Representations of Positive Integers by a Direct Sum of Quadratic forms

The number of representation of positive integers by quadratic forms $ F_{1}=x_{1}^{2}+3x_{1}x_{2}+8x_{2}^{2} $ and $ G_{1}=2x_{1}^{2}+3x_{1}x_{2}+4x_{2}^{2} $ of discriminant —23 are given. Moreover, a basis for the cusp form space S ₄(Γ₀(23), 1) are constructed. Furthermore, formulas for the representation of positive integers by direct sum of copies of F ₁ and G ₁, i.e. formulas for $ r(n; F_{4}), r(n; G_{4}), r(n; F_{3} \oplus G_{1}), r(n; F_{2} \oplus G_{2}), {\rm and}\ r(n; F_{1} \oplus G_{3}) $ , are derived using the elements of the space S ₄(Γ(23), 1).     

An unusual case of acute disseminated encephalomyelitis confined to brainstem

Acute disseminated encephalomyelitis (ADEM) is an immune-mediated demyelinating disorder usually encountered in children or adolescents and characterized by multifocal neurological deficits of rapid onset. Typical target areas of demyelination include the corona radiata, centrum semiovale, periventricular white matter, cerebellar peduncles and brainstem. Involvement of deep gray matter nuclei is also frequent. We report a 6-year-old boy with ADEM who had only brainstem involvement. Serial magnetic resonance images representing the stage of disease and response to steroid treatment are presented.     

The variational iteration method for solitary patterns solutions of gBBM equation

We consider solitary patterns solutions of generalized Benjamin–Bona–Mahony equations (shortly gBBM). The variational iteration method (shortly VIM) is applied for the numerical solution subject to appropriate initial condition. The numerical solutions of our model equation are calculated in the form of convergence power series with easily computable components. The VIM performs extremely well in terms of accuracy, efficiently, simplicity, stability and reliability.     

Synthesis, crystal structure, EPR and electrochemical studies of copper(II) dipicolinate complex with 2,2′-dipyridylamine ligand

The (2,2′-dipyridylamine)(pyridine-2,6-dicarboxylato)copper(II) trihydrate complex was synthesized and characterized by spectroscopic (IR, UV-vis, EPR), X-ray diffraction technique and electrochemical methods. The copper(II) center is surrounded by one bidentate 2,2′-dipyridylamine (dpa) and one tridentate dipicolinate (dpc) ligand, and exhibits a distorted square-pyramidal geometry. The crystal packing involves both hydrogen-bonding and π-π interactions. The solvent water molecules link monomers to one another through hydrogen-bonding interactions, forming ladder-type chains in the ab plane. π-π interactions also occur between the dpa rings of neighboring molecules and are responsible for interchain packing. Based on EPR and optical absorption studies, spin-Hamiltonian and bonding parameters have been calculated. The g-values, calculated for title complex in polycrystalline state at 298 K and in frozen DMF (110 K), indicate the presence of the unpaired electron in the d_x²-y² orbital. The evaluated metal-ligand bonding parameters showed strong in-plane σ- and π-bonding. The cyclic voltammogram of the title complex investigated in DMF (dimethylformamide) solution exhibits only metal centered electroactivity in the potential range ±1.25 V versus Ag/AgCl reference electrode.     

Wavelet packet based analysis of sound fields in rooms using coincident microphone arrays

This paper presents a passive analysis method for determining the spatio-temporal characteristics of sound fields in small rooms. The analysis finds an approximate directional reflectogram (ADR) which reveals the approximate arrival directions, time delays and amplitudes of the direct sound and early reflections without using a special or known sound source. A coincident microphone array is used to obtain directional recordings. The recordings are analysed by wavelet packet decomposition to determine the direction of the sound source and select wavelet packet coefficients to reconstruct the estimate of the direct sound. ADR is then computed via deconvolution using this estimate. Experiments have been carried out using synthesized recordings that were obtained from actual room impulse responses measured in two rooms for various source locations. The method estimates the source direction with a mean absolute error of about 7°. Calculated ADRs provide a good estimate of the time delays and arrival directions of acoustical reflections, whereas the amplitudes differ slightly.     

Soluble alkyl substituted poly(3,4‐propylenedioxyselenophene)s: A new platform for optoelectronic materials

Optical and electrochemical properties of regiosymmetric and soluble alkylenedioxyselenophene‐based electrochromic polymers, namely poly(3,3‐dibutyl‐3,4‐dihydro‐2H‐selenopheno[3,4‐b][1,4]dioxephine) (PProDOS‐C₄), poly(3,3‐dihexyl‐3,4‐dihydro‐2H‐selenopheno[3,4‐b][1,4]dioxephine) (PProDOS‐C₆), and poly(3,3‐didecyl‐3,4‐dihydro‐2H‐selenopheno[3,4‐b][1,4]dioxephine) (PProDOS‐C₁₀), are highlighted. It is noted that these unique polymers have low bandgaps (1.57–1.65 eV), and they are exceptionally stable under ambient atmospheric conditions. Polymer films retained 82–97% of their electroactivity after 5000 cycles. The percent transmittance of PProDOS‐C_n (n = 4, 6, 10) films found to be between 55 and 59%. Furthermore, these novel soluble PProDOS‐C_n polymers showed electrochromic behavior: a color change form pure blue to highly transparent state in a low switching time (1.0 s) during oxidation with high coloration efficiencies (328–864 cm² C^?1) when compared to their thiophene analogues. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Aspects of fatigue failure mechanisms in polymer fuel cell membranes

The swelling‐driven fatigue behavior of polymer fuel cell membranes during relative humidity (RH) cycling is investigated. In particular, swelling‐induced membrane stresses are obtained from a numerical model simulating fuel cell RH cycle tests, and compared to the lifetimes obtained experimentally from tests conducted in the absence of electrochemical effects. A strong correlation between the lifetimes of the membranes in the actual tests and model results is obtained. In general, higher RH (or swelling) amplitude results in larger stress amplitudes and shorter lifetime, that is, fewer cycles to failure. Tensile stresses are needed for forming local cavities in the membrane, which may eventually lead to craze formation. Cavitation is less likely to occur in compressed membrane at high humidities. The stress–lifetime plots for polymer fuel cell membranes exhibit similar features to those observed for other polymers. The crazing criterion for polymers suggests that craze initiation during RH cycling is more likely to occur in the low compression regions, such as under the channels, which is in agreement with experimental observations. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1506–1517, 2011     

Bis­(acesulfamato)­tetra­aqua­cobalt(II)

The crystal structure of the first acesulfame–metal complex, namely tetra­aqua­bis­[6‐methyl‐1,2,3‐oxa­thia­zin‐4(3H)‐onato 2,2‐dioxide‐κN]­cobalt(II), [Co(C₄H₄NO₄S)₂(H₂O)₄], is re­ported. The Co^II ion resides on a twofold axis and is coordinated by four aqua ligands defining the basal plane and by two monodentate acesulfamate ligands, via their ring N atoms, in the axial positions. Two intra‐ and three intermolecular hydrogen‐bonding interactions stabilize the crystal structure and form an infinite three‐dimensional lattice.