A maximum-minimum principle for bang-bang systems

1970 ◽  
pp. 225-247
Author(s):  
B. Fraeijs de Veubeke
Keyword(s):  
Minimum Principle ◽  
Maximum Minimum

ON THE MAXIMUM PRINCIPLE FOR GENERALIZED SOLUTIONS TO THE TRICOMI PROBLEM

2000 ◽  
Vol 02 (04) ◽  
pp. 535-557 ◽  
Author(s):  
DANIELA LUPO ◽  
KEVIN R. PAYNE
Keyword(s):  
Existence And Uniqueness ◽  
Boundary Data ◽  
Minimum Principle ◽  
Generalized Solutions ◽  
Tricomi Problem ◽  
Convexity Condition ◽  
Parabolic Boundary ◽  
The Maximum Principle ◽  
Right Hand ◽  
Maximum Minimum

A maximum/minimum principle for weighted W1,2 solutions to the Tricomi problem with L2 right hand side and homogeneous boundary data is established for normal Tricomi domains. In addition, the existence and uniqueness of such generalized solutions is established for arbitrary L2 right hand sides in normal domains which satisfy a convexity condition near the parabolic boundary points.

A Cluster Analysis of the D 2 Matrix of White Spruce Stands in Saskatchewan Based on the Maximum-Minimum Principle

1972 ◽  
Vol 60 (3) ◽  
pp. 873 ◽  
Author(s):  
T. Frey ◽  
H. van Groenewoud
Keyword(s):  
Cluster Analysis ◽  
Minimum Principle ◽  
White Spruce ◽  
Spruce Stands ◽  
Maximum Minimum

scholarly journals AN APPLICATION OF HAMILTONIAN NEURODYNAMICS USING PONTRYAGIN’S MAXIMUM (MINIMUM) PRINCIPLE

1995 ◽  
Vol 06 (04) ◽  
pp. 425-433
Author(s):  
TAKAMASA KOSHIZEN ◽  
JOHN FULCHER
Keyword(s):  
Minimum Principle ◽  
Learning Rule ◽  
Control Methods ◽  
Continuous Time Systems ◽  
Xor Problem ◽  
New Learning ◽  
Feedback Networks ◽  
Time Systems ◽  
Optimal Control Methods ◽  
Maximum Minimum

Classical optimal control methods, notably Pontryagin’s Maximum (Minimum) Principle (PMP) can be employed, together with Hamiltonians, to determine optimal system weights in Artificial Neural dynamical systems. A new learning rule based on weight equations derived using PMP is shown to be suitable for both discrete- and continuous-time systems, and moreover, can also be applied to feedback networks. Preliminary testing shows that this PMP learning rule compares favorably with Standard BackPropagation (SBP) on the XOR problem.

A New Nonlinear Two-Point Flux Approximation Method for Solving the Anisotropic Diffusion Equation with Reduced Violations of the Discrete Maximum/Minimum Principle

SPE Journal ◽  
2021 ◽  
pp. 1-19
Author(s):  
Wenjuan Zhang ◽  
Mohammed Al Kobaisi
Keyword(s):  
Diffusion Equation ◽  
Anisotropic Diffusion ◽  
Convex Combination ◽  
Minimum Principle ◽  
Coefficient Matrix ◽  
Finite Volume Methods ◽  
System Of Nonlinear Equations ◽  
Flux Approximation ◽  
Anisotropic Diffusion Equation ◽  
Maximum Minimum

