In 1978, Rivest, Adleman and Dertouzos asked for algebraic systems for which useful privacy homomorphisms exist. To date, the only acknownledged result is noise based encryption combined with bootstrapping. Before that, there were several failed attempts. We prove that fully homomorphic schemes are impossible for several algebraic structures. Then we develop a characterisation of all fully homo...

Let I[f ] = ∫ 1 −1 f(x) dx, where f ∈ C ∞(−1, 1), and let Gn[f ] = ∑n i=1 wnif(xni) be the n-point Gauss–Legendre quadrature approximation to I[f ]. In this paper, we derive an asymptotic expansion as n → ∞ for the error En[f ] = I[f ]−Gn[f ] when f(x) has general algebraic-logarithmic singularities at one or both endpoints. We assume that f(x) has asymptotic expansions of the forms f(x) ∼ ∞ ∑ ...

A wide variety of scientiic settings involve indirect noisy measurements where one faces a linear inverse problem in the presence of noise. Primary interest is in some function f(t) but the data is accessible only about some transform (Kf)(t), where K is some linear operator, and (Kf)(t) is in addition corrupted by noise. The usual linear methods for such inverse problems, for example those bas...

Fragmin/protamine nanoparticles (F/P NPs) have been used as carriers for the preservation and controlled release of fibroblast growth factor (FGF)-2 and various cytokines in human plasma (HP). This study tested an HP-Dulbecco's modified Eagle's medium (DMEM) gel as a three-dimensional (3D) culture for the expansion of adipose tissue-derived multilineage stromal cells (ASCs) and bone marrow-deri...

the aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. the method is a combination of the asymptotic expansion technique and the reproducing kernel method (rkm). first an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. then the reduced regular delayed diffe...

BACKGROUND Automatic extracting protein entity interaction information from biomedical literature can help to build protein relation network and design new drugs. There are more than 20 million literature abstracts included in MEDLINE, which is the most authoritative textual database in the field of biomedicine, and follow an exponential growth over time. This frantic expansion of the biomedica...

Based on the traveling wave reduction method with a perturbed initial solution and F-expansion method, class of explicit exact solutions (2+1)-dimensional CDGKS equation are obtained through symbolic computation. Moreover, both interaction behavior between parameters perturbation degree periodic Gauss to rational pulse wave, correlation superposition energy solitary discussed. Finally, numerica...

Avram Sidi Computer Science Department, Technion – Israel Institute of Technology, Haifa 32000, Israel E-mail: [email protected]; URL: http://www.cs.technion.ac.il/~asidi/ Abstract. Let ∑∞ n=0 en[f ]Pn(x) be the Legendre expansion of a function f (x) on (−1, 1). In this work, we derive an asymptotic expansion as n → ∞ for en[f ], assuming that f ∈ C∞(−1, 1), but may have arbitrary algebra...

A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method provides a more systematical and convenient handling of the solution process of nonlinear equations, unifying the tanhfunction type methods, the homogeneous balance method, the exp-function method, the mapping method, and the F-expansion type m...