A composition of an integer constrained to have decreasing then increasing parts is called concave. We prove that the generating function for the number of concave compositions, denoted v(q), is a mixed mock modular form in a more general sense than is typically used. We relate v(q) to generating functions studied in connection with “Moonshine of the Mathieu group” and the smallest parts of a p...

During the late stages of cranial neurulation in mammalian embryos, the neural epithelium becomes concave. A thick subapical band of microfilament bundles, attached to junctions which are both vertical and horizontal in orientation, can be seen by TEM. Prior to this the neural epithelium is first biconvex and then V-shaped in transverse section, microfilament bundles are absent, and the subapic...

‎In this paper‎, ‎we shall establish some extended Simpson-type inequalities‎ ‎for differentiable convex functions and differentiable concave functions‎ ‎which are connected with Hermite-Hadamard inequality‎. ‎Some error estimates‎ ‎for the midpoint‎, ‎trapezoidal and Simpson formula are also given‎.

BACKGROUND The dynamic changes of anterior mitral leaflet (AML) curvature are of primary importance for optimal left ventricular filling and emptying but are incompletely characterized. METHODS AND RESULTS Sixteen radiopaque markers were sutured to the AML in 11 sheep, and 4-dimensional marker coordinates were acquired with biplane videofluoroscopy. A surface subdivision algorithm was applied...

Flattening of the preimplantation rod contour in the sagittal plane influences thoracic kyphosis (TK) restoration in adolescent idiopathic scoliosis (AIS) surgery. The effects of multilevel facetectomy and screw density on postoperative changes in spinal rod contour have not been documented. This study aimed to evaluate the effects of multilevel facetectomy and screw density on changes in spina...

This paper shows that if a game satisfies the sufficient condition for the existence and uniqueness of a pure-strategy Nash equilibrium provided by Rosen (1965) then the game has a unique correlated equilibrium, which places probability one on the unique pure-strategy Nash equilibrium. In addition, it shows that a weaker condition suffices for the uniqueness of a correlated equilibrium. The con...

Preface These lecture notes grew out of several years of teaching a course on Advanced Microeconomics, first at the Indian Institute of Management, Ahmedabad and subsequently at the University of Witwatersrand, Johannesburg. When we were students at graduate schools in US (during the mid 1980's), a typical first year graduate Microeconomics course, revolved around Hal Varian's classic on the su...

A simple gripper with two vertical cylindrical jaws can make contact with external or internal concavities in polygonal and polyhedral parts to align and grip parts in form closure. Such grippers are inexpensive, lightweight, and their small footprint facilitates access and insertion for industrial applications. We refer to this as a v-grip. We begin by defining 2D v-grips, where a pair of fric...

The present paper shows that any sequence of integers laying along a finite ray in any Pascal-pyramid is log-concave, consequently unimodal. Further, we describe an algorithm which provides the plateaus of the diagonal sequences locating on layer n of the regular Pascal pyramid.

Let S be a finite set with some rank function r such that the Whitney numbers w i = I { x e S I r ( x ) = i}l are log-concave. Given k, me N so that Wk-1 < Wk <~ Wk+m, set W = w k + w k + 1 + "'" + Wk + ~" Generalizing a theorem of Kleitman and Milner, we prove that every F ~ S with cardinality IFI/> Whas average rank at least ( k w k + ... + (k + m)wk+m)/W, provided the normalized profile vect...