Properties of noninteger moments in a first passage time problem

We calculate the moments t ^q , whereq is not necessarily an integer, of the first passage time to trapping for a simple diffusion problem in one dimension. If a characteristic length of the system isL and t _q ~L (q) asL, then we show that there is a phase transition atq=q _c such that whenq<q _c ,(g)=0, and forq>q _c , (q) is a linear function ofq. These analytical results can be used to explain results for large moments for diffusion on a hierarchic structure. We also show how to calculate noninteger moments in terms of characteristic functions.     

A non-Schurian coherent configuration on 14 points exists

For a few decades the smallest known non-Schurian coherent configuration was the association scheme on 15 points, coming from a doubly regular tournament. Last year the second author, using a computer, enumerated all coherent configurations of order up to 15. A consequence of the enumeration is that all coherent configurations up to 13 points are Schurian and a unique non-Schurian rank 11 coherent configuration of order 14 exists. This coherent configuration has two fibers of sizes 6 and 8, and an automorphism group of order 24 isomorphic to SL(2, 3). We provide a computer free interpretation of this new object, relying on some simple interplay between group theoretical and combinatorial arguments.     

An integral model structure and truncation theory for coherent group actions

In this work we study the homotopy theory of coherent group actions from a global point of view, where we allow both the group and the space acted upon to vary. Using the model of Segal group actions and the model categorical Grothendieck construction we construct a model category encompassing all Segal group actions simultaneously. We then prove a global rectification result in this setting. We proceed to develop a general truncation theory for the model-categorical Grothendieck construction and apply it to the case of Segal group actions. We give a simple characterization of n-truncated Segal group actions and show that every Segal group action admits a convergent Postnikov tower built out of its n-truncations.     

Polarized neutron scattering studies of the kagomé lattice antiferromagnet

We report polarized neutron scattering studies of spin-wave excitations and spin fluctuations in the lattice antiferromagnet KFe₃(OH)₆(SO₄)₂ (jarosite). Inelastic polarized neutron scattering measurements at 10 K on a single crystal sample reveal two spin gaps, associated with in-plane and out-of-plane excitations. The polarization analysis of quasi-elastic scattering at 67 K shows in-plane spin fluctuations with XY symmetry, consistent with the disappearance of the in-plane gap above the Néel temperature . Our results suggest that jarosite is a promising candidate for studying the 2D XY universality class in magnetic systems.     

Effects of Thai Local Ingredient Odorants,Litsea cubeba and Garlic Essential Oils,on Brainwaves and Moods

The functional food market is growing with a compound annual growth rate of 7.9%. Thai food recipes use several kinds of herbs. Lemongrass, garlic, and turmeric are ingredients used in Thai curry paste. Essential oils released in the preparation step create the flavor and fragrance of the famous tom yum and massaman dishes. While the biological activities of these ingredients have been investigated, including the antioxidant, anti-inflammatory, and antimicrobial activities, there is still a lack of understanding regarding the responses to the essential oils of these plants. To investigate the effects of essential oil inhalation on the brain and mood responses, electroencephalography was carried out during the non-task resting state, and self-assessment of the mood state was performed. The essential oils were prepared in several dilutions in the range of the supra-threshold level. The results show that Litsea cubeba oil inhalation showed a sedative effect, observed from alpha and beta wave power reductions. The frontal and temporal regions of the brain were involved in the wave alterations. Garlic oil increased the alpha wave power at lower concentrations; however, a sedative effect was also observed at higher concentrations. Lower dilution oil induced changes in the fast alpha activity in the frontal region. The alpha and beta wave powers were decreased with higher dilution oils, particularly in the temporal, parietal, and occipital regions. Both Litsea cubeba and turmeric oils resulted in better positive moods than garlic oil. Garlic oil caused more negative moods than the others. The psychophysiological activities and the related brain functions require further investigation. The knowledge obtained from this study may be used to design functional food products.     

