scholarly journals Polyhedral Embeddings of Snarks with Arbitrary Nonorientable Genera

10.37236/2539 ◽  
2012 ◽  
Vol 19 (3) ◽  
Author(s):  
Wenzhong Liu ◽  
Yichao Chen
Keyword(s):  
Positive Solution ◽  
Klein Bottle ◽  
Infinite Family ◽  
Polyhedral Embedding

Mohar and Vodopivec [Combinatorics, Probability and Computing (2006) 15, 877-893] proved that for every integer $k$ ($k \geq 1$ and $k\neq 2$), there exists a snark which polyhedrally embeds in $\mathbb{N}_k$ and presented the problem: Is there a snark that has a polyhedral embedding in the Klein bottle? In the paper, we give a positive solution of the problem and strengthen Mohar and Vodopivec's  result. We prove that for every integer $k$ ($k\geq 2$), there exists an infinite family of snarks with nonorientable genus $k$ which polyhedrally embed in $\mathbb{N}_k$. Furthermore, for every integer $k$ ($k> 0$), there exists a snark with nonorientable genus $k$ which polyhedrally embeds in $\mathbb{N}_k$.

On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value

2006 ◽  
Vol 11 (4) ◽  
pp. 323-329 ◽  
Author(s):  
G. A. Afrouzi ◽  
S. H. Rasouli
Keyword(s):  
Boundary Value Problems ◽  
Positive Solution ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Smooth Bounded Domain ◽  
Elliptic Boundary Value ◽  
Existence Of Positive Solutions

This study concerns the existence of positive solutions to classes of boundary value problems of the form−∆u = g(x,u), x ∈ Ω,u(x) = 0, x ∈ ∂Ω,where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u).

Advancing Women in Local Government: The Case of Illinois

Public Voices ◽  
2016 ◽  
Vol 13 (2) ◽  
pp. 89
Author(s):  
Rachel Lange ◽  
Kimberly Nelson
Keyword(s):  
Local Government ◽  
Positive Solution ◽  
Gender Gap ◽  
Family Life ◽  
Online Survey ◽  
Work Life ◽  
Time Commitment ◽  
Survey Results ◽  
Local Government Management ◽  
Professional Fields

Despite gains by women in many professional fields, the top level of local government management ranks continues to be populated primarily by man. The percentage of females serving as local government chief administrators has not increased since the 1980s. Little empirical research exists that attempts to uncover the reason for the gender gap. The purpose of this research is to identify some of the obstacles and barriers that affect a woman’s decision to advance her career in local government. Utilizing an online survey, the authors surveyed female chief administrative officers (CAOs), assistant CAOs, assistant to the CAOs, and deputy CAOs in Illinois. The survey results show that barriers such as a male dominated culture and time commitment to work life and family life are preventing females from achieving higher authority. Mentoring proves to be a positive solution to many of the barriers facing women in local government.

Positive solution of a class of equations involving noncompact mappings

1988 ◽  
Vol 9 (8) ◽  
pp. 727-736
Author(s):  
Lan Kun-quan ◽  
Ding Xie-ping
Keyword(s):  
Positive Solution

scholarly journals More on holographic correlators: twisted and dimensionally reduced structures

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Connor Behan ◽  
Pietro Ferrero ◽  
Xinan Zhou
Keyword(s):  
Field Theory ◽  
Theoretical Data ◽  
Infinite Family ◽  
Tree Level ◽  
Chiral Algebra ◽  
Perfect Agreement ◽  
Four Dimensions ◽  
Independent Field ◽  
Superconformal Theories ◽  
Emergent Structure

Abstract Recently four-point holographic correlators with arbitrary external BPS operators were constructively derived in [1, 2] at tree-level for maximally superconformal theories. In this paper, we capitalize on these theoretical data, and perform a detailed study of their analytic properties. We point out that these maximally supersymmetric holographic correlators exhibit a hidden dimensional reduction structure à la Parisi and Sourlas. This emergent structure allows the correlators to be compactly expressed in terms of only scalar exchange diagrams in a dimensionally reduced spacetime, where formally both the AdS and the sphere factors have four dimensions less. We also demonstrate the superconformal properties of holographic correlators under the chiral algebra and topological twistings. For AdS5× S5 and AdS7× S4, we obtain closed form expressions for the meromorphic twisted correlators from the maximally R-symmetry violating limit of the holographic correlators. The results are compared with independent field theory computations in 4d $$ \mathcal{N} $$ N = 4 SYM and the 6d (2, 0) theory, finding perfect agreement. For AdS4× S7, we focus on an infinite family of near-extremal four-point correlators, and extract various protected OPE coefficients from supergravity. These OPE coefficients provide new holographic predictions to be matched by future supersymmetric localization calculations. In deriving these results, we also develop many technical tools which should have broader applicability beyond studying holographic correlators.

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 AdS2 × S2 × CY2 solutions in Type IIB with 8 supersymmetries

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yolanda Lozano ◽  
Carlos Nunez ◽  
Anayeli Ramirez
Keyword(s):  
Quantum Mechanics ◽  
Riemann Surface ◽  
Central Charge ◽  
Global Solutions ◽  
Infinite Family ◽  
Dimensional System ◽  
One Dimensional

Abstract We present a new infinite family of Type IIB supergravity solutions preserving eight supercharges. The structure of the space is AdS2 × S2 × CY2 × S1 fibered over an interval. These solutions can be related through double analytical continuations with those recently constructed in [1]. Both types of solutions are however dual to very different superconformal quantum mechanics. We show that our solutions fit locally in the class of AdS2 × S2 × CY2 solutions fibered over a 2d Riemann surface Σ constructed by Chiodaroli, Gutperle and Krym, in the absence of D3 and D7 brane sources. We compare our solutions to the global solutions constructed by Chiodaroli, D’Hoker and Gutperle for Σ an annulus. We also construct a cohomogeneity-two family of solutions using non-Abelian T-duality. Finally, we relate the holographic central charge of our one dimensional system to a combination of electric and magnetic fluxes. We propose an extremisation principle for the central charge from a functional constructed out of the RR fluxes.

Sign in / Sign up

Export Citation Format

Share Document