Summary A class of monotone cell-centered nonlinear finite-volume methods has been proposed in the past decade to solve the anisotropic diffusion equation. The nonlinear two-point flux approximation (TPFA) (NTPFA) method preserves the nonnegativity of the solution values but can violate the discrete maximum/minimum principle (DMP). To enforce DMP, the nonlinear multipoint flux approximation (NMPFA) method ought to be used. In this work, we propose a novel NTPFA method that can reduce the severity of DMP violations significantly compared with the standard NTPFA method. The new formulation uses conormal decomposition for the construction of the one-sided fluxes. To define the unique flux through a connection between two cells, we choose a convex combination of the two one-sided fluxes such that the absolute differences of the magnitudes of the two transmissibility terms associated with the two neighboring cells are minimized, thus bringing the discrete coefficient matrix closer to having the zero row-sum property. Numerical experiments are conducted to test the performance of the new NTPFA method. The results demonstrate that the new scheme has comparable convergence order for both the solution and the flux compared with the standard NTPFA method or the classical multi-point flux approximation (MPFA-O) method. Moreover, the new NTPFA formulation shows marked improvements over the standard NTPFA in terms of reducing DMP violations. However, depending on the specific problem configuration, our new NTPFA formulation can lead to a system of nonlinear equations that is more difficult to solve.

Stereokinetic phenomena with rotating ellipses follow a minimum principle

1991 ◽  
Author(s):  
Mario Zanforlin
Keyword(s):  
Minimum Principle

The build of nonlinear quantum mechancs and variations of feature of microscopic particles as well as their experimental affirmation

2014 ◽  
Vol 5 (3) ◽  
pp. 871-981 ◽  
Author(s):  
Pang Xiao Feng
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Lagrange Equation ◽  
Minimum Principle ◽  
Superposition Principle ◽  
Type Equation ◽  
Experimental Results ◽  
Traditional Concept ◽  
Nonlinear Quantum ◽  
Nonlinear Quantum Mechanics

We establish the nonlinear quantum mechanics due to difficulties and problems of original quantum mechanics, in which microscopic particles have only a wave feature, not corpuscle feature, which are completely not consistent with experimental results and traditional concept of particle. In this theory the microscopic particles are no longer a wave, but localized and have a wave-corpuscle duality, which are represented by the following facts, the solutions of dynamic equation describing the particles have a wave-corpuscle duality, namely it consists of a mass center with constant size and carrier wave, is localized and stable and has a determinant mass, momentum and energy, which obey also generally conservation laws of motion, their motions meet both the Hamilton equation, Euler-Lagrange equation and Newton-type equation, their collision satisfies also the classical rule of collision of macroscopic particles, the uncertainty of their position and momentum is denoted by the minimum principle of uncertainty. Meanwhile the microscopic particles in this theory can both propagate in solitary wave with certain frequency and amplitude and generate reflection and transmission at the interfaces, thus they have also a wave feature, which but are different from linear and KdV solitary wave’s. Therefore the nonlinear quantum mechanics changes thoroughly the natures of microscopic particles due to the nonlinear interactions. In this investigation we gave systematically and completely the distinctions and variations between linear and nonlinear quantum mechanics, including the significances and representations of wave function and mechanical quantities, superposition principle of wave function, property of microscopic particle, eigenvalue problem, uncertainty relation and the methods solving the dynamic equations, from which we found nonlinear quantum mechanics is fully new and different from linear quantum mechanics. Finally, we verify further the correctness of properties of microscopic particles described by nonlinear quantum mechanics using the experimental results of light soliton in fiber and water soliton, which are described by same nonlinear Schrödinger equation. Thus we affirm that nonlinear quantum mechanics is correct and useful, it can be used to study the real properties of microscopic particles in physical systems.

Simulation of continuous random process according to the specified sequence of extremes

2020 ◽  
Vol 86 (7) ◽  
pp. 65-71
Author(s):  
I. V. Gadolina ◽  
R. I. Zainetdinov ◽  
T. P. Gryzlova ◽  
I. M. Petrova
Keyword(s):  
Spectral Density ◽  
Random Process ◽  
Continuous Process ◽  
Continuous Processes ◽  
Regression Formula ◽  
Bending Stresses ◽  
Development And Validation ◽  
Irregular Loading ◽  
Cosine Functions ◽  
Maximum Minimum

