Cenap Ozel

Geometry of warped product pointwise semi-slant submanifolds of cosymplectic manifolds and its applications

It is known from [K. Yano and M. Kon, Structures on Manifolds (World Scientific, 1984)] that the integration of the Laplacian of a smooth function defined on a compact orientable Riemannian manifold without boundary vanishes with respect to the volume element. In this paper, we find out the some potential applications of this notion, and study the concept of warped product pointwise semi-slant submanifolds in cosymplectic manifolds as a generalization of contact CR-warped product submanifolds. Then, we prove the existence of warped product pointwise semi-slant submanifolds by their characterizations, and give an example supporting to this idea. Further, we obtain an interesting inequality in terms of the second fundamental form and the scalar curvature using Gauss equation and then, derive some applications of it with considering the equality case. We provide many trivial results for the warped product pointwise semi-slant submanifolds in cosymplectic space forms in various mathematical and physical terms such as Hessian, Hamiltonian and kinetic energy, and generalize the triviality results for contact CR-warped products as well.

A new generalization of Apostol type Hermite–Genocchi polynomials and its applications

By using the modified Milne-Thomson’s polynomial given in Araci et al. (Appl Math Inf Sci 8(6):2803–2808, 2014), we introduce a new concept of the Apostol Hermite–Genocchi polynomials. We also perform a further investigation for aforementioned polynomial and derive some implicit summation formulae and general symmetric identities arising from different analytical means and generating functions method. The results obtained here are an extension of Hermite–Bernoulli polynomials (Pathan and Khan in Mediterr J Math 12:679–695, 2015a) and Hermite–Euler polynomials (Pathan and Khan in Mediterr J Math 2015b, doi:10.1007/s00009-015-0551-1) to Apostol type Hermite–Genocchi polynomials defined in this paper.

On solvability of the integrodifferential hyperbolic equation with purely nonlocal conditions

In this study, we prove the existence, uniqueness, and continuous dependence upon the data of solution to integro-differential hyperbolic equation with purely nonlocal (integral) conditions. The proofs are based on a priori estimates and Laplace transform method. Finally, we obtain the solution using a numerical technique (Stehfest algorithm) by inverting the Laplace transform.

Recent Trends in Special Numbers and Special Functions and Polynomials

1Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, 27410 Gaziantep, Turkey 2Department of Mathematics, Faculty of Arts and Sciences, University of Gaziantep, 27310 Gaziantep, Turkey 3Department of Mathematics, Dokuz Eylul University, 35160 Izmir, Turkey 4Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3R4 5Department of Mathematics, Howard University, 2441 6th, Street NW, Washington, DC 20059, USA

Gröbner–Shirshov basis and reduced words for affine Weyl group Ãn

Using Buchberger–Shirshov Algorithm, Composition–Diamond Lemma and partitions of integers we obtain the reduced Grobner–Shirshov basis of An and classify all reduced words of the affine Weyl group An.

Combinatorial integers (m,nj) and schubert calculus in the integral cohomology ring of infinite smooth flag manifolds

We discuss the calculation of integral cohomology ring of LG/T and ΩG. First we describe the root system and Weyl group of LG, then we give some homotopy equivalences on the loop groups and homogeneous spaces, and calculate the cohomology ring structures of LG/T and ΩG for affine group A^2. We introduce combinatorial integers (m,nj) which play a crucial role in our calculations and give some interesting identities among these integers. Last we calculate generators for ideals and rank of each module of graded integral cohomology algebra in the local coefficient ring ℤ[1/2].