A Baire-type theorem for cardinals

1983 ◽  
Vol 48 (4) ◽  
pp. 1082-1089 ◽  
Author(s):  
Kurt Wolfsdorf
Keyword(s):  
Type Theorem ◽  
Infinite Cardinal ◽  
Power Set ◽  
Partition Class

AbstractWe shall prove the following theorem: If κ is an infinite cardinal and Γ: P(κ) → cf κ a partition of the power-set of κ then we can find a homogeneous ⊿-system of size κ such that the kernel of the ⊿-system is in the same partition class as all the members of the ⊿-system.

scholarly journals Partitioning the Power Set of $[n]$ into $C_k$-free parts

10.37236/8385 ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Eben Blaisdell ◽  
András Gyárfás ◽  
Robert A. Krueger ◽  
Ronen Wdowinski
Keyword(s):  
Upper Bound ◽  
Connected Graph ◽  
Type Problem ◽  
Color Class ◽  
Power Set ◽  
Ramsey Type ◽  
Partition Class ◽  
Cycle Path

We show that for $n \geq 3, n\ne 5$, in any partition of $\mathcal{P}(n)$, the set of all subsets of $[n]=\{1,2,\dots,n\}$, into $2^{n-2}-1$ parts, some part must contain a triangle — three different subsets $A,B,C\subseteq [n]$ such that $A\cap B,A\cap C,B\cap C$ have distinct representatives. This is sharp, since by placing two complementary pairs of sets into each partition class, we have a partition into $2^{n-2}$ triangle-free parts.  We also address a more general Ramsey-type problem: for a given graph $G$, find (estimate) $f(n,G)$, the smallest number of colors needed for a coloring of $\mathcal{P}(n)$, such that no color class contains a Berge-$G$ subhypergraph. We give an upper bound for $f(n,G)$ for any connected graph $G$ which is asymptotically sharp when $G$ is a cycle, path, or star. Additional bounds are given when $G$ is a $4$-cycle and when $G$ is a claw.

Migration and family change in Egypt: a comparative approach to social remittances

2013 ◽  
Vol 10 (1) ◽  
pp. 71-80 ◽  
Author(s):  
Lucile Gruntz ◽  
Delphine Pagès-El Karoui
Keyword(s):  
Public Discourse ◽  
Comparative Approach ◽  
Structural Factors ◽  
Host Countries ◽  
Return Policies ◽  
Social Remittances ◽  
Power Set ◽  
Gender Ideals ◽  
Gulf States ◽  
And Gender

Based on two ethnographical studies, our article explores social remittances from France and from the Gulf States, i.e. the way Egyptian migrants and returnees contribute to social change in their homeland with a focus on gender ideals and practices, as well as on the ways families cope with departure, absence and return. Policies in the home and host countries, public discourse, translocal networks, and individual locations within evolving structures of power, set the frame for an analysis of the consequences of migration in Egypt. This combination of structural factors is necessary to grasp the complex negotiations of family and gender norms, as asserted through idealized models, or enacted in daily practices in immigration and back home.

A Perron-Frobenius-type Theorem for Positive Matrix Semigroups

Positivity ◽  
2016 ◽  
Vol 21 (1) ◽  
pp. 61-72
Author(s):  
L. Livshits ◽  
G. MacDonald ◽  
H. Radjavi
Keyword(s):  
Type Theorem ◽  
Positive Matrix ◽  
Matrix Semigroups

scholarly journals A singular eigenvalue problem for the Dirichlet (p, q)-Laplacian

2021 ◽  
Author(s):  
Yunru Bai ◽  
Nikolaos S. Papageorgiou ◽  
Shengda Zeng
Keyword(s):  
Dirichlet Problem ◽  
Eigenvalue Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Singular Term ◽  
Type Theorem ◽  
Solution Map ◽  
Continuity Properties ◽  
Variational Tools ◽  
Superlinear Reaction

AbstractWe consider a parametric nonlinear, nonhomogeneous Dirichlet problem driven by the (p, q)-Laplacian with a reaction involving a singular term plus a superlinear reaction which does not satisfy the Ambrosetti–Rabinowitz condition. The main goal of the paper is to look for positive solutions and our approach is based on the use of variational tools combined with suitable truncations and comparison techniques. We prove a bifurcation-type theorem describing in a precise way the dependence of the set of positive solutions on the parameter $$\lambda $$ λ . Moreover, we produce minimal positive solutions and determine the monotonicity and continuity properties of the minimal positive solution map.

