This paper has two parts. The first part surveys Euler’s work on the constant γ = 0.57721 · · · bearing his name, together with some of his related work on the gamma function, values of the zeta function, and divergent series. The second part describes various mathematical developments involving Euler’s constant, as well as another constant, the Euler–Gompertz constant. These developments inclu...

In this paper, we make Euler inequality, Chen first inequality and Chen-Ricci for non-integrable distributions in statistical manifolds with constant curvatures. Moreover, investigate the conditions equality cases.

(a) Show that for the solution x(t, x0) of the IVP with initial value x0 holds: ‖x(t, x0)‖ = ‖x(t0, x0)‖ . What is the geometric interpretation? Hint: Differentiate 1/2 ‖x(t)‖ and try to formulate the derivative as a scalar product! (b) Formulate an IVP in C (i.e. for complex-valued functions) equivalent (?) to the one in R in (a). (c) Consider now the numerical approximation x∆ to the IVP, whe...

The piecewise constant level set method (PCLSM) has recently emerged as a variant of the level set method for variational interphase problems. Traditionally, the Euler-Lagrange equations are solved by some iterative numerical method for PDEs. Normally the speed is slow. In this work, we focus on the piecewise constant level set method (PCLSM) applied to the multiphase Mumford-Shah model for ima...

For linear partial differential equations, there exist well-developed classical methods of their analytical solution, which, in particular, includes the separation of variables, different integral transforms, Fourier series and their generalizations. At the same time, the study of symmetry properties of such equations is important, first of all, for the development of methods of symmetry analys...

2014 We describe a continuous-flow cryostat system with spherical geometry and full 360° freedom of motion for all three Euler angles. The cryostat does not increase the dead angular zones of the Euler-cradle itself. Any sample temperature between 3 K and 300 K can be set and kept gradient-free and constant by a computer controlled temperature regulation. The time constant of the device is in t...

1. INTRODUCTION. Edge detection and the detection of discontinuities are important in many fields. In image processing, for example, one often needs to determine the boundaries of the items of which a picture is composed. (For more information about edge detection in image processing, see [10].) We consider the problem of detecting the edges present in a function when given the Fourier coeffici...

The main contribution of this paper is to propose a closed expression for the Ramanujan constant alternating series, based on Euler–Boole summation formula. Such an not present in literature. We also highlight only choice parameter formula proposed by Hardy series positive terms, so value obtained as agrees with other methods divergent series. Additionally, we derive closed-formula chosen, unde...