Determination of periodic solutions for nonlinear oscillators with fractional powers by He’s modified Lindstedt-Poincaré method

He’s modified Lindstedt-Poincaré method is applied to nonlinear oscillatiors with fractional powers. Comparison of the obtained results with exact solutions provides confirmation for the validity of He’s modified Lindstedt-Poincaré method.     

Excitation functions of the analyzing power in elastic proton-proton scattering from 0.45 to 2.5 GeV

Excitation functions A_N(p_lab,_c.m.) of the analyzing power in elastic proton-proton scattering have been measured in an internal target experiment at the Cooler Synchrotron COSY with an unpolarized proton beam and a polarized atomic hydrogen target. Data were taken continuously during the acceleration and deceleration for proton kinetic energies T_lab (momenta p_lab) between 0.45 and 2.5 GeV (1.0 and 3.3 GeV/c) and scattering angles 30 ^° _c.m. 90^°. The results provide excitation functions and angular distributions of high precision and internal consistency. The data can be used as calibration standard between 0.45 and 2.5 GeV. They have significant impact on phase shift solutions, in particular on the spin triplet phase shifts between 1.0 and 1.8 GeV.     

Simple high-performance liquid chromatographic method for determination of atropine and obidoxime in a parenteral injection device

Atropine and obidoxime in a parenteral injection device are determined by simple HPLC method simultaneously without any pretreatment at 228 nm. The relative standard deviations (R.S.D.) were below 1.6% for the compounds. The correlation coefficient was greater than 0.999 for both compounds in the calibration range. The recoveries at 5 mg/L concentration averaged as 95% for atropine and 102% for obidoxime. The uncertainty of the measurements for atropine and obidoxime was 2.8% and 2.4%, respectively.     

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.     

Role of copper species in the oxidative dimerization of arylboronic acids: synthesis of symmetrical biaryls

Certain Cu(I) and Cu(II) salts are able to mediate the dimerization of arylboronic acids in DMF. They provide the corresponding symmetrical biaryls in moderate to very good yields. It is possible to run the reaction catalytically under an oxygen atmosphere without a significant loss of yields.     

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.