scholarly journals B-maximal commutators, commutators of B-singular integral operators and B-Riesz potentials on B-Morrey spaces

2020 ◽  
Vol 18 (1) ◽  
pp. 715-730
Author(s):  
Javanshir J. Hasanov ◽  
Rabil Ayazoglu ◽  
Simten Bayrakci
Keyword(s):  
Differential Operator ◽  
Singular Integral ◽  
Riesz Potential ◽  
Type Theorem ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Sobolev Type ◽  
Riesz Potentials ◽  
Bessel Differential Operator

Abstract In this article, we consider the Laplace-Bessel differential operator {\Delta }_{{B}_{k,n}}=\mathop{\sum }\limits_{i=1}^{k}\left(\frac{{\partial }^{2}}{\partial {x}_{i}^{2}}+\frac{{\gamma }_{i}}{{x}_{i}}\frac{\partial }{\partial {x}_{i}}\right)+\mathop{\sum }\limits_{i=k+1}^{n}\frac{{\partial }^{2}}{\partial {x}_{i}^{2}},{\gamma }_{1}\gt 0,\ldots ,{\gamma }_{k}\gt 0. Furthermore, we define B-maximal commutators, commutators of B-singular integral operators and B-Riesz potentials associated with the Laplace-Bessel differential operator. Moreover, we also obtain the boundedness of the B-maximal commutator {M}_{b,\gamma } and the commutator {[}b,{A}_{\gamma }] of the B-singular integral operator and Hardy-Littlewood-Sobolev-type theorem for the commutator {[}b,{I}_{\alpha ,\gamma }] of the B-Riesz potential on B-Morrey spaces {L}_{p,\lambda ,\gamma } , when b\in {\text{BMO}}_{\gamma } .

scholarly journals Online Learning Algorithms for the Real-Time Set-Point Tracking Problem

2021 ◽  
Vol 11 (14) ◽  
pp. 6620
Author(s):  
Arman Alahyari ◽  
David Pozo ◽  
Meisam Farrokhifar
Keyword(s):  
Decision Making ◽  
Power Systems ◽  
Real Time ◽  
Demand Response ◽  
Tracking Problem ◽  
Smart Meters ◽  
Set Point ◽  
Point Tracking ◽  
Power Set ◽  
Decision Making Framework

With the recent advent of technology within the smart grid, many conventional concepts of power systems have undergone drastic changes. Owing to technological developments, even small customers can monitor their energy consumption and schedule household applications with the utilization of smart meters and mobile devices. In this paper, we address the power set-point tracking problem for an aggregator that participates in a real-time ancillary program. Fast communication of data and control signal is possible, and the end-user side can exploit the provided signals through demand response programs benefiting both customers and the power grid. However, the existing optimization approaches rely on heavy computation and future parameter predictions, making them ineffective regarding real-time decision-making. As an alternative to the fixed control rules and offline optimization models, we propose the use of an online optimization decision-making framework for the power set-point tracking problem. For the introduced decision-making framework, two types of online algorithms are investigated with and without projections. The former is based on the standard online gradient descent (OGD) algorithm, while the latter is based on the Online Frank–Wolfe (OFW) algorithm. The results demonstrated that both algorithms could achieve sub-linear regret where the OGD approach reached approximately 2.4-times lower average losses. However, the OFW-based demand response algorithm performed up to twenty-nine percent faster when the number of loads increased for each round of optimization.

scholarly journals A Class of Integral Operators that Fix Exponential Functions

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini ◽  
Gumrah Uysal ◽  
Basar Yilmaz
Keyword(s):  
General Class ◽  
Pointwise Convergence ◽  
Type Theorem ◽  
Integral Operators ◽  
Exponential Functions ◽  
Convergence Theorems ◽  
Korovkin Type Theorem ◽  
Type Formula

AbstractIn this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified operators of Gauss–Weierstrass, or Picard or moment type operators. Pointwise convergence theorems are studied, using a Korovkin-type theorem and a Voronovskaja-type formula is obtained.

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