On the calculation of generalized binomial coefficients

The generalized binomial coefficients (_κ^λ) are defined by

$\text{Cλ(I}{}_{\mathrm{m}}\text{+ R)}\text{Cλ(I}{}_{\mathrm{m}}\text{)}\text{=}\text{Σ}\text{k=0}\text{l}\text{Σ}\text{κ}\text{(}\text{λ}\text{κ}\text{)}\text{C}{}_{\mathrm{\kappa }}\text{(R)}\text{C}{}_{\mathrm{\kappa }}\text{(I}{}_{\mathrm{m}}\text{)}$

, where the C_k(R) are the zonal polynomials of the m × m matrix R. In this paper some simple expressions are derived which allow straightforward calculation of a large number of these coefficients.     

A multireference energy decomposition scheme with respect to fragment valence states

In this paper we describe a multi-reference energy decomposition scheme defined with respect to specific valence states of the interacting fragments. The orbitals of these fragments are computed with a new iterative procedure involving MC-SCF computations with the fragments at infinite separation and CI computations at the internuclear distance of interest. This procedure is applied here for the analysis of the rotational barrier in methylamine.     

Inference in canonical correlation analysis

The asymptotic behavior, for large sample size, is given for the distribution of the canonical correlation coefficients. The result is used to examine the Bartlett-Lawley test that the residual population canonical correlation coefficients are zero. A marginal likelihood function for the population coefficients is obtained and the maximum marginal likelihood estimates are shown to provide a bias correction.     

The mechanism of magnetic interactions in the bulk ferromagnet para-(methylthio)phenyl nitronyl nitroxide (YUJNEW): a first principles, bottom-up, theoretical study

The mechanism of magnetic interactions in the bulk ferromagnet para-(methylthio)phenyl nitronyl nitroxide crystal (YUJNEW) has been theoretically reinvestigated, using only data from ab initio calculations and avoiding any a priori assumptions. We first calculate the microscopic magnetic interactions (JAB exchange couplings) between all unique radical pairs in the crystal, and then generate the macroscopic magnetic properties from the energy levels of the corresponding Heisenberg Hamiltonian. We thus propose a first principles, bottom-up (i.e. micro-to-macro) approach that brings theory and experiment together. We have applied this strategy to study the magnetism of YUJNEW using data from the previously reported 298 and 114 K crystal structures, and also data from a 10 K neutron diffraction structure fully reported in this work. The magnetic topology at 298 K is two-dimensional: noninteracting planes, with three different in-plane JAB pair interactions (+0.24, +0.09, and -0.11 cm(-1)) and one numerically negligible (+0.02 cm(-1)) inter-plane JAB interaction. In contrast, the magnetic topology at 114 and 10 K is three-dimensional, with two non-negligible in-plane JAB constants (+0.11 and +0.07 cm(-1) at 114 K; +0.22 and +0.07 cm(-1) at 10 K) and one inter-plane pair interaction (+0.07 cm(-1) at 114 K; +0.08 cm(-1) at 10 K). Although this three-dimensional magnetic topology is consistent with YUJNEW being a bulk ferromagnet, there is only a qualitative agreement between computed and experimental magnetic susceptibility chiT(T) data at 114 K. However, the experimental chiT(T) curve is quantitatively reproduced at 10 K. The heat capacity curve presents a peak at around 0.12 K, close to the estimated experimental peak (0.20 K).     

Avalanches and scaling in plastic deformation

Plastic deformation of crystalline materials is a complex nonhomogeneous process characterized by avalanches in the motion of dislocations. We study the evolution of dislocation loops using an analytically solvable phase-field model of dislocations for ductile single crystals during monotonic loading. The distribution of dislocation loop sizes is given by P(A) approximately A-sigma, with sigma=1.8+/-0.1. The exponent is in agreement with those found in acoustic emission experiments. This model also predicts a range of macroscopic behaviors in agreement with observation, including hardening with monotonic loading, and a maximum in the acoustic emission signal at the onset of yielding.     

A study of sentence stress production in Mandarin speakers of American English

Acoustic characteristics of American English sentence stress produced by native Mandarin speakers are reported. Fundamental frequency (F0), vowel duration, and vowel intensity in the sentence-level stress produced by 40 Mandarin speakers were compared to those of 40 American English speakers. Results obtained from two methods of stress calculation indicated that Mandarin speakers of American English are able to differentiate stressed and unstressed words according to features of F0, duration, and intensity. Although the group of Mandarin speakers were able to signal stress in their sentence productions, the acoustic characteristics of stress were not identical to the American speakers. Mandarin speakers were found to produce stressed words with a significantly higher F0 and shorter duration compared to the American speakers. The groups also differed in production of unstressed words with Mandarin speakers using a higher F0 and greater intensity compared to American speakers. Although the acoustic differences observed may reflect an interference of L1 Mandarin in the production of L2 American English, the outcome of this study suggests no critical divergence between these speakers in the way they implement American English sentence stress.     

