scholarly journals Some Intrinsic Properties of Tadmor–Tanner Functions: Related Problems and Possible Applications

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1963 ◽  
Author(s):  
Nikolay Kyurkchiev
Keyword(s):  
Hausdorff Metric ◽  
Optimal Filter ◽  
Activation Functions ◽  
Intrinsic Properties ◽  
Exponential Functions ◽  
Numerical Examples

In this paper, we study some properties of an exponentially optimal filter proposed by Tadmor and Tanner. More precisely, we consider the problem for approximating the function of rectangular type F(t) by the class of exponential functions σadapt(t) about the Hausdorff metric. We prove upper and lower estimates for “saturation”—d (in the case q=2). New activation and “semi-activation” functions based on σadapt(t) are defined. Some related problems are discussed. We also consider modified families of functions with “polynomial variable transfer”. Numerical examples, illustrating our results using CAS MATHEMATICA are given.

scholarly journals Matrix Measure Approach for Stability and Synchronization of Complex-Valued Neural Networks with Deviating Argument

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Wenbo Zhou ◽  
Biwen Li ◽  
Jin-E Zhang
Keyword(s):  
Neural Networks ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Activation Functions ◽  
Matrix Measure ◽  
Numerical Examples ◽  
Coupled Neural Networks ◽  
Deviating Argument ◽  
Exponentially Stable ◽  
Complex Valued

This paper concentrates on global exponential stability and synchronization for complex-valued neural networks (CVNNs) with deviating argument by matrix measure approach. The Lyapunov function is no longer required, and some sufficient conditions are firstly obtained to ascertain the addressed system to be exponentially stable under different activation functions. Moreover, after designing a suitable controller, the synchronization of two complex-valued coupled neural networks is realized, and the derived condition is easy to be confirmed. Finally, some numerical examples are given to demonstrate the superiority and feasibility of the presented theoretical analysis and results.

scholarly journals New LMI-Based Conditions on Neural Networks of Neutral Type with Discrete Interval Delays and General Activation Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Guoquan Liu ◽  
Shumin Zhou ◽  
He Huang
Keyword(s):  
Neural Networks ◽  
Neutral Type ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Activation Functions ◽  
Numerical Examples ◽  
Discrete Interval ◽  
General Activation ◽  
The Stability ◽  
Delay Dependent

The stability analysis of global asymptotic stability of neural networks of neutral type with both discrete interval delays and general activation functions is discussed. New delay-dependent conditions are obtained by using more general Lyapunov-Krasovskii functionals. Meanwhile, these conditions are expressed in terms of a linear matrix inequality (LMI) and can be verified using the MATLAB LMI toolbox. Numerical examples are used to illustrate the effectiveness of the proposed approach.

scholarly journals Some Notes on the Omega Distribution and the Pliant Probability Distribution Family

Algorithms ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 324
Author(s):  
Maria T. Vasileva
Keyword(s):  
Open Access ◽  
Probability Distribution ◽  
Hausdorff Distance ◽  
Hausdorff Metric ◽  
Software Module ◽  
Numerical Examples ◽  
Horizontal Asymptote ◽  
Dynamic Software ◽  
Distribution Family

In 2020 Dombi and Jónás (Acta Polytechnica Hungarica 17:1, 2020) introduced a new four parameter probability distribution which they named the pliant probability distribution family. One of the special members of this family is the so-called omega probability distribution. This paper deals with one of the important characteristic “saturation” of these new cumulative functions to the horizontal asymptote with respect to Hausdorff metric. We obtain upper and lower estimates for the value of the Hausdorff distance. A simple dynamic software module using CAS Mathematica and Wolfram Cloud Open Access is developed. Numerical examples are given to illustrate the applicability of obtained results.

MULTILAYER PERCEPTRONS TO APPROXIMATE COMPLEX VALUED FUNCTIONS

1995 ◽  
Vol 06 (04) ◽  
pp. 435-446 ◽  
Author(s):  
P. ARENA ◽  
L. FORTUNA ◽  
R. RE ◽  
M.G. XIBILIA
Keyword(s):  
Neural Networks ◽  
Computational Complexity ◽  
Feedforward Neural Networks ◽  
Density Theorem ◽  
Multilayer Perceptrons ◽  
Activation Functions ◽  
Approximation Properties ◽  
Numerical Examples ◽  
Continuous Complex ◽  
Complex Valued

In this paper the approximation capabilities of different structures of complex feedforward neural networks, reported in the literature, have been theoretically analyzed. In particular a new density theorem for Complex Multilayer Perceptrons with complex valued non-analytic sigmoidal activation functions has been proven. Such a result makes Multilayer Perceptrons with complex valued neurons universal interpolators of continuous complex valued functions. Moreover the approximation properties of superpositions of analytic activation functions have been investigated, proving that such combinations are not dense in the set of continuous complex valued functions. Several numerical examples have also been reported in order to show the advantages introduced by Complex Multilayer Perceptrons in terms of computational complexity with respect to the classical real MLP.

