scholarly journals Biharmonic Maps and Laguerre Minimal Surfaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yusuf Abu Muhanna ◽  
Rosihan M. Ali
Keyword(s):  
Minimal Surface ◽  
Gaussian Curvature ◽  
Minimal Surfaces ◽  
Complete Characterization ◽  
Necessary Condition ◽  
Biharmonic Maps ◽  
Laguerre Minimal Surfaces ◽  
Laguerre Minimal Surface ◽  
Sufficient And Necessary Condition

A Laguerre surface is known to be minimal if and only if its corresponding isotropic map is biharmonic. For every Laguerre surfaceΦis its associated surfaceΨ=1+u2Φ, whereulies in the unit disk. In this paper, the projection of the surfaceΨassociated to a Laguerre minimal surface is shown to be biharmonic. A complete characterization ofΨis obtained under the assumption that the corresponding isotropic map of the Laguerre minimal surface is harmonic. A sufficient and necessary condition is also derived forΨto be a graph. Estimates of the Gaussian curvature to the Laguerre minimal surface are obtained, and several illustrative examples are given.

scholarly journals Null Wave Front and Ryu–Takayanagi Surface

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1297
Author(s):  
Jun Tsujimura ◽  
Yasusada Nambu
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Cosmological Constant ◽  
Minimal Surface ◽  
Wave Front ◽  
Entanglement Entropy ◽  
Necessary Condition ◽  
Quantum Field ◽  
Wave Fronts ◽  
Sufficient And Necessary Condition

The Ryu–Takayanagi formula provides the entanglement entropy of quantum field theory as an area of the minimal surface (Ryu–Takayanagi surface) in a corresponding gravity theory. There are some attempts to understand the formula as a flow rather than as a surface. In this paper, we consider null rays emitted from the AdS boundary and construct a flow representing the causal holographic information. We present a sufficient and necessary condition that the causal information surface coincides with Ryu–Takayanagi surface. In particular, we show that, in spherical symmetric static spacetimes with a negative cosmological constant, wave fronts of null geodesics from a point on the AdS boundary become extremal surfaces and therefore they can be regarded as the Ryu–Takayanagi surfaces. In addition, from the viewpoint of flow, we propose a wave optical formula to calculate the causal holographic information.

scholarly journals On Characterization of Distortion Premium Principle

2003 ◽  
Vol 33 (01) ◽  
pp. 1-10 ◽  
Author(s):  
Xianyi Wu ◽  
Jinglong Wang
Keyword(s):  
Distribution Function ◽  
Integral Representation ◽  
Necessary Condition ◽  
Additive Measure ◽  
Insurance Risk ◽  
Sufficient And Necessary Condition

In this paper, based on the additive measure integral representation of a non-additive measure integral, it is shown that any comonotonically additive premium principle can be represented as an integral of the distorted decumulative distribution function of the insurance risk. Furthermore, a sufficient and necessary condition that a premium principle is a distortion premium principle is given.

CHARACTERIZATION OF THE EXISTENCE OF GALLED-TREE NETWORKS

2006 ◽  
Vol 04 (06) ◽  
pp. 1309-1328 ◽  
Author(s):  
ARVIND GUPTA ◽  
JÁN MAŇUCH ◽  
XIAOHONG ZHAO ◽  
LADISLAV STACHO
Keyword(s):  
Necessary Conditions ◽  
Simple Algorithm ◽  
Complete Characterization ◽  
Necessary Condition ◽  
Tree Networks ◽  
Tree Network ◽  
Sufficient And Necessary Conditions

In this paper, we give a complete characterization of the existence of a galled-tree network in the form of simple sufficient and necessary conditions for both root-known and root-unknown cases. As a by-product we obtain a simple algorithm for constructing galled-tree networks. We also introduce a new necessary condition for the existence of a galled-tree network similar to bi-convexity.

The isoperimetric inequality for minimal surfaces in a Riemannian manifold

1999 ◽  
Vol 1999 (506) ◽  
pp. 205-214 ◽  
Author(s):  
Jaigyoung Choe
Keyword(s):  
Riemannian Manifold ◽  
Minimal Surface ◽  
Sectional Curvature ◽  
Isoperimetric Inequality ◽  
Gaussian Curvature ◽  
Minimal Surfaces ◽  
Constant Gaussian Curvature ◽  
Simply Connected

Abstract It is proved that every minimal surface with one or two boundary components in a simply connected Riemannian manifold with sectional curvature bounded above by a nonpositive constant K satisfies the sharp isoperimetric inequality 4π A ≦ L2 + K A2. Here equality holds if and only if the minimal surface is a geodesic disk in a surface of constant Gaussian curvature K.

