Magic rectangles are well-known for its very interesting and entertaining combinatorics. In a magic rectangle, the numbers 1 to mn are arranged in an array of m rows and n columns so that each row adds to the same total M and each column to the same total N . In the present paper we provide a new systematic method for constructing any even by even magic rectangle. The method proposed is extreme...

The first MAGIC telescope is close to completion and soon will start to collect data. Parallel to the ongoing MAGIC construction we pursuit studies for the future 2nd phase of the MAGIC observatory project. We have been considering 3 choices for the extension of the project: a) To build a ∼30 m diameter telescope in the vicinity of MAGIC. b) To give MAGIC another camera based on very high quant...

Using computational algebraic geometry techniques and Hilbert bases of polyhedral cones we derive explicit formulas and generating functions for the number of magic squares and magic cubes. Magic cubes and squares are very popular combinatorial objects (see [2, 15, 17] and their references). A magic square is a square matrix whose entries are nonnegative integers and whose row sums, column sums...

Background—Endovascular aortic repairs have been developed as less invasive treatments for aortic aneurysms. Some aneurismal cavities, however, remain without organization, causing a re-expansion of the aneurysms. We studied cell transplantation into the aneurismal sac to promote the organization of thrombus for the complete healing of aneurysms. Methods and Results—Skin fibroblasts and skeleta...

We use multispeckle dynamic light scattering to measure the dynamic structure factor, f(q,tau), of gels formed by aggregation of colloids. Although the gel is an elastic solid, f(q,tau) nearly completely decays on long time scales, with an unusual form, f(q, tau) approximately exp{-(tau/tau(f))(mu)}, with mu approximately 1.5 and with tau(f) proportional variant q(-1). A model for restructuring...

This crossover study with 46 child dental patients compared two topical APF products, a gel and a foam, with respect to the amounts of product and fluoride (F) applied, salivary F concentrations, and enamel F uptake. Half the subjects were treated for 4 min with the gel first and the other half with the foam. After approximately 16 days, each patient received a second treatment using the other ...

Servedio et al. [1], following Gavrilets [2], define a magic trait as ‘a trait subject to divergent selection and a trait contributing to non-random mating that are pleiotropic expressions of the same gene(s)’. This clarified definition is certainly helpful, but we outline here several pivotal questions for empirical research, particularly surrounding the crucial concept of effect size. The eff...

An arc colored eulerian multidigraph with l colors is rainbow eulerian if there is an eulerian circuit in which a sequence of l colors repeats. The digraph product that refers the title was introduced by Figueroa-Centeno et al. as follows: let D be a digraph and let Γ be a family of digraphs such that V (F ) = V for every F ∈ Γ. Consider any function h : E(D) −→ Γ. Then the product D⊗hΓ is the ...

Magic illusions provide the perceptual and cognitive scientist with a toolbox of experimental manipulations and testable hypotheses about the building blocks of conscious experience. Here we studied several sleight-of-hand manipulations in the performance of the classic "Cups and Balls" magic trick (where balls appear and disappear inside upside-down opaque cups). We examined a version inspired...

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