Ones Of Order Research Articles

Fast calculation of gravitational effects using tesseroids with a polynomial density of arbitrary degree in depth

Fast and accurate calculation of gravitational effects on a regional or global scale with complex density environment is a critical issue in gravitational forward modelling. Most existing significant developments with tessroid-based modelling are limited to homogeneous density models or polynomial ones of a limited order. Moreover, the total gravitational effects of tesseroids are often calculated by pure summation in these methods, which makes the calculation extremely time-consuming. A new efficient and accurate method based on tesseroids with a polynomial density up to an arbitrary order in depth is developed for 3D large-scale gravitational forward modelling. The method divides the source region into a number of tesseroids, and the density in each tesseroid is assumed to be a polynomial function of arbitrary degree. To guarantee the computational accuracy and efficiency, two key points are involved: (1) the volume Newton’s integral is decomposed into a one-dimensional integral with a polynomial density in the radial direction, for which a simple analytical recursive formula is derived for efficient calculation, and a surface integral over the horizontal directions evaluated by the Gauss–Legendre quadrature (GLQ) combined with a 2D adaptive discretization strategy; (2) a fast and flexible discrete convolution algorithm based on 1D fast Fourier transform (FFT) and a general Toepritz form of weight coefficient matrices is adopted in the longitudinal dimension to speed up the computation of the cumulative contributions from all tesseroids. Numerical examples show that the gravitational fields predicted by the new method have a good agreement with the corresponding analytical solutions for spherical shell models with both polynomial and non-polynomial density variations in depth. Compared with the 3D GLQ methods, the new algorithm is computationally more accurate and efficient. The calculation time is significantly reduced by 3 orders of magnitude as compared with the traditional 3D GLQ methods. Application of the new algorithm in the global crustal CRUST1.0 model further verifies its reliability and practicability in real cases. The proposed method will provide a powerful numerical tool for large-scale gravity modelling and also an efficient forward engine for inversion and continuation problems.

Understanding key factors controlling the duration of river flow intermittency: Case of Burkina Faso in West Africa

Study regionThis study focused mainly on Burkina Faso in West Africa. Study focusThis study aims to identify environmental variables that best explain the geographic variations of the flow intermittency regime, focusing on intermittency duration. Discharge data from 49 gauging stations were considered, mostly over large rivers. The mean number of dry months (Ndry¯) was used as a predictor to define four classes of flow intermittency, for which the potential explanatory environmental variables were assessed based on correlation analysis and principal component analysis (PCA). New hydrological insights for the regionThe first two components (PCs) account for 82 % of the total variance with PC1 (52 %), and most of the catchments with similar flow intermittency are ordered according to PC2 (30 %), predominantly related to catchment permeability. Moreover, permeability was highly correlated with Ndry¯ (r = - 0.75). Results suggest that catchment permeability and catchment areas are the most critical variables in determining flow intermittency classes in Burkina Faso, as the effect of precipitation can be overruled by the ones of permeability, catchment area, and Strahler order. This study is a first step in understanding the controls of river intermittency in data-scarce and poorly gauged regions of West Africa. The identified variables could be used as input in statistical models to predict and map river intermittency and provide valuable information for stream conservation.

Discrete-Time Super-Twisting Fractional-Order Differentiator With Implicit Euler Method

This brief proposes a discrete-time fractional-order differentiator based on the super-twisting algorithm for second-order systems. The differentiator achieves higher performance with respect to the classical ones of integer order in terms of convergence time and robustness. It relaxes the classical boundedness condition required to be satisfied by the second-order derivatives of the functions in conventional differentiators. The numerical integration is performed by an implicit Euler discretization technique based on the Fractional Adams-Moulton method, which significantly suppresses the chattering. The significance of the proposed differentiator is demonstrated through a simulation example, comparing with the classical ones.

L p polyharmonic Robin problems on Lipschitz domains

ABSTRACT In this paper, we study a class of boundary value problems (BVPs) with Robin conditions in some spaces for polyharmonic equation on Lipschitz domains. Utilizing polyharmonic fundamental solutions, these Robin BVPs are solved by the method of layer potentials. The crucial ingedients of our approach are the classical single layer potential and its higher order analog (which are called multi-layer S-potentials), and the main results generalize ones of second order (Laplacian) case to higher order (polyharmonic) case.

