Vanishing corrections on the intermediate scale and implications for unification of forces

In two-step breaking of a class of grand unified theories including SO(10),we prove a theorem showing that the scale $M_I$ where the Pati-Salam gauge symmetry with parity breaks down to the standard gauge group,has vanishing corrections due to all sources emerging from higher scales $\mu >M_I$ such as the one-loop and all higher loop effects,the GUT-threshold,gravitational smearing,and string threshold effects. Implications of such a scale for the unification of gauge couplings with small Majorana neutrino masses are discussed.In string inspired SO(10) we show that $M_I \simeq 5\times 10^{12}$,needed for neutrino masses,with the GUT scale $M_U \simeq M_{str}$ can be realized provided certain particle states in the predicted spectum are light.Comment: 21 pages, Late

Optical properties of AlGaN nanowires synthesized via ion beam techniques

AlGaN plays a vital role in hetero-structure high electron mobility transistor by employing a two-dimensional electron gas and as electron blocking layer in the multi quantum well light emitting diodes. Nevertheless, the incorporation of Al in GaN for the formation of AlGaN alloy is limited by the diffusion barrier formed by instant nitridation of Al adatoms by reactive atomic N. Incorporation of Al above the miscibility limit, however can be achieved by ion beam technique. The well known ion beam mixing (IBM) technique was carried out with the help of Ar+ irradiation for different fluences. A novel approach was also adopted for the synthesis of AlGaN by the process of post irradiation diffusion (PID) as a comparative study with the IBM technique. The optical investigations of AlGaN nanowires, synthesized via two different methods of ion beam processing are reported. The effect of irradiation fluence and post irradiation annealing temperature on the random alloy formation were studied by the vibrational and photoluminescence (PL) spectroscopic studies. Vibrational studies show one-mode phonon behavior corresponding to longitudinal optical (LO) mode of A1 symmetry (A1(LO)) for the wurtzite phase of AlGaN nanowires in the random alloy model. Maximum Al atomic percentage ~6.3-6.7% was calculated with the help of band bowing formalism from the Raman spectral analysis for samples synthesized in IBM and PID processes. PL studies show the extent of defects present in these samples

New Uncertainties in QCD-QED Rescaling Factors using Quadrature Method

In this paper we briefly outline the quadrature method for estimating uncertainties in a function of several variables and apply it to estimate the numerical uncertainties in QCD-QED rescaling factors. We employ here the one-loop order in QED and three-loop order in QCD evolution equations of fermion mass renormalization. Our present calculations are found to be new and also reliable compared to the earlier values employed by various authors.Comment: 14 page

Normal, Abby Normal, Prefix Normal

A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. This class of words is important in the context of binary jumbled pattern matching. In this paper we present results about the number $pnw(n)$ of prefix normal words of length $n$, showing that $pnw(n) =\Omega\left(2^{n - c\sqrt{n\ln n}}\right)$ for some $c$ and $pnw(n) = O \left(\frac{2^n (\ln n)^2}{n}\right)$. We introduce efficient algorithms for testing the prefix normal property and a "mechanical algorithm" for computing prefix normal forms. We also include games which can be played with prefix normal words. In these games Alice wishes to stay normal but Bob wants to drive her "abnormal" -- we discuss which parameter settings allow Alice to succeed.Comment: Accepted at FUN '1

Sistem Pendukung Keputusan Penentuan Penilaian Karyawan Berprestasi Menggunakan Metode Saw dan Ahp

STAI Ibnu Rusyd kotabumi adalah sebuah perguruan tinggi yang selalu berupaya dalam peningkatan mutu internal secara berkelanjutan agar dapat bersaing dengan perguruan tinggi swasta lain. Salah satu upaya yang dilakukan adalah dengan melakukan penilaian terhadap karyawan. Penilaian tersebut dilakukan untuk mengetahui karyawan berprestasi, akan tetapi penilaian karyawan yang dilakukan selama ini masih menggunakan metode manual. Berdasarkan kondisi tersebut maka diperlukan adanya metode yang tepat dan akurat dalam mengelola data penilaian karyawan.Menggunakan metode Simple Additive Weighting (SAW) dengan Analytic Hierarchy Process (AHP) di hitung nilai masing-masing karyawan yang melibatkan beberapa kriteria yaitu kriteria komitmen, manajemen, kerjasama dan hasil kerja setelah perhitungan dilakukan maka ditentukan manakah metode yang paling tepat.Dari penelitian ini dapat disimpulkan bahwa metode Analytic Hierarchy Process (AHP) lebih tepat untuk studi kasus pemilihan karyawan berprestasi karena pemilihan karyawan berprestasi ini melibatkan banyak subkriteria, dimana AHP dianggap tepat untuk mewakili pemikiranalamiah yang cenderung mengelompokkan elemen sistemke level-level yang berbeda dari masing-masing level berisi elemen yang serupa dan juga menyediakan skala pengukuran

Neutrino Mixings and Leptonic CP Violation from CKM Matrix and Majorana Phases

The high scale mixing unification hypothesis recently proposed by three of us (R. N. M., M. K. P. and G. R.) states that if at the seesaw scale, the quark and lepton mixing matrices are equal then for quasi-degenerate neutrinos, radiative corrections can lead to large solar and atmospheric mixings and small reactor angle at the weak scale in agreement with data. Evidence for quasi-degenerate neutrinos could, within this framework, be interpreted as a sign of quark-lepton unification at high scale. In the current work, we extend this model to show that the hypothesis works quite successfully in the presence of CP violating phases (which were set to zero in the first paper). In the case where the PMNS matrix is identical to the CKM matrix at the seesaw scale, with a Dirac phase but no Majorana phase, the low energy Dirac phase is predicted to be ($\simeq 0.3^{\circ}$) and leptonic CP-violation parameter $J_{CP} \simeq (4 - 8)\times 10^{-5}$ and $\theta_{13} = 3.5^{\circ}$. If on the other hand, the PMNS matrix is assumed to also have Majorana phases initially, the resulting theory damps radiative magnification phenomenon for a large range of parameters but nevertheless has enough parameter space to give the two necessary large neutrino mixing angles. In this case, one has $\theta_{13} = 3.5^{\circ} - 10^{\circ}$ and $|J_{CP}|$ as large as $0.02-0.04$ which are accessible to long baseline neutrino oscillation experiments.Comment: 15 pages and 10 figures, typo correcte

Quark lepton complementarity and renormalization group effects

We consider a scenario for the Quark-Lepton Complementarity relations between mixing angles in which the bi-maximal mixing follows from the neutrino mass matrix. According to this scenario in the lowest order the angle \theta_{12} is \sim 1\sigma (1.5 - 2^\circ) above the best fit point coinciding practically with the tri-bimaximal mixing prediction. Realization of this scenario in the context of the seesaw type-I mechanism with leptonic Dirac mass matrices approximately equal to the quark mass matrices is studied. We calculate the renormalization group corrections to \theta_{12} as well as to \theta_{13} in the standard model (SM) and minimal supersymmetric standard model (MSSM). We find that in large part of the parameter space corrections \Delta \theta_{12} are small or negligible. In the MSSM version of the scenario the correction \Delta \theta_{12} is in general positive. Small negative corrections appear in the case of an inverted mass hierarchy and opposite CP parities of \nu_1 and \nu_2 when leading contributions to \theta_{12} running are strongly suppressed. The corrections are negative in the SM version in a large part of the parameter space for values of the relative CP phase of \nu_1 and \nu_2: \phi > \pi/2.Comment: version as published in PRD, 14 pages, 12 figure