Development of one-dimensional integral photography

2019 ◽  
pp. 1253
Author(s):  
Akira Hasegawa ◽  
Sumio Yano
Keyword(s):  
One Dimensional ◽  
Dimensional Integral

State-of-the-Art of Modeling Surface Water Impoundments

1982 ◽  
Vol 14 (1-2) ◽  
pp. 241-261 ◽  
Author(s):  
P A Krenkel ◽  
R H French
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
State Of The Art ◽  
Rate Coefficients ◽  
Two Dimensional ◽  
One Dimensional ◽  
Integral Energy ◽  
Range Of Values ◽  
Dimensional Integral ◽  
Water Impoundment

The state-of-the-art of surface water impoundment modeling is examined from the viewpoints of both hydrodynamics and water quality. In the area of hydrodynamics current one dimensional integral energy and two dimensional models are discussed. In the area of water quality, the formulations used for various parameters are presented with a range of values for the associated rate coefficients.

scholarly journals The on-axis magnetic well and Mercier's criterion for arbitrary stellarator geometries

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
P. Kim ◽  
R. Jorge ◽  
W. Dorland
Keyword(s):  
Magnetic Field ◽  
Original Work ◽  
Three Dimensional ◽  
Radial Distance ◽  
Analytical Form ◽  
One Dimensional ◽  
Modern Notation ◽  
Magnetic Well ◽  
First Time ◽  
Dimensional Integral

A simplified analytical form of the on-axis magnetic well and Mercier's criterion for interchange instabilities for arbitrary three-dimensional magnetic field geometries is derived. For this purpose, a near-axis expansion based on a direct coordinate approach is used by expressing the toroidal magnetic flux in terms of powers of the radial distance to the magnetic axis. For the first time, the magnetic well and Mercier's criterion are then written as a one-dimensional integral with respect to the axis arclength. When compared with the original work of Mercier, the derivation here is presented using modern notation and in a more streamlined manner that highlights essential steps. Finally, these expressions are verified numerically using several quasisymmetric and non-quasisymmetric stellarator configurations including Wendelstein 7-X.

Geometric Factors for Radiative Heat Transfer Through an Absorbing Medium in Cartesian Co-ordinates

1960 ◽  
Vol 82 (4) ◽  
pp. 360-368 ◽  
Author(s):  
A. K. Oppenheim ◽  
J. T. Bevans
Keyword(s):  
Radiative Heat ◽  
Unit Area ◽  
Diffuse Radiation ◽  
Radiation Beam ◽  
Actual Distribution ◽  
Absorbing Medium ◽  
One Dimensional ◽  
Geometric Factors ◽  
Absorption Law ◽  
Dimensional Integral

Heat flux conveyed by diffuse radiation from surface A1 and A2 through an absorbing medium is expressed by the relation Q1−2=J1 ∫A1×A2f(l12)(cosθ1cosθ2/πl122)dA1dA2 where J1 is the radiosity of A1 (sum of the emitted, reflected, and transmitted flux per unit area), l12 is the radiation beam (the distance between surface elements dA1 and dA2), θ1 and θ2 are the angles between the radiation beam and the normals to the surface elements, and f(l12) is the function describing the absorption law. The foregoing four-dimensional integral is transformed into a sum of one-dimensional integrals for the cases of opposite-parallel and adjoining-perpendicular rectangles. The results are suitable for numerical integration with any total absorption law obtained from the actual distribution of monochromatic absorptivities over the whole spectrum.

scholarly journals A Fast-Converging Scheme for the Electromagnetic Scattering from a Thin Dielectric Disk

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1451
Author(s):  
Mario Lucido ◽  
Mykhaylo V. Balaban ◽  
Sergii Dukhopelnykov ◽  
Alexander I. Nosich
Keyword(s):  
Integral Equations ◽  
Electromagnetic Scattering ◽  
Disk Surface ◽  
Hankel Transform ◽  
Transform Domain ◽  
One Dimensional ◽  
Analytical Technique ◽  
Generalized Boundary Conditions ◽  
Dielectric Disk ◽  
Dimensional Integral

