Let A be a 3D symmetric elasticity tensor not necessary isotropic. If μ is an invariant measure on SO(3), then μ is a convex combinaison of the Haar measure. The nearest isotropic elasticity tensor is obtained by integrating the tensor A on the rotation group SO(3). For the numerical approach, we integrate the elasticity tensor on the unit ordinary ball B(0, 1).
The main purpose of this paper is to construct a new class of second order differential equation at infinity. To solve the problem, we generate the auxiliary equation via a pre-auxiliary equation and obtain the general solution of it. We express the higher order of the differential equation in a matrix form. We have also studied the problem with a change in variable. We prove the sufficient condition of the solutions for the 2nd order differential equation under certain conditions for existence of the problem.
In this paper, we give some relations in terms of k- Balancing number which generalize some well known results concerning the relation between the determinant and Chebyshev polynomials which is due to tridiagonal matrix B(n)(k). Also for the other tridiagonal matrix W(n)(k); we deduce the cofactor matrix of it then we nd another relations for k- Balancing number.
By using xed point theorem we studied the mild solution of fractional integro- differential equations with non-local and impulsive conditions, also we studied the sucient conditions of controllability for this system.
Let∗ be an involution over some ring. In this note∗- skew polynomial rings over commutative rings are studied along with ∗- rigidity and ∗ - Armendariz property. Some interesting applications are demonstrated for uniserial rings.
In recent years, enhancement in wireless and mobile technologies, location based services (LBSs) has become more and more popular. Location based services provide enhanced functionalities, they open up new vulnerabilities that can be exploited to cause security and privacy breaches of mobile (wireless) users. Privacy of personal location information in location-based services of vehicular ad-hoc networks (VANETs) users (over road networks) is becoming an increasingly important issue. However, as vehicle users with mobile devices are highly autonomous and heterogeneous. So it is challenging to design generic location privacy protection techniques with desired level of protection. Therefore, here one big question arises “How to secure user’s privacy information must be taken into consideration”? Various approaches have been proposed to protect mobile user’s privacy, including his/her identity, location and so on. This paper reviews and analyzes existing privacy protection research works (according to goals, techniques, etc.) from an integrated perspective and discusses the challenges of securing privacy information. At last, our suggestions for future research work are presented.