and that the same holds if any n— 1 of the signs are replaced by strict inequality. Those unimodular lattices, such as Z , which have only the origin in common with the open cube shall be called critical, as shall the corresponding matrices. Minkowski conjectured, and Hajos [ l ] proved in 1938, that a critical lattice must contain one of the points (5»i, • • • , 5,-»), i = 1, • • • , n. If A i...

Using the Serre construction, we give examples of stable rank 2 vector bundles on principally polarized abelian threefolds (X,Θ) with Picard number 1. The Chern classes (c1, c2) of these examples realize roughly one half of the classes that are a priori allowed by the Bogomolov inequality and Riemann-Roch (the latter gives a certain divisibility condition). In the case of even c1, we study defo...

The U.K. skill premium fell from the 1950s to the late 1970s and then rose very sharply. This paper examines the contributions to these relative wage movements of international trade and technical change. We first measure trade as changes in product prices and technical change as TFP growth. Then we relate price and TFP changes to a set of underlying factors. Among a number of results, we find ...

In this paper, strongly (α ,T ) -convex functions, i.e., functions f : D → R satisfying the functional inequality f (tx+(1− t)y) t f (x)+(1− t) f (y)− tα(1− t)(x− y)− (1− t)αt(y− x) for x,y ∈ D and t ∈ T ∩ [0,1] are investigated. Here D is a convex set in a linear space, α is a nonnegative function on D−D , and T ⊆ R is a nonempty set. The main results provide various characterizations of stron...

and Applied Analysis 3 Remark 1.5. If f x /x is increasing on I and 1.6 holds, then the Petrović-type functional P1 is nonnegative, that is, inequality 1.4 is valid. Conversely, if f x /x is increasing on I and conditions as in 1.7 are fulfilled, then relation 1.5 holds. In order to define another Petrović-type functional, we cite the following Petrović-type inequality involving a convex functi...

In this paper we prove uniqueness of blow-ups and C-regularity for the freeboundary of minimizers of the Alt-Caffarelli functional at points where one blow-up has an isolated singularity. We do this by establishing a (log-)epiperimetric inequality for the Weiss energy for traces close to that of a cone with isolated singularity, whose free-boundary is graphical and smooth over that of the cone ...

in this paper, two pairs of new inequalities are given, which decompose two hilbert-type inequalities.

There is a popular belief that Chinese imports have devastated US and European manufacturing and contributed to rising inequality. Somewhat paradoxically, the consensus amongst empirical economists is that trade has not been a major cause of rising wage inequality (although this is largely based on datasets predating China’s rise). We argue that both views have underestimated the positive impac...

The attracting set of dynamical systems have been extensively studied over the past few decades and various results are reported. It is well known that one of the most researching tools is inequality technique. With the establishment of various differential and integral inequalities 1–12 , the sufficient conditions on the attracting sets for different differential systems are obtained 12–16 . H...