ORTHOGONALITY

In this paper, second order rotatable designs of second type using symmetrical unequal block arrangements with two
unequal block sizes is suggested. This design is compared with second order rotatable designs of first type using symmetrical
unequal block arrangements with two unequal block sizes (Raghavarao, 1963) on the basis of efficiency

In this paper a new logical operation method called "orthogonalizing difference-buliding" is presented. It is used to calculate the difference, but also the complement of a function as well as the EXOR and EXNOR of two minterms respectively two ternary-vectors or two functions respectively two ternary-vector-lists is presented. On the basis of this new method a further logical operation method called "orthogonal OR-ing" is going to be introduced. The advantages of both methods are their results, which are already available in an orthogonal form that has an essential advantage for continuing calculations. Since it applies, an orthogonal disjunctive normal form is equal to orthogonal antivalence normal form, subsequent Boolean differential calculus will be simplified.

A discussion of the Creation of the Cosmos is presented, herein, which makes a particular reference to the quantum mechanics of the fundamental Expansive-Electric and Contractive-Magnetic Quanta of Energy that together give rise to the overall Electromagnetic Field of the Cosmos. The quantum mechanics of the Electromagnetic Cosmos asserts the formation of energetic contours around the SOURCE which are equivalent to, or consistent with, the author’s previously published work concerning the ‘Nested Spheres Model of Cosmos,’ in which the surfaces of each sphere portray a set of the main space-time dimensions of Cosmos comprised of a conjugate or double layered-edifice giving rise to the Worlds of Matter and Antimatter.  This way,  the energetic contours of the Cosmos that, in essence, define the very space-time energetic dimensions of the Cosmos, closely resemble the structure of an atom in which negatively charged Electrons being confined within well-defined energetic orbitals spin in opposition to one another, when they are observed from either Worlds of Matter or Antimatter. Yet, these Electrons spin counterclockwise about their (Time) Axis, creating correspondingly two Expansive Electric ‘Fields.’ And, conformant with the Dualism Principle of Creation, the Expansive Electrodynamic Field of Electrons immediately symbiotically creates a Magnetodynamic Field perpendicular to the former with the fundamental Energetic Quanta (may be referred to as ‘Magnetons’) this time spinning clockwise about their magnetic (time) axis as well as rotating clockwise about the central SOURCE, forming a symbiotic, yet contractive, Magnetodynamic Field of Energy. And, it is the resultant of the two fields generated that gives rise to the Electromagnetic Field of a particular dimensional space-time within the Cosmos.  In this respect, the space-time fabrics composed of the Electromagnetic Quanta of Energy that spin about their resultant (Time) axes, overall rotate about the center of the Cosmos (the SOURCE) that may be visualized as two groups with one group spinning in an opposite manner to the other, essentially epitomize mirroring one another. And, these give rise to the separate worlds of Matter and Antimatter with the Zero-Point Field located in between that essentially divides the two worlds like a Time Wall. As a result, these Worlds of Matter and Antimatter never ‘meet,’ and thus, are stealth to one another, perceived as one being the ‘ethereal’ aspect of the other.

In this paper we propose a method for perspective distortion correction of rectangular documents. This scheme exploits the orthogonality of the document edges, allowing to recover the aspect ratio of the original document. The results obtained after correcting the perspective of several document images captured with a mobile phone are compared with those achieved by digitizing the same documents with several scanner models.

The theme of this short article is to investigate an orthogonal decomposition of the Sobolev space W 1,2 (Ω) as W 1,2 (Ω) = A 2,2 (Ω) ⊕ D 2 W 3,2 0 (Ω) and look at some of the properties of the inner product therein and the distance defined by the inner product. We also determine the dimension of the orthogonal difference space W 1,2 (Ω) W 1,2 0 (Ω) ⊥ and show the expansion of Sobolev spaces as their regularity increases.

Motivated by some results on Orthogonal Derivations and Biderivations, in [5], the authors defined the notion of  orthogonality between the Derivation and Biderivation in ring and some interesting results.In this paper we also introduce the notion of Derivations and Biderivations are orthogonal in semiprime semiring and giving some necessary and sufficient conditions for Derivations and Biderivations are Orthogonal.

