scholarly journals Existence of Multispike Positive Solutions for a Nonlocal Problem in ℝ3

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jing Yang ◽  
Qiuxiang Bian ◽  
Na Zhao
Keyword(s):  
Positive Integer ◽  
Positive Solution ◽  
Reduction Method ◽  
Nonlocal Problem ◽  
Local Maximum ◽  
Maximum Point ◽  
Choquard Equation ◽  
Local Maximum Point ◽  
Continuous Potential ◽  
Nonlinear Choquard Equation

In this paper, we study the following nonlinear Choquard equation −ϵ2Δu+Kxu=1/8πϵ2∫ℝ3u2y/x−ydyu,x∈ℝ3, where ϵ>0 and Kx is a positive bounded continuous potential on ℝ3. By applying the reduction method, we proved that for any positive integer k, the above equation has a positive solution with k spikes near the local maximum point of Kx if ϵ>0 is sufficiently small under some suitable conditions on Kx.

Multi-peak positive solutions for the fractional Schrödinger–Poisson system

2018 ◽  
Vol 20 (03) ◽  
pp. 1750017
Author(s):  
Weiming Liu ◽  
Miaomiao Niu
Keyword(s):  
Small Parameter ◽  
Positive Solution ◽  
Positive Solutions ◽  
Local Maximum ◽  
Positive Function ◽  
Maximum Point ◽  
Poisson System ◽  
Local Maximum Point

In this paper, we study the existence of positive multi-peak solutions to the fractional Schrödinger–Poisson system [Formula: see text] where [Formula: see text] is a small parameter, [Formula: see text] is a positive function, [Formula: see text] and [Formula: see text] Under some given conditions which are given in Sec. ??, we prove the existence of a positive solution with m-peaks and concentrating near a given local maximum point of [Formula: see text]

scholarly journals On the query complexity of finding a local maximum point

2002 ◽  
Vol 84 (6) ◽  
pp. 327-332 ◽  
Author(s):  
A.L. Rastsvetaev ◽  
L.D. Beklemishev
Keyword(s):  
Local Maximum ◽  
Query Complexity ◽  
Maximum Point ◽  
Local Maximum Point

scholarly journals Strict convexity of the objective function and uniqueness of the maximum point in a model with three arbitrary random priorities

2021 ◽  
Vol 2131 (3) ◽  
pp. 032001
Author(s):  
I V Pavlov ◽  
N V Neumerzhitskaia ◽  
S I Uglich ◽  
T A Volosatova
Keyword(s):  
Objective Function ◽  
Local Maximum ◽  
Integral Form ◽  
Strict Convexity ◽  
Global Maximum ◽  
Maximum Point ◽  
Expert Opinions ◽  
Local Maximum Point ◽  
Significant Generalization ◽  
Strict Concavity

Abstract The main result of this paper is the proof of the strict concavity of some function of integral form depending on three random variables, which we call priorities. This function is an objective function in the so-called model with priorities, in which the arbiter, following expert opinions, distributes funds among the enterprises and institutions under his jurisdiction. This result implies an important corollary about the existence and uniqueness of a local maximum point (which is also a global maximum point) of the objective function. This is a significant generalization of the corresponding result of N.V. Neumezhitskaia, S.I. Uglich and T.A. Volosatova, published in December 2020.

scholarly journals Investigation of voltage regulation in grid–connected PV system

2020 ◽  
Vol 19 (3) ◽  
pp. 1131
Author(s):  
Soumen Gorai ◽  
Sattianadan D ◽  
V. Shanmugasundaram ◽  
S. Vidyasagar ◽  
G. R. Prudhvi Kumar ◽  
...  
Keyword(s):  
Carbon Dioxide Emissions ◽  
Local Maximum ◽  
Tidal Energy ◽  
Voltage Regulation ◽  
Voltage Source ◽  
Maximum Point ◽  
Power Demand ◽  
Pv System ◽  
Local Maximum Point ◽  
Park Transformation