Highly efficient family of iterative methods for solving nonlinear models

In this study, we present a new highly efficient sixth-order family of iterative methods for solving nonlinear equations along with convergence properties. Further, we extend this family to the multidimensional case preserving the same order of convergence. In order to illustrate the applicability of our methods, we choose some real world problems namely, kinematic syntheses, boundary value, Bratu’s 2D, Fisher’s and Hammerstein integral problems in the case of nonlinear systems (see Farhane et al., 2017 [ 1 ]; Kaur and Arora, 2017 [ 2 ] for more applications) . In addition, numerical comparisons are made to show the performance of our iterative techniques with the existing ones. Moreover, we find that our techniques perform better as compared to the existing ones of same order in terms of residual error and the errors between two consecutive iterations. Finally, the stability analysis of our methods also support this to great extent.

Some higher-order iteration functions for solving nonlinear models

In this paper, we present a new efficient sixth-order family of Jarratt type methods for solving scalar equations. Then, we extend this family to the multidimensional case preserving the same order of convergence. We also discuss the theoretical convergence properties of the proposed scheme in the case of scalar as well as multidimensional case. The derivation of these schemes are based on weight function approach and free disposable parameters. We also demonstrate the applicability of them on total six number of problems: first five are real life problems namely, continuous stirred tank reactor (CSTR), chemical engineering, the trajectory of an electron in the air gap between two parallel plates, Hammerstein integration and boundary value problems; last one is the standard academic test problem. In addition, numerical comparisons are made to show the performance of the proposed iterative techniques with the existing techniques of the same order in the scalar as well as multi-dimensional case. Finally on the basis of numerical results, we conclude that our techniques perform better in terms of residual error, error between the two consecutive iterations, asymptotic error constant term and approximated root as compared to the existing ones of same order in scalar as well as multidimensional case.

Some novel and optimal families of King’s method with eighth and sixteenth-order of convergence

In this study, our principle aim is to provide some novel eighth and sixteenth-order families of King’s method for solving nonlinear equations which should be superior than the existing schemes of same order. The relevant optimal orders of the proposed families satisfy the classical Kung–Traub conjecture which was made in 1974. The derivations of the proposed schemes are based on the weight function and rational approximation approaches, respectively. In addition, convergence properties of the proposed families are fully investigated along with one lemma and two main theorems describing their order of convergence. We consider a concrete variety of real life problems e.g. the trajectory of an electron in the air gap between two parallel plates, chemical engineering problem, Van der Waal’s equation which explains the behavior of a real gas by introducing in the ideal gas equations and fractional conversion in a chemical reactor, in order to check the validity, applicability and effectiveness of our proposed methods. Further, it is found from the numerical results that our proposed methods perform better than the existing ones of the same order when the accuracy is checked in the multi precision digits.

On the Analysis of Multistep-Out-of-Grid Method for Celestial Mechanics Tasks

Abstract Occasionally, there is a necessity in high-accurate prediction of celestial body trajectory. The most common way to do that is to solve Kepler’s equation analytically or to use Runge-Kutta or Adams integrators to solve equation of motion numerically. For low-orbit satellites, there is a critical need in accounting geopotential and another forces which influence motion. As the result, the right side of equation of motion becomes much bigger, and classical integrators will not be quite effective. On the other hand, there is a multistep-out-of-grid (MOG) method which combines Runge-Kutta and Adams methods. The MOG method is based on using m on-grid values of the solution and n × m off-grid derivative estimations. Such method could provide stable integrators of maximum possible order, O (hm + mn + n− 1). The main subject of this research was to implement and analyze the MOG method for solving satellite equation of motion with taking into account Earth geopotential model (ex. EGM2008 (Pavlis at al., 2008)) and with possibility to add other perturbations such as atmospheric drag or solar radiation pressure. Simulations were made for satellites on low orbit and with various eccentricities (from 0.1 to 0.9). Results of the MOG integrator were compared with results of Runge-Kutta and Adams integrators. It was shown that the MOG method has better accuracy than classical ones of the same order and less right-hand value estimations when is working on high orders. That gives it some advantage over ”classical” methods.

