Multiple agents finitely repeated inspection game with dismissals

Decision makers usually have to face a budget and other type of constraints when they have to decide which projects are going to be undertaken (to satisfy their requirements and guarantee profitable growth). Our purpose is to assist them in the task of selecting project portfolios. We have approached this problem by proposing a general nonlinear binary multi-objective mathematical model, which takes into account all the most important factors mentioned in the literature related with Project Portfolio Selection and Scheduling. Due to the existence of uncertainty in different aspects involved in the aforementioned decision task, we have also incorporated into the model some fuzzy parameters, which allow us to represent information not fully known by the decision maker/s. The resulting problem is both fuzzy and multiobjective. The results are complemented with graphical tools, which show the usefulness of the proposed model to assist the decision maker/s.     

Block decomposition of permutations and Schur-positivity

The block number of a permutation is the maximum number of components in its expression as a direct sum. We show that, for 321-avoiding permutations, the set of left-to-right maxima has the same distribution when the block number is assumed to be k, as when the last descent of the inverse is assumed to be at position \(n - k\). This result is analogous to the Foata–Schützenberger equidistribution theorem, and implies that the quasi-symmetric generating function of the descent set over 321-avoiding permutations with a prescribed number of blocks is Schur-positive.     

Tensor Products and Support Varieties for Some Noncocommutative Hopf Algebras

We explore questions of projectivity and tensor products of modules for finite dimensional Hopf algebras. We construct many classes of examples in which tensor powers of nonprojective modules are projective and tensor products of modules in one order are projective but in the other order are not. Our examples are smash coproducts with duals of group algebras, some having algebra and coalgebra structures twisted by cocycles. We apply support variety theory for these Hopf algebras as a tool in our investigations.     

Hydrodynamic pair attractions between driven colloidal particles

Colloidal spheres driven through water along a circular path by an optical ring trap display unexpected dynamical correlations. We use Stokesian dynamics simulations and a simple analytical model to demonstrate that the path's curvature breaks the symmetry of the two-body hydrodynamic interaction, resulting in particle pairing. The influence of this effective nonequilibrium attraction diminishes as either the temperature or the stiffness of the radial confinement increases. We find a well-defined set of dynamically paired states whose stability relies on hydrodynamic coupling in curving trajectories.     

Optical forces arising from phase gradients

We demonstrate both theoretically and experimentally that phase gradients in a light field can be used to create a new category of optical traps complementary to the more familiar intensity-gradient traps known as optical tweezers. We further show that the work done by phase-gradient forces is path dependent and briefly discuss some ramifications of this nonconservativity.     

Characterization of water distribution in bread during storage using magnetic resonance imaging

A soy bread of fully acceptable quality and containing 49% soy ingredients (with or without 5% almond powder) has been recently developed in our laboratory.

An investigation on water distribution and mobility, as probed by proton signal intensity and T₂ magnetic resonance images, during storage was designed to examine possible relations between water states and hindered staling rate upon soy or soy–almond addition.

Water proton distribution throughout soy-containing loaves was found to be very homogeneous in fresh breads with and without almond, with minimal water migration occurring during prolonged storage. In contrast, traditional wheat bread displayed an inhomogeneous water proton population that tended to change (with higher moisture migration towards the outer perimeter of the slice) during storage. Similar results were found for water mobility throughout the loaves, as depicted in T₂ images. On intensity images of all considered bread varieties, the outer perimeter corresponding to the crust exhibited lower signal intensity due to decreased water content. Higher T₂ values were found in the crust of soy breads with and without almond, which were attributed to lipids.

The results indicated that the addition of soy to bread improved the homogeneous distribution of water molecules, which may hinder the staling rate of soy-containing breads. However, incorporation of almond had little effect on the water proton distribution or mobility of soy breads.     

Upper bound on the characters of the symmetric groups

Let C be a conjugacy class in the symmetric group S _n , and λ be a partition of n. Let f ^λ be the degree of the irreducible representation S ^λ , χ ^λ (C)– the character of S ^λ at C, and r ^λ (C)– the normalized character χ ^λ (C) f ^λ . We prove that there exist constants b > 0 and 1 > q > 0 such that for n > 4, for every conjugacy class C in S _n and every irreducible representation S ^λ of S _n ∣r ^λ (C)∣≦ ( max {q,λ ₁ n, λ ₁ ′ n}) ^{b ⋅ supp(C)} where supp (C) is the number of non-fixed digits under the action of a permutation in C, λ ₁ is the size of the largest part in λ, and λ ₁ ′ is the number of parts in λ. The proof is obtained by enumeration of rim hook tableaux, the Hook formula and probabilistic arguments. Combinatorial, algebraic and statistical applications follow this result. In particular, we estimate the rate of mixing of random walks on the alternating groups with respect to conjugacy classes. Oblatum 14-III-1995 & 30-X-1995     

Electronic and vibrational signatures of the Au102(p-MBA)44 cluster

Optical absorption of a gold nanocluster of 102 Au atoms protected by 44 para-mercaptobenzoic acid (p-MBA) ligands is measured in the range of 0.05-6.2 eV (mid-IR to UV) by a combination of several techniques for purified samples in solid and solution phases. The results are compared to calculations for a model cluster Au(102)(SMe)(44) based on the time-dependent density functional theory in the linear-response regime and using the known structure of Au(102)(p-MBA)(44). The measured and calculated molar absorption coefficients in the NIR-vis region are comparable, within a factor of 2, in the absolute scale. Several characteristic features are observed in the absorption in the range of 1.5-3.5 eV. The onset of the electronic transitions in the mid-IR region is experimentally observed at 0.45 ± 0.05 eV which compares well with the lowest calculated transition at 0.55 eV. Vibrations in the ligand layer give rise to fingerprint IR features below the onset of low-energy metal-to-metal electronic transitions. Partial exchange of the p-MBA ligand to glutathione does not affect the onset of the electronic transitions, which indicates that the metal core of the cluster is not affected by the ligand exchange. The full spectroscopic characterization of the Au(102)(p-MBA)(44) reported here for the first time gives benchmarks for further studies of manipulation and functionalization of this nanocluster to various applications.     

Assembly of crystalline halogen-bonded materials by physical vapor deposition

Polycrystalline halogen-bonded assemblies fabricated by physical vapor deposition (PVD) exhibit controllable morphologies and microstructures. Although the solid-state packing may vary going from a solution crystal growth process (used for chromophore single-crystal determination) to a vapor-phase deposition process (used for PVD film fabrication), the corresponding film microstructures are independent of the substrate surface chemistry.