On ∗-clean group rings over abelian groups

2016 ◽  
Vol 16 (08) ◽  
pp. 1750152 ◽  
Author(s):  
Dongchun Han ◽  
Yuan Ren ◽  
Hanbin Zhang
Keyword(s):  
Cyclic Group ◽  
Prime Power ◽  
Associative Ring ◽  
Finite Abelian Group ◽  
Sufficient Conditions ◽  
Complete Characterization ◽  
Necessary Condition ◽  
Group Rings ◽  
Prime Power Order

An associative ring with unity is called clean if each of its elements is the sum of an idempotent and a unit. A clean ring with involution ∗ is called ∗-clean if each of its elements is the sum of a unit and a projection (∗-invariant idempotent). In a recent paper, Huang, Li and Yuan provided a complete characterization that when a group ring [Formula: see text] is ∗-clean, where [Formula: see text] is a finite field and [Formula: see text] is a cyclic group of an odd prime power order [Formula: see text]. They also provided a necessary condition and a few sufficient conditions for [Formula: see text] to be ∗-clean, where [Formula: see text] is a cyclic group of order [Formula: see text]. In this paper, we extend the above result of Huang, Li and Yuan from [Formula: see text] to [Formula: see text] and provide a characterization of ∗-clean group rings [Formula: see text], where [Formula: see text] is a finite abelian group and [Formula: see text] is a field with characteristic not dividing the exponent of [Formula: see text].

scholarly journals On Characterization of Distortion Premium Principle

2003 ◽  
Vol 33 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Xianyi Wu ◽  
Jinglong Wang
Keyword(s):  
Distribution Function ◽  
Integral Representation ◽  
Necessary Condition ◽  
Additive Measure ◽  
Insurance Risk ◽  
Sufficient And Necessary Condition

In this paper, based on the additive measure integral representation of a non-additive measure integral, it is shown that any comonotonically additive premium principle can be represented as an integral of the distorted decumulative distribution function of the insurance risk. Furthermore, a sufficient and necessary condition that a premium principle is a distortion premium principle is given.

scholarly journals Affine spheres with prescribed Blaschke metric

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5967-5975
Author(s):  
Barbara Opozda
Keyword(s):  
Gaussian Curvature ◽  
Harmonic Functions ◽  
Necessary Condition ◽  
Dimensional Manifold ◽  
Affine Sphere ◽  
Metric Tensor ◽  
Affine Spheres ◽  
Pick Invariant ◽  
Sufficient And Necessary Condition

It is proved that the equality ?ln |k-?| = 6k, where k is the Gaussian curvature of a metric tensor 1 on a 2-dimensional manifold is a sufficient and necessary condition for local realizability of the metric as the Blaschke metric of some affine sphere. Consequently, the set of all improper local affine spheres with nowhere-vanishing Pick invariant can be parametrized by harmonic functions.

Disjoint topological transitivity for weighted translations generated by group actions

2021 ◽  
Vol 71 (5) ◽  
pp. 1229-1240
Author(s):  
Chung-Chuan Chen ◽  
Seyyed Mohammad Tabatabaie ◽  
Ali Mohammadi
Keyword(s):  
Group Actions ◽  
Group Element ◽  
Necessary Condition ◽  
Compact Groups ◽  
Topological Transitivity ◽  
Locally Compact ◽  
Topological Mixing ◽  
Quotient Spaces ◽  
Sufficient And Necessary Condition

Abstract In this note, we give a sufficient and necessary condition for weighted translations, generated by group actions, to be disjoint topologically transitive in terms of the weights, the group element and the measure. The characterization of disjoint topological mixing is obtained as well. Moreover, we apply the results to the quotient spaces of locally compact groups and hypergroups.

A CHARACTERIZATION OF THE CATENOID AND HELICOID

2013 ◽  
Vol 24 (06) ◽  
pp. 1350045 ◽  
Author(s):  
CARLOS M. C. RIVEROS ◽  
ARMANDO M. V. CORRO
Keyword(s):  
Minimal Surface ◽  
Minimal Surfaces ◽  
Geodesic Curvature ◽  
Lines Of Curvature ◽  
Asymptotic Lines

In this paper we show that a connected non-planar minimal surface whose asymptotic lines have the same geodesic curvature up to sign is a catenoid. As an application of this result we show that a connected non-planar minimal surface whose lines of curvature have the same geodesic curvature up to sign is a helicoid. Moreover, we show that the coordinates curves of the associate minimal surfaces to catenoid have the same geodesic curvature up to sign.

Full characterization of quantum correlated equilibria

2013 ◽  
Vol 13 (9&10) ◽  
pp. 846-860
Author(s):  
Zhaohui Wei ◽  
Shengyu Zhang
Keyword(s):  
Necessary Condition ◽  
Quantum Game ◽  
Quantum Devices ◽  
Full Characterization ◽  
Positive Gain ◽  
Conflicting Interests ◽  
Correlated Equilibria ◽  
Sufficient And Necessary Condition ◽  
Quantum Strategies

Quantum game theory aims to study interactions of people (or other agents) using quantum devices with possibly conflicting interests. Recently Zhang studied some quantitative questions in general quantum strategic games of growing sizes~\cite{Zha12}. However, a fundamental question not addressed there is the characterization of quantum correlated equilibria (QCE). In this paper, we answer this question by giving a sufficient and necessary condition for an arbitrary state $\rho$ being a QCE. In addition, when the condition fails to hold for some player $i$, we give an explicit positive-operator valued measurement (POVM) for that player to achieve a strictly positive gain of payoff. Finally, we give some upper bounds for the maximum gain by playing quantum strategies over classical ones, and the bounds are tight for some games.

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