<p>In the present scenario the power demand on the load side is increasing day by day, so to balance the power demand and power supply various renewable energy comes to picture as the additional source of electricity generation. The power generated by various renewable resources such as solar, wind, tidal energy and geothermal sources is environmentally clean and have a less emission impact. Out of which PV system draws more attention because it generates energy with a much lower level of carbon dioxide emissions. In the proposed work the objective is to investigate the synchronisation of the grid-connected PV system in terms of voltage and frequency. It includes the P-V characteristics under the circumstances of MPPT technique such as perturb &amp; observe (P&amp;O) method can able to track the local maximum point. The proposed inverter is a voltage source H-Bridge inverter which is controlled using a Clarke and Park transformation to drive a controlled current into the grid to maintain the THD value within the standards. As the grid frequency is fluctuating between SRF-PLL is generally used to fix the output frequency and phase of the grid. It also includes with the design of a three-phase H-bridge inverter as an interface between PV system and grid system. The proposed work is designed and simulated in MATLAB SIMULINK 2017b environment.</p>

scholarly journals POINT CLOUD GENERATION FROM GAUSSIAN DECOMPOSITION OF THE WAVEFORM LASER SIGNAL WITH GENETIC ALGORITHMS

2018 ◽  
Vol 24 (2) ◽  
pp. 270-287
Author(s):  
Andrey Augusto Alves de Oliveira ◽  
Jorge Antonio Silva Centeno ◽  
Fabiano Scheer Hainosz
Keyword(s):  
Genetic Algorithms ◽  
Point Cloud ◽  
Detection Method ◽  
Local Maximum ◽  
Maximum Point ◽  
Decomposition Approach ◽  
Laser Signal ◽  
Recent Developments ◽  
Local Maximum Point ◽  
Gaussian Decomposition

Abstract: Recent developments in LIDAR technology lead to the availability of the waveform systems, which capture and digitize the whole return of the emitted LASER pulse. As many objects may cause multiple returns in the same echo, one task is to detect and separate different echoes within the same digitized measurement. In this paper the results of a study aimed at LASER signal waveform decomposition using genetic algorithms are introduced. The proposed method is based on the Gaussian decomposition approach and analyzes each digitized return to compute one or more points. Initially, the number of peaks contained in the waveform is determined by a simple peak detection method, with a local maximum point algorithm. When more than one peak is detected, genetic algorithms are applied to estimate the amplitude, time and standard deviation of each peak within the digitized signal. With this methodology it was possible to increase the number of points by approximately 17 % compared to the point cloud obtained using commercial software. The best results were obtained in areas with high vegetation, and thus the methodology can be applied to the generation of denser points cloud in forest areas.

Multi-peak Positive Solutions of a Nonlinear Schrödinger–Newton Type System

2020 ◽  
Vol 20 (1) ◽  
pp. 53-75 ◽  
Author(s):  
Billel Gheraibia ◽  
Chunhua Wang
Keyword(s):  
Positive Integer ◽  
Local Minimum ◽  
Reduction Method ◽  
Type System ◽  
Finite Dimensional Reduction ◽  
Nonlinear Schrödinger ◽  
Finite Dimensional ◽  
Local Minimum Point ◽  
Dimensional Reduction Method ◽  
Continuous Potential

AbstractIn this paper, we study the following nonlinear Schrödinger–Newton type system:\left\{\begin{aligned} &\displaystyle{-}\epsilon^{2}\Delta u+u-\Phi(x)u=Q(x)|u% |u,&&\displaystyle x\in\mathbb{R}^{3},\\ &\displaystyle{-}\epsilon^{2}\Delta\Phi=u^{2},&&\displaystyle x\in\mathbb{R}^{% 3},\end{aligned}\right.where {\epsilon>0} and {Q(x)} is a positive bounded continuous potential on {\mathbb{R}^{3}} satisfying some suitable conditions. By applying the finite-dimensional reduction method, we prove that for any positive integer k, the system has a positive solution with k-peaks concentrating near a strict local minimum point {x_{0}} of {Q(x)} in {\mathbb{R}^{3}}, provided that {\epsilon>0} is sufficiently small.

