scholarly journals Equality of Ultradifferentiable Classes by Means of Indices of Mixed O-regular Variation

2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Javier Jiménez-Garrido ◽  
Javier Sanz ◽  
Gerhard Schindl
Keyword(s):  
Weight Function ◽  
Regular Variation ◽  
Weight Functions ◽  
Growth Indices ◽  
Ultradifferentiable Function ◽  
Weight Sequence ◽  
Function Classes ◽  
Comparison Results

AbstractWe characterize the equality between ultradifferentiable function classes defined in terms of abstractly given weight matrices and in terms of the corresponding matrix of associated weight functions by using new growth indices. These indices, defined by means of weight sequences and (associated) weight functions, are extending the notion of O-regular variation to a mixed setting. Hence we are extending the known comparison results concerning classes defined in terms of a single weight sequence and of a single weight function and give also these statements an interpretation expressed in O-regular variation.

scholarly journals Solid hulls and cores of classes of weighted entire functions defined in terms of associated weight functions

2020 ◽  
Vol 114 (4) ◽  
Author(s):  
Gerhard Schindl
Keyword(s):  
Weight Function ◽  
Entire Functions ◽  
Growth Behavior ◽  
Weight Functions ◽  
Additional Information ◽  
Function Classes ◽  
Regularity Properties

Abstract In the spirit of very recent articles by J. Bonet, W. Lusky and J. Taskinen we are studying the so-called solid hulls and cores of spaces of weighted entire functions when the weights are given in terms of associated weight functions coming from weight sequences. These sequences are required to satisfy certain (standard) growth and regularity properties which are frequently arising and used in the theory of ultradifferentiable and ultraholomorphic function classes (where also the associated weight function plays a prominent role). Thanks to this additional information we are able to see which growth behavior the so-called ”Lusky-numbers”, arising in the representations of the solid hulls and cores, have to satisfy resp. if such numbers can exist.

Moving Weighted Averages

1993 ◽  
Vol 45 (3) ◽  
pp. 449-469 ◽  
Author(s):  
M. A. Akcoglu ◽  
Y. Déniel
Keyword(s):  
Weight Function ◽  
Sufficient Conditions ◽  
Nonnegative Function ◽  
Finite Measure ◽  
Weight Functions ◽  
Ergodic Averages ◽  
Fixed Weight ◽  
Finite Measure Space ◽  
Image Position ◽  
Necessary And Sufficient

AbstractLet ℝ denote the real line. Let {Tt}tєℝ be a measure preserving ergodic flow on a non atomic finite measure space (X, ℱ, μ). A nonnegative function φ on ℝ is called a weight function if ∫ℝ φ(t)dt = 1. Consider the weighted ergodic averagesof a function f X —> ℝ, where {θk} is a sequence of weight functions. Some sufficient and some necessary and sufficient conditions are given for the a.e. convergence of Akf, in particular for a special case in whichwhere φ is a fixed weight function and {(ak, rk)} is a sequence of pairs of real numbers such that rk > 0 for all k. These conditions are obtained by a combination of the methods of Bellow-Jones-Rosenblatt, developed to deal with moving ergodic averages, and the methods of Broise-Déniel-Derriennic, developed to deal with unbounded weight functions.

Numerical solutions and analysis of diffusion for new generalized fractional Burgers equation

2013 ◽  
Vol 16 (3) ◽  
Author(s):  
Yufeng Xu ◽  
Om Agrawal
Keyword(s):  
Finite Difference ◽  
Diffusion Process ◽  
Weight Function ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Weight Functions ◽  
Linear Recurrence ◽  
Scale Function ◽  
Special Cases ◽  
Wide Range

AbstractIn this paper, numerical solutions of Burgers equation defined by using a new Generalized Time-Fractional Derivative (GTFD) are discussed. The numerical scheme uses a finite difference method. The new GTFD is defined using a scale function and a weight function. Many existing fractional derivatives are the special cases of it. A linear recurrence relationship for the numerical solutions of the resulting system of linear equations is found via finite difference approach. Burgers equations with different fractional orders and coefficients are computed which show that this numerical method is simple and effective, and is capable of solving the Burgers equation accurately for a wide range of viscosity values. Furthermore, we study the influence of the scale and the weight functions on the diffusion process of Burgers equation. Numerical simulations illustrate that a scale function can stretch or contract the diffusion on the time domain, while a weight function can change the decay velocity of the diffusion process.

