In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

ABSTRACT The effect of tensile fracture in a vertical borehole under anisotropic horizontal stress conditions is numerically investigated terms the dispersion flexural wave generated dipole sonic logging. Our three?dimensional model comprises filled with water and intersecting axial direction. Two shear waves are excited individually to produce particle displacements polarized two orthogonal ra...

‎In this paper, generalized convex contractions on orthogonal metric spaces are stablished in whath  might be called their  definitive versions. Also, we show that there are examples which show that our main theorems are  genuine generalizations of Theorem 3.1 and 3.2 of [M.A. Miandaragh, M. Postolache and S. Rezapour,  {it Approximate fixed points of generalized convex contractions}, Fixed Poi...

Let H be a graph on n vertices and G a collection of n subgraphs of H, one for each vertex, where G is an orthogonal double cover (ODC) of H if every edge of H occurs in exactly two members of G and any two members share an edge whenever the corresponding vertices are adjacent in H and share no edges whenever the corresponding vertices are nonadjacent in H. In this paper, we are concerned with ...

This Article is brought to you for free and open access by the Center for Coastal Physical Oceanography at ODU Digital Commons. It has been accepted for inclusion in CCPO Publications by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. Repository Citation Hamlington, B. D.; Leben, R. R.; Strassburg, M. W.; and Kim, K.-Y., "Cyclosta...

Orthogonal wavelet bases have been developed using multiple mother wavelet functions. Applying the discrete multiwavelet transform requires the input data to be preprocessed to obtain a more economical decomposition. Four characteristics of a preprocessing method are presented: length, degree, orthogonality and frequency response. A minimal preelter is deened to have length one and highest atta...

The main goal of the paper is to show that wavelet transforms and packets have the multiparametric representation in the form of a product of the rotation Jacobi matrices. These representations we call the third and the fourth canonical multiparametric form. Each multiparametric wavelet transform (MPWT) depends on several free Jacobi parameters. When parameters are changed multiparametric trans...

Gronau, Mullin, and Rosa conjectured that for every tree T with n vertices except for P4 there exists an ODC of Kn by T . They also proved the conjecture for all caterpillars of diameter 3. Later, Leck and Leck proved it for all caterpillars of diameter 4 and all trees with up to 14 vertices. We prove the conjecture for all carerpillars of diameter 5 and order n ≥ 24; for orders 15 ≤ n ≤ 23 we ...