An atomic decomposition is considered in Banach space.  A method for constructing an atomic decomposition of Banach  space, starting with atomic decomposition of  subspaces  is presented. Some relations between them are established. The proposed method is used in the  study  of the  frame  properties of systems of eigenfunctions and associated functions of discontinuous differential operators.

introduction various factors like climatic conditions, vegetation, soil properties, topography, time, plant residue quality and crop management strategies affect the decomposition rate of organic carbon (oc) and its residence time in soil. plant residue management concerns nutrients recycling, carbon recycling in ecosystems and the increasing co2 concentration in the atmosphere. plant residue d...

‎‎in this article‎, ‎a new method is introduced to give approximate solution to van der pol equation‎. ‎the proposed method is based on the combination of two different methods‎, ‎the spectral adomian decomposition method (sadm) and piecewise method‎, ‎called the piecewise adomian decomposition method (psadm)‎. ‎the numerical results obtained from the proposed method show that this method is an...

the potential energy hyper surfaces (fes) of the unimolecular rearrangements of a) nitromethane itei totrans acknitromethane b) nitrometharie (/) to methyl nitrite (3) and c) naromethane decomposition tomethyl and nitrogen dioxide were searched using the ab !nth° mp2 method. split valence 6-310(d.p) basisset was used for geometry optimizations, frequency and 1rc computations along each reaction...

A hole in a graph is a chordless cycle of length at least 4. A theta is a graph formed by three paths between the same pair of distinct vertices so that the union of any two of the paths induces a hole. A wheel is a graph formed by a hole and a node that has at least 3 neighbors in the hole. In this paper we obtain a decomposition theorem for the class of graphs that do not contain an induced s...

Let G be a simple graph with vertex set V (G) = {1, 2, . . . , n} and (0, 1)adjacency matrix A. The eigenvalue μ of A is said to be a main eigenvalue of G if the eigenspace E(μ) is not orthogonal to the all-1 vector j. An eigenvector x is a main eigenvector if xj 6= 0. The main eigenvalues of the connected graphs of order ≤ 5 are listed in [12, Appendix B], and those of all the connected graphs...

Introduction and the Statement. In [A] S. Akbulut obtained an example of the exotic manifold cutting off the contractible submanifold from the standard manifold and regluing it via nontrivial involution of the boundary. In these notes we give a proof of a decomposition theorem stated below. It generalizes the example of Akbulut. Another proof of the theorem was independently obtained by C.L. Cu...

We characterize infrared spectral energy distributions of 343 (Ultra) Luminous Infrared Galaxies from z = 0.3− 2.8. We diagnose the presence of an AGN by decomposing individual Spitzer mid-IR spectroscopy into emission from star-formation and an AGN-powered continuum; we classify sources as star-forming galaxies (SFGs), AGN, or composites. Composites comprise 30% of our sample and are prevalent...

This paper is concerned with the fast computation of a relation d on the edge set of connected graphs that plays a decisive role in the recognition of approximate Cartesian products, the weak reconstruction of Cartesian products, and the recognition of Cartesian graph bundles with a triangle free basis. A special case of d is the relation δ, whose convex closure yields the product relation σ th...

Cross-correlation function (CCF) has become the standard tool for extraction of radial-velocity and broadening information from high resolution spectra. It permits integration of information which is common to many spectral lines into one function which is easy to calculate, visualize and interpret. However, CCF is not the best tool for many applications where it should be replaced by the prope...