A discontinuous Galerkin method for time fractional diffusion equations with variable coefficients

We propose a piecewise-linear, time-stepping discontinuous Galerkin method to solve numerically a time fractional diffusion equation involving Caputo derivative of order μ ∈ (0, 1) with variable coefficients. For the spatial discretization, we apply the standard continuous Galerkin method of total degree ≤ 1 on each spatial mesh elements. Well-posedness of the fully discrete scheme and error analysis will be shown. For a time interval (0, T) and a spatial domain Ω, our analysis suggest that the error in \(L^{2}\left ((0,T),L^{2}({\Omega })\right )\)-norm is \(O(k^{2-\frac {\mu }{2}}+h^{2})\) (that is, short by order \(\frac {\mu }{2}\) from being optimal in time) where k denotes the maximum time step, and h is the maximum diameter of the elements of the (quasi-uniform) spatial mesh. However, our numerical experiments indicate optimal O(k² + h²) error bound in the stronger \(L^{\infty }\left ((0,T),L^{2}({\Omega })\right )\)-norm. Variable time steps are used to compensate the singularity of the continuous solution near t = 0.     

A new site‐selective route for synthesis of functionalized imidazo[2,1‐c][1,2,4]triazoles

Reactions of 4‐arylhydrazono‐2‐methylthio‐imidazolin‐5(1H)‐one 3 with various hydrazonoyl halides 1 proved to be site‐selective and yielded the respective imidazo[2,1‐c][1,2,4]triazole derivatives 8 . The structure of the latter was elucidated by X‐ray analysis and the mechanism of the studied reactions was discussed.     

Studies of relativistic backward-wave oscillator operation in thecross-excitation regime

We first reported the operation of a relativistic backward-wave oscillator (BWO) in the so-called cross-excitation regime in 1998. This instability, whose general properties were predicted earlier through numerical studies, resulted from the use of a particularly shallow rippled-wall waveguide [slow wave structure (SWS)] that was installed in an experiment to diagnose pulse shortening in a long-pulse electron beam-driven high-power microwave (HPM) source. This SWS was necessary to accommodate laser interferometry measurements along the SWS during the course of microwave generation. Since those early experiments, we have studied this regime in greater detail using two different SWS lengths. We have invoked time-frequency analysis, the smoothed-pseudo Wigner-Ville distribution in particular, to interpret the heterodyned signals of the radiated power measurements. These recent results are consistent with earlier theoretical predictions for the onset and voltage scaling for this instability. This paper presents data for a relativistic BWO operating in the single-frequency regime for two axial modes, operating in the cross-excitation regime, and discusses the interpretation of the data, as well as the methodology used for its analysis. Although operation in the cross-excitation regime is typically avoided due to its poorer efficiency, it may prove useful for future HPM effects studies     

Synthesis,refinement of the structure,and AC conductivity behavior of sodium lithium orthonavadates

The Na _x Li_1-x CdVO₄ (x = 0.5, 1) orthovanadates were prepared using a solid-state reaction method. The x-ray diffraction patterns (XRDP) of both materials reveal the formation of the Na₂CrO₄ structure. Vibrational study confirms the existence of [VO₄]^3? group. Electrical measurements of our compounds have been investigated using complex impedance spectroscopy (CIS) in the frequency and temperature range 209 Hz–1 MHz and 589–703 K, respectively. Nyquist plots reveal the presence of tow contributions, an equivalent circuit was proposed. DC conductivity shows electrical conduction in the material as a thermally activated process. The AC conductivity is explained using the non-overlapping small polaron tunneling (NSPT) conduction mechanism. A relationship between crystal structure and ionic conductivity was established and discussed.     

Theoretical study of the structures,conformations, and spectroscopic properties of 2‐formylthiophene‐N‐acetylhydrazone and 2‐thiophenecarboxaldehyde‐2‐thienylhydrazone

2‐Formylthiophene‐N‐acetylhydrazone (Hait) and 2‐thiophenecarboxaldehyde‐2‐thienylhydrazone (Htit) in the cis and trans conformations were investigated in the gas‐phase by density functional method using B3LYP as the functional set and 6‐311++G(d,p) as the basis set. The cis and trans structures were fully optimized in the C₁ and C_s symmetries. Transition states were also modeled for the cis–trans isomerization of the title compounds and the barriers to internal rotation were calculated. This work reports the structural, energetics, and spectroscopic parameters of all the optimized geometries. Some of the structural parameters are in good agreement with experimental literature data. The computed parameters for these compounds are also in good agreement with a related molecule, namely, acetohydrazide. For both Hait and Htit, the trans conformers are more stable than the cis conformers and the energy barriers are larger compared with the energy differences between the cis and trans conformers. This accounts for Hait and Htit existing mostly in the trans conformation. © 2009 Wiley Periodicals, Inc. Heteroatom Chem 20:144–150, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20526     

Development and Validation of HPLC,TLC and Derivative Spectrophotometric Methods for the Analysis of Ezetimibe in the Presence of Alkaline Induced Degradation Products