Exploring the synthesis and impact of end‐functional poly(3‐hexylthiophene)

In recent years, end‐functional poly(3‐hexylthiophene) (P3HT) has proven to be instrumental in the continued development and innovation within the broad conjugated polymer arena, enabling a variety of applications, particularly in organic electronics. The availability of P3HT with controlled molecular weights, low polydispersity, and importantly, a wide range of reactive end‐groups not only serves as a key building block for the preparation of conjugated block copolymers but also facilitates the development of hybrid nanocomposite materials via inorganic surface modification strategies. This Highlight focuses on the synthetic approaches to end‐functional P3HT and the impact of these systems in emerging technologies. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 831–841     

Inventory management with periodic ordering and minimum order quantities

Periodic review systems are commonly employed by distributors and retailers to replenish their inventories (for example, to co-ordinate in-bound transportation). It is also often the case that vendors specify minimum purchase quantities for physical (for example, packaging) or strategic reasons. When inventory systems recommend order quantities below the prescribed minimum, a decision must be made on whether or not to order. We describe how this environment can be modelled, and employ an extensive factorial experiment involving a simulation to demonstrate situations in which a common simple ‘rounding up’ decision rule performs poorly. In this paper, we discuss financial implications and implementation issues.     

Effects of solvent flow,dopant flow,and lamp current on dopant-assisted atmospheric pressure photoionization (DA-APPI) for LC-MS. Ionizationvia proton transfer

In this paper, the effects of solvent flow, dopant flow, and lamp power on proton transfer ionization in dopant-assisted (DA) atmospheric pressure photoionization (APPI) are investigated. A broad theoretical framework is presented, describing the primary photoionization process, the formation of protonated-solvent cluster ions, and the balance between analyte ion creation via proton transfer and loss via recombination. The principal experimental test system utilized methanol as the solvent, toluene as the dopant, and acridine as the analyte. Comparisons are made between acridine and a less basic compound, 9-methylanthracene (9-MA). Experimental determinations of the trends in the analyte MH⁺ signal and the total ion current (TIC) with variations in the subject parameters are provided. Experimental results and theory demonstrate that both the analyte signal and the TIC approach asymptotic limits with increases in dopant flow and/or lamp current (two factors which dictate the rate of photoion generation). The data show that these limits are lowered at higher solvent flow rates. These results are attributed to the recombination loss process, the rate of which increases with the second power of ion concentration. We deduce that the recombination rate constant increases with solvent flow rate, a consequence of the growth of ion-solvent clusters. Cluster growth is also believed to be a factor in the dramatic loss of sensitivity for 9-MA that occurs as the solvent flow is raised, because larger protonated-solvent cluster ions have greater solvation energies and may be unreactive with compounds having low gas-phase basicity and/or low solvation energy.     

Magnetic and spectroscopic investigation of partially reduced vanadium pentoxides. II. β′-CuxV2O5

The magnetic, electron paramagentic resonance (EPR), infrared (ir), and optical properties of β′-Cu_xV₂O₅ have been measured and interpreted. Magentic susceptibility studies indicate that β′-Cu_xV₂O₅ undergoes a semiconductor → metal transition near x = 0.60. For x ? 0.40, the magnetic data interpreted in terms of a ligand-field model in which the octahedral ²T_2g term of V⁴⁺ is split by the combined perturbations of axial distortion and spin-oribt coupling, with the result that the ²T_2g term is split into a magnetic ground level, a weakly magentic intermediate level, and a magnetic highest level. The results of the magnetic analysis further support the transition to metallic behavior with increasing x. The EPR spectra are motionally narrowed by electronic hopping at low temperatures, and the g-tensor and linewidth data are in good agreement with the magnetic results. The ir spectra are independent of x and exhibit narrow bands at 1020 and 995 cm^?1, which are attributed to the stretching vibration of multiple VO bonds. The optical spectra consist of two main bands whose peak positions shift to higher frequencies with increasing x, implying that the V⁴⁺O bond distances decrease with increasing x. The results of this study are in excellent agreement with Goodenough's interpretation of β-M_xV₂O₅.