O (re)nascimento de um corpo professoral: os estatutos do magistério público do Estado de Santa Catarina de 1960 e 1975

O presente artigo analisa uma das dimensões do processo histórico de democratização da educação no Estado de Santa Catarina, a saber: os estatutos do magistério público dos anos de 1960 e 1975, que regulamentaram a carreira do magistério, contribuindo, assim, para uma (re)definição da identidade dos professores e a consolidação da profissão docente. Dentre muitos aspectos que compõem a identidade profissional, destacam-se os de ordem moral, considerando-se três categorias: os requisitos para ingresso na carreira, as regras de permanência no magistério e as sanções disciplinares. Os documentos, por intermédio da instituição de competências e condutas que deveriam ser seguidas por todos, estabelecem uma ordem moral e inauguram uma ordem professoral. Constata-se a continuidade de grande parte das prerrogativas legais que orientaram a constituição do corpo docente no início dos anos 1960 e o estabelecimento de novas regras para o exercício do magistério nos anos 1975. Verifica-se também que os dois dispositivos apresentam um caráter normativo fortemente fundado em regras morais, o que levou a buscar os escritos de Émile Durkheim (1858-1917) relacionados ao elemento disciplinar da moralidade.

Functional representation of the negative DNLS hierarchy

This paper is devoted to the negative flows of the derivative nonlinear Schrödinger hierarchy (DNLSH). The main result of this work is the functional representation of the extended DNLSH, composed of both positive (classical) and negative flows. We derive a finite set of functional equations, constructed by means of the Miwa's shifts, which contains all equations of the hierarchy. Using the obtained functional representation we convert the nonlocal equations of the negative subhierarchy into local ones of higher order, derive the generating function of the conservation laws and the N-soliton solutions for the extended DNLSH under non-vanishing boundary conditions.

Post-Lesson Observation Conferencing of University Supervisors and Physical Education Teacher Education Students

The purpose of our descriptive study was to examine post-lesson observation conferencing discourse between university supervisors (USs) and physical education teacher education students (PTs). Three USs completed a questionnaire related to demographic information and their perceptions of their role as a supervisor. These USs then audio-recorded post-lesson observation conferences that they held with their PTs. A total of 54 conferences were audio-recorded and transcribed for analysis. Results revealed that the USs believed in a collaborative approach to supervision and that is what occurred as PTs spoke slightly more than USs. Of all of the idea units spoken by USs, 31% of them were questions. USs had far more higher order questions and offerings than they did lower order ones. PTs also had far more higher order offerings than ones of lower order.

A recursive construction of nonbinary de Bruijn sequences

This paper presents a method to find new de Bruijn sequences based on ones of lesser order. This is done by mapping a de Bruijn cycle to several vertex disjoint cycles in a de Bruijn digraph of higher order and then connecting these cycles into one full cycle. We present precise formulae for the locations where those cycles can be rejoined into one full cycle. We obtain an exponentially large class of distinct de Bruijn cycles. This method generalizes the Lempel construction of binary de Bruijn sequences as well as its efficient implementation by Annextein.

Relativity constraints on the two-nucleon contact interaction

We construct the most general, relativistically invariant, contact Lagrangian at order Q^2 in the power counting, Q denoting the low momentum scale. A complete, but non-minimal, set of (contact) interaction terms is identified, which upon non-relativistic reduction generate 2 leading independent operator combinations of order Q^0 and 7 sub-leading ones of order Q^2 - a result derived previously in the heavy-baryon formulation of effective field theories (EFT's). We show that Poincare covariance of the theory requires that additional terms with fixed coefficients be included, in order to describe the two-nucleon potential in reference frames other than the center-of-mass frame. These terms will contribute in systems with mass number A>2, and their impact on EFT calculations of binding energies and scattering observables in these systems should be studied.

Fine gradings on the Lie algebra

As it is well known, there is an element in the family of classical Lie algebras which presents more symmetries than the others. We are speaking, of course, about the algebra which, together with the usual two-fold symmetry which is common to the whole family, presents an order three symmetry which makes of it an “exceptional” classical Lie algebra. In this work we describe the fine group gradings induced by outer automorphisms of the Lie algebra . The qualitative approach used here emphasizes some algebraic aspects, as triality, and it is devoted to gradings involving the outer automorphisms of order three. The computation of the remaining fine group gradings, the ones induced by inner automorphisms and outer ones of order two, follows the same pattern as the classical case with n ≥ 5 and so it has been previously considered in the literature.

Manifestation of Work Function Difference in High Order Gundlach Oscillation

Gundlach oscillation (or the standing-wave state) is a general phenomenon manifesting in the tunneling spectrum acquired from a metal surface using scanning tunneling spectroscopy. Previous studies relate the energy shift between peaks of the lowest-order Gundlach oscillation observed on the thin film and the metal substrate to the difference in their work functions. By observing Gundlach oscillations on Ag/Au(111), Ag/Cu(111), and Co/Cu(111) systems, we demonstrate that the work function difference is not the energy shift of the lowest order but the ones of higher order where a constant energy shift exhibits. Higher order Gundlach oscillations can thus be applied to determine the work function of thin metal films precisely.