Reversed phase‐high performance liquid chromatography (RP‐HPLC), thin layer chromatography (TLC) densitometry and first derivative spectrophotometry (1D) techniques are developed and validated as a stability‐indicating assay of ezetimibe in the presence of alkaline induced degradation products. RP‐HPLC method involves an isocratic elution on a Phenomenex Luna 5μ C₁₈ column using acetonitrile: water: glacial acetic acid (50:50:0.1 v/v/v) as a mobile phase at a flow rate of 1.5 mL/min. and a UV detector at 235 nm. TLC densitometric method is based on the difference in Rf‐values between the intact drug and its degradation products on aluminum‐packed silica gel 60 F₂₅₄ TLC plates as stationary phase with isopropanol: ammonia 33% (9:1 v/v) as a developing mobile phase. On the fluorescent plates, the spots were located by fluorescence quenching and the densitometric analysis was carried out at 250 nm. Derivative spectrophotometry, the zero‐crossing method, ezetimibe was determined using first derivative at 261 nm in the presence of its degradation products. Calibration graphs of the three suggested methods are linear in the concentration ranges 1–10 mcg/mL, 0.1–1 mg/mL and 1–16 mcg/mL with a mean percentage accuracy of 99.05 ± 0.54%, 99.46 ± 0.63% and 99.24 ± 0.82% of bulk powder, respectively. The three proposed methods were successfully applied for the determination of ezetimibe in raw material and pharmaceutical dosage form; the results were statistically analyzed and compared with those obtained by the reported method. Validation parameters were determined for linearity, accuracy and precision; selectivity and robustness and were assessed by applying the standard addition technique.     

Long-Time Behavior for Second Order Lattice Dynamical Systems

Many researchers examined the existence of global attractors for various types of first and second order lattice dynamical systems. Here we prove the existence of a global attractor for a new type of second order lattice dynamical systems in the Hilbert space l ²×l ². For specific choices of the linear operators this system can be regraded as a spatial discretization of a continuous damped nonlinear Boussinesq equation on ℝ ^m ,m≥1.      

Measurement and simulations of hollow atom X-ray spectra of solid-density relativistic plasma created by high-contrast PW optical laser pulses

K-shell spectra of solid Al excited by petawatt picosecond laser pulses have been investigated at the Vulcan PW facility. Laser pulses of ultrahigh contrast with an energy of 160 J on the target allow studies of interactions between the laser field and solid state matter at 10²⁰ W/cm². Intense X-ray emission of KK hollow atoms (atoms without n = 1 electrons) from thin aluminum foils is observed from optical laser plasma for the first time. Specifically for 1.5 μm thin foil targets the hollow atom yield dominates the resonance line emission. It is suggested that the hollow atoms are predominantly excited by the impact of X-ray photons generated by radiation friction to fast electron currents in solid-density plasma due to Thomson scattering and bremsstrahlung in the transverse plasma fields. Numerical simulations of Al hollow atom spectra using the ATOMIC code confirm that the impact of keV photons dominates the atom ionization. Our estimates demonstrate that solid-density plasma generated by relativistic optical laser pulses provide the source of a polychromatic keV range X-ray field of 10¹⁸ W/cm² intensity, and allows the study of excited matter in the radiation-dominated regime. High-resolution X-ray spectroscopy of hollow atom radiation is found to be a powerful tool to study the properties of high-energy density plasma created by intense X-ray radiation.     

Lowest electronic states of neutral and ionic LiN

We have investigated the potential energy curves (PECs) of the LiN heteronuclear diatomic molecule, including its ionic species LiN⁺ and LiN⁻, using explicitly correlated multi-reference configuration interaction (MRCI-F12) calculations in conjunction with the correlation consistent quintuple-𝜁 basis set. The effect of core–valence correlation, scalar relativistic effects, and the size of the basis sets has been investigated. A comprehensive set of spectroscopic constants determined based on the above-mentioned calculations are also reported for the lowest electronic states and all systems, including dissociation energies, harmonic and anharmonic vibrational frequencies, and rotational constants. Additional parameters, such as the dipole moments, equilibrium spin-orbit constants, excitation energies, and rovibrational energy levels, are also documented. We found that the three triplet states of LiN, namely, X ³∑⁻, A ³Π, and 2 ³∑⁻, exhibit substantial potential wells in the PEC diagrams, while the quintet states are repulsive in nature. The ground state of the anion also shows a deep potential well in the vicinity of its equilibrium geometry. In contrast, the ground and excited states of the cation are very loosely bound. Charge transfer properties of each of these states are also analyzed to obtain an in-depth understanding of the interatomic interactions. We found that the core–valence correlation has a substantial effect on the calculated spectroscopic constants.     

Measurement of the top quark pair production cross section in pp collisions at s=7TeV in dilepton final states with ATLAS

A measurement of the production cross section of top quark pairs ($t\overline{t}$) in proton–proton collisions at a center-of-mass energy of 7 TeV recorded with the ATLAS detector at the Large Hadron Collider is reported. Candidate events are selected in the dilepton topology with large missing transverse energy and at least two jets. Using a data sample corresponding to an integrated luminosity of $35{\mathrm{pb}}^{?1}$, a $t\overline{t}$ production cross section ${\sigma }_{t\overline{t}}=177\pm 20(\text{stat.})\pm 14(\text{syst.})\pm 7(\text{lum.})\text{pb}$ is measured for an assumed top quark mass of $m_t=172.5\text{GeV}$. A second measurement requiring at least one jet identified as coming from a b quark yields a comparable result, demonstrating that the dilepton final states are consistent with being accompanied by b-quark jets. These measurements are in good agreement with Standard Model predictions.