scholarly journals Notes on the Szegő minimum problem. II. Singular measures

2020 ◽  
Vol 240 (2) ◽  
pp. 745-767
Author(s):  
Alexander Borichev ◽  
Anna Kononova ◽  
Mikhail Sodin
Keyword(s):  
Minimum Problem ◽  
Singular Measures

Rurality and Party System Fragmentation in the Nigerian Presidential Elections of the Fourth Republic

2020 ◽  
Vol 11 (1) ◽  
pp. 59-85
Author(s):  
Cletus Famous Nwankwo
Keyword(s):  
Presidential Elections ◽  
Party System ◽  
Party Systems ◽  
Voting Behaviour ◽  
Composite Measure ◽  
Singular Measures ◽  
Rural And Urban ◽  
Fourth Republic ◽  
Cast Doubt ◽  
Negative Effect

AbstractThis paper examines the effect of rurality on party system fragmentation in the Nigerian presidential elections of the fourth republic. The findings show that party system fragmentation (PSF) has been characteristically low in the Nigerian presidential elections and rurality does not significantly predict party system fragmentation. Rurality has a negative effect on PSF in all the elections studied except the 2003 election but only significant in the 2011 poll. Thus, the paper cast doubt on previous studies that indicate that striking rural-urban differences manifest in party system fragmentation in African elections and attribute it to previous studies’ measure of rurality. The paper argues that the use of a composite measure of rurality instead of singular measures of rurality might provide better analysis that helps us understand the effect of rurality on party systems. Also, it argues that in the study of the rural-urban difference in voting behaviour or political behaviours more broadly, data should be aggregated based on cities and non-city areas because cities have distinctive urban characters compared with non-city places. Analyses done on states or constituencies level may not reveal the rural-urban difference because states and constituencies usually have a mix of rural and urban population and other characteristics.

scholarly journals Optimal control in liver kinetics

1986 ◽  
Vol 27 (3) ◽  
pp. 361-369 ◽  
Author(s):  
A. M. Fink
Keyword(s):  
Optimal Control ◽  
Minimization Problem ◽  
Enzymatic Reaction ◽  
The Body ◽  
Minimum Problem ◽  
Density Functions ◽  
Intermediate Form

AbstractWe solve a minimization problem in liver kinetics posed by Bass, et al., in this journal, (1984), pages 538–562. The problem is to choose the density functions for the location of two enzymes, in order to minimize the concentration of an intermediate form of a substance at the outlet of the liver. This form may be toxic to the rest of the body, but the second enzyme renders it harmless. It seems natural that the second enzyme should be downstream from the first. However, we can show that the minimum problem is sometimes solved by an overlap of the supports of the two density functions. Even more surprising is that, for certain forms of the kinetic functions and high levels of transformation of the first enzymatic reaction, some of the first enzyme should be located downstream from all the second enzyme. This suggests that the first reaction should be relatively slow.

scholarly journals Fuzzy Formation Control and Collision Avoidance for Multiagent Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Yeong-Hwa Chang ◽  
Chun-Lin Chen ◽  
Wei-Shou Chan ◽  
Hung-Wei Lin ◽  
Chia-Wen Chang
Keyword(s):  
Collision Avoidance ◽  
Multiagent Systems ◽  
Formation Control ◽  
Descent Method ◽  
Minimum Problem ◽  
Gradient Descent Method ◽  
Consensus Formation ◽  
Distributed Information ◽  
Graph Theoretic ◽  
Learning Rules

This paper aims to investigate the formation control of leader-follower multiagent systems, where the problem of collision avoidance is considered. Based on the graph-theoretic concepts and locally distributed information, a neural fuzzy formation controller is designed with the capability of online learning. The learning rules of controller parameters can be derived from the gradient descent method. To avoid collisions between neighboring agents, a fuzzy separation controller is proposed such that the local minimum problem can be solved. In order to highlight the advantages of this fuzzy logic based collision-free formation control, both of the static and dynamic leaders are discussed for performance comparisons. Simulation results indicate that the proposed fuzzy formation and separation control can provide better formation responses compared to conventional consensus formation and potential-based collision-avoidance algorithms.

