Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators

Ground state energies and wave functions of quartic and pure quartic oscillators are calculated by first casting the Schr\"{o}dinger equation into a nonlinear Riccati form and then solving that nonlinear equation analytically in the first iteration of the quasilinearization method (QLM). In the QLM the nonlinear differential equation is solved by approximating the nonlinear terms by a sequence of linear expressions. The QLM is iterative but not perturbative and gives stable solutions to nonlinear problems without depending on the existence of a smallness parameter. Our explicit analytic results are then compared with exact numerical and also with WKB solutions and it is found that our ground state wave functions, using a range of small to large coupling constants, yield a precision of between 0.1 and 1 percent and are more accurate than WKB solutions by two to three orders of magnitude. In addition, our QLM wave functions are devoid of unphysical turning point singularities and thus allow one to make analytical estimates of how variation of the oscillator parameters affects physical systems that can be described by the quartic and pure quartic oscillators.Comment: 8 pages, 12 figures, 1 tabl

Network Security Investment

Analysing potential risk and the allocation of resources for computer network security and business continuity require strategic, long-term planning. Most companies tend to be reactive and respond with quick infrastructure solutions. The purpose of risk analysis should be to assist managers in making informed decisions about investment and developing risk management policies. High countermeasures expenditure on every aspect of an information system is out of question in a commercial organisation. Therefore, this expenditure must be directed to reduce corporate exposure to information system risks in the context of overall business risks. The aim of this paper is to report the on going research to justify funding for network security expenditure through risk assessment practice

Masses and Mixings in a Grand Unified Toy Model

The generation of the fermion mass hierarchy in the standard model of particle physics is a long-standing puzzle. The recent discoveries from neutrino physics suggests that the mixing in the lepton sector is large compared to the quark mixings. To understand this asymmetry between the quark and lepton mixings is an important aim for particle physics. In this regard, two promising approaches from the theoretical side are grand unified theories and family symmetries. In this note we try to understand certain general features of grand unified theories with Abelian family symmetries by taking the simplest SU(5) grand unified theory as a prototype. We construct an SU(5) toy model with $U(1)_F \otimes Z'_2\otimes Z''_2 \otimes Z'''_2$ family symmetry that, in a natural way, duplicates the observed mass hierarchy and mixing matrices to lowest approximation. The system for generating the mass hierarchy is through a Froggatt-Nielsen type mechanism. One idea that we use in the model is that the quark and charged lepton sectors are hierarchical with small mixing angles while the light neutrino sector is democratic with larger mixing angles. We also discuss some of the difficulties in incorporating finer details into the model without making further assumptions or adding a large scalar sector.Comment: 21 pages, 2 figures, RevTeX, v2: references updated and typos corrected, v3: updated top quark mass, comments on MiniBooNE result, and typos correcte

Neutrino induced reactions related to the ν\nu-process nucleosynthesis of 92{}^{92}Nb and 98{}^{98}Tc

It has recently been proposed that ${}^{92}_{41}$Nb and ${}^{98}_{43}$Tc may have been formed in the $\nu$-process. We investigate the neutrino induced reactions related to the $\nu$-process origin of the two odd-odd nuclei. The main neutrino reactions for ${}^{92}_{41}$Nb are the charged-current (CC) $^{92}$Zr($\nu_e,e^{-}$)$^{92}$Nb and the neutral-current (NC) $^{93}$Nb(${\nu} ({\bar \nu}), {\nu}^{'} ({\bar \nu})^{'}$ n)$^{92}$Nb reactions. The main reactions for ${}^{98}_{43}$Tc, are the CC reaction $^{98}$Mo($\nu_e,e^-$)$^{98}$Tc and the NC reaction $^{99}$Ru(${\nu} ({\bar \nu}), {\nu}^{'} ({\bar \nu})^{'}$ p)$^{98}$Tc. Our calculations are carried out using the quasi-particle random phase approximation. Numerical results are presented for the energy and temperature dependent cross sections. Since charge exchange reactions by neutrons may also lead to the formation of ${}^{92}_{41}$Nb and ${}^{98}_{43}$Tc, we discuss the feasibility of the $^{92}$Mo(n,p)$^{92}$Nb and $^{98}$Ru(n,p)$^{98}$Tc reactions to produce these nuclei.Comment: 21 pages, 8 figure

Information and network management security Investment

In today’s business environment it is difficult to obtain senior management approval for the expenditure of valuable resources to “guarantee “that a potentially disastrous event will not occur that could affect the organisation performance. Analysing potential risk and the allocation of resources for computer network security and business continuity require strategic, long-term planning. Most companies tend to be reactive and respond with quick infrastructure solutions. A strategic approach to computer network security leads to a more efficient plan and a less expensive risk-management strategy. Financial modelling is a fundamental component of all business investment cases. IT security investment proposals have unique qualities that can pose expenditure justification challenges. This paper aims to explore various financial models and to develop one that IT managers can effectively use to support their business cases

On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation

The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations. Here we investigate the integrability properties of a generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e singularity structure analysis singles out a special case ($m=2$) as integrable. More interestingly, a B\"acklund transformation is shown to give rise to a linearizing transformation for the integrable case. A Lie symmetry analysis again separates out the same $m=2$ case as the integrable one and hence we report several physically interesting solutions via similarity reductions. Thus we give a group theoretical interpretation for the system under study. Explicit and numerical solutions for specific cases of nonintegrable systems are also given. In particular, the system is found to exhibit different types of travelling wave solutions and patterns, static structures and localized structures. Besides the Lie symmetry analysis, nonclassical and generalized conditional symmetry analysis are also carried out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004

OligoWalk: an online siRNA design tool utilizing hybridization thermodynamics

Given an mRNA sequence as input, the OligoWalk web server generates a list of small interfering RNA (siRNA) candidate sequences, ranked by the probability of being efficient siRNA (silencing efficacy greater than 70%). To accomplish this, the server predicts the free energy changes of the hybridization of an siRNA to a target mRNA, considering both siRNA and mRNA self-structure. The free energy changes of the structures are rigorously calculated using a partition function calculation. By changing advanced options, the free energy changes can also be calculated using less rigorous lowest free energy structure or suboptimal structure prediction methods for the purpose of comparison. Considering the predicted free energy changes and local siRNA sequence features, the server selects efficient siRNA with high accuracy using a support vector machine. On average, the fraction of efficient siRNAs selected by the server that will be efficient at silencing is 78.6%. The OligoWalk web server is freely accessible through internet at http://rna.urmc.rochester.edu/servers/oligowalk

Direct Signals for Large Extra Dimensions in the Production of Fermion Pairs at Linear Colliders

We analyze the potentiality of the new generation of $e^+e^-$ linear colliders to search for large extra dimensions via the production of fermion pairs in association with Kaluza-Klein gravitons (G), i.e. $e^+e^- \leftarrow f\bar{f}G$. This process leads to a final state exhibiting a significant amount of missing energy in addition to acoplanar lepton or jet pairs. We study in detail this reaction using full tree level contibutions due to the graviton emission and the standard model backgrounds. After choosing the cuts to enhance the signal, we show that a linear collider with a center-of-mass energy of 500 GeV will be able to probe quantum gravity scales from 0.96(0.86) up to 4.1(3.3) TeV at 2(5)$\sigma$ level, depending on the number of extra dimensions.Comment: 19 pages, 5 figures. Using RevTex, axodraw.sty. Discussion was extended. No changes in the results. Accepted for publication by Phys. Rev.