The volume of the Lp-centroid body of a convex body K ⊂ Rd is a convex function of a time-like parameter when each chord of K parallel to a fixed direction moves with constant speed. This fact is used to study extrema of some affine invariant functionals involving the volume of the Lp-centroid body and related to classical open problems like the slicing problem. Some variants of the Lp-Busemann...

Freakonomics is more about “entertainment” than it is a serious attempt at popularization. Consequently, rather than conduct a comprehensive fact check, I use the book as a springboard for a broader inquiry into social science research and take issue with the book’s surprising premise that “Economics is a science with excellent tools for gaining answers but a serious shortage of interesting que...

Abstract. The main result includes features of a Hardy-type inequality and an inequality of either Sobolev or Gagliardo-Nirenberg type. It is inspired by the method of proof of a recent improved Sobolev inequality derived by M. Ledoux which brings out the connection between Sobolev embeddings and heat kernel bounds. Here Ledoux’s technique is applied to the operator L := x · ∇ and the analysis ...

Want to get experience? Want to get any ideas to create new things in your life? Read reason and rationality in health and human services delivery now! By reading this book as soon as possible, you can renew the situation to get the inspirations. Yeah, this way will lead you to always think more and more. In this case, this book will be always right for you. When you can observe more about the ...

In this paper, we establish some weighted fractional inequalities for differentiable mappings whose derivatives in absolute value are convex. These results are connected with the celebrated Hermite-Hadamard-Fejér type integral inequality. The results presented here would provide extensions of those given in earlier works.

The Schur-convexity at the upper and lower limits of the integral for the mean of a convex function is researched. As applications, a form with a parameter of Stolarsky’s mean is obtained and a relevant double inequality that is an extension of a known inequality is established. © 2009 Elsevier Ltd. All rights reserved.

We consider collaborative systems where users make contributions across multiple available projects and are rewarded for their contributions in individual projects according to a local sharing of the value produced. This serves as a model of online social computing systems such as online Q&A forums and of credit sharing in scientific co-authorship settings. We show that the maximum feasible pro...

Let M be a complete Riemannian manifold and N a complete noncompact Riemannian manifold. Let φ : M → N be a surjective harmonic morphism. We prove that if N admits a subharmonic function with finite Dirichlet integral which is not harmonic, and φ has finite energy, then φ is a constant map. Similarly, if f is a subharmonic function on N which is not harmonic and such that |df | is bounded, and ...

IN THE LITERATURE OF monopolistic third-degree price discrimination, it has been widely held that a change in aggregate Marshallian social welfare by price discrimination is negative if total output decreases. Among others, Schwartz [1990] verifies this conjecture for any total cost function that depends only on total output, not on its distribution among markets. Letting ∆X and ∆W denote a cha...