Origin shifts in divergent Feynman integrals

1969 ◽  
Vol 47 (12) ◽  
pp. 1263-1269 ◽  
Author(s):  
Robert E. Pugh
Keyword(s):  
Sum Rules ◽  
Tensor Rank ◽  
Linear Quadratic ◽  
Arbitrary Degree ◽  
Recursion Relations ◽  
Feynman Integrals ◽  
Shift Of Origin

The surface terms arising from a shift of origin in divergent Feynman integrals are considered. Sum rules and recursion relations between these terms are derived for an arbitrary degree of divergence and tensor rank. These relations are explicitly solved for linear, quadratic, cubic, and quartic divergences.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Glucose Calibration Modeling in Blood with Spline Regression Approaching to Non-Invasive Tools

2018 ◽  
pp. 144-149
Author(s):  
Ria Hayatun Nur ◽  
Indahwati A ◽  
Erfiani A
Keyword(s):  
Diabetes Mellitus ◽  
Linear Regression ◽  
Good Health ◽  
Cubic Spline ◽  
The Body ◽  
Spline Regression ◽  
Linear Quadratic ◽  
Important Thing ◽  
Non Invasive

In this globalization era, health is the most important thing to be able to run various activities. Without good health, this will hinder many activities. Diabetes mellitus is one of the diseases caused by unhealty lifestyle.There are many treatments that can be done to prevent the occurrence of diabetes. The treatments are giving the insulin and also checking the glucose rate to the patients.Checking the glucose rate needs the tools which is safety to the body. This research want to develop non invasive tool which is safety and do not injure the patient. The purpose of this research is also finding the best model which derived from Linear, Quadratic, and Cubic Spline Regression. Some respondents were taking to get the glucose measuring by invasive and non invasive tools. It could be seen clearly that Spline Linear Regression was the best model than Quadratic and Cubic Spline Regression. It had 70% and 33.939 for R2 and RMSEP respectively.

Quadratic Discriminant Analysis of Spatially Correlated Data

2001 ◽  
Vol 6 (2) ◽  
pp. 15-28 ◽  
Author(s):  
K. Dučinskas ◽  
J. Šaltytė
Keyword(s):  
Discriminant Function ◽  
Error Rate ◽  
Gaussian Random Field ◽  
Correlated Data ◽  
Covariance Matrices ◽  
Classification Rule ◽  
Spatial Correlations ◽  
Linear Quadratic ◽  
Spatial Correlation Function ◽  
Spatially Correlated

The problem of classification of the realisation of the stationary univariate Gaussian random field into one of two populations with different means and different factorised covariance matrices is considered. In such a case optimal classification rule in the sense of minimum probability of misclassification is associated with non-linear (quadratic) discriminant function. Unknown means and the covariance matrices of the feature vector components are estimated from spatially correlated training samples using the maximum likelihood approach and assuming spatial correlations to be known. Explicit formula of Bayes error rate and the first-order asymptotic expansion of the expected error rate associated with quadratic plug-in discriminant function are presented. A set of numerical calculations for the spherical spatial correlation function is performed and two different spatial sampling designs are compared.

A Study on Linear Quadratic Regulator with the Desired Low-Pass Property

2013 ◽  
Vol 133 (12) ◽  
pp. 2167-2175 ◽  
Author(s):  
Katsuhiko Fuwa ◽  
Satoshi Murayama ◽  
Tatsuo Narikiyo
Keyword(s):  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Low Pass
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