On the Principle of Transference In Three-Dimensional Kinematics

1981 ◽  
Vol 103 (3) ◽  
pp. 652-656 ◽  
Author(s):  
L. M. Hsia ◽  
A. T. Yang
Keyword(s):  
Rigid Body ◽  
Three Dimensional ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Intrinsic Properties ◽  
Numerical Examples ◽  
Systematic Procedure ◽  
Point Trajectories

In this paper, the principle of transference is developed and applied to the establishment of a systematic procedure for the determination, via screw calculus, of a prescribed rigid body motion. This is an essential first step toward the study of the intrinsic properties of point trajectories in three-dimensional kinematics. Two numerical examples are presented for illustrative purposes.

Implications due to Different Loading Programs in Inelastic Materials

2011 ◽  
Vol 422 ◽  
pp. 726-733 ◽  
Author(s):  
Fabio de Angelis ◽  
Donato Cancellara
Keyword(s):  
Solution Method ◽  
Model Problem ◽  
Intrinsic Properties ◽  
Viscoplastic Model ◽  
Numerical Examples ◽  
Inelastic Behaviour ◽  
Loading Procedure

In the present paper the effects of different loading procedures on the response of rate-sensitive inelastic materials are analysed. The elasto/viscoplastic model problem is developed by taking advantage of the postulate of maximum dissipation in order to derive an associated formulation of the evolutive laws. A non-dimensional loading program parameter is introduced which accounts for the loading procedure and the intrinsic properties of the material. An appropriate solution method is applied and specific numerical examples are reported so that the implications due to different loading programs on the inelastic behaviour of rate-sensitive materials are suitably illustrated.

Results of Distinct Modes of Loading Procedures in the Nonlinear Inelastic Behaviour of Solids

2012 ◽  
Vol 482-484 ◽  
pp. 1004-1011 ◽  
Author(s):  
Fabio de Angelis ◽  
Donato Cancellara
Keyword(s):  
Mechanical Behaviour ◽  
Integration Scheme ◽  
Nonlinear Behaviour ◽  
Intrinsic Properties ◽  
Numerical Examples ◽  
Loading Rates ◽  
Application Rates ◽  
Inelastic Behaviour

The consequences of distinct modes of loading procedures on the mechanical behaviour of elasto/viscoplastic materials are analyzed in the present work. An associated formulation of the evolutive laws is adopted based on the existence of a non-negative convex closed function representing the dissipative mechanisms. Distinct modes of loading modalities are suitably taken into account by considering different loading application rates and the intrinsic properties of the material. An adequate integration scheme is adopted and the effectiveness of the procedure is shown by analyzing specific computational applications with different loading programs. Numerical examples and results are also illustrated in order to show the significance of different loading procedures and different loading rates on the nonlinear behaviour of inelastic materials.

God's Being Is in Becoming: An Essay in Theological Idealism

2016 ◽  
Vol 8 (3) ◽  
pp. 145-157
Author(s):  
Hartmut Von Sass
Keyword(s):  
Intrinsic Properties

God’s being is becoming – the title is the thesis. The first section of this paper will be dedicated to the problem of radical historicity in sketching three dogmatic approaches dealing with the relation between God and history. After critically introducing the concept of relational – in contrast to intrinsic – properties in the second section I will apply a revised version of this concept theologically in integrating it into the architecture of Trinitarian thinking. Accordingly, and on that basis, the last section can address the ambivalent as well as precarious question in which sense God’s ultimate being is in real (be) coming.

Quantitative Conditions and Convergent Operations That Are Compatible With the Universe as a Persistent Generator of Successive Simulations

2016 ◽  
Vol 12 (1) ◽  
pp. 4178-4187
Author(s):  
Michael A Persinger ◽  
Stanley A Koren
Keyword(s):  
Structural Organization ◽  
Total Duration ◽  
Human Cognition ◽  
Intrinsic Properties ◽  
Basic Assumptions ◽  
Electron Orbit ◽  
Quantitative Analyses ◽  
Massive Information ◽  
The Universe

                The capacity for computer-like simulations to be generated by massive information processing from electron-spin potentials supports Bostrom’s hypothesis that matter and human cognition might reflect simulations. Quantitative analyses of the basic assumptions indicate the universe may display properties of a simulation where photons behave as pixels and gravitons control the structural organization. The Lorentz solution for the square of the light and entanglement velocities converges with the duration of a single electron orbit that ultimately defines properties of matter. The approximately one trillion potential states within the same space with respect to the final epoch of the universe indicate that a different simulation, each with intrinsic properties, has been and will be generated as a type of tractrix defined by ±2 to 3 days (total duration 5 to 6 days). It may define the causal limits within a simulation. Because of the intrinsic role of photons as the pixel unit, phenomena within which flux densities are enhanced, such as human cognition (particularly dreaming) and the cerebral regions associated with those functions, create the conditions for entanglement or excess correlations between contiguous simulations. The consistent quantitative convergence of operations indicates potential validity for this approach. The emergent solutions offer alternative explanations for the limits of predictions for multivariate phenomena that could be coupled to more distal simulations.

Conservative solute transport with periodic velocity and sinusoidal source concentration in semi-infinite porous media: An analytical solution

2014 ◽  
Vol 6 (1) ◽  
pp. 1024-1031
Author(s):  
R R Yadav ◽  
Gulrana Gulrana ◽  
Dilip Kumar Jaiswal
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Laplace Transformation ◽  
Seepage Velocity ◽  
Transformation Technique ◽  
Numerical Examples ◽  
One Dimensional ◽  
Porous Domain ◽  
Conservative Solute Transport ◽  
Source Concentration

The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.

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