An Auxiliary 'Differential Measure' for SU(3)SU(3)

A 'differential measure' is used to cast our calculus for the group $SU(3)$ into a form similar to Schwinger's boson operator calculus for the group $SU(2)$. It is then applied to compute (i) the inner product between the basis states and (ii) an algebraic formula for the Clebsch-Gordan coefficients. These were obtained earlier by us using Gaussian integration techniques.Comment: RevTex 3.0, 30 pages, no figures; Latex error correcte

An Explicit and Simple Relationship Between Two Model Spaces

An explicit and simple correspondence, between the basis of the model space of $SU(3)$ on one hand and that of $SU(2)\otimes SU(2)$ or $SO(1,3)$ on the other, is exhibited for the first time. This is done by considering the generating functions for the basis vectors of these model spaces.Comment: RevTex 3.0, 21 pages, no figure

Weyl's Character Formula for SU(3)SU(3) - A Generating Function Approach

Using a generating function for the Wigner's $D$-matrix elements of $SU(3)$ Weyl's character formula for $SU(3)$ is derived using Schwinger's technique.Comment: RevTex 3.0, 30 pages, no figure

Thinning Algorithm Using Hypergraph Based Morphological Operators

The object recognition is a complex problem in the image processing. Mathematical morphology is Shape oriented operations, that simplify image data, preserving their essential shape characteristics and eliminating irrelevancies. This paper briefly describes morphological operators using hypergraph and its applications for thinning algorithms. The morphological operators using hypergraph method is used to preventing errors and irregularities in skeleton, and is an important step recognizing line objects. The morphological operators using hypergraph such as dilation, erosion, opening, closing is a novel approach in image processing and it act as a filter remove the noise and errors in the images.Comment: Advance Computing Conference (IACC), 2015 IEEE International,Banglore Indi

Disk Scheduling: Selection of Algorithm

The objective of this paper is to take some aspects of disk scheduling and scheduling algorithms. The disk scheduling is discussed with a sneak peak in general and selection of algorithm in particular.Comment: 9 pages; http://www.ijascse.in/publications-2012--

A Calculus for SU(3)SU(3) Leading to an Algebraic Formula for Clebsch-Gordan Coefficients

We develop a simple computational tool for $SU(3)$ analogous to Bargmann's calculus for $SU(2)$. Crucial new inputs are, (i) explicit representation of the Gelfand-Zetlin basis in terms of polynomials in four variables and positive or negative integral powers of a fifth variable (ii) an auxiliary Gaussian measure with respect to which the Gelfand-Zetlin states are orthogonal but not normalized (iii) simple generating functions for generating all basis states and also all invariants. As an illustration of our techniques, an algebraic formula for the Clebsch-Gordan coefficients is obtained for the first time. This involves only Gaussian integrations. Thus $SU(3)$ is made as accessible for computations as $SU(2)$ is.Comment: RevTex 3.0, 104 pages, one figure. To Appear in J.M.

On the Polarization of non-Guassian optical quantum field: higher-order optical-polarization

Polarization of light signifies transversal, anisotropic and asymmetrical statistical property of electromagnetic radiation about direction of propagation. Traditionally, optical-polarization is characterized by Stokes theory susceptible to be insufficient in assessing polarization structure of optical quantum fields and, also, does not decipher twin characteristic polarization parameters (ratio of real amplitudes and difference in phases). An alternative way, in spirit of classical description of optical-polarization, is introduced which can be generalized to deal higher-order polarization of quantum light, particularly, prepared in non-Guassian Schrodinger Cat or Cat-like states and entangled bi-modal coherent states. On account of pseudo mono-modal or multi-modal nature of such optical quantum field, higher-order polarization is seen to be highly sensitive to the basis of description.Comment: 15 pages, To appear in Annals of Physic

The Large Sieve Inequality for Quadratic Polynomial Amplitudes

We provide here a modest improvement upon a large sieve inequality for quadratic polynomial amplitudes orginally due to Liangyi Zhao.Comment: 7 pages comments welcom

Degree of Polarization in Quantum Optics through second generalization of Intensity

Classical definition of degree of polarization is expressed in quantum domain by replacing intensities through quantum mechanical average values of relevant number operators and is viewed as first generalization of Intensity. This definition assigns inaccurately the unpolarized status to some typical optical fields such as amplitude coherent phase randomized and hidden polarized, which are not truly unpolarized light. The apparent paradoxical trait is circumvented by proposing a new definition of degree of polarization in Quantum Optics through second generalization of Intensity. The correspondence of new degree of polarization to usual degree of polarization in Quantum Optics is established. It is seen that the two definitions disagree significantly for intense optical fields but coincides for weak light (thermal light) or for optical fields in which occupancy of photons in orthogonal mode is very feeble. Our proposed definition of degree of polarization, similar to other proposals in literature, reveals an interesting feature that states of polarization of optical quantum fields depend upon the average photons (intensity) present therein.Comment: 17 pages, Accepted in PR

The Large Sieve Inequality for Integer Polynomial Amplitudes

We obtain a close to the best possible version of the large sieve inequality with amplitudes given by the values of a polynomial with integer coefficients of degree $\geq 2$.Comment: 6 page