Weight functions method for stability analysis applied as design tool for Hawker 800XP aircraft

2015 ◽  
Vol 119 (1218) ◽  
pp. 981-998 ◽  
Author(s):  
N. Anton ◽  
R. M. Botez
Keyword(s):  
Stability Analysis ◽  
Weight Function ◽  
Flight Test ◽  
Design Tool ◽  
System Stability ◽  
Weight Functions ◽  
Geometrical Parameters ◽  
System Modelling ◽  
Stable Model ◽  
Stability Derivatives

Abstract A new method for system stability analysis, the weight functions method, is applied to estimate the longitudinal and lateral stability of a Hawker 800XP aircraft. This paper assesses the application of the weight functions method to a real aircraft and a method validation with an eigenvalues stability analysis of the linear small-perturbation equations. The method consists of finding the weight functions that are equal to the number of differential equations required for system modelling. The aircraft’s stability is determined from the sign of the total weight function – the sign should be negative for a stable model. Aerodynamic coefficients and stability derivatives of the mid-size twin-engine corporate aircraft Hawker 800XP are obtained using the in-house FDerivatives code, recently developed at our laboratory of applied research in active controls, avionics and aeroservoelasticity LARCASE. The results are validated with the flight test data supplied by CAE Inc. for all considered flight cases. This aircraft model was chosen because it was part of a research project for FDerivatives code and continued with weight function method for stability analysis in order to develop a design tool, based only on the aircraft geometrical parameters for subsonic regime. The following flight cases are considered: Mach numbers = 0·4 and 0·5, altitudes = 3,000m, 5,000m, 8,000m and 10,000m, and angles-of-attack α = –5° to 20°.

scholarly journals Fixed Point Root-Finding Methods of Fourth-Order of Convergence

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 769 ◽  
Author(s):  
Alicia Cordero ◽  
Lucía Guasp ◽  
Juan R. Torregrosa
Keyword(s):  
Weight Function ◽  
Dynamical Behavior ◽  
Nonlinear Problems ◽  
Dynamical Analysis ◽  
Function Technique ◽  
Weight Functions ◽  
Good Tool ◽  
Quadratic Polynomials ◽  
Root Finding ◽  
The Stability

In this manuscript, by using the weight-function technique, a new class of iterative methods for solving nonlinear problems is constructed, which includes many known schemes that can be obtained by choosing different weight functions. This weight function, depending on two different evaluations of the derivative, is the unique difference between the two steps of each method, which is unusual. As it is proven that all the members of the class are optimal methods in the sense of Kung-Traub’s conjecture, the dynamical analysis is a good tool to determine the best elements of the family in terms of stability. Therefore, the dynamical behavior of this class on quadratic polynomials is studied in this work. We analyze the stability of the presented family from the multipliers of the fixed points and critical points, along with their associated parameter planes. In addition, this study enables us to select the members of the class with good stability properties.

Grey cluster evaluation models based on mixed triangular whitenization weight functions

2015 ◽  
Vol 5 (3) ◽  
pp. 410-418 ◽  
Author(s):  
Si-feng Liu ◽  
Yingjie Yang ◽  
Zhi-geng Fang ◽  
Naiming Xie
Keyword(s):  
Weight Function ◽  
Evaluation Model ◽  
Weight Functions ◽  
The Novel ◽  
Content Type ◽  
Clustering Model ◽  
Cluster Evaluation ◽  
Fixed Weight ◽  
Variable Weight ◽  
Evaluation Models

Purpose – The purpose of this paper is to present two novel grey cluster evaluation models to solve the difficulty in extending the bounds of each clustering index of grey cluster evaluation models. Design/methodology/approach – In this paper, the triangular whitenization weight function corresponding to class 1 is changed to a whitenization weight function of its lower measures, and the triangular whitenization weight function corresponding to class s is changed to a whitenization weight function of its upper measures. The difficulty in extending the bound of each clustering indicator is solved with this improvement. Findings – The findings of this paper are the novel grey cluster evaluation models based on mixed centre-point triangular whitenization weight functions and the novel grey cluster evaluation models based on mixed end-point triangular whitenization weight functions. Practical implications – A practical evaluation and decision problem for some projects in a university has been studied using the new triangular whitenization weight function. Originality/value – Particularly, compared with grey variable weight clustering model and grey fixed weight clustering model, the grey cluster evaluation model using whitenization weight function is more suitable to be used to solve the problem of poor information clustering evaluation. The grey cluster evaluation model using endpoint triangular whitenization weight functions is suitable for the situation that all grey boundary is clear, but the most likely points belonging to each grey class are unknown; the grey cluster evaluation model using centre-point triangular whitenization weight functions is suitable for those problems where it is easier to judge the most likely points belonging to each grey class, but the grey boundary is not clear.

