Multidecompositions of Several Graph Products

We find necessary and sufficient conditions for (C ₄, E ₂) multidecompositions of the cartesian product and tensor product of paths, cycles, and complete graphs.     

Coloring Cubic Graphs by Point‐Intransitive Steiner Triple Systems

An ‐coloring of a cubic graph G is an edge coloring of G by points of a Steiner triple system such that the colors of any three edges meeting at a vertex form a block of . A Steiner triple system that colors every simple cubic graph is said to be universal. It is known that every nontrivial point‐transitive Steiner triple system that is neither projective nor affine is universal. In this article, we present the following results.

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Density matrix tomography through sequential coherent optical rotations of an exciton qubit in a single quantum dot

We demonstrate single qubit density matrix tomography in a single semiconductor quantum dot system through consecutive phase sensitive rotations of the qubit via ultrafast coherent optical excitations. The result is important for quantifying gate operations in quantum information processing in the quantum dot systems as well as demonstrating consecutive arbitrary qubit rotations.     

Conformational stability of a model macrocycle tetraamide: an ab initio study

Ab initio calculations are carried out to investigate the conformational stability of a model macrocyle tetraamide. The four amide groups in the selected model are present in the sequence: -(O=CNH)-Ph-(NHC=O)-CH=CH-(O=CNH)-Ph-(NHC=O)-CH=CH-. In this sequence, two phenyl rings and two ethene groups act as bridges between the amide units. Each amide motif bonds to a phenyl ring through its amide nitrogen and to an ethene group through its amide carbon. Four clearly distinct minimum-energy conformations are found upon full geometry optimization using the B3LYP/6-31+G(d) method. Frequency calculations using the same method confirm that the four conformations are indeed minima in the macrocycle potential energy surface. Relative to the most stable conformer, the other conformations are higher in energy by 0.86, 2.09, and 9.17 kcal/mol, respectively, at the MP2/6-31+G(d,p) level. The stability of the macrocycle conformations is correlated primarily to the existence and strength of intramolecular N-H...O=C hydrogen bonds. Additional stability to the conformations is found to come from weak Ph-H...O=C hydrogen bonding between a carbonyl oxygen and a hydrogen atom of a phenyl group. Solvent effects play an important role in the relative energies of the various conformations, as indicated by the simple SCRF = dipole model calculations for the case of aqueous solution.     

Chiral heterocyclic ligands. XIV. Control of directionality in silver coordination polymers through ligand design

Four C(2)-symmetric homochiral ligands derived from (+)-camphor are shown to produce linear chain and ladder silver coordination polymers wherein the directionality and polarisation can be controlled by subtle differences in ligand design.     

Physisorption of N2, O2, and CO on fully oxidized TiO2(110)

Physisorption of N(2), O(2), and CO was studied on fully oxidized TiO(2)(110) using beam reflection and temperature-programmed desorption (TPD) techniques. Sticking coefficients for all three molecules are nearly equal (0.75 +/- 0.05) and approximately independent of coverage suggesting that adsorption occurs via a precursor-mediated mechanism. Excluding multilayer coverages, the TPD spectra for all three adsorbates exhibit three distinct coverage regimes that can be interpreted in accord with previous theoretical studies of N(2) adsorption. At low coverages (0-0.5 N(2)/Ti(4+)), N(2) molecules bind head-on to five-coordinated Ti(4+) ions. The adsorption occurs preferentially on the Ti(4+) sites that do not have neighboring adsorbates. This arrangement minimizes the repulsive interactions between the adsorbed molecules along the Ti(4+) rows resulting in a relatively small shift of the TPD peak (105 --> 90 K) with increasing coverage. At higher N(2) coverages (0.5-1.0 N(2)/Ti(4+)) the nearest-neighbor Ti(4+) sites become occupied. The close proximity of the adsorbates results in strong repulsion thus giving rise to a significant shift of the TPD leading edges (90 --> 45 K) with increasing coverage. For N(2)/Ti(4+) > 1, an additional low-temperature peak (approximately 43 K) is present and is ascribed to N(2) adsorption on bridge-bonded oxygen rows. The results for O(2) and CO are qualitatively similar. The repulsive adsorbate-adsorbate interactions are largest for CO, most likely due to alignment of CO dipole moments. The coverage-dependent binding energies of O(2), N(2), and CO are determined by inverting TPD profiles.     

A nonlinear mesh-warping technique for correcting brain deformation after stroke

This article presents a warping technique for correcting brain tissue distortion on magnetic resonance imaging (MRI) scans due to stroke lesion growth and for mapping MRI scans to histological sections. Meshes are imposed upon the images for feature specification, and these features are exactly matched in the different images to be mapped, while the other voxels are matched by interpolation. This technique was tested on serial MR images and histological sections that were acquired in a nonhuman primate model of stroke. This technique was able to deliver satisfactory warping results. It is simple and robust and can be utilized in many applications for comparison of multimodality medical images and histological sections.     

Dimensions of Tight Spans

Given a finite metric, one can construct its tight span, a geometric object representing the metric. The dimension of a tight span encodes, among other things, the size of the space of explanatory trees for that metric; for instance, if the metric is a tree metric, the dimension of the tight span is one. We show that the dimension of the tight span of a generic metric is between

Coherent two-dimensional infrared spectroscopy: quantitative analysis of protein secondary structure in solution

We present a method to quantitatively determine the secondary structure composition of globular proteins using coherent two-dimensional infrared (2DIR) spectroscopy of backbone amide I vibrations (1550-1720 cm(-1)). Sixteen proteins with known crystal structures were used to construct a library of 2DIR spectra, and the fraction of residues in α-helix, β-sheet, and unassigned conformations was determined by singular value decomposition (SVD) of the measured two-dimensional spectra. The method was benchmarked by removing each individual protein from the set and comparing the composition extracted from 2DIR against the composition determined from the crystal structures. To highlight the increased structural content extracted from 2DIR spectra a similar analysis was also carried out using conventional infrared absorption of the proteins in the library.     

Structure sheaves of definable additive categories

We prove that the 2-category of small abelian categories with exact functors is anti-equivalent to the 2-category of definable additive categories. We define and compare sheaves of localisations associated to the objects of these categories. We investigate the natural image of the free abelian category over a ring in the module category over that ring and use this to describe a basis for the Ziegler topology on injectives; the last can be viewed model-theoretically as an elimination of imaginaries result.