Existence theorem for a minimum problem with free discontinuity set

1989 ◽  
Vol 108 (4) ◽  
pp. 195-218 ◽  
Author(s):  
E. De Giorgi ◽  
M. Carriero ◽  
A. Leaci
Keyword(s):  
Existence Theorem ◽  
Minimum Problem

Singular measures with absolutely continuous convolution squares

1966 ◽  
Vol 62 (3) ◽  
pp. 399-420 ◽  
Author(s):  
Edwin Hewitt ◽  
Herbert S. Zuckerman
Keyword(s):  
Abelian Groups ◽  
Natural Order ◽  
Continuous Measure ◽  
Locally Compact ◽  
Absolutely Continuous ◽  
Character Group ◽  
Locally Compact Abelian Groups ◽  
Singular Measures ◽  
Compact Abelian Groups ◽  
Nikodym Derivative

Introduction. A famous construction of Wiener and Wintner ((13)), later refined by Salem ((11)) and extended by Schaeffer ((12)) and Ivašev-Musatov ((8)), produces a non-negative, singular, continuous measure μ on [ − π,π[ such thatfor every ∈ > 0. It is plain that the convolution μ * μ is absolutely continuous and in fact has Lebesgue–Radon–Nikodým derivative f such that For general locally compact Abelian groups, no exact analogue of (1 · 1) seems possible, as the character group may admit no natural order. However, it makes good sense to ask if μ* μ is absolutely continuous and has pth power integrable derivative. We will construct continuous singular measures μ on all non-discrete locally compact Abelian groups G such that μ * μ is a absolutely continuous and for which the Lebesgue–Radon–Nikodým derivative of μ * μ is in, for all real p > 1.

A Robust Method with High Time Resolution for Estimating the Cortico-Thalamo-Cortical Loop Strength and the Delay when Using a Scalp Electroencephalography Applied to the Wake-Sleep Transition

2018 ◽  
Vol 57 (03) ◽  
pp. 122-128 ◽  
Author(s):  
Akifumi Kishi ◽  
Fumiharu Togo ◽  
Toru Nakamura ◽  
Yoshiharu Yamamoto ◽  
Ikuhiro Yamaguchi
Keyword(s):  
Transfer Function ◽  
Time Resolution ◽  
Physiological Model ◽  
High Time ◽  
Ar Model ◽  
Minimum Problem ◽  
High Time Resolution ◽  
Robust Method ◽  
Loop Delay ◽  
Sleep Transition

Summary Objectives: This study aimed to describe a robust method with high time resolution for estimating the cortico-thalamo-cortical (CTC) loop strength and the delay when using a scalp electroencephalography (EEG) and to illustrate its applicability for analyzing the wake-sleep transition. Methods: The basic framework for the proposed method is the parallel use of a physiological model and a parametric phenomenological model: a neural field theory (NFT) of the corticothalamic system and an autoregressive (AR) model. The AR model is a “stochastic” model that shortens the time taken to extract spectral features and is also a “linear” model that is free from the local-minimum problem. From the relationship between the transfer function of the AR model and the transfer function of the NFT in the low frequency limit, we successfully derived a direct expression of CTC loop strength and the loop delay using AR coefficients. Results: Using this method to analyze sleep-EEG data, we were able to clearly track the wake-to-sleep transition, as the estimated CTC loop strength (c 2) decreased to almost zero. We also found that the c 2-distribution during nocturnal sleep is clearly bimodal in nature, which can be well approximated by the superposition of two Gaussian distributions that correspond to sleep and wake states, respectively. The estimated loop delay distributed ∼0.08 s, which agrees well with the previously reported value estimated by other methods, confirming the validity of our method. Conclusions: A robust method with high time resolution was developed for estimating the cortico-thalamo-cortical loop strength and the delay when using a scalp electroencephalography. This method can contribute not only to detecting the wake-sleep transition, but also to further understanding of the transition, where the cortico-thalamo-cortical loop is thought to play an important role.

