In this paper, by introducing four parameters A,B,?,? and using the Euler-Maclaurin expansion for Riemann zeta function, we establish an inequality of a weight coefficient. Using inequality, derive generalizations Hilbert?s type inequality.

Design methods of adaptive H∞ formation control of multi-agent systems composed of Euler-Lagrange systems by utilizing neural network approximators are presented in this paper. The proposed control schemes are derived as solutions of certain H∞ control problems, where estimation errors of tuning parameters, error terms in potential functions, and approximate and algorithmic errors in neural net...

This paper presents closed form solutions for the inverse and direct dynamic models of the Gough-Stewart parallel robot. The models are obtained in terms of the Cartesian dynamic model elements of the legs and of the Newton-Euler equation of the platform. The final form has an interesting and intuitive physical interpretation. The base inertial parameters of the robot, which constitute the mini...

Thermal buckling behavior of functionally graded Euler-Bernoulli beams in thermal conditions is investigated analytically. The beam with material and thermal properties dependent on the temperature and position is considered. Based on the transformed-section method, the functionally graded beam is considered as an equivalent homogeneous Euler-Bernoulli beam with an effective bending rigidity un...

One of the simplest and, at the same time, most important invariants of a topological space is the Euler characteristic. A generalization of the notion of the Euler characteristic to the equivariant setting, that is, to spaces with an action of a group (say, finite) is far from unique. An equivariant analogue of the Euler characteristic can be defined as an element of the ring of representation...

Nonlocally related systems for the Euler and Lagrange systems of twodimensional dynamical nonlinear elasticity are constructed. Using the continuity equation, i.e., conservation of mass of the Euler system to represent the density and Eulerian velocity components as the curl of a potential vector, one obtains the Euler potential system that is nonlocally related to the Euler system. It is shown...

Recently the new q-Euler numbers and polynomials related to Frobenius-Euler numbers and polynomials are constructed by Kim (see[3]). In this paper, we study the generalized q-Euler numbers and polynomials attached to χ related to the new q-Euler numbers and polynomials which is constructed in [3]. Finally, we will derive some interesting congruence on the generalized q-Euler numbers and polynom...

We investigate the equilibrium configurations of closed planar elastic curves fixed length, whose stiffness, also known as bending rigidity, depends on an additional density variable. The underlying variational model relies minimisation a energy with respect to shape and can be considered one-dimensional analogue Canham–Helfrich for heterogeneous biological membranes. present generalised Euler–...

We consider the Euler–Darboux equation with parameters such that their absolute values are equal to $$ \frac{1}{2} . Since Cauchy problem in classical formulation is ill-posed for of parameters, we propose formulations and solutions modified Cauchy-type problems following parameters: (a) \alpha =\beta =\frac{1}{2}; (b) =-\frac{1}{2}\ \mathrm{and}\ \beta (c) =-\frac{1}{2}. In case (a), solved by...

The theory of domination in graphs is an emerging area of research in graph theory today. It has been studied extensively and finds applications to various branches of Science & Technology.Products are often viewed as a convenient language with which one can describe structures, but they are increasingly being applied in more substantial ways. In this paper, we consider lexicographic product gr...