Simple Compact Form Research Articles

Generalized Darboux transformation for nonlinear Schrödinger system on general Hermitian symmetric spaces and rogue wave solutions

In this paper, a generalized Darboux transformation is obtained for Fordy–Kulish NLS (nonlinear Schrödinger) systems on general Hermitian symmetric spaces in order to rigorously obtain rogue wave solutions for these systems. In particular, we express the generalized algebraic relations in a simple and elegant compact form. As an illustration, we derive multi-soliton, breather-type and mainly rogue wave solutions of triangular patterns for single- and multi-component NLS systems on [Formula: see text] and [Formula: see text] respectively. We also analyze the modulation instability of proper plane wave solutions. In order to get visual intuition for the dynamics of the result and solutions for the running examples, the associated simulations of profiles are furnished as well.

A bispinor formalism for spinning Witten diagrams

We develop a new embedding-space formalism for AdS4 and CFT3 that is useful for evaluating Witten diagrams for operators with spin. The basic variables are Killing spinors for the bulk AdS4 and conformal Killing spinors for the boundary CFT3. The more conventional embedding space coordinates XI for the bulk and PI for the boundary are bilinears in these new variables. We write a simple compact form for the general bulk-boundary propagator, and, for boundary operators of spin ℓ ≥ 1, we determine its conservation properties at the unitarity bound. In our CFT3 formalism, we identify an mathfrak{so} (5, 5) Lie algebra of differential operators that includes the basic weight-shifting operators. These operators, together with a set of differential operators in AdS4, can be used to relate Witten diagrams with spinning external legs to Witten diagrams with only scalar external legs. We provide several applications that include Compton scattering and the evaluation of an R4 contact interaction in AdS4. Finally, we derive bispinor formulas for the bulk-to-bulk propagators of massive spinor and vector gauge fields and evaluate a diagram with spinor exchange.

Ab initio dielectronic recombination rate coefficients for highly-charged Ar-like ions

Employing the independent-processes isolated-resonance distorted-wave approximation, we have made a comprehensive study on dielectronic recombination (DR) for 19 highly-charged Ar-like ions with nuclear charge number Z=23–30, 36, 42, 50, 54, 60, 64, 70, 74, 79, 85 and 92. For the convenience of usage, the ab initio level-by-level total rate coefficients for DR initially from both the ground state 3s23p6 1S0 and the metastable state 3s23p53d 3P0 are presented in a simple compact fitting form. We include the 3 → 3 (Δn=0), 2 → 3 and 3 → 4 (Δn=1), and 3 → 5 (Δn=2) core-excitations resonances as well as the decays from the resonances toward low-lying autoionizing levels followed possibly by radiative cascade effects in our ab initio DR results. The detailed configuration interaction analysis and comparisons with both theoretical and experimental results show that present total DR rate coefficients are reliable at both low (with a typical uncertainty of a factor of 2 in the photoionized plasma zone) and high (with an uncertainty of about 20% in the collisional plasma zone) temperature. To our knowledge, these are the first ab initio DR results for most of ions with Z > 30.

The most general \u03bb-deformation of CFTs and integrability

We show that the CFT with symmetry group {G}_{k_1}times {G}_{k_2}times cdots times {G}_{k_n} consisting of WZW models based on the same group G, but at arbitrary integer levels, admits an integrable deformation depending on 2(n − 1) continuous parameters. We derive the all-loop effective action of the deformed theory and prove integrability. We also calculate the exact in the deformation parameters RG flow equations which can be put in a particularly simple compact form. This allows a full determination and classification of the fixed points of the RG flow, in particular of those that are IR stable. The models under consideration provide concrete realizations of integrable flows between CFTs. We also consider non-Abelian T-duality type limits.

A semi-analytical approach for SH guided wave mode conversion from evanescent into propagating

Conversion of evanescent shear horizontal (SH) guided waves into propagating is presented in this paper. The conversion is exemplified by a time-harmonic SH evanescent displacement prescribed on a narrow aperture at an edge of a semi-infinite isotropic plate. The conversion efficiency in terms of the amplitude of the propagating SH mode converted from evanescent can be expressed in a very simple compact form. The magnitude of the conversion efficiency can be quantified through a derived semi-analytical form based on the complex reciprocity theorem in conjunction with a two-dimensional (2-D) finite element analysis (FEA). Through power conversion analysis, it can be shown that the power flow generated into the plate due to evanescent incident is complex valued. It is theoretically proved that the real part of the complex power flow is associated with the propagating SH modes, while the imaginary part is confined due to the evanescent modes at the plate edge. The conversion efficiency and converted modes are dependent on the geometric configuration of the aperture as well as the selection of the excitation frequency.

Two-loop gravity amplitudes from four dimensional unitarity

We compute the polylogarithmic parts of the two-loop four and five-graviton amplitudes where the external helicities are positive and express these in a simple compact analytic form. We use these to extract the $\ln(\mu^2)$ terms from both the four and five-point amplitudes and show that these match the same $R^3$ counterterm.

