A Perturbative Approach to the Relativistic Harmonic Oscillator

A quantum realization of the Relativistic Harmonic Oscillator is realized in terms of the spatial variable $x$ and {\d\over \d x} (the minimal canonical representation). The eigenstates of the Hamiltonian operator are found (at lower order) by using a perturbation expansion in the constant $c^{-1}$. Unlike the Foldy-Wouthuysen transformed version of the relativistic hydrogen atom, conventional perturbation theory cannot be applied and a perturbation of the scalar product itself is required.Comment: 9 pages, latex, no figure

Experimental investigation of Paper Honeycomb subjected to quasi-static loading

Three point bending test is performed to investigate the collapse load of paper honeycomb sandwich panel. Three panel thickness were considered; 9.1 mm, 35.84 mm and 41.92 mm with an eight span length. Eight span lengths range from 50 mm to 120 mm with 10 mm increment are compressed with 2 mm/min. The Paik’s theoretical collapse load is adapted and compared with experimental results.The agreement between experiment and theory are only found at d= 50mm,70 mm and 120 mm

Big q-Laguerre and q-Meixner polynomials and representations of the algebra U_q(su(1,1))

Diagonalization of a certain operator in irreducible representations of the positive discrete series of the quantum algebra U_q(su(1,1)) is studied. Spectrum and eigenfunctions of this operator are found in an explicit form. These eigenfunctions, when normalized, constitute an orthonormal basis in the representation space. The initial U_q(su(1,1))-basis and the basis of eigenfunctions are interrelated by a matrix with entries, expressed in terms of big q-Laguerre polynomials. The unitarity of this connection matrix leads to an orthogonal system of functions, which are dual with respect to big q-Laguerre polynomials. This system of functions consists of two separate sets of functions, which can be expressed in terms of q-Meixner polynomials M_n(x;b,c;q) either with positive or negative values of the parameter b. The orthogonality property of these two sets of functions follows directly from the unitarity of the connection matrix. As a consequence, one obtains an orthogonality relation for q-Meixner polynomials M_n(x;b,c;q) with b<0. A biorthogonal system of functions (with respect to the scalar product in the representation space) is also derived.Comment: 15 pages, LaTe

Rare Decay of the Top t -> cgg in the Standard Model

We calculate the one-loop flavor changing neutral current top quark decay t -> cgg in the Standard Model. We demonstrate that the rate for t -> cgg exceeds the rate for a single gluon emission t -> cg by about two orders of magnitude, while the rate for t -> cq barq (q=u) is slightly smaller than for t -> cg.Comment: 22 pages, 4 figures and 2 tables. Typo in Eq.2.1 corrected, text slightly modified, references added. Version to appear in Phys.Rev.

The Friedreich ataxia GAA repeat expansion mutation induces comparable epigenetic changes in human and transgenic mouse brain and heart tissues

Friedreich ataxia (FRDA) is caused by a homozygous GAA repeat expansion mutation within intron 1 of the FXN gene, leading to reduced expression of frataxin protein. Evidence suggests that the mutation may induce epigenetic changes and heterochromatin formation, thereby impeding gene transcription. In particular, studies using FRDA patient blood and lymphoblastoid cell lines have detected increased DNA methylation of specific CpG sites upstream of the GAA repeat and histone modifications in regions flanking the GAA repeat. In this report we show that such epigenetic changes are also present in FRDA patient brain, cerebellum and heart tissues, the primary affected systems of the disorder. Bisulfite sequence analysis of the FXN flanking GAA regions reveals a shift in the FRDA DNA methylation profile, with upstream CpG sites becoming consistently hypermethylated and downstream CpG sites becoming consistently hypomethylated. We also identify differential DNA methylation at three specific CpG sites within the FXN promoter and one CpG site within exon 1. Furthermore, we show by chromatin immunoprecipitation (ChIP) analysis that there is overall decreased histone H3K9 acetylation together with increased H3K9 methylation of FRDA brain tissue. Further studies of brain, cerebellum and heart tissues from our GAA repeat expansion-containing FRDA YAC transgenic mice reveal comparable epigenetic changes to those detected in FRDA patient tissue. We have thus developed a mouse model that will be a valuable resource for future therapeutic studies targeting epigenetic modifications of the FXN gene to increase frataxin expression