scholarly journals An ingenious invasive weed optimization (IWO) aided maximum power tracking for partially shaded photovoltaic array

2019 ◽  
Vol 15 (2) ◽  
pp. 543
Author(s):  
Sridhar R ◽  
Boopathi C.S ◽  
Deepanjali Das ◽  
Sakshi Agrawal ◽  
Hardik Choubisa
Keyword(s):  
Local Maximum ◽  
Maximum Power ◽  
Hill Climbing ◽  
Global Maximum ◽  
Maximum Point ◽  
Invasive Weed ◽  
Photovoltaic Array ◽  
Perturb And Observe ◽  
Local Maximum Point ◽  
Power Point

<p>The inborn non-direct power voltage trademark bends concerning barometrical temperature and light makes the photovoltaic (PV) source a discontinuous one. Maximum power point (MPPT) following is a procedure through which most extreme accessible power is yielded from the PV for the given purpose of time. Prior, the customary MPPT methods, for example, perturb and observe, incremental conductance, hill climbing and so forth strategies were utilized and these methods stayed inadequate when the PV source is partially shaded (PS), since amid (PS) the power voltage (P-V) bends show different power crests. There wins each possibility that the ordinary calculations will stall out to the local maximum point and the global maximum point won't be accomplished and in this way control misfortune is brought about. The metaheuristic calculations give better arrangements however confront the downside of high weight on processor and enormous number of information prerequisites. In this way, in this paper, a novel calculation in light of invasive weed optimisation (IWO) technique is utilized to locate the Global maximum point for MPPT under in part shaded condition and it is contrasted and its nearby partner differential evolution(DE) MPPT algorithm and furthermore with the very much settled in perturb and observe (P&amp;O) calculation. The proposed calculation is actualized in MATLAB condition and tried on a 3-board PV cluster arrangement of 150 W. The flexibility of the calculation is tried through various experiments and the outcomes demonstrate the effectiveness and exactness of the proposed calculation in finding the global maximum point.</p>

Application of Identification Method of Swirling Motion by Swirl Function

2004 ◽  
Author(s):  
Katsuyuki Nakayama ◽  
Kenji Umeda
Keyword(s):  
Velocity Field ◽  
Complex Number ◽  
Swirling Flow ◽  
Local Maximum ◽  
Complex Eigenvalue ◽  
Maximum Point ◽  
Gradient Tensor ◽  
Velocity Gradient Tensor ◽  
Local Maximum Point

A method of identification and estimation of swirling motion in complicated flow and its application are presented. Classification of flow can be performed with velocity gradient tensor and its eigenvalue, and complex eigenvalue indicates that flow is swirling motion. Here the complex number of the eigenvalue is defined as swirling function, and the local maximum point of swirling function is assumed to be the axis of swirling. This method enables to identify the swirling motion hidden in complicated flow, which is impossible to identify with velocity field or streamline. This definition prevents misunderstanding between swirling flow and non-swirling flow with (non-zero) vorticity, and the intensity of swirling can be estimated.

scholarly journals Infinitely Many Solutions for the Prescribed Boundary Mean Curvature Problem in 𝔹N

2013 ◽  
Vol 65 (4) ◽  
pp. 927-960 ◽  
Author(s):  
Liping Wang ◽  
Chunyi Zhao
Keyword(s):  
Positive Solutions ◽  
Mean Curvature ◽  
Local Maximum ◽  
Infinitely Many Solutions ◽  
Maximum Point ◽  
Euclidean Metric ◽  
Rotationally Symmetric ◽  
Local Maximum Point ◽  
Curvature Problem ◽  
Boundary Mean Curvature

AbstractWe consider the prescribed boundary mean curvature problem in 𝔹N with the Euclidean metric where ã(x) is positive and rotationally symmetric on We show that if K∽(x) has a local maximum point, then this problemhas infinitely many positive solutions that are not rotationally symmetric on 𝕊N−1.

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