free matrix balls to dimension-free matrix balls and carry the boundary to the boundary; such maps we call “NC ball maps”. In this paper we turn to a more general dimension-free ball BL, called a “pencil ball”, associated with a homogeneous linear pencil

     

Homogenization limit of a parabolic equation with nonlinear boundary conditions

Consider the parabolic equation

(E)     

Large-time geometric properties of solutions of the evolution p-Laplacian equation

We establish the behavior of the solutions of the degenerate parabolic equation

     

Blow up rate for a porous medium equation with power nonlinearity

The present paper is concerned with the blow up rate of a solution to the following Cauchy problem

     

Superstability and rigorous asymptotics in singularly perturbed state-dependent delay-differential equations

We study the singularly perturbed state-dependent delay-differential equation

(?)     

On the validity of the Euler-Lagrange equation in a nonlinear case

We prove the validity of the Euler-Lagrange equation for the class of functionals of the type

     

On source-type solutions and the Cauchy problem for a doubly degenerate sixth-order thin film equation, I: Local oscillatory properties

As a key example, the sixth-order doubly degenerate parabolic equation from thin film theory,