An improved upper bound on the density of universal random graphs

We give a polynomial time randomized algorithm that, on receiving as input a pair (H, G) of n‐vertex graphs, searches for an embedding of H into G. If H has bounded maximum degree and G is suitably dense and pseudorandom, then the algorithm succeeds with high probability. Our algorithm proves that, for every integer and a large enough constant C = C_d, as , asymptotically almost all graphs with n vertices and at least edges contain as subgraphs all graphs with n vertices and maximum degree at most d. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 2014     

Characterization of Biodiesel by Infrared Spectroscopy with Partial Least Square Discriminant Analysis

This paper reports a method to simultaneously classify 7% biodiesel and 93% diesel based on vegetable oil as the source of the biodiesel. Mafurra, moringa, and cotton biodiesel blends were characterized by infrared spectroscopy with partial least square discriminant analysis. The efficiency of model was evaluated based on the sensitivity and specificity. The model showed excellent results as all samples were correctly classified based on the raw material. Hence, the sensitivity and specificity parameters showed values of 1, which means 100% correct characterization of the samples in the calibration and prediction sets. Therefore, infrared spectroscopy with partial least square discriminant analysis is suitable for the characterization of biodiesel/diesel blends.     

(R)-Binaphthoxy diiodide lanthanides

The synthesis and characterization of novel enantiopure binaphthoxy-diiodo lanthanides [(R)-2-(1-naphthol)-1′-naphthoxide)LnI₂(THF)₃] (Ln=Sm (4a), Yb (4b), La (4c)) are described. These complexes have been prepared by reacting the mono potassium salt of (R)-binaphthol with the corresponding lanthanide triiodides and were characterized by elemental analysis, IR and NMR spectroscopies. Recrystallization of 4c from THF–hexane led to monocrystals of [(R)-2-(1-naphthol)-1′-naphthoxide)]-diiodolanthane-tetrakistetrahydrofurane] (4c*). Complex 4c* crystallizes in the orthorhombic space group, P2₁2₁2₁ with cell parameters a=13.086(1) Å, b=15.496(1) Å, c=18.854(1) Å, V=3823.2(6) ų, and Z=4.     

Synthesis and characterization of uranium(III) compounds supported by the hydrotris(3,5-dimethyl-pyrazolyl)borate ligand: Crystal structures of [U(Tp)2(X)] complexes (X = OC6H2-2,4,6-Me3, dmpz, Cl)

Reaction of [U(Tp^Me2)₂(NR₂)] (R = Ph, SiMe₃) with protic substrates such as 2,4,6-trimethylphenol (HOC₆H₂-2,4,6-Me₃), 3,5-dimethylpyrazole (Hdmpz), 2-mercaptopyridine (HSC₅H₄N) and phenylacetylene (HCCPh) afforded the corresponding [U(Tp^Me2)₂(OAr)] (Ar = C₆H₂-2,4,6-Me₃) (1), [U(Tp^Me2)₂(dmpz)] (2), [U(Tp^Me2)₂(η²-SC₅H₄N)] (3), and [U(Tp^Me2)₂(CCPh)] (4) compounds. Reaction of [U(Tp^Me2)₂(NR₂)] with Me₃SnCl or Me₃SiBr gave [U(Tp^Me2)₂Cl] (5) and [U(Tp^Me2)₂Br] (6), respectively, in high yield. The amido precursors failed to react with cyclopentadiene, but metathesis of [U(Tp^Me2)₂I] with NaCp yielded [U(κ³-Tp^Me2)(κ²-Tp^Me2)(η⁵-Cp)] (7). Thermolysis of 7 resulted in oxidation of the metal centre and redistribution of the ligands, giving [UCp₃(dmpz)] (8), pyrazabole (9) and [U(Tp^Me2)(dmpz)₃] (10). The complexes have been fully characterized by spectroscopic methods and the structures of 1, 2, and 5 were confirmed by X-ray crystallographic studies. In the solid state the complexes exhibit distorted pentagonal bipyramidal geometries.     

Interplay of Exciton Coupling and Large‐Amplitude Motions in the Vibrational Circular Dichroism Spectrum of Dehydroquinidine

A detailed analysis of the computed structure, energies, vibrational absorption (VA) and circular dichroism (VCD) spectra of 30 low‐energy conformers of dehydroquinidine reveals the existence of families of pseudo‐conformers, the structures of which differ mostly in the orientation of a single O?H bond. The pseudo‐conformers in a family are separated by very small energy barriers (i.e., 1.0 kcal mol^?1 or smaller) and have very different VCD spectra. First, we demonstrate the unreliable character of the Boltzmann factors predicted with DFT. Then, we show that the large differences observed between the VCD spectra of the pseudo‐conformers in a family are caused by large‐amplitude motions involving the O?H bond, which trigger the appearance/disappearance of strong VCD exciton‐coupling bands in the fingerprint region. This interplay between exciton coupling and large‐amplitude‐motion phenomena demonstrates that when dealing with flexible molecules with polar bonds, vibrational averaging of VCD spectra should not be neglected. In this regard, the dehydroquinidine molecule considered here is expected to be a typical example and not the exception to the rule.     

From the classical field with sources to the multipole matrix elements

Starting with the classical interaction of the electromagnetic field with sources and then quantizing, the interaction Hamiltonian is expanded in multipoles. Explicit expressions for the multipole operators are obtained. Transformation properties, under time reversal and Hermitian conjugation, of nuclear states and multipole operators are studied.     

Spectral results on graphs with regularity constraints

Graphs with (k, τ)-regular sets and equitable partitions are examples of graphs with regularity constraints. A (k, τ)-regular set of a graph G is a subset of vertices S ⊆ V(G) inducing a k-regular subgraph and such that each vertex not in S has τ neighbors in S. The existence of such structures in a graph provides some information about the eigenvalues and eigenvectors of its adjacency matrix. For example, if a graph G has a (k₁, τ₁)-regular set S₁ and a (k₂, τ₂)-regular set S₂ such that k₁ − τ₁ = k₂ − τ₂ = λ, then λ is an eigenvalue of G with a certain eigenvector. Additionally, considering primitive strongly regular graphs, a necessary and sufficient condition for a particular subset of vertices to be (k, τ)-regular is introduced. Another example comes from the existence of an equitable partition in a graph. If a graph G, has an equitable partition π then its line graph, L(G), also has an equitable partition, , induced by π, and the adjacency matrix of the quotient graph is obtained from the adjacency matrix of G/π.