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.

scholarly journals Extreme points and rotundity of Orlicz-Sobolev spaces

2002 ◽  
Vol 32 (5) ◽  
pp. 293-299
Author(s):  
Shutao Chen ◽  
Changying Hu ◽  
Charles Xuejin Zhao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Sobolev Spaces ◽  
Necessary Conditions ◽  
Nonlinear Partial Differential Equations ◽  
Extreme Points ◽  
Necessary Condition ◽  
Partial Differential ◽  
Sufficient And Necessary Conditions ◽  
Sufficient And Necessary Condition

It is well known that Sobolev spaces have played essential roles in solving nonlinear partial differential equations. Orlicz-Sobolev spaces are generalized from Sobolev spaces. In this paper, we present sufficient and necessary conditions of extreme points of Orlicz-Sobolev spaces. A sufficient and necessary condition of rotundity of Orlicz-Sobolev spaces is obtained.

Efficient Constrained Combinatorial Auctions

2016 ◽  
Vol 18 (03) ◽  
pp. 1650007
Author(s):  
Anat Lerner ◽  
Rica Gonen
Keyword(s):  
Necessary Conditions ◽  
Dominant Strategy ◽  
Single Item ◽  
Constrained Efficiency ◽  
Incentive Compatible ◽  
Sufficient And Necessary Conditions ◽  
Multidimensional Types ◽  
The Individual ◽  
Efficient Mechanisms

The seminal work by Green and Laffont [(1977) characterization of satisfactory mechanisms for the revelation of preferences for public goods, Econometrica 45, 427–438] shows that efficient mechanisms with Vickrey–Clarke–Groves prices satisfy the properties of dominant-strategy incentive compatible (DSIC) and individually rational in the quasilinear utilities model. Nevertheless in many real-world situations some players have a gap between their willingness to pay and their ability to pay, i.e., a budget. We show that once budgets are integrated into the model then Green and Laffont’s theorem ceases to apply. More specifically, we show that even if only a single player has budget constraints then there is no deterministic efficient mechanism that satisfies the individual rationality and DSIC properties. Furthermore, in a quasilinear utilities model with [Formula: see text] nonidentical items and [Formula: see text] players with multidimensional types, we characterize the sufficient and necessary conditions under which Green and Laffont’s theorem holds in the presence of budget-constrained players. Interestingly our characterization is similar in spirit to that of Maskin [(2000) Auctions, development and privatization: Efficient auctions with liquidity-constrained buyers, Eur. Econ. Rev. 44, 667–681] for Bayesian single-item constrained-efficiency auctions.

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 Optimality for E-[0,1] convex multi-objective programming

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 529-541 ◽  
Author(s):  
Tarek Emama
Keyword(s):  
Feasible Solution ◽  
Necessary Conditions ◽  
Optimal Solution ◽  
Efficient Solutions ◽  
Properly Efficient Solution ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Sufficient And Necessary Conditions ◽  
Objective Programming

In this paper, we interest with deriving the sufficient and necessary conditions for optimal solution of special classes of Programming. These classes involve generalized E-[0,1] convex functions. Characterization of efficient solutions for E-[0,1] convex multi-objective Programming are obtained. Finally, sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are derived.

Grazing Bifurcations and Parametric Characterization of a Hysterically Damped Semi-Active Suspension System

2007 ◽  
Author(s):  
Albert C. J. Luo ◽  
Arun Rajendran
Keyword(s):  
Necessary Conditions ◽  
Active Suspension ◽  
Suspension System ◽  
Local Theory ◽  
Final States ◽  
Discontinuous System ◽  
Comprehensive Investigation ◽  
System Parameters ◽  
Sufficient And Necessary Conditions

The criterion for grazing motions in a hysterically damped semi-active suspension system is obtained from the local theory of non-smooth dynamical systems on the connectable and accessible domains. The generic mappings for such a suspension system are introduced. The sufficient and necessary conditions for grazing at the final states of mappings are expressed. The initial and final switching sets of grazing mapping, varying with system parameters, are illustrated for the grazing parametric characteristics. The initial and grazing, switching manifolds in the switching sets are defined through grazing mappings. Finally, numerical illustrations of grazing motions are very easily carried out with help of the analytical predictions. This paper provides a comprehensive investigation of grazing motions in the suspension system for a better understanding of the grazing mechanism of such a discontinuous system.

scholarly journals Combined structural and topological stability are equivalent to Axiom A and the strong transversality condition

1984 ◽  
Vol 4 (1) ◽  
pp. 81-88 ◽  
Author(s):  
Mike Hurley
Keyword(s):  
Necessary Conditions ◽  
Transversality Condition ◽  
Complete Characterization ◽  
Compact Manifolds ◽  
Topological Stability ◽  
Axiom A ◽  
Recent Theorem ◽  
Structurally Stable

AbstractThe purpose of this paper is to develop necessary conditions for a diffeomorphism to be topologically stable (lower semistable). Our results combine with a recent theorem of R. Mañé and with earlier results of J. Robbin, C. Robinson, and Z. Nitecki to give a complete characterization of diffeomorphisms of compact manifolds that are both topologically and structurally stable: they are precisely the Axiom A diffeomorphisms that satisfy the strong transversality condition.

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 On Sufficient and Necessary Conditions in Bounded CTL: A Forgetting Approach

2020 ◽  
Author(s):  
Renyan Feng ◽  
Erman Acar ◽  
Stefan Schlobach ◽  
Yisong Wang ◽  
Wanwei Liu
Keyword(s):  
Computational Complexity ◽  
System Design ◽  
Formal Verification ◽  
Information Content ◽  
Necessary Conditions ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Computation Tree ◽  
Sufficient And Necessary Conditions ◽  
Points Of View

Computation Tree Logic (CTL) is one of the central formalisms in formal verification. As a specification language, it is used to express a property that the system at hand is expected to satisfy. From both the verification and the system design points of view, some information content of such property might become irrelevant for the system due to various reasons, e.g., it might become obsolete by time, or perhaps infeasible due to practical difficulties. Then, the problem arises on how to subtract such piece of information without altering the relevant system behaviour or violating the existing specifications over a given signature. Moreover, in such a scenario, two crucial notions are informative: the strongest necessary condition (SNC) and the weakest sufficient condition (WSC) of a given property. To address such a scenario in a principled way, we introduce a forgetting-based approach in CTL and show that it can be used to compute SNC and WSC of a property under a given model and over a given signature. We study its theoretical properties and also show that our notion of forgetting satisfies existing essential postulates of knowledge forgetting. Furthermore, we analyse the computational complexity of some basic reasoning tasks for the fragment CTLAF in particular.

scholarly journals Weak Sharp Minima in Set-Valued Optimization Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Ming-hao Jin ◽  
Jun-xiang Wang ◽  
Shu Xu
Keyword(s):  
Necessary Conditions ◽  
Optimization Problems ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Outer Limit ◽  
Sufficient And Necessary Conditions ◽  
Scalarization Function ◽  
Weak Sharp ◽  
Sharp Minima

We introduce the notion of a weakψ-sharp minimizer for set-valued optimization problems. We present some sufficient and necessary conditions that a pair point is a weakψ-sharp minimizer through the outer limit of set-valued map and develop the characterization of the weakψ-sharp minimizer in terms of a generalized nonlinear scalarization function. These results extend the corresponding ones in Studniarski (2007).

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