On a geometric inequality

An inequality is obtained connecting the characteristics of a figureG with the characteristics of similar images of a convex figureg contained inG and containingG. In the case wheng is a disk the well-known inequality of Bonnesen is obtained.Translated from Ukrainskií Geometricheskií Sbornik, No. 30, 1987, pp. 49–52.     

On bilinear Hardy inequality and corresponding geometric mean inequality

Ricerche di Matematica - The main aim of this paper to provide several scales of equivalent conditions for the bilinear Hardy inequalities in the case $$1< q, p_1, p_2<infty $$ with...     

On the loop space of a geometric realization

In this paper we discuss a model for the loop sace of a geometric realization. We present a geometric proof of a result of Baues and thereby obtain a stronger version. The concepts used are the theory of cofibrations, fibrations and homotopy cartesian squares. As a consequence, we also get a geometric proof of a result of Adams concerning the homology of the loop space of a simply connected space.     

Lagrangian non-squeezing and a geometric inequality

We prove that if the unit codisc bundle of a closed Riemannian manifold embeds symplectically into a symplectic cylinder of radius one then the length of the shortest non-trivial closed geodesic is at most half the area of the unit disc.     

A geometric inequality on mixed volumes

We develop some geometric inequality for a kind of generalized convex set. The integral of (n – 2)-th mean curvature of the generalized convex set, the mixed volume of the convex hull of the set, and a reference convex set are involved in the inequality.Partially supported by grants from Kosef and BSRI-95-1419.     

Matrix Wielandt inequality via the matrix geometric mean

In this paper, by virtue of the matrix geometric mean and the polar decomposition, we present new Wielandt type inequalities for matrices of any size. To this end, based on results due to J.I. Fujii, we reform a matrix Cauchy–Schwarz inequality, which differs from ones due to Marshall and Olkin. As an application, we show a new block matrix version of Wielandt type inequalities under the block rank additivity condition.     

A geometric inequality and the complexity of computing volume

The volume of the convex hull of anym points of ann-dimensional ball with volumeV is at mostV·m/2 ⁿ . This implies that no polynomial time algorithm can compute the volume of a convex set (given by an oracle) with less than exponential relative error. A lower bound on the complexity of computing width can also be deduced.Dedicated to my teacher Kõváry Károly     

A geometric inequality on hypersurface in hyperbolic space

In this paper, we use the inverse curvature flow to prove a sharp geometric inequality on star-shaped and two-convex hypersurface in hyperbolic space.     

On the Gromov-Hitchin-Thorpe inequality

The purpose of this Note is to prove an inequality which 4-dimensional Einstein manifolds must satisfy, relating the Euler characteristic, the signature, and the simplicial volume. The inequality sharpens Gromov's generalization [3] of the Hitchin-Thorpe inequality [4].     

On the Clausius-Duhem inequality

Zusammenfassung Die der Kontinuumsmechanik angemessene Form des zweiten thermodynamischen Hauptsatzes wird auf eine sehr allgemeine Weise hergeleitet. Dabei werden zwei Temperaturen eingeführt und eine Verallgemeinerung der Clausius-Duhemschen Ungleichung erhalten.Zunächst wird bewiesen, dass für eine bestimmte Klasse von Stoffen die Ungleichung nur gültig ist, wenn beide Temperaturen gleich sind, so dass solchen Stoffen die gewöhnliche Form der Clausius-Duhemschen Ungleichung angemessen ist.Schliesslich wird gezeigt, dass ein einfaches Material mit Erinnerung dieser Stoffart angehört.     

On the width-length inequality

This paper was written at the Rensselaer Polytechnic Institute in 1963. A lecture based on it was given at the Rand Corporation in 1965 and this version is in the form in which Ray Fulkerson received it at Rand.The paper is the underpinning for results on resistor network inequalities (Reference [4]) which has not been published. A specific example, however, appears inProceedings of the IEEE 51 (1963) 1047–1048.More is known about minimal non-W—L matrices. U. Peled has found several additional classes of matrices which are also classically known in other contexts. A consequence of a recent matrix theorem is apparently that the degenerate projection planes are the only minimal matrices requiring unequal weights.The preparation of this paper was supported by the National Science Foundation under grant GP-14. Editor's Note: This paper, although written in 1963, was sought for inclusion inMathematical Programming Study 8—Polyhedral Combinatorics, which was dedicated to the memory of D.R. Fulkerson. Unfortunately, an editorial mishap prevented its inclusion. Nevertheless, the historical importance of the paper, the fact that it has been widely referenced and influenced Fulkerson's and others' work in the area has convinced the Editor that it should be published and hence made readily available. Alfred Lehman has given his assent to this despite his reluctance to publish a paper which is not current.     

On the Schur inequality

We generalize to a large class of functions the conditions of equality in the Schur inequality.     

An optimal double inequality between geometric and identric means

We find the greatest value p and least value q in (0,1/2) such that the double inequality G(pa+(1−p)b,pb+(1−p)a)<I(a,b)<G(qa+(1−q)b,qb+(1−q)a) holds for all a,b>0 with a≠b. Here, G(a,b), and I(a,b) denote the geometric, and identric means of two positive numbers a and b, respectively.