scholarly journals Upper level sets of Lelong numbers on $$\mathbb P^2$$ and cubic curves

2021 ◽  
Author(s):  
Ali Ulas Ozgur Kisisel ◽  
Ozcan Yazici
Keyword(s):  
Level Sets ◽  
Cubic Curves ◽  
Lelong Numbers ◽  
Upper Level

scholarly journals On Construction of Positive Closed Currents with Prescribed Lelong Numbers

2020 ◽  
pp. 331-341
Author(s):  
Hedi Khedhiri
Keyword(s):  
Growth Condition ◽  
Compact Subset ◽  
Level Set ◽  
Level Sets ◽  
Plurisubharmonic Function ◽  
Lelong Numbers ◽  
The Family ◽  
Closed Current ◽  
Upper Level ◽  
Positive Closed Current

We establish that a sequence (Xk)k∈N of analytic subsets of a domain Ω in Cn, purely dimensioned, can be released as the family of upper-level sets for the Lelong numbers of some positive closed current. This holds whenever the sequence (Xk)k∈N satisfies, for any compact subset L of Ω, the growth condition Σ k∈N Ck mes(Xk ∩ L) < ∞. More precisely, we built a positive closed current Θ of bidimension (p, p) on Ω, such that the generic Lelong number mXk of Θ along each Xk satisfies mXk = Ck. In particular, we prove the existence of a plurisubharmonic function v on Ω such that, each Xk is contained in the upper-level set ECk (ddcv)

scholarly journals Geometric properties of upper level sets of Lelong numbers on projective spaces

2014 ◽  
Vol 361 (3-4) ◽  
pp. 981-994 ◽  
Author(s):  
Dan Coman ◽  
Tuyen Trung Truong
Keyword(s):  
Level Sets ◽  
Projective Spaces ◽  
Geometric Properties ◽  
Lelong Numbers ◽  
Upper Level

scholarly journals A Property of upper level sets of Lelong numbers of currents on ℙ2

2017 ◽  
Vol 28 (14) ◽  
pp. 1750110 ◽  
Author(s):  
James J. Heffers
Keyword(s):  
Projective Space ◽  
Level Set ◽  
Level Sets ◽  
Complex Projective Space ◽  
Lelong Number ◽  
Lelong Numbers ◽  
Closed Current ◽  
Upper Level ◽  
Complex Projective ◽  
Positive Closed Current

Let [Formula: see text] be a positive closed current of bidimension [Formula: see text] with unit mass on the complex projective space [Formula: see text]. For [Formula: see text] and [Formula: see text] we show that if [Formula: see text] has four points with Lelong number at least [Formula: see text], the upper level set [Formula: see text] of points of [Formula: see text] with Lelong number strictly larger than [Formula: see text] is contained within a conic with the exception of at most one point.

Finding upper-level sets in cellular surface data using echelons and saTScan

2006 ◽  
Vol 13 (4) ◽  
pp. 379-390 ◽  
Author(s):  
Wayne L. Myers ◽  
Koji Kurihara ◽  
Ganapati P. Patil ◽  
Ryan Vraney
Keyword(s):  
Level Sets ◽  
Surface Data ◽  
Upper Level

scholarly journals Administrative corruption in the static model of balancing common and private interests

2021 ◽  
pp. 9-19
Author(s):  
Olga Ivanovna Gorbaneva
Keyword(s):  
Level Sets ◽  
Lower Boundary ◽  
Static Model ◽  
Optimization Approach ◽  
Level System ◽  
Private Interests ◽  
Descriptive Approach ◽  
Upper Level ◽  
The Impact

&nbsp; This article is dedicated to examination of corruption in the previously researched static model of balancing common and private interests (SOCHI-models). In the previously considered two-level system, between the upper non-corrupted level and the lower &ndash; agents, is introduced the average level which in exchange for a bribe, can weaken the influence of the upper level. The upper level sets the minimum amount of resources for an agent to spend on general purposes. A supervisor, in exchange for a bribe, the role of which is played by the share of agent&rsquo;s private income, can reduce this lower boundary, allowing the latter to spend more resources on private purposes. This article reviews the three-level hierarchical system &ldquo;Principal-Supervisor-Agents&rdquo;, where the supervisor uses the administrative corruption mechanism, which requires two descriptive and optimization approaches towards its examination. The descriptive approach suggests that the considered functions of bribery are known; while the optimization approach implies the use of Germeyer&rsquo;s theorem. The author explores the impact of administrative corruption upon systemic congruence of the SOCHI-model: it is proven that the administrative corruption can only reduce congruence. The author finds the conditions that can beat or reduce administrative corruption can, as well as conditions when corruption is disadvantageous for supervisor or agent. The article determines the circle of agents that supervisor can exert influence upon. &nbsp;

Administrative corruption in the static model of balancing common and private interests

2021 ◽  
pp. 9-19
Author(s):  
Olga Ivanovna Gorbaneva
Keyword(s):  
Level Sets ◽  
Lower Boundary ◽  
Static Model ◽  
Optimization Approach ◽  
Level System ◽  
Private Interests ◽  
Descriptive Approach ◽  
Upper Level ◽  
The Impact

&nbsp; This article is dedicated to examination of corruption in the previously researched static model of balancing common and private interests (SOCHI-models). In the previously considered two-level system, between the upper non-corrupted level and the lower &ndash; agents, is introduced the average level which in exchange for a bribe, can weaken the influence of the upper level. The upper level sets the minimum amount of resources for an agent to spend on general purposes. A supervisor, in exchange for a bribe, the role of which is played by the share of agent&rsquo;s private income, can reduce this lower boundary, allowing the latter to spend more resources on private purposes. This article reviews the three-level hierarchical system &ldquo;Principal-Supervisor-Agents&rdquo;, where the supervisor uses the administrative corruption mechanism, which requires two descriptive and optimization approaches towards its examination. The descriptive approach suggests that the considered functions of bribery are known; while the optimization approach implies the use of Germeyer&rsquo;s theorem. The author explores the impact of administrative corruption upon systemic congruence of the SOCHI-model: it is proven that the administrative corruption can only reduce congruence. The author finds the conditions that can beat or reduce administrative corruption can, as well as conditions when corruption is disadvantageous for supervisor or agent. The article determines the circle of agents that supervisor can exert influence upon. &nbsp;

scholarly journals A Novel Method for Solving the Fully Fuzzy Bilevel Linear Programming Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Aihong Ren
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Level Sets ◽  
Fuzzy Numbers ◽  
Main Idea ◽  
Bilevel Linear Programming ◽  
Decision Variables ◽  
Upper Level

We address a fully fuzzy bilevel linear programming problem in which all the coefficients and variables of both objective functions and constraints are expressed as fuzzy numbers. This paper is to develop a new method to deal with the fully fuzzy bilevel linear programming problem by applying interval programming method. To this end, we first discretize membership grade of fuzzy coefficients and fuzzy decision variables of the problem into a finite number ofα-level sets. By usingα-level sets of fuzzy numbers, the fully fuzzy bilevel linear programming problem is transformed into an interval bilevel linear programming problem for eachα-level set. The main idea to solve the obtained interval bilevel linear programming problem is to convert the problem into two deterministic subproblems which correspond to the lower and upper bounds of the upper level objective function. Based on theKth-best algorithm, the two subproblems can be solved sequentially. Based on a series ofα-level sets, we introduce a linear piecewise trapezoidal fuzzy number to approximate the optimal value of the upper level objective function of the fully fuzzy bilevel linear programming problem. Finally, a numerical example is provided to demonstrate the feasibility of the proposed approach.

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