Stable silylenes with acyclic, cyclic, and unsaturated cyclic structures: Effects of heteroatoms and cyclopropyl α-substituents at DFT

The effects of alkyl, amino, phosphino, oxy, and thio moieties on the stability, multiplicity and reactivity of α-cyclopropylsilylenes with acyclic, cyclic, and unsaturated cyclic structures are compared and contrasted at B3LYP/AUG-cc-pVTZ//B3LYP/6-31G∗ level. The simultaneous stabilizing effects of heteroatom and cyclopropyl α-substituents on the above silylenes create the following trend of singlet-triplet energy gaps (?E_S-T): amino ≈ oxy > thio > alkyl > phosphino. The ΔE_S-T values for all the above silylenes increase through cyclization, because cyclization stabilizes singlet states of all our α-heteroatom substitued silylenes while destabilizes their corresponding triplet states. The ΔE_S-T values for all the heteroatom substituted cyclic silylenes decrease upon unsaturation, due to the higher stabilization of triplet compared to the singlet state. Interestingly, isodesmic reactions showed the phosphino substituents stabilize the triplet more than the corresponding singlet states, not only in the unsaturated form but also in the acyclic and cyclic structures. This is in contrast to cyclopropyl which stabilizes singlet considerably more than the corresponding triplet states. The reactivity of the above silylenes is discussed in terms of nucleophilicity, and electrophilicity; showing phosphino- and aminocyclopropylsilylenes more nucleophilic than oxy- and thiocyclopropylsilylenes.     

Molecular dynamics simulation of NMR powder lineshapes of linear guests in structure I clathrate hydrates

We perform molecular dynamics simulations (up to 6 ns) for the structure I clathrate hydrates of linear molecules CS, CS(2), OCS, and C(2)H(2) in large cages at different temperatures in the stability range to determine the angular distribution and dynamics of the guests in the large cages. The long axes of linear guest molecules in the oblate large structure I clathrate hydrate cages are primarily confined near the equatorial plane of the cage rather than axial regions. This non-uniform spatial distribution leads to well-known anisotropic lineshapes in the solid-state NMR spectra of the guest species. We use the dynamic distribution of guest orientations in the cages during the MD simulations at different temperatures to predict the (13)C NMR powder lineshapes of the guests in the large cages. The length of the guests and intermolecular interactions of the guests in the water cages determine the angular distribution and the mobility of the guests in the sI large cages at different temperatures. At low temperatures the range of motion of the guests in the cages are limited and this is reflected in the skew of the predicted (13)C lineshapes. As the guest molecules reach the fast motion limit at higher temperatures, the lineshapes for CS, OCS, and C(2)H(2) are predicted to have the "standard" powder lineshapes of guest molecules.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.     

Phonon-mediated anomalous dynamics of defects

Dynamics of an array of line defects interacting with a background elastic medium is studied in the linear regime. It is shown that the inertial coupling between the defects and the ambient phonons leads to an anomalous response behavior for the deformation modes of a defect-lattice, in the form of anisotropic and anomalous mass and elastic constants, resonant dissipation through excitation of phonons, and instabilities. The case of a single fluctuating line defect is also studied, and it is shown that it could lead to formation of shock waves in the elastic medium for sufficiently high frequency deformation modes.Received: 18 February 2003, Published online: 23 July 2003PACS: 63.20.Mt Phonon-defect interactions - 61.72.Bb Theories and models of crystal defects - 66.30.Lw Diffusion of other defects     

Accurate gamma ray spectrum analysis

The problem of gamma ray spectrum analysis has been is studied. The difficulties encountered by different methods are explained. An empirical method which uses an experimental peak for the analysis of spectrum is developed. This method utilizes the simple algorithm of linear least squares and is able to analyze the multiplets. It gives more accurate results than other ones. It is well adapted for automatic treatment of gamma ray spectra by small computers.     

Interaction of the mu-opioid receptor with GPR177 (Wntless) inhibits Wnt secretion: potential implications for opioid dependence

Background  

Opioid agonist drugs produce analgesia. However, long-term exposure to opioid agonists may lead to opioid dependence. The analgesic and addictive properties of opioid agonist drugs are mediated primarily via the mu-opioid receptor (MOR). Opioid agonists appear to alter neuronal morphology in key brain regions implicated in the development of opioid dependence. However, the precise role of the MOR in the development of these neuronal alterations remains elusive. We hypothesize that identifying and characterizing novel MOR interacting proteins (MORIPs) may help to elucidate the underlying mechanisms involved in the development of opioid dependence.     

Weakly Douglas Finsler metrics

Periodica Mathematica Hungarica - In this paper, we define a weaker notion of Douglas metrics, namely weakly Douglas metrics. A Finsler metric satisfies a projectively invariant equation...     

Operator maps of Jensen-type

Let \(\mathbb {B}_J({\mathcal {H}})\) denote the set of self-adjoint operators acting on a Hilbert space \(\mathcal {H}\) with spectra contained in an open interval J. A map \(\Phi :\mathbb {B}_J({\mathcal {H}})\rightarrow {{\mathbb {B}}}({\mathcal {H}})_\text {sa} \) is said to be of Jensen-type if

$$\begin{aligned} \Phi (C^*AC+D^*BD)\le C^*\Phi (A)C+D^*\Phi (B)D \end{aligned}$$

for all \( A, B \in \mathbb {B}_J({\mathcal {H}})\) and bounded linear operators C, D acting on \( \mathcal {H} \) with \( C^*C+D^*D=I\), where I denotes the identity operator. We show that a Jensen-type map on an infinite dimensional Hilbert space is of the form \(\Phi (A)=f(A)\) for some operator convex function f defined in J.

     

A note on “A new method for solving fully fuzzy linear programming problems”

This note shows that solving fully fuzzy linear programming (FFLP) model presented by Kumar et al. [A. Kumar, J. Kaur, P. Singh, A new method for solving fully fuzzy linear programming problems, Appl. Math. Model. 35 (2011) 817–823] needs some corrections to make the model well in general. A new version is provided in this note. A simple example is also presented to demonstrate the new form.