The direct energy functional minimization problem in electronic structure theory, where the single-particle orbitals are optimized under the constraint of orthogonality, is explored. We present an orbital transformation based on an efficient expansion of the inverse factorization of the overlap matrix that keeps orbitals orthonormal. The orbital transformation maps the orthogonality constrained...

In this article the notions of semi weak orthogonality and semi weak factorization structure in a category $mathcal X$ are introduced. Then the relationship between semi weak factorization structures and quasi right (left) and weak factorization structures is given. The main result is a characterization of semi weak orthogonality, factorization of morphisms, and semi weak factorization structur...

An extension of the metric space in which distance same point is not always zero called a partial space. Orthogonality relation two perpendicular lines at one intersection forming right angle. There are several ways to define orthogonality, including Pythagorean Orthogonality, Isosceles and Birkhoff-James Orthogonality. The purpose this research study consistency definition orthogonality Based ...

We introduce a new stopping-time argument, adapted to handle linear sums of noncompactly-supported functions that satisfy fairly weak decay, smoothness, and cancellation conditions. We use the argument to obtain a new Littlewood-Paley-type result for such sums. 0. Introduction. First, an apology. The title, though correct, is somewhat misleading. It should be “Global almostorthogonality implies...

In this study, we investigate the problem of partially overlapping channel assignment to improve the performance of 802.11 wireless networks. We first derive a novel interference model that takes into account both the adjacent channel separation and the physical distance of the two nodes employing adjacent channels. This model defines “node orthogonality”, which states that two nodes over adjac...

In this paper, a computational goal for a monaural speech separation system is proposed. Since this goal is derived by maximizing the signal-to-noise ratio (SNR), it is called the optimal ratio mask (ORM). Under the approximate W-Disjoint Orthogonality assumption which almost always holds due to the sparse nature of speech, theoretical analysis shows that the ORM can improve the SNR about 10log...

In previous work, we have successfully used an ideal joint sparseness assumption: W-Disjoint Orthogonality (WDO). This assumption, that the time-frequency representations of the sources have disjoint support, is satisfied in an approximate sense by many signals of practical interest, including speech. Here we discuss results derived from a stochastic model of speech signals that justify the WDO...

We derive a posteriori error estimates, which exhibit optimal global order, for a class of time stepping methods of any order that include Runge–Kutta Collocation (RK-C) methods and the continuous Galerkin (cG) method for linear and nonlinear stiff ODEs and parabolic PDEs. The key ingredients in deriving these bounds are appropriate one-degree higher continuous reconstructions of the approximat...