Effect of cation size and charge on the interaction between silica surfaces in 1:1, 2:1, and 3:1 aqueous electrolytes

Application of two complementary AFM measurements, force vs separation and adhesion force, reveals the combined effects of cation size and charge (valency) on the interaction between silica surfaces in three 1:1, three 2:1, and three 3:1 metal chloride aqueous solutions of different concentrations. The interaction between the silica surfaces in 1:1 and 2:1 salt solutions is fully accounted for by ion-independent van der Waals (vdW) attraction and electric double-layer repulsion modified by cation specific adsorption to the silica surfaces. The deduced ranking of mono- and divalent cation adsorption capacity (adsorbability) to silica, Mg(2+) < Ca(2+) < Na(+) < Sr(2+) < K(+) < Cs(+), follows cation bare size as well as cation solvation energy but does not correlate with hydrated ionic radius or with volume or surface ionic charge density. In the presence of 3:1 salts, the coarse phenomenology of the force between the silica surfaces as a function of salt concentration resembles that in 1:1 and 2:1 electrolytes. Nevertheless, two fundamental differences should be noticed. First, the attraction between the silica surfaces is too large to be attributed solely to vdW force, hence implying an additional attraction mechanism or gross modification of the conventional vdW attraction. Second, neutralization of the silica surfaces occurs at trivalent cation concentrations that are 3 orders of magnitude smaller than those characterizing surface neutralization by mono- and divalent cations. Consequently, when trivalent cations are added to our cation adsorbability series the correlation with bare ion size breaks down abruptly. The strong adsorbability of trivalent cations to silica contrasts straightforward expectations based on ranking of the cationic solvation energies, thus suggesting a different adsorption mechanism which is inoperative or weak for mono- and divalent cations.     

Affine and Projective Tree Metric Theorems

The tree metric theorem provides a combinatorial four-point condition that characterizes dissimilarity maps derived from pairwise compatible split systems. A related weaker four point condition characterizes dissimilarity maps derived from circular split systems known as Kalmanson metrics. The tree metric theorem was first discovered in the context of phylogenetics and forms the basis of many tree reconstruction algorithms, whereas Kalmanson metrics were first considered by computer scientists, and are notable in that they are a non-trivial class of metrics for which the traveling salesman problem is tractable. We present a unifying framework for these theorems based on combinatorial structures that are used for graph planarity testing. These are (projective) PC-trees, and their affine analogs, PQ-trees. In the projective case, we generalize a number of concepts from clustering theory, including hierarchies, pyramids, ultrametrics, and Robinsonian matrices, and the theorems that relate them. As with tree metrics and ultrametrics, the link between PC-trees and PQ-trees is established via the Gromov product.     

Spin waves in the frustrated kagomé lattice antiferromagnet KFe3(OH)6(SO4)2

The spin wave excitations of the S=5/2 kagomé lattice antiferromagnet KFe3(OH)6(SO4)2 have been measured using high-resolution inelastic neutron scattering. We directly observe a flat mode which corresponds to a lifted "zero energy mode," verifying a fundamental prediction for the kagomé lattice. A simple Heisenberg spin Hamiltonian provides an excellent fit to our spin wave data. The antisymmetric Dzyaloshinskii-Moriya interaction is the primary source of anisotropy and explains the low-temperature magnetization and spin structure.     

On Optimality of a Class of Dynamic Myopic Policies for Continuous-Time Replenishment with Periodic Updates

This paper is motivated by inventory problems arising in supply chains characterized by continuous replenishment programs based on information exchanged (reviewed) only intermittently between a manufacturing system (supplier) and a customer (retailer). When the replenishment is once-per-period, rather than at any point of time, a well-known result is the optimality of the so-called myopic base-stock policy. We generalize the notion of the base-stock policy and study the optimality of the corresponding class of dynamic myopic policies. We identify a myopic policy and prove that although the replenishment rule is dynamic, this policy is optimal when the demands are stationary and the number of review periods tends to infinity.