Franklin's identity generalizes Euler's and states that the number of partitions n with j different parts divisible by r equals repeated at least times. In this article, we give a refinement when j=1. We prove j=1, r=2 for fixed perimeter, i.e., largest hook. also derive Beck-type perimeter: excess in all into odd perimeter M over distinct whose set even is singleton. provide analytic combinato...

We consider the problem of removing c points from a set S of n points so that the remaining point set is optimal in some sense. Definitions of optimality we consider include having minimum diameter, having minimum area (perimeter) bounding box, having minimum area (perimeter) convex hull. For constant values of c, all our algorithms run in O(n log n) time.

In two dimensions, a polyform is a finite set of edge-connected cells on a square, triangular, or hexagonal grid. A layer is the set of grid cells that are vertex-adjacent to the polyform and not part of the polyform. A bumped-body polyform has two parts: a body and a bump. Adding a layer to a bumped-body polyform with minimum perimeter constructs a bumped-body polyform with min perimeter; the ...

the purpose of this study was to identify daily changes in body weight of broiler chickens using image processing and multi-regression analysis. therefore, thirty 1-day-old broiler chickens were reared under standard rearing condition and after acquiring images they were weighted, individually. from 2490 digital images, six features (perimeter, area convex, major axis, minor axis, eccentricity)...

BACKGROUND Previous studies have shown cross-sectional 3-dimensional (3D) transesophageal echocardiographic (TEE) measurements to severely underestimate multidetector row computed tomographic (MDCT) measurements for the assessment of aortic annulus before transcatheter aortic valve replacement. This study compares annulus measurements from 3D-TEE using off-label use of commercially available so...

OBJECTIVE To determine the prevalence of metabolic syndrome (MS) and the hypertriglyceridemic waist phenotype (HW) in a representative adolescent sample; as well as to establish which anthropometric indicator better identifies MS and HW, according to gender and adolescent age. METHODS This cross sectional study had the participation of 800 adolescents (414 girls) from 10-19 years old. Anthrop...

We return to a classic problem of structural optimization whose solution requires microstructure. It is well-known that perimeter penalization assures the existence of an optimal design. We are interested in the regime where the perimeter penalization is weak, i. e. in the effect of perimeter as a selection mechanism in structural optimization. To explore this topic in a simple yet challenging ...

Dilatation of infarcted segments (infarct expansion) may occur during recovery from myocardial infarction, but the fate of noninfarcted segments is uncertain. Accordingly, left ventricular geometric changes were assessed by left ventricular angiography and M mode echocardiography on admission and 2 weeks later in 30 patients with their first acute transmural myocardial infarction. All patients ...