Under standard approach, locational marginal prices (LMPs) are generally decomposed into system marginal (energy) price (SMP), marginal congestion cost (MCC), and marginal loss cost (MLC). However, earlier work has shown that it is not possible to separate the standard decompositions of LMPs into three mutually orthogonal subspaces. It is also found that MLC term of standard LMP inherently depends on the selection of reference bus, due to their association with only a single direction (one dimensional space) in the set of admissible LMPs. On the other hand, the MCC term, constructed by the null space approach, is found to be independent of choice of reference bus. A key goal of this research is to develop efficient algorithms that provide conceptual and computational simplicity in characterizing the admissible set of LMPs. The key outcome of this work is an efficient algorithm that only requires the identification of a single null vector in a matrix known to be column-rank deficient by one, and hence achieves the goal of low cost computation. In this paper, we illustrate the usefulness of this fundamental null space approach by applying it on well-known PJM network by invoking one constraint at a time. The objective is to analyze the admissible LMP pattern in PJM network, by observing the behavior and relationship of MCC term - both magnitude and direction - to combined SMP/MLC term (marginal energy/loss basis vector).

Int. J. Machining and Machinability of Materials, Vol. 8, Nos. 1/2, 2010 ... Intelligent process modelling using radial basis neural network ... Department of Operations Research, Institute of Statistical Studies and Research, Cairo University, 5 Tharwat Street, Orman, Dokki, Giza, 12613 ...

Let H be a separable infinite dimensional complex Hilbert space, and let L(H) denote the algebra of all bounded linear operators on H. Let A,B 2 L(H) we define the generalized derivation A,B : L(H) 7! L(H) by A,B(X) = AX XB, we note A,A = A. If for all X 2 L(H) and for all T 2 ker A the inequality ||T (AX XA)|| || T||(*) holds, then we say that the range of A is orthogonal to kernel A in the sense of Birkho. The operator A 2 L(H) is said to be finite (17) if ||I (AX XA)|| 1(**) for all X 2 L(H), where I is the identity operator. The well-known Inequality (**) due to J.P.Williams (17) is the starting point of the topic of commutator approximation (a topic which has its roots in quantum theory (18)). This topic deals with minimizing the distance, measured by some norms or other, between a varying commutator XX X X and some fixed operator (12). In this paper we prove that a paranormal operator is finite and we present some generalized finite operators. An extension of Inequality (*) is...

DRAFT - Generally, a theory is understood to be a system of concepts (variables) along with the connections between them. In order to create more useful theories we must attempt to choose the “best” concepts. Ideally, we strive to identify “independent” variables; however, that is problematic on two fronts. First, because we live in a world where everything is connected. Second, to obtain even nominally independent variables may require sophisticated analytical methodologies available only to well-funded researchers and practitioners. Others, in contrast, would benefit from a more pragmatic guide for developing better theories (understood as being more useful or effective in practical application for reaching desired goals). Here, we explore the notion of orthogonality as a path for re-thinking concepts in a theory to enable the more effective development of more useful theories for improved practice.

A resistance network is a weighted graph (G,c) with intrinsic (resistance) metric R. We embed the resistance network into the Hilbert space H_ E of functions of finite energy. We use the resistance metric to study H_ E, and vice versa and show that the embedded images of the vertices {v_x} form a reproducing kernel for this Hilbert space. We also obtain a discrete version of the Gauss-Green formula for resistance networks and show that resistance networks which support nonconstant harmonic functions of finite energy have a certain type of boundary. We obtain an analytic boundary representation for the harmonic functions of finite energy in a sense analogous to the Poisson or Martin boundary representations, but with different hypotheses, and for a different class of functions. In the process, we construct a dense space of "smooth" functions of finite energy and obtain a Gel'fand triple for H_ E. This allows us to represent the resistance network as a system of Gaussian...

xtivreg28 implements IV/GMM estimation of the fixed-effects and first-differences panel data models with possibly endogenous regressors. It is essentially a wrapper for ivreg28, which must be installed for xtivreg28 to run. Users of Stata versions 9+ should use xtivreg2. xtivreg28 supports all the estimation and reporting options of ivreg28; see help ivreg28 for full descriptions and examples. In particular, all the statistics available with ivreg28 (heteroskedastic, cluster- and autocorrelation-robust covariance matrix and standard errors, overidentification and orthogonality tests, first-stage and weak/underidentification statistics, etc.) are also supported by xtivreg2 and will be reported with any degrees-of-freedom adjustments required for a panel data estimation.