scholarly journals Pfister’s Theorem Fails in the Free Case

2012 ◽  
pp. 189-194
Author(s):  
Martin Harrison
Keyword(s):  
Free Case

scholarly journals A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 62
Author(s):  
Zhengwei Liu ◽  
Fukang Zhu
Keyword(s):  
Likelihood Estimation ◽  
Real Data ◽  
Autoregressive Models ◽  
Superior Performance ◽  
Data Sets ◽  
Binomial Thinning ◽  
Free Case ◽  
Two Parameters ◽  
Conditional Maximum ◽  
Thinning Operator

The thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended binomial is introduced, which is a general case of the binomial thinning. Compared to the binomial thinning operator, the extended binomial thinning operator has two parameters and is more flexible in modeling. Based on the proposed operator, a new integer-valued autoregressive model is introduced, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares (CLS) estimation is investigated for the innovation-free case and the conditional maximum likelihood estimation is also discussed. We have also obtained the asymptotic property of the two-step CLS estimator. Finally, three overdispersed or underdispersed real data sets are considered to illustrate a superior performance of the proposed model.

scholarly journals A Numerical Solution to Fractional Diffusion Equation for Force-Free Case

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
O. Tasbozan ◽  
A. Esen ◽  
N. M. Yagmurlu ◽  
Y. Ucar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Exact Analytical Solution ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Spline Functions ◽  
B Spline ◽  
Numerical Examples ◽  
Free Case

A collocation finite element method for solving fractional diffusion equation for force-free case is considered. In this paper, we develop an approximation method based on collocation finite elements by cubic B-spline functions to solve fractional diffusion equation for force-free case formulated with Riemann-Liouville operator. Some numerical examples of interest are provided to show the accuracy of the method. A comparison between exact analytical solution and a numerical one has been made.

Variational thermodynamic derivation of the formula for pressure difference across a charged conducting liquid surface and its relation to the thermodynamics of electrical capacitance

1995 ◽  
Vol 450 (1938) ◽  
pp. 177-192 ◽  
Keyword(s):  
Free Energy ◽  
Pressure Difference ◽  
Liquid Surface ◽  
Field Energy ◽  
Conducting Liquid ◽  
Difference Formula ◽  
Direct Energy ◽  
Free Case ◽  
Definition Of ◽  
Work Done

The formula for pressure difference across a charged conducting liquid surface has conventionally been derived by adding a Maxwell stress term to the pressure-difference formula for the field-free case. As far as can be established, no derivation applying direct energy-based methods to the charged-surface case has ever been clearly formulated. This paper presents a first-principles variational derivation, starting from the laws of thermodynamics and modelled on Gibbs’s (1875) approach to the field-free case. The derivation applies to the static equilibrium situation. The method is to treat the charged liquid and its environment as a heterogeneous system in thermodynamic equilibrium, and consider the effects of a small virtual variation in the shape of the conducting-liquid surface. Expressions can be obtained for virtual changes in the free energies of relevant system components and for the virtual electrical work done on the system. By converting the space integral of the variation in electrostatic field energy to an integral over the surface of the liquid electrode, the usual pressure-difference formula is retrieved. It is also shown how the problem can be formulated, in various ways, as a free-energy problem in a situation involving electric stresses and capacitance. The most satisfactory approach involves the definition of an unfamiliar form of free energy, that can be seen as the electrical analogue of the Gibbs free energy and may have use in other contexts.

scholarly journals Effect of Residual Stresses on the Elastoplastic Behavior of Welded Steel Plates

2020 ◽  
Vol 8 (9) ◽  
pp. 702
Author(s):  
José Manuel Gordo
Keyword(s):  
Residual Stresses ◽  
Bending Strength ◽  
Steel Plates ◽  
Finite Elements Analysis ◽  
Elastoplastic Behavior ◽  
Welded Steel ◽  
Plate Elements ◽  
Tension And Compression ◽  
Free Case ◽  
Range Of Variation

A robust methodology to simulate virtually the residual stresses pattern in welded steel plates is presented. The methodology is applied to the structural analysis of typical welded plates belonging to ship structures, and the effect of residual stresses on the elastoplastic behavior of plates loaded axially is analyzed in comparison to the residual stress free case, both for tension and compression and including initial imperfections. Residual stresses affect in different manner plates with different geometries; thus a parametric study is performed covering the usual range of variation of the most important plate parameters that control the strength of the plates, more precisely the slenderness and the aspect ratio. The results from finite elements analysis are compared with codes and most established formulations and recommendations of applicability in the prediction of load-shortening curves for hull’s bending strength evaluation, ultimate strength and ultimate strain of plate elements are made.

scholarly journals The measurements results adjustment by the Least Square Method

