Conditional linearizability criteria for a system of third-order ordinary differential equations

We provide linearizability criteria for a class of systems of two third-order ordinary differential equations that is cubically nonlinear in the first derivative, by differentiating a system of second-order quadratically nonlinear ordinary differential equations and using the original system to replace the second derivatives. The procedure developed splits into two cases: those for which the coefficients are constant and those for which they are variables. Both cases are discussed and examples given.     

Affine compact almost-homogeneous manifolds of cohomogeneity one

This paper is one in a series generalizing our results in [12, 14, 15, 20] on the existence of extremal metrics to the general almost-homogeneous manifolds of cohomogeneity one. In this paper, we consider the affine cases with hypersurface ends. In particular, we study the existence of Kähler-Einstein metrics on these manifolds and obtain new Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metrics. As a consequence of our study, we also give a solution to the problem posted by Ahiezer on the nonhomogeneity of compact almost-homogeneous manifolds of cohomogeneity one; this clarifies the classification of these manifolds as complex manifolds. We also consider Fano properties of the affine compact manifolds.     

On C *-Extreme Maps and *-Homomorphisms of a Commutative C *-Algebra

The generalized state space of a commutative C^*-algebra, denoted , is the set of positive unital maps from C(X) to the algebra of bounded linear operators on a Hilbert space . C^*-convexity is one of several non-commutative analogs of convexity which have been discussed in this context. In this paper we show that a C^*-extreme point of satisfies a certain spectral condition on the operators in the range of the associated positive operator-valued measure. This result enables us to show that C^*-extreme maps from C(X) into , the algebra generated by the compact and scalar operators, are multiplicative. This generalizes a result of D. Farenick and P. Morenz. We then determine the structure of these maps. This paper constitutes a part of the author’s Ph.D. thesis at the University of Nebraska-Lincoln.     

Stability results for properly quasi convex vector optimization problems

In this paper, we discuss the stability of the sets of (weak) minimal points and (weak) efficient points of vector optimization problems. Assuming that the objective functions are (strictly) properly quasi convex, and the data ofthe approximate problems converges to the data of the original problems in the sense of Painlevé–Kuratowski, we establish the Painlevé–Kuratowski set convergence of the sets of (weak) minimal points and (weak) efficient points of the approximate problems to the corresponding ones of original problem. Our main results improve and extend the results of the recent papers.     

Relations between the convexity of a set and the differentiability of its support function

It is known that, in finite dimensions, the support function of a compact convex set with nonempty interior is differentiable excepting the origin if and only if the set is strictly convex. In this paper, we realize a thorough study of the relations between the differentiability of the support function on the interior of its domain and the convexity of the set, mainly for unbounded sets. Then, we revisit some results related to the differentiability of the cost function associated to a production function.     

The James constant for the <Emphasis Type="Italic">l</Emphasis><Subscript>3</Subscript> − <Emphasis Type="Italic">l</Emphasis><Subscript>1</Subscript> space

In this note, the exact value of the James constant for the l₃-l₁ space is obtained, J(l₃-l₁)=1.5573…. This result improves the known inequality, J(l₃-l₁)≤4/³√10, which was given by Dhompongsa, Piraisangjun and Saejung.     

On Nash Equilibria for Noncooperative Games Governed by the Burgers Equation

Existence of a Nash equilibrium in a noncooperative game governed by the one-dimensional Burgers equation, proposed in the case of pointwise controls in Ref. 1, is proved under data qualifications that guarantee the diffusion term in the Burgers’ equation to be dominant enough with respect to the uniform convexity of the payoffs. This work was partly supported by Grants 201/03/0934 (GA čR) and MSM 0021620839 (MšMT čR). Inspiring discussions with Angel M. Ramos are acknowledged.     

The fixed point property for multivalued nonexpansive mappings

We show some properties concerning geometrical constants of Banach spaces which imply the existence of fixed points for multivalued nonexpansive mappings and we study the relationship between these properties.