An analytical model of triple‐material double‐gate metal–oxide–semiconductor field‐effect transistor to suppress short‐channel effects

SummaryThis paper presents an analytical subthreshold model for surface potential and threshold voltage of a triple‐material double‐gate (DG) metal–oxide–semiconductor field‐effect transistor. The model is developed by using a rectangular Gaussian box in the channel depletion region with the required boundary conditions at the source and drain end. The model is used to study the effect of triple‐material gate structure on the electrical performance of the device in terms of changes in potential and electric field. The device immunity against short‐channel effects is evaluated by comparing the relative performance parameters such as drain‐induced barrier lowering, threshold voltage roll‐off, and subthreshold swing with its counterparts in the single‐material DG and double‐material DG metal–oxide–semiconductor field‐effect transistors. The developed surface potential model not only provides device physics insight but is also computationally efficient because of its simple compact form that can be utilized to study and characterize the gate‐engineered devices. Furthermore, the effects of quantum confinement are analyzed with the development of a quantum‐mechanical correction term for threshold voltage. The results obtained from the model are in close agreement with the data extracted from numerical Technology Computer Aided Design device simulation. Copyright © 2015 John Wiley & Sons, Ltd.

Multiple scattering effects on inclusive particle production in the large-xregime

We study the multiple scattering effects on inclusive particle production in $\mathrm{p}+\mathrm{A}$ and $\ensuremath{\gamma}+\mathrm{A}$ collisions. Specifically, we concentrate on the region where the parton momentum fraction in the nucleus $x\ensuremath{\sim}\mathcal{O}(1)$ and incoherent multiple interactions are relevant. By taking into account both initial-state and final-state double scattering, we derive the nuclear size-enhanced power corrections to the differential cross section for single inclusive hadron production in $\mathrm{p}+\mathrm{A}$ and $\ensuremath{\gamma}+\mathrm{A}$ reactions, and for prompt photon production in $\mathrm{p}+\mathrm{A}$ reactions. We find that the final result can be written in a simple compact form in terms of four-parton correlation functions, in which the second-derivative, first-derivative and nonderivative terms of the correlation distributions share the same hard-scattering functions. We expect our result to be especially relevant for understanding the nuclear modification of particle production in the backward rapidity regions in $\mathrm{p}+\mathrm{A}$ and $\mathrm{e}+\mathrm{A}$ collisions.

Small-sample likelihood inference in extreme-value regression models

We deal with a general class of extreme-value regression models introduced by Barreto-Souza and Vasconcellos [Bias and skewness in a general extreme-value regression model, Comput. Statist. Data Anal. 55 (2011), pp. 1379–1393]. Our goal is to derive an adjusted likelihood ratio statistic that is approximately distributed as χ2 with a high degree of accuracy. Although the adjusted statistic requires more computational effort than its unadjusted counterpart, it is shown that the adjustment term has a simple compact form that can be easily implemented in standard statistical software. Further, we compare the finite-sample performance of the three classical tests (likelihood ratio, Wald, and score), the gradient test that has been recently proposed by Terrell [The gradient statistic, Comput. Sci. Stat. 34 (2002), pp. 206–215], and the adjusted likelihood ratio test obtained in this article. Our simulations favour the latter. Applications of our results are presented.

Some restriction tests in a new class of regression models for proportions

The main purpose of this work is to study the behaviour of Skovgaard’s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian Journal of Statistics 28, 3–32] adjusted likelihood ratio statistic in testing simple hypothesis in a new class of regression models proposed here. The proposed class of regression models considers Dirichlet distributed observations, and the parameters that index the Dirichlet distributions are related to covariates and unknown regression coefficients. This class is useful for modelling data consisting of multivariate positive observations summing to one and generalizes the beta regression model described in Vasconcellos and Cribari-Neto [Vasconcellos, K.L.P., Cribari-Neto, F., 2005. Improved maximum likelihood estimation in a new class of beta regression models. Brazilian Journal of Probability and Statistics 19, 13–31]. We show that, for our model, Skovgaard’s adjusted likelihood ratio statistics have a simple compact form that can be easily implemented in standard statistical software. The adjusted statistic is approximately chi-squared distributed with a high degree of accuracy. Some numerical simulations show that the modified test is more reliable in finite samples than the usual likelihood ratio procedure. An empirical application is also presented and discussed.

Skovgaard’s adjustment to likelihood ratio tests in exponential family nonlinear models

Likelihood ratio tests can be substantially size distorted in small- and moderate-sized samples. In this paper, we apply Skovgaard’s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian Journal of Statistics 28, 3–32] adjusted likelihood ratio statistic to exponential family nonlinear models. We show that the adjustment term has a simple compact form that can be easily implemented from standard statistical software. The adjusted statistic is approximately distributed as χ 2 with high degree of accuracy. It is applicable in wide generality since it allows both the parameter of interest and the nuisance parameter to be vector-valued. Unlike the modified profile likelihood ratio statistic obtained from Cox and Reid [Cox, D.R., Reid, N., 1987. Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society B 49, 1–39], the adjusted statistic proposed here does not require an orthogonal parameterization. Numerical comparison of likelihood-based tests of varying dispersion favors the test we propose and a Bartlett-corrected version of the modified profile likelihood ratio test recently obtained by Cysneiros and Ferrari [Cysneiros, A.H.M.A., Ferrari, S.L.P., 2006. An improved likelihood ratio test for varying dispersion in exponential family nonlinear models. Statistics and Probability Letters 76 (3), 255–265].