Finite Discrete, Shift-Invariant, Directional Filterbanks for Visual Information Processing, I : Construction

As is well known in neuroscience, simple cells of the mammalian’s striate cortex possess both orientation and spatial-frequency selectivity, and are similar to the Gabor filters or Gaussian derivative filters in shape. The purpose of this paper is to propose a method of designing perfect reconstruction 2D filterbanks which act on finite dimensional linear spaces consisting of 2D signals of a certain size, and have several analogous features to simple cells: (1) the filterbanks consist of several spatial-frequency channels with orientation selectivity, (2) the filterbanks have shift-invariant multiresolution (multiscale) structures, (3) filters contained in them are FIR, and are similar in appearance to not only Gaussian derivatives of 1st and 2nd order, but also ones of higher order. Moreover, they are constructed by finite linear combinations of separable filters. As is described in the text, by virtue of these properties, our 2D filterbanks can become bases of constructing computational nonlinear models of visual information processing. In this paper we construct the 2D filterbanks, and discuss them from the viewpoint of vision science. For example we disclose a possible role of “Gaussian-derivative-like” filters of higher order in our filterbanks. Practical applications of our 2D filterbanks to vision science and image processing will be given in our subsequent papers.

Some Eighth Order Mock Theta Functions

A method is developed for obtaining Ramanujan's mock theta functions from ordinary theta functions by performing certain operations on their q-series expansions. The method is then used to construct several new mock theta functions, including the first ones of eighth order. Summation and transformation formulae for basic hypergeometric series are used to prove that the new functions actually have the mock theta property. The modular transformation formulae for these functions are obtained.

Method for measuring properties of high relative dielectric constant materials in a cutoff waveguide cavity

In this paper, a method for measuring properties of ceramic materials with relative dielectric constant value of 20-150 is proposed. It permits us to eliminate the operating TM/sub 01/spl delta//-mode degeneration due to its frequency coincidence with other modes, including ones of higher order. Both that fact and the possibility of precise calculation of an unloaded quality factor for a cavity permit one to execute the accurate measurements of loss tangent values as low as (1/spl divide/0, 5)/spl times/10/sup -4/, the error of dielectric constant measurement being equal to or less than 1%. The feasibility of precise measurement of the loaded Q-factor of a cavity by the readings of micrometric probe makes the use of frequency meters unnecessary.

On The Thermoelectric Power And Transport Properties Of Quasicrystals

Stable quasicrystals exhibit specific and unusual physical properties, such as, diamagnetism, low electrical conductivity, low thermal conductivity, and large themoelectric power at room temperature. These properties can be understood with a Bragg's reflexions scheme due to their dense filled reciprocal space.This leads to small gaps on the Fermi surface (some tenths of eV), much narrower than the usual Hume-Rothery ones (of order of 0.5 eV) which explain their stability. These gaps lead to the existence of quasi Umklapp processes, crucial for the interpretation of thermoelectric power. In some cases, the positive phonon drag contribution due to Umklapp processes, add with the electronic one's and dominates at room temperature with a large positive thermoelectric power. A crude estimate of the figure of merit gives some hope for applications of some quasicrystals and high approximants as new thermoelectric materials.

Krylov Subspace Methods for Solving Large Lyapunov Equations

This paper considers several methods for calculating low-rank approximate solutions to large-scale Lyapunov equations of the form $AP + PA' + BB' = 0$. The interest in this problem stems from model reduction where the task is to approximate high-dimensional models by ones of lower order. The two recently developed Krylov subspace methods exploited in this paper are the Arnoldi method [Saad, Math. Comput., 37 (1981), pp. 105–126] and the Generalised Minimum Residual method (GMRES) [Saad and Schultz, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856–869]. Exact expressions for the approximation errors incurred are derived in both cases. The numerical solution of the low-dimensional linear matrix equation arising from the GMRES method is discussed and an algorithm for its solution is proposed. Low rank solutions of discrete time Lyapunov equations and continuous time algebraic Riccati equations are also considered. Throughout this paper, the authors tackle problems in which B has more than one column with the use of block Krylov schemes.