In this paper, the analysis of the electromagnetic scattering from a thin dielectric disk is formulated as two sets of one-dimensional integral equations in the vector Hankel transform domain by taking advantage of the revolution symmetry of the problem and by imposing the generalized boundary conditions on the disk surface. The problem is further simplified by means of Helmholtz decomposition, which allows to introduce new scalar unknows in the spectral domain. Galerkin method with complete sets of orthogonal eigenfunctions of the static parts of the integral operators, reconstructing the physical behavior of the fields, as expansion bases, is applied to discretize the integral equations. The obtained matrix equations are Fredholm second-kind equations whose coefficients are efficiently numerically evaluated by means of a suitable analytical technique. Numerical results and comparisons with the commercial software CST Microwave Studio are provided showing the accuracy and efficiency of the proposed technique.

scholarly journals Motion Reliability Modeling and Evaluation for Manipulator Path Planning Task

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Tong Li ◽  
Qingxuan Jia ◽  
Gang Chen ◽  
Hanxu Sun
Keyword(s):  
Path Planning ◽  
Maximum Entropy ◽  
Model Calculation ◽  
Reliability Evaluation ◽  
Modeling Method ◽  
One Dimensional ◽  
Position Accuracy ◽  
Planning Task ◽  
Multidimensional Integral ◽  
Dimensional Integral

Motion reliability as a criterion can reflect the accuracy of manipulator in completing operations. Since path planning task takes a significant role in operations of manipulator, the motion reliability evaluation of path planning task is discussed in the paper. First, a modeling method for motion reliability is proposed by taking factors related to position accuracy of manipulator into account. In the model, multidimensional integral for PDF is carried out to calculate motion reliability. Considering the complex of multidimensional integral, the approach of equivalent extreme value is introduced, with which multidimensional integral is converted into one dimensional integral for convenient calculation. Then a method based on the maximum entropy principle is proposed for model calculation. With the method, the PDF can be obtained efficiently at the state of maximum entropy. As a result, the evaluation of motion reliability can be achieved by one dimensional integral for PDF. Simulations on a particular path planning task are carried out, with which the feasibility and effectiveness of the proposed methods are verified. In addition, the modeling method which takes the factors related to position accuracy into account can represent the contributions of these factors to motion reliability. And the model calculation method can achieve motion reliability evaluation with high precision and efficiency.

scholarly journals Applications of one- and two-dimensional Volterra inequalities in differential equations of the hyperbolic type

2003 ◽  
Vol 2003 (53) ◽  
pp. 3373-3383
Author(s):  
Lechosław Hącia
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Hyperbolic Type ◽  
Integral Inequalities ◽  
Two Dimensional ◽  
Volterra Type ◽  
One Dimensional ◽  
Dimensional Integral ◽  
Hyperbolic Differential Equations

Some variants of one-dimensional and two-dimensional integral inequalities of the Volterra type are applied to study the behaviour properties of the solutions to various boundary value problems for partial differential equations of the hyperbolic type. Moreover, new types of integral inequalities for one and two variables, being a generalization of the Gronwall inequality, are presented and used in the theory of nonlinear hyperbolic differential equations.

scholarly journals BN-invariant Sharpness Regularizes the Training Model to Better Generalization

2019 ◽  
Author(s):  
Mingyang Yi ◽  
Huishuai Zhang ◽  
Wei Chen ◽  
Zhi-Ming Ma ◽  
Tie-Yan Liu
Keyword(s):  
Neural Networks ◽  
Scale Invariance ◽  
Training Model ◽  
Scale Invariant ◽  
One Dimensional ◽  
Batch Normalization ◽  
Dimensional Integral ◽  
Consistent Measurement

It is arguably believed that flatter minima can generalize better. However, it has been pointed out that the usual definitions of sharpness, which consider either the maxima or the integral of loss over a delta ball of parameters around minima, cannot give consistent measurement for scale invariant neural networks, e.g., networks with batch normalization layer. In this paper, we first propose a measure of sharpness, BN-Sharpness, which gives consistent value for equivalent networks under BN. It achieves the property of scale invariance by connecting the integral diameter with the scale of parameter. Then we present a computation-efficient way to calculate the BN-sharpness approximately i.e., one dimensional integral along the "sharpest" direction. Furthermore, we use the BN-sharpness to regularize the training and design an algorithm to minimize the new regularized objective. Our algorithm achieves considerably better performance than vanilla SGD over various experiment settings.

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