Asymptotic representation of weighted L∞- and L1-minimal polynomials

2008 ◽  
Vol 144 (1) ◽  
pp. 241-254 ◽  
Author(s):  
ANDRÁS KROÓ ◽  
FRANZ PEHERSTORFER
Keyword(s):  
Weight Function ◽  
Chebyshev Polynomial ◽  
Asymptotic Representation ◽  
Minimal Polynomial ◽  
Maximum Norm ◽  
Weight Functions ◽  
Second Derivative ◽  
Minimal Polynomials ◽  
Minimum Deviation ◽  
Point Of Interest

AbstractIn 1858 Chebyshev, and some years later his students Korkin and Zolotarev, determined the polynomial which deviates least from zero among all polynomials of degree n with leading coefficient one with respect to the maximum- and the L1-norm, respectively; these are now called the Chebyshev polynomial of first and second kind.The next natural step which is to find, at least asymptotically, the minimal polynomial with respect to a given weight function has not been settled until today. Indeed, Bernstein gave asymptotics for the minimum deviation of weighted minimal polynomials, Fekete and Walsh found nth root asymptotics and, recently, Lubinsky and Saff provided asymptotics outside [−1, 1]. But the main point of interest: the asymptotic representation of the weighted minimal polynomials on the interval of approximation [−1, 1] remained open. Here we settle this problem with respect to the maximum norm for weight functions whose second derivative is Lipα, α ∈ (0, 1), and with respect to the L1-norm under somewhat stronger differentiability conditions.

True‐amplitude weight functions in 3D limited‐aperture migration revisited

Geophysics ◽  
2004 ◽  
Vol 69 (4) ◽  
pp. 1025-1036 ◽  
Author(s):  
Jianguo Sun
Keyword(s):  
Weight Function ◽  
Order Approximation ◽  
Velocity Model ◽  
Seismic Signal ◽  
Weight Functions ◽  
Image Point ◽  
Depth Migration ◽  
Amplitude Distortion ◽  
Pulse Distortion ◽  
Paraxial Ray

The true‐amplitude weight function in 3D limited‐aperture migration is obtained by extending its formula at an actual reflection point to any arbitrary subsurface point. This implies that the recorded seismic signal is a delta impulse. When the weight function is used in depth migration, it results in an amplitude distortion depending on the vertical distance from the target reflector. This distortion exists even if the correct velocity model is used. If the image point lies at a depth shallower than the half‐offset, the distortion cannot be ignored, even for a spatial wavelet having a short length. Using paraxial ray theory, I find a formula for the true‐amplitude weight function causing no amplitude distortion, under the condition that the earth's surface is smoothly curved. However, the formula is reflector dependent. As a result, amplitude distortion, in parallel with pulse distortion, is an intrinsic effect in depth migration, and true‐amplitude migration without amplitude distortion is possible only when the position of the target reflector is known. If this is the case, true‐amplitude migration without amplitude distortion can be realized by filtering the output of a simple unweighted diffraction stack with the weight function presented here. Also, using Taylor expansions with respect to the vertical, I derive an alternative formula for the true‐amplitude weight function that causes no amplitude distortion. Starting from this formula, I show that the previously published reflector‐independent true‐amplitude weight function is a zero‐order approximation to the one given here.

Time Complexity Research on the Second Type Neural Networks of Padé Weight Functions

2014 ◽  
Vol 989-994 ◽  
pp. 2667-2670
Author(s):  
Dai Yuan Zhang ◽  
Lei Yang
Keyword(s):  
Neural Network ◽  
Weight Function ◽  
Time Complexity ◽  
Weight Functions ◽  
Matlab Simulation ◽  
Training Samples ◽  
Neural Network Algorithm ◽  
Output Dimension ◽  
Key Steps ◽  
Second Category

Time complexity is an important measure of algorithm. The main purpose of this paper is to research the time complexity of the second category of Padé weight function neural network and find out the factors which affect its time complexity. In this paper, firstly, the second category of Padé weight function neural network algorithm is introduced. Then through the analysis of the key steps of the algorithm, the time complexity is given. After MATLAB simulation, the experimental results verify the theoretical analysis of the results. Therefore, its time complexity is related to input dimension, output dimension and the number of training samples.

scholarly journals WEIGHTED STATISTICAL CONVERGENCE OF REAL VALUED SEQUENCES

2020 ◽  
pp. 887
Author(s):  
Abdu Awel Adem ◽  
Maya Altınok
Keyword(s):  
Weight Function ◽  
Statistical Convergence ◽  
Initial Conditions ◽  
Weight Functions ◽  
Weighted Density ◽  
Natural Density ◽  
Convergent Sequences

Functions defined in the form ``$g:\mathbb{N}\to[0,\infty)$ such that $\lim_{n\to\infty}g(n)=\infty$ and $\lim_{n\to\infty}\frac{n}{g(n)}=0$'' are called weight functions. Using the weight function, the concept of weighted density, which is a generalization of natural density, was defined by Balcerzak, Das, Filipczak and Swaczyna in the paper ``Generalized kinsd of density and the associated ideals'', Acta Mathematica Hungarica 147(1) (2015), 97-115.In this study, the definitions of $g$-statistical convergence and $g$-statisticalCauchy sequence for any weight function $g$ are given and it is proved that these two concepts are equivalent. Also some inclusions of the sets of all weight $g_1$-statistical convergent and weight $g_2$-statistical convergent sequences for $g_1,g_2$ which have the initial conditions are given.

Sign in / Sign up

Export Citation Format

Share Document