A method has been developed for converting a discrete sequence of extrema into a continuous process. The relevancy of the problem is attributed to the necessity of an approximate estimation of spectral density in in testing materials and structures under random (irregular) loading. A great bulk of available experimental data thus can be used in development and validation of calculation methods for assessing durability in the multi-cycle region. Postulating the continuity of random stress processes and their first derivative we propose to connect piecewise the available starting points (namely, the extrema of the random process) with half-cosine functions under the condition of compatibility at the points of extrema. A distinctive feature of the method is the provision of 100% coincidence of the values and sequences of extrema in the initial discrete and simulated continuous processes. The issue of choosing the magnitude of half-periods for these half-cosine functions is addressed on the basis of information obtained from the analysis of real stress records in the form of a regression equation linking half-periods and half-ranges for some realizations of the random process for transport vehicles. The regression dependences of the half-periods and semi-ranges of bending stresses (part of a railway train) and torsion (torsion shaft of a tracked vehicle) are shown as an example. An analysis of the correlation of two random variables (half-periods and half-ranges) according to empirical data has shown that the correlation exists and is significant for the observed number of points thus providing the basis for using the regression formula for an approximate choice of the frequency composition of the process. Moreover, the lower restrictions are imposed on the number of points (at least 5) in the half-period. Since the extrema of the initial and simulated processes coincide in accordance with the principle of the proposed simulation, the distribution of the amplitudes of complete cycles, as well as the results of schematization by other known methods are identical, therefore, the estimate of the durability by hypotheses based on a linear one is also identical. The validation of the method consists in consideration of the chain: 1) the initial continuous process; 2) the discrete process of extrema; 3) simulated continuous process according to the proposed method. Auxiliary distributions, such as distributions of maximum, minimum and average cycle values also coincide in accordance with the principle of modeling. The method is proposed to be used in analysis of the comparability of two competing approaches in assessing the loading in the problems of assessing durability, namely: those that use cycle-counting methods and methods based on the spectral density of processes. Since the spectral densities of the processes can differ due to an approximate choice of the frequencies on the basis of a regression formula, methods on their base can give estimates of the durability that differ from those obtained by schematization methods. To study this phenomenon, further computational experiments are required. The developed method can be very useful for the experiment design.

A Defense Mechanism Based on Improved Allocation Strategy of VMs Co-Resident Attack in Power Cloud Platform

2020 ◽  
Vol 13 ◽  
Author(s):  
Yuancheng Li ◽  
Pan Zhang ◽  
Daoxing Li ◽  
Jing Zeng
Keyword(s):  
Virtual Machine ◽  
Simulation Experiment ◽  
Virtual Machines ◽  
Defense Mechanism ◽  
Security Threats ◽  
Allocation Strategy ◽  
Cloud Platform ◽  
Deployment Strategy ◽  
Dbscan Algorithm ◽  
Maximum Minimum

Background: Cloud platform is widely used in electric power field. Virtual machine co-resident attack is one of the major security threats to the existing power cloud platform. Objective: This paper proposes a mechanism to defend virtual machine co-resident attack on power cloud platform. Method: Our defense mechanism uses the DBSCAN algorithm to classify and output the classification results through the random forest and uses improved virtual machine deployment strategy which combines the advantages of random round robin strategy and maximum/minimum resource strategy to deploy virtual machines. Results: we made a simulation experiment on power cloud platform of State Grid and verified the effectiveness of proposed defense deployment strategy. Conclusion: After the virtual machine deployment strategy is improved, the coverage of the virtual machine is remarkably reduced which proves that our defense mechanism achieves some effect of defending the virtual machine from virtual machine co-resident attack.

One-layer feedforward neural network for fast maximum/minimum determination

1992 ◽  
Vol 28 (17) ◽  
pp. 1583 ◽  
Author(s):  
H.K. Kwan
Keyword(s):  
Neural Network ◽  
Feedforward Neural Network ◽  
Maximum Minimum
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