‎We show that for all normalized Hecke eigenforms $f$‎ ‎with weight one and of CM type‎, ‎the number $(f,f)$ where $(cdot‎, ‎cdot )$ denotes‎ ‎the Petersson inner product‎, ‎is a linear form in logarithms and‎ ‎hence transcendental‎.

the adhesion molecules are involved in adhesion of leukocytes to endothelial cells and other immune cells. not only adhesion molecules have membrane form, but they also have soluble form. in this paper, we attempted to investigate the concen¬tration of soluble adhesion molecules in the type 1 diabetic patients (n = 40) and healthy subjects (n = 10). the results indicated that there was an incre...

In this paper, a fuzzy version of the analytic form of Hahn-Banachextension theorem is given. As application, the Hahn-Banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

In this paper, we study linear fuzzy time-variant optimal control systems using the generalized differentiability concept and we present the general form of optimal controls and states. Some examples are provided to illustrate our results.

Fuzzy quasi-interpolations help to reduce the complexity of solving a linear system of equations compared with fuzzy interpolations. Almost all fuzzy quasi-interpolations are focused on the form of $widetilde{f}^{*}:mathbb{R}rightarrow F(mathbb{R})$ or $widetilde{f}^{*}:F(mathbb{R})rightarrow mathbb{R}$.  In this paper, we intend to offer a novel fuzzy radial basis function by the concept of so...

In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than sol...

The general linear quaternion function of degree one is a sum of terms with quaternion coefficients on the left and right. The paper considers the canonic form of such a function, and builds on the recent work of Todd Ell, who has shown that any such function may be represented using at most four quaternion coefficients. In this paper, a new and simple method is presented for obtaining these co...

 Background: Background and Objectives: The biological variation of body mass index (BMI) and waist circumference (WC) with age may vary by gender. The objective of this study was to investigate the functional relationship of anthropometric measures with age and sex.Methods: The data were collected from a population-based cross-sectional study of 1800 men and 1800 women aged 20-70 years in...

Abstract. It is shown how Andrews’ multidimensional extension of Watson’s transformation between a very-well-poised 8φ7-series and a balanced 4φ3-series can be used to give a straightforward proof of a conjecture of Zudilin and the second author on the arithmetic behaviour of the coefficients of certain linear forms of 1 and Catalan’s constant. This proof is considerably simpler and more stream...