(x,y)),x,y∈I,aregiven.SimilarconsiderationsforatheoremaccompanyingtheLagrangemean-valuetheoremarepresented.Keywords:Lagrangemean-valuetheorem,mean,Darbouxpropertyofderivative,vector-valuedfunctionMSC2010:26A24,26E601.IntroductionLetI⊂Rbeaninterval.RecallthatafunctionM:I2→RissaidtobeameaninIif,forallx,y...
(x):x∈D}istheimagesetofDbyf.Themaincontributionofthispaperistopresentthefirstmethodabletosolvetheimagesetproblemforcontinuouslydifferentiablenonlinearvector-valuedfunctionsf:Rn−→Rn(bothdomainandco-domainhavethesamedimension).Intervalanalysisprovidesalargenumberofmethodsabletocomputeefficientlyanouter...
Vector-ValuedFunctions131向量值函数
VECTOR-VALUED FUNCTIONSMATH 195, SECTION 59 (VIPUL NAIK)Corresponding material in the book: Sections 14.1. 14.2.What students should denitely get: Denition of vector-valued function, relation with paramet-ric description of curves, basic operations on vector-valued functions, limit and continuity ...
We study the weighted average consensus problem for a gossip network of agents with vector-valued states. For a given matrix-weighted graph, the gossip process is described by a sequence of pairs of adjacent agents communicating and updating their states based on the edge matrix weight. Our key...
VECTOR-VALUED LAPLACE TRANSFORMSAND CAUCHY PROBLEMS 向量值拉普拉斯变换 柯西问题.pdf,ISRAELJOURNAL OF MATHEMATICS,Vol. 59, No. 3, 1987 VECTOR-VALUED LAPLACE TRANSFORMS AND CAUCHY PROBLEMS BY WOLFGANG ARENDT Mathematisches Institut der Universitat, D- 7400
not just the strictly convex ones. The Converse to the Four Vertex Theorem says that any continuous real- valued function on the circle which has at least two local maxima and two local minima is the curvature function of a simple closed curve in the plane. In 1971 Herman Gluck proved this...
paper, we adopt the point of view that the real figure of merit in H∞-feedback systems design is the vector-valued performance measure (∥W1S∥∞,∥W2T∥∞), where W1S is the frequency-weighted sensitivity function and W2T:= W2 (I−S) the weighted complementary sensitivity function....
We extend the V BG* property to the context of vector-valued functions and give some characterizations of this property. Necessary and sufficient conditions for vector-valued VBG* functions to be continuous or weakly continuous, except at most on a countable set, are obtained. MSC: Primary 26A4...
Let D be a domain of holomorphy in G (where C denotes the complex plane), let A be a complex Banach algebra with identity e (where A is in general non-commutative) and denote by A (D) the algebra of all holomorphic A-valued functions on D. This paper isdoi:10.1112/jlms/s1-42.1....