We consider the family of 3D minimal polyominoes inscribed in a rectanglar prism. These objects are polyominos and so they are connected sets of unitary cubic cells inscribed in a given rectangular prism of size b×k×h and of minimal volume equal to b + k + h − 2. They extend the concept of minimal 2D polyominoes inscribed in a rectangle studied in a previous work. Using their geometric structur...

A tropical curve Γ is a metric graph with possibly unbounded edges, and tropical rational functions are continuous piecewise linear functions with integer slopes. We define the complete linear system |D| of a divisor D on a tropical curve Γ analogously to the classical counterpart. We investigate the structure of |D| as a cell complex and show that linear systems are quotients of tropical modul...

We first generalize an identity involving the generalized Fibonacci numbers and then apply it to establish some general identities concerning special sums. We also give a sufficient condition on a generalized Fibonacci sequence {Un} such that Un is divisible by an arbitrary prime r for some 2 < n ≤ r − 2. 1. Preliminaries The generalized Fibonacci and Lucas numbers are defined, respectively, by...

We present a revised estimate of Earth’s surface heat flux that is based upon a heat flow data-set with 38 347 measurements, which is 55% more than used in previous estimates. Our methodology, like others, accounts for hydrothermal circulation in young oceanic crust by utilising a half-space cooling approximation. For the rest of Earth’s surface, we estimate the average heat flow for different ...

We propose a generalization of the notion of R-split mixed Hodge structure by defining a Rsplitting level for mixed Hodge structures. This is a discrete invariant taking values in positive integers and equal to 0 for R-split mixed Hodge structures. We describe some properties of this invariant for classical operations on these structures and give some explicit calculation. Résumé Nous proposons...

Technical limitations in image capturing usually impose defective, such as contrast degradation. There are different approaches to improve the contrast of an image. Among the exiting approaches, un-sharp masking is a popular method due to its simplicity in implementation and computation. There is an important parameter in un-sharp masking, named gain factor, which affects the quality of the enh...

We introduce k-crossings and k-nestings of permutations. We show that the crossing number and the nesting number of permutations have a symmetric joint distribution. As a corollary, the number of k-noncrossing permutations is equal to the number of k-nonnesting permutations. We also provide some enumerative results for k-noncrossing permutations for some values of k. Résumé. Nous introduisons l...

1. For the phototropic reaction of bees, the stimulating effects of two illuminated fields differing in intensity and area become equal when the product of area and intensity is the same for both fields. 2. The effect of two areas differing in size and flicker frequency is the same for the bee, when the product of area and flicker frequency is equal for both fields. 3. If two patterns of the sa...