scholarly journals Generalized powers and measures

2021 ◽  
Vol 41 (6) ◽  
pp. 747-754
Author(s):  
Zbigniew Burdak ◽  
Marek Kosiek ◽  
Patryk Pagacz ◽  
Krzysztof Rudol ◽  
Marek Słociński
Keyword(s):  
Invariant Subspaces ◽  
Unitary Operators ◽  
Singular Measures ◽  
Special Classes

Using the winding of measures on torus in "rational directions" special classes of unitary operators and pairs of isometries are defined. This provides nontrivial examples of generalized powers. Operators related to winding Szegö-singular measures are shown to have specific properties of their invariant subspaces.

scholarly journals Modified Elman Neural-PID Controller Design for DC-DC Buck Converter System Based on Dolphin Echolocation Optimization

2018 ◽  
Vol 14 (3) ◽  
pp. 129-140
Author(s):  
Khulood E. Dagher
Keyword(s):  
Pid Controller ◽  
Controller Design ◽  
Load Resistance ◽  
Buck Converter ◽  
Minimum Problem ◽  
Portable Devices ◽  
Elman Neural Network ◽  
Pid Controller Design ◽  
On Line ◽  
Local Minimum Problem

This paper describes a new proposed structure of the Proportional Integral Derivative (PID) controller based on modified Elman neural network for the DC-DC buck converter system which is used in battery operation of the portable devices. The Dolphin Echolocation Optimization (DEO) algorithm is considered as a perfect on-line tuning technique therefore, it was used for tuning and obtaining the parameters of the modified Elman neural-PID controller to avoid the local minimum problem during learning the proposed controller. Simulation results show that the best weight parameters of the proposed controller, which are taken from the DEO, lead to find the best action and unsaturated state that will stabilize the Buck converter system performance and achieve the desired output. In addition, there is a minimization for the tracking voltage error to zero value of the Buck converter output, especially when changing a load resistance by 10%.

Asymptotically compatible discretization of multidimensional nonlocal diffusion models and approximation of nonlocal Green’s functions

2018 ◽  
Vol 39 (2) ◽  
pp. 607-625 ◽  
Author(s):  
Qiang Du ◽  
Yunzhe Tao ◽  
Xiaochuan Tian ◽  
Jiang Yang
Keyword(s):  
Green's Functions ◽  
Numerical Solutions ◽  
Green’S Functions ◽  
Diffusion Equations ◽  
Nonlocal Diffusion ◽  
Optimal Order ◽  
Numerical Approximations ◽  
Splitting Technique ◽  
Singular Measures ◽  
Nonlocal Models

AbstractNonlocal diffusion equations and their numerical approximations have attracted much attention in the literature as nonlocal modeling becomes popular in various applications. This paper continues the study of robust discretization schemes for the numerical solution of nonlocal models. In particular, we present quadrature-based finite difference approximations of some linear nonlocal diffusion equations in multidimensions. These approximations are able to preserve various nice properties of the nonlocal continuum models such as the maximum principle and they are shown to be asymptotically compatible in the sense that as the nonlocality vanishes, the numerical solutions can give consistent local limits. The approximation errors are proved to be of optimal order in both nonlocal and asymptotically local settings. The numerical schemes involve a unique design of quadrature weights that reflect the multidimensional nature and require technical estimates on nonconventional divided differences for their numerical analysis. We also study numerical approximations of nonlocal Green’s functions associated with nonlocal models. Unlike their local counterparts, nonlocal Green’s functions might become singular measures that are not well defined pointwise. We demonstrate how to combine a splitting technique with the asymptotically compatible schemes to provide effective numerical approximations of these singular measures.

Sign in / Sign up

Export Citation Format

Share Document