Properties of boundaries of an ND convex cone

2002 ◽  
Author(s):  
Chia-Lun J. Hu
Keyword(s):  
Convex Cone

Fluctuations of random walk in R d and storage systems

1977 ◽  
Vol 9 (03) ◽  
pp. 566-587 ◽  
Author(s):  
Priscilla Greenwood ◽  
Moshe Shaked
Keyword(s):  
Random Walk ◽  
Unique Solution ◽  
Convex Cone ◽  
Storage Systems ◽  
Queueing Systems ◽  
Convolution Equation ◽  
Stopping Times ◽  
Multivariate Distributions ◽  
Explicit Formulas ◽  
And Storage

Two Wiener-Hopf type factorization identities for multivariate distributions are introduced. Properties of associated stopping times are derived. The structure that produces one factorization also provides the unique solution of the Wiener-Hopf convolution equation on a convex cone in R d . Some applications for multivariate storage and queueing systems are indicated. For a few cases explicit formulas are obtained for the transforms of the associated stopping times. A result of Kemperman is extended.

Remarks on CCR and CAR flows over closed convex cones

2022 ◽  
Author(s):  
Anbu Arjunan
Keyword(s):  
Convex Cone ◽  
Convex Cones ◽  
Closed Convex Cone ◽  
Cocycle Conjugacy

For a closed convex cone [Formula: see text] in [Formula: see text] which is spanning and pointed, i.e. [Formula: see text] and [Formula: see text] we consider a family of [Formula: see text]-semigroups over [Formula: see text] consisting of a certain family of CCR flows and CAR flows over [Formula: see text] and classify them up to the cocycle conjugacy.

Equilibrium with Constant Returns

2011 ◽  
Author(s):  
Yves Balasko
Keyword(s):  
General Equilibrium ◽  
Equilibrium Model ◽  
Convex Cone ◽  
Supply And Demand ◽  
Returns To Scale ◽  
Price System ◽  
Production Sector ◽  
The One ◽  
Constant Returns To Scale ◽  
Privately Owned

This chapter analyzes an equilibrium model where privately owned firms feature either smooth decreasing or constant returns to scale. Profit of the constant returns to scale firms being equal to zero at equilibrium, the equilibrium of the model does not depend on the ownership structure of these firms. In addition, the convex conical production sets of these firms sum up into a convex cone. It is as if the production sector operating under constant returns consists of a unique firm. The general equilibrium model with decreasing and constant returns to scale firms is essentially the same model as the one considered in Chapter 10 with the addition of a unique firm operating under constant returns to scale. Nevertheless, this addition is enough to hamstring the approach of the preceding chapters based on the concept of price system that equates aggregate supply and demand. The solution is to add to that price system the activity of the constant returns to scale firm.

Cone-Monotone Functions: Differentiability and Continuity

2005 ◽  
Vol 57 (5) ◽  
pp. 961-982 ◽  
Author(s):  
Jonathan M. Borwein ◽  
Xianfu Wang
Keyword(s):  
Banach Spaces ◽  
Convex Cone ◽  
Continuous Functions ◽  
Monotone Functions ◽  
Empty Interior ◽  
Space Of Continuous Functions

AbstractWe provide a porosity-based approach to the differentiability and continuity of real-valued functions on separable Banach spaces, when the function is monotone with respect to an ordering induced by a convex cone K with non-empty interior. We also show that the set of nowhere K-monotone functions has a σ-porous complement in the space of continuous functions endowed with the uniform metric.

scholarly journals Lipschitz and differentiable dependence of solutions on a parameter in a scalarization method

1987 ◽  
Vol 42 (3) ◽  
pp. 353-364 ◽  
Author(s):  
Alicia Sterna-Karwat
Keyword(s):  
Vector Optimization ◽  
Normed Space ◽  
Convex Cone ◽  
Optimization Problem ◽  
Vector Optimization Problem ◽  
Optimal Solutions ◽  
Scalar Problem ◽  
Lipschitz Continuous ◽  
Scalarization Method ◽  
Convexity Assumptions

AbstractThis paper is concerned with a vector optimization problem set in a normed space where optimality is defined through a convex cone. The vector problem can be solved using a parametrized scalar problem. Under some convexity assumptions, it is shown that dependence of optimal solutions on the parameter is Lipschitz continuous. Hence differentiable dependence on the solutions on the parameter is derived.

Holomorphic Functions with Positive Real Part

1982 ◽  
Vol 34 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Eric Sawyer
Keyword(s):  
Unit Ball ◽  
Hardy Spaces ◽  
Convex Cone ◽  
Holomorphic Functions ◽  
Positive Real Part ◽  
Positive Real ◽  
Spaces Of Holomorphic Functions ◽  
Extreme Element ◽  
Image Position ◽  
Special Case

The main purpose of this note is to prove a special case of the following conjecture.Conjecture. If F is holomorphic on the unit ball Bn in Cn and has positive real part, then F is in Hp(Bn) for 0 < p < ½(n + 1).Here Hp(Bn) (0 < p < ∞) denote the usual Hardy spaces of holomorphic functions on Bn. See below for definitions. We remark that the conjecture is known for 0 < p < 1 and that some evidence for it already exists in the literature; for example [1, Theorems 3.11 and 3.15] where it is shown that a particular extreme element of the convex cone of functionsis in Hp(B2) for 0 < p < 3/2.

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