The Bivariate Rogers-Szeg\"{o} Polynomials

We present an operator approach to deriving Mehler's formula and the Rogers formula for the bivariate Rogers-Szeg\"{o} polynomials $h_n(x,y|q)$. The proof of Mehler's formula can be considered as a new approach to the nonsymmetric Poisson kernel formula for the continuous big $q$-Hermite polynomials $H_n(x;a|q)$ due to Askey, Rahman and Suslov. Mehler's formula for $h_n(x,y|q)$ involves a ${}_3\phi_2$ sum and the Rogers formula involves a ${}_2\phi_1$ sum. The proofs of these results are based on parameter augmentation with respect to the $q$-exponential operator and the homogeneous $q$-shift operator in two variables. By extending recent results on the Rogers-Szeg\"{o} polynomials $h_n(x|q)$ due to Hou, Lascoux and Mu, we obtain another Rogers-type formula for $h_n(x,y|q)$. Finally, we give a change of base formula for $H_n(x;a|q)$ which can be used to evaluate some integrals by using the Askey-Wilson integral.Comment: 16 pages, revised version, to appear in J. Phys. A: Math. Theo

Assessment of Some Clay Deposits from Fatha Formation (M. Miocene) for Brick Manufacturing in Koya Area, NE Iraq

This paper deals with the evaluation of physical, chemical and mineralogical properties of claystone sediments of Miocene age (Fatha Formation) and their suitability to use them as raw materials in manufacturing of building clay brick in Kurdistan (Koya city). The study based on the field reconnaissance for three sites of claystones which were selected from three different locations within Fatha Formation in Koya city, includes Haibat-Sultan area, Koya-Sulaimania road and central of Koya city. The clay samples were subjected to particle size distribution, chemical composition, mineralogical analysis, plasticity index and XRD tests. Clay tiles were produced by using Semi-dry method under load 78 kN/mm² and fired at 950 C°. The produced clay tiles were subjected to water absorption, efflorescence, shrinkage and compressive strength tests. The research has shown that the plasticity index depends on the mineral composition of the raw materials. The grain size analysis of raw materials, physical properties and mechanical properties of the produced tiles has shown the suitability of the used raw materials in producing class bricks of class A (first class) according to the requirements of specification of the Iraqi Standard (1993)

Impact of localization on Dyson's circular ensemble

A wide variety of complex physical systems described by unitary matrices have been shown numerically to satisfy level statistics predicted by Dyson's circular ensemble. We argue that the impact of localization in such systems is to provide certain restrictions on the eigenvalues. We consider a solvable model which takes into account such restrictions qualitatively and find that within the model a gap is created in the spectrum, and there is a transition from the universal Wigner distribution towards a Poisson distribution with increasing localization.Comment: To be published in J. Phys.

The Suitability of Limestone from Pilaspi Formation (Middle-Late Eocene) for Building Stone in Koya Area, NE Iraq

Suitability of limestone rocks has a crucial importance when stones are used for constructing modern structure. The purpose of this study is to clarify the links between physical, mechanical properties of limestone rocks, also their quality to use as building materials. A total of six limestone rock samples were collected from three different outcrops locations within Pilaspi Formation in Koya area. Engineering geological and geotechnical properties of the limestone rocks in the study area were determined based on the field studies and laboratory tests. The field studies included observations/ measurements of rock mass characteristics such as color, grain size, orientation, bedding thickness and weathering state of the rock materials also spacing, persistence, roughness and infilling material of the discontinuities. Laboratory tests were carried out for determining water content, water absorption, density, uniaxial compressive strength, slake durability and porosity of the rock materials. The study results go well with the national and international standards (Iraqi Standards, 1989; American Society for Testing and Materials, 2004; International Society for Rock Mechanics, 1981) and have shown that the limestone rocks are acceptable for building stone