• ÖZ

In this study, the frequency response of a pre-stressed slab, which stands on a rigid foundation, subject to a timely harmonic loadingwas considered. The investigation is implemented according to the piecewise homogeneous body model utilizing the threedimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB). The considered body was designed joiningto three discrete slabs side-by-side. It was assumed that there exists a rigidly clamping state at all interface planes on the system.A mathematical model of the problem is constructed and the system related to equations of motion is numerically solved using thefinite element method (FEM). Particularly, the effect the ratio of the layer length has on the frequency response of the slab waspresented.

• ÖZ

In this paper, we study Horadam hybrid numbers. For these numbers, we give the exponential generatingfunction, Poisson generating function, generating matrix, Vajda’s, Catalan’s, Cassini’s, and d’Ocagne’s identities. Inaddition, we offer Honsberger formula, general bilinear formula, and some summation formulas for these numbers.

• ÖZ

I n this study, a new generalization of the usual Jacobsthal sequence is presented, which is called the generalized Jacobsthal p-sequence. The generating matrix, the generalized Binet formula, the generating functions and the combinatorial representations of the generalized Jacobsthal p-sequence are investigated. Moreover, certain sum formula consisting of the terms of the generalized Jacobsthal p-sequence are given