In this paper we consider the generalized Jacobsthal Jn,m and Jacobsthal-Lucas numbers jn,m. Also, introduce new sequences of An,m, Bn,m, Cn,m Dn,m. Namely, these are convolutions Further, find generating functions some recurrence relations for numbers.

We establish abstract inequalities that give, as particular cases, many previously established Hölder-like inequalities. In addition to unifying the proofs of these inequalities, which, in most cases, tend to be technical and obscure, the proofs of our inequalities are quite simple and basic. Moreover, we show that sharper inequalities can be obtained by applying our results.

The calculus of generalized p-forms,−1 p n, is developed further. On an n-dimensional manifold with metric, M, a (Hodge) star operator, inner product, co-differential and Laplacian operators are introduced. The inner product and Lie derivative with respect to vector fields on M are defined. Applications are made to Hamiltonian mechanics, field theories and Einstein’s vacuum equations. PACS numb...

To achieve a resilient society, the reliability of core engineering systems should be evaluated accurately. However, this remains challenging due to complexity and large scale real-world systems. Such can efficiently modelled by Bayesian network (BN), which formulates probability distribution through graph-based representation. On other hand, issue addressed matrix-based (MBN), allows for effic...

The generalized vector is defined on an n dimensional manifold. Interior product, Lie derivative acting on generalized p-forms, −1 ≤ p ≤ n are introduced. Generalized commutator of two generalized vectors are defined. Adding a correction term to Cartan’s formula the generalized Lie derivative’s action on a generalized vector field is defined. We explore various identities of the generalized Lie...

New ultrahard rhombohedral B2N2 and BC2N – or hexagonal B6N6 B3C6N3 are derived from 3R graphite based on crystal chemistry rationale schematizing a mechanism for 2D → 3D transformation. Full unconstrained geometry optimizations leading to ground state energy structures quantities as energy-volume equation of states (EOS) the elastic constants were computations within density functional theory ...

Background. Different studies indicate a high prevalence of eating disorders in athletes. These disorders represent a serious defect in many areas of life. Eating disorders can lead to changes in consumer or intake of food and significant damage to physical health and psychosocial sports performance. Objectives. The aim of the present study was examining the effects of Cognitive Behavior Thera...