Smallest weak and smallest totally weak critical sets in the latin squares of order at most seven

A critical set in a latin square of order n is a set of entries in a latin square which can be embedded in precisely one latin square of order n. Also, if any element of the critical set is deleted, the remaining set can be embedded in more than one latin square of order n. In this paper we find smallest weak and smallest totally weak critical sets for all the latin squares of orders six and seven. Moreover, we computationally prove that there is no (totally) weak critical set in the back circulant latin square of order five and we find a totally weak critical set of size seven in the other main class of latin squares of order five.

On the direct product of two weak uniquely completable partial latin squares

In this note we show by counter-example that the direct product of two weak uniquely completable partial latin squares is not necessarily a uniquely completable partial latin square. This counter-example rejects a conjecture by Gower (see [3]) on the direct product of two uniquely completable partial latin squares.

Steiner trades that give rise to completely decomposable latin interchanges

In this paper we focus on the representation of Steiner trades of volume less than or equal to nine and identify those for which the associated partial latin square can be decomposed into six disjoint latin interchanges.

Overlarge sets of 2-(11, 5, 2) designs and related configurations

We consider the construction of several configurations, including: • overlarge sets of 2-(11,5,2) designs, that is, partitions of the set of all 5-subsets of a 12-set into 72 2-(11,5,2) designs; • an indecomposable doubly overlarge set of 2-(11,5,2) designs, that is, a partition of two copies of the set of all 5-subsets of a 12-set into 144 2-(11,5,2) designs, such that the 144 designs can be arranged into a 12 × 12 square with interesting row and column properties; • a partition of the Steiner system S(5,6,12) into 12 disjoint 2-(11,6,3) designs arising from the diagonal of the square; • bidistant permutation arrays and generalized Room squares arising from the doubly overlarge set, and their relation to some new strongly regular graphs.

Communication: The criticality of self-assembled rigid rods on triangular lattices

The criticality of self-assembled rigid rods on triangular lattices is investigated using Monte Carlo simulation. We find a continuous transition between an ordered phase, where the rods are oriented along one of the three (equivalent) lattice directions, and a disordered one. We conclude that equilibrium polydispersity of the rod lengths does not affect the critical behavior, as we found that the criticality is the same as that of monodisperse rodson the same lattice, in contrast with the results of recently published work on similar models. (C) 2011 American Institute of Physics. [doi:10.1063/1.3556665]

Square-wave voltametric method for determination of molinate concentration in a biological process using a hanging mercury drop electrode

A square-wave voltammetric (SWV) method using a hanging mercury drop electrode (HMDE) has been developed for determination of the herbicide molinate in a biodegradation process. The method is based on controlled adsorptive accumulation of molinate for 10 s at a potential of -0.8 V versus AgCl/Ag. An anodic peak, due to oxidation of the adsorbed pesticide, was observed in the cyclic voltammogram at ca. -0.320 V versus AgCl/Ag; a very small cathodic peak was also detected. The SWV calibration plot was established to be linear in the range 5.0x10-6 to 9.0x10-6 mol L-1; this corresponded to a detection limit of 3.5x10-8 mol L-1. This electroanalytical method was used to monitor the decrease of molinate concentration in river waters along a biodegradation process using a bacterial mixed culture. The results achieved with this voltammetric method were compared with those obtained by use of a chromatographic method (HPLC–UV) and no significant statistical differences were observed.

Square-wave adsorptive-stripping voltammetric detection in the quality control of fluoxetine

Electroanalytical methods based on square-wave adsorptive-stripping voltammetry (SWAdSV) and flow-injection analysis with square-wave adsorptive-stripping voltammetric detection (FIA-SWAdSV) were developed for the determination of fluoxetine (FXT). The methods were based on the reduction of FXT at a mercury drop electrode at -1.2 V versus Ag/AgCl, in a phosphate buffer of pH 12.0, and on the possibility of accumulating the compound at the electrode surface. The SWAdSV method was successfully applied in the quantification of FXT in pharmaceutical products, human serum samples, and in drug dissolution studies. Because the presence of dissolved oxygen did not interfere significantly with the analysis, it was possible to quantify FXT in several pharmaceutical products using FIA-SWAdSV. This method enables analysis of up to 120 samples per hour at reduced costs.

On lattices from combinatorial game theory modularity and a representation theorem: finite case

We show that a self-generated set of combinatorial games, S. may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question "Is there a set which will give a non-distributive but modular lattice?" appears. A useful necessary condition for the existence of a finite non-distributive modular L(S) is proved. We show the existence of S such that L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented. (C) 2014 Elsevier B.V. All rights reserved.

Partial Least Square – Path Modeling: metodologia, software e aplicação

Trabalho de Projeto apresentado como requisito parcial para obtenção do grau de Mestre em Estatística e Gestão de Informação

Experiments in square lattice with a common treatment in all blocks

This paper deals with a generalization of square lattice designs, with k² treatments in blocks of k + 1 plots, the extra plot in each block receiving a standard treatment, the same for all blocks. The new design leads to lower variances for contrasts between adjusted treatment means

Shellability of noncrossing partition lattices

We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type Dn and those of exceptional type and rank at least three.

On square permutations

Severini and Mansour introduced in [4]square polygons, as graphical representations of square permutations, that is, permutations such that all entries are records (left or right, minimum or maximum), and they obtained a nice formula for their number. In this paper we give a recursive construction for this class of permutations, that allows to simplify the derivation of their formula and to enumerate the subclass of square permutations with a simple record polygon. We also show that the generating function of these permutations with respect to the number of records of each type is algebraic, answering a question of Wilf in a particular case.

Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

The Brezis-Nirenberg type problem involving the square root of the Laplacian

We establish existence and non-existence results to the Brezis-Nirenberg type problem involving the square root of the Laplacian in a bounded domain with zero Dirichlet boundary condition.