Operationally, index functions of variable Hilbert scales can be viewed as generators for families of spaces and norms and, thereby, associated scales of interpolatory inequalities. Using one parameter families of index functions based on the dilations of given index functions, new classes of interpolatory inequalities, dilational interpolatory inequalities (DII), are constructed. They have ord...

Traditional encryption schemes, both symmetric and asymmetric, were not designed to respect the algebraic structure of the plaintext and ciphertext spaces. Many schemes, such as Elgamal (resp. e.g. Paillier), are multiplicatively homomorphic (resp. additively homomorphic), so that one can perform certain limited types of computations directly on the encrypted data and have them pass through the...

We propose a general framework to develop fully homomorphic encryption schemes (FHE) without using Gentry’s technique. Initially, a private-key cryptosystem is built over Zn (n being an RSA modulus). An encryption of x ∈ Zn is a randomly chosen vector e such that Φ(e) = x where Φ is a secret multivariate polynomial. This private-key cryptosystem is not homomorphic in the sense that the vector s...

Introduction Several deconvolution methods have been proposed to increase the angular resolution of HARDI or QBI [1][2]. However, there is no deconvolution method directly applied to diffusion ODF without resorting to spherical decomposition. In this study, we developed a deconvolution method that could be directly applied to diffusion ODF, thus extending its applicability to other q-space meth...

Introduction: Renal dynamic study is a well-established and popular test in routine practice of nuclear medicine. The test is non-invasive, rapid and unique in evaluation of the kidney function. In despite of its clinical values, the parameters derived from renogram are physiologically meaningless. That is due to the fact that renogram is not the true kidney function. From mathematical po...