Delamination Analysis of Layered Shells

This article provides a theoretical and numerical treatment of delaminations in composite shells. A large deformation theory for layered shells of arbitrarily varying thickness, including interface delamination and transverse shear effects, is developed. Asystem of layer coordinates and conjugate coordinates is introduced which allows the results to be presented in a simple compact form analogous to the theory of monocoque shells. To validate the feasibility and the accuracy of the developed theory, a numerical example is provided. The results of the present theory are compared for a one dimensional beam with results obtained from two dimensional finite element analysis and excellent agreement is observed.

Delamination Analysis of Layered Shells

This article provides a theoretical and numerical treatment of delaminations in composite shells. A large deformation theory for layered shells of arbitrarily varying thickness, including interface delamination and transverse shear effects, is developed. Asystem of layer coordinates and conjugate coordinates is introduced which allows the results to be presented in a simple compact form analogous to the theory of monocoque shells. To validate the feasibility and the accuracy of the developed theory, a numerical example is provided. The results of the present theory are compared for a one dimensional beam with results obtained from two dimensional finite element analysis and excellent agreement is observed.

The photogravitational three-body problem: The approximation of the collinear equilibria in a simple compact form

The collinear equilibrium points of the three-body problem for cases where the moving particle is further acted upon by a weak radiation pressure are given approximately in a simple compact form.

Moment-method determination of the surface currents and fields radiated by rectangular microstrip patch-antennas

A quantitative solution is presented of the surface currents and the corresponding fields generated in free space by electrically thin microstrip patch-antennas of rectangular configuration. Use is made of a versatile analytical tool known as the method of moments, in which the surface current density is approximated by a series expansion involving piece wise linear basis functions and weighted superposition coefficients which are to be determined. It is shown that when the governing integro-diflerential equations are reformulated in matrix form involving generalized network parameters, the desired current distribution emerges in a simple compact form. A remarkable feature of the result of the present analysis is the fact that the field induced in the substrate is due to a finite charge distribution rather than the previously implied phenomenon, viz. the influence of an infinite charge distribution. Indeed, the charge distribution responsible is directly derivable from the time-harmonic continuity equatio...

Evaluation of the spectra of sum and product functions

The derivation is given of a simple compact form for evaluating the spectra for the sum and product of two functions in terms of their individual spectra alone. The method avoids the reintroduction of the transform. The results are extended to include the exclusive-OR function and are easily applied for the computation of the spectra of more complex Boolean functions in terms of their individual spectra.

Evaluation of the spectra of sum and product functions

The derivation is given of a simple compact form for evaluating the spectra for the sum and product of two functions in terms of their individual spectra alone. The method avoids the reintroduction of the transform. The results are extended to include the exclusive-OR function and are easily applied for the computation of the spectra of more complex Boolean functions in terms of their individual spectra.

Nonlinear analysis of multilayered shells

A large deformation theory for layered shells of arbitrarily varying thickness and using a piecewise smooth displacement field is developed. A system of layer coordinates is introduced which allows the results to be presented in a simple compact form analogous to the theory of monocoque shells.

Analytic and Numeric Integration for Quadrilaterals

Two-dimensional finite element analysis uses linear edge arbitrary quadrilaterals with hyperbolic paraboloid shape functions as an important element. To obtain the element stiffness matrix, such a procedure leads to evaluation of integrals involving irrational polynomials and analytic evaluation of such expressions presents considerable difficulty. Almost without exception, the evaluation of integrals has either been done or suggested by using a numerical quadrature of the Legendre-Gauss type. However, what is clearly lacking is quantitative information pertaining to the order of the quadrature formula to be used for various degrees of artibrariness in a quadrilateral. In the subsequent development, it is shown how the equations can be manipulated to yield a simple compact form amenable to closed-form solution, yielding simple programmable expressions, and how they compare with the quadrature formula.

General Hydrodynamic Equations from the Linear Boltzmann Equation

A derivation of hydrodynamic equations from the linearized Boltzmann equation is presented which is based upon Zwanzig's projection operator method. This is obtained in the simple compact form of linearized Burnett equations with frequency and wavelength dependent transport coefficients, for which explicit expressions are given for well-behaved intermolecular potentials. The effects of the initial distribution function may be included, although for long times the initial state terms disappear. This disappearance of the initial state terms implies that for long times the general hydrodynamic equations and the Chapman-Enskog hydrodynamic equations agree. The latter are exact for all times for a special initial state. As an application of the theory, an expression is found for the dispersion equation for sound propagating in a gas, that holds for any well-behaved intermolecular potential.