2021 ◽  
Vol 1 ◽  
pp. 1-8
Author(s):  
Oleksandr Samoilenko ◽  
Yurii Kuzmenko
Keyword(s):  
Reference Value ◽  
Least Square Method ◽  
Systematic Errors ◽  
Least Square ◽  
Key Comparisons ◽  
System Of Equations ◽  
The Third ◽  
Measurement Results ◽  
Free Case ◽  
Degrees Of Equivalence

The method for processing of the measurement results obtained from Comite International des Poids et Measures (CIPM) Key, Regional Metrology Organizations (RMO) or supplementary comparisons, from the proficiency testing by interlaboratory comparisons and the calibrations is proposed. It is named by authors as adjustment by least square method (LSM). Additive and multiplicative parameters for each measuring standard of every particular laboratory will be the results of this adjustment. As well as the parameters for each artifact. The parameters of the measurements standards are their additive and multiplicative degrees of equivalence from the comparison and the estimations of the systematic errors (biases) from calibrations. The parameters of the artifacts are the key comparisons reference value from the comparison and the assigned quantity values from the calibrations. The adjustment is considered as a way to solving a problem of processing the great amount of homogeneous measurements with many measuring standards at a different comparison levels (CIPM, RMO or supplementary), including connected problems. Four different cases of the adjustments are considered. The first one is a free case of adjustment. It was named so because of the fact that none of participants has any advantage except their uncertainties of measurements. The second one is a fixed case of adjustment. Measuring results of RMO and supplementary comparisons are rigidly linked to additive and multiplicative parameters of measuring standards of particular laboratories participated in CIPM key comparisons. The third one is a case of adjustment with dependent equations. This one is not so rigidly linked of the new comparisons results to previous or to some other comparisons as for fixed case. It means that the new results of comparisons are influenced by the known additive and multiplicative parameters and vice versa. The fourth one is a free case of adjustment with additional summary equations. In that case certain checking equations are added to the system of equations. So, the sum of parameters multiplied by their weights of all measurement standards for particular laboratories participated in comparisons should be equal to zero.

scholarly journals AN UNCERTAINTY PRINCIPLE FOR SOLUTIONS OF THE SCHRÖDINGER EQUATION ON -TYPE GROUPS

2020 ◽  
pp. 1-16
Author(s):  
AINGERU FERNÁNDEZ-BERTOLIN ◽  
PHILIPPE JAMING ◽  
SALVADOR PÉREZ-ESTEVA
Keyword(s):  
Schrödinger Equation ◽  
Uncertainty Principle ◽  
Schrodinger Equation ◽  
Schrodinger Equations ◽  
Nilpotent Lie Groups ◽  
Schrödinger Equations ◽  
Uncertainty Principles ◽  
Uniqueness Of Solutions ◽  
Free Case ◽  
Formula Type

In this paper we consider uncertainty principles for solutions of certain partial differential equations on $H$ -type groups. We first prove that, on $H$ -type groups, the heat kernel is an average of Gaussians in the central variable, so that it does not satisfy a certain reformulation of Hardy’s uncertainty principle. We then prove the analogue of Hardy’s uncertainty principle for solutions of the Schrödinger equation with potential on $H$ -type groups. This extends the free case considered by Ben Saïd et al. [‘Uniqueness of solutions to Schrödinger equations on H-type groups’, J. Aust. Math. Soc. (3)95 (2013), 297–314] and by Ludwig and Müller [‘Uniqueness of solutions to Schrödinger equations on 2-step nilpotent Lie groups’, Proc. Amer. Math. Soc.142 (2014), 2101–2118].

Characterization of Nb-Microsegregation and Eutectic Carbide in As-Cast Nb-Microalloyed Al-Free Case Hardening Steel

2017 ◽  
Vol 88 (10) ◽  
pp. 1700092 ◽  
Author(s):  
Mamta Sharma ◽  
Silvia Richter ◽  
Ulrich Prahl ◽  
Wolfgang Bleck
Keyword(s):  
Case Hardening ◽  
Eutectic Carbide ◽  
Free Case ◽  
Case Hardening Steel

scholarly journals A rigorous mathematical treatment of the shape of a dissipative rope fountain

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190612
Author(s):  
Jonathan J. Bevan ◽  
Jonathan H. B. Deane
Keyword(s):  
Energy Conservation ◽  
Drag Force ◽  
Numerical Study ◽  
Analytical Description ◽  
Mathematical Treatment ◽  
Numerical Treatment ◽  
Constant Tension ◽  
Free Case ◽  
Parameter Values

This is a theoretical and numerical study of a model of a rope fountain subject to a drag force that depends linearly on the rope velocity. A precise, analytical description of the long-term shape adopted by the rope is given, and various consequences are derived from it. Using parameters that naturally appear in the model, we distinguish between cases wherein energy is conserved by means of a constant tension far from the rope source (the ‘free’ case) and where energy conservation is a consequence of a non-constant tension (the ‘braked’ case). The model is used, among other things, to generate rope fountain shapes based on approximate experimental estimates of the parameter values and a careful numerical treatment.

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