High spin states in120Xe

High spin states in ¹²⁰Xe, populated via¹⁰⁷Ag(¹⁶O, p2n) and¹⁰⁸Pd(¹⁶O, 4n)reactions have been studied using γ-ray spectroscopic techniques. 21 new transitions have been added to extend the level scheme. Two S-bands are extended upto 26⁺ and 22⁺;these bands are found to cross the g. s band at hΩ=0. 39 and 0. 47 MeV. The band structures have been discussed within the framework of CSM.     

Shell model study of high spin states in theN=50 nucleus93Tc

High spin states in theN=50 nucleus⁹³Tc were reinvestigated by using the reaction⁶⁴Zn (³⁵Cl,4p 2n) at a beam energy of 140 MeV. This was done particularly with a view to observe anyγ rays upto 2.7 MeV which may have been missed in our earlier study where the experimental conditions were set to observeγ rays upto 2 MeV. We found four newγ rays of energy: 2484, 2164, 2130 and 69 keV. We have placed theseγ rays in the level scheme and it now gets extended to 49/2^?. Though there is no substantial change in the level scheme, placing theγ rays in the level scheme has resulted into two important conclusions: (1) We have performed shell model calculations for⁹³Tc nucleus within a model space which encompasses an enlarged proton configuration and allows for the excitation of the neutron across theN=50 core. The excitation of a single neutron across theN=50 core satisfactorily explains the new level scheme. (2) The energy of the 17/2^? isomeric state is now unambiguously placed at 2185 keV.     

A parametric investigation of the friction performance of PC‐ABS parts processed by FDM additive manufacturing process

The friction performance is an important factor of parts processed by fused deposition modeling (FDM) for various engineering applications. It is one type of failure made of surface contact. The proper use of FDM process parameters can bring a significant reduction in friction and the amount of wear, thereby leading to a reduction in the material waste. To date, very little studies have been performed in this area. This paper investigates the effect of FDM manufacturing parameters on the friction performance of polycarbonate‐acrylonitrile butadiene styrene prototypes processed by FDM using definitive screening design and partial least squares method. The observation of surface morphology was obtained by the scanning electron microscopy to examine the effect of process parameters on the microstructure. The experimental results have shown that layer thickness, air gap, raster angle, and build orientation are the most influential factors affecting the friction performance of FDM manufactured parts. The proposed approach presented in this study provides an impetus to develop analytical modeling and functional relationships between FDM manufacturing parameters and friction performance. Copyright © 2017 John Wiley & Sons, Ltd.     

Control of molecular architecture by steric factors: mononuclear vs polynuclear manganese(III) compounds with tetradentate N2O2 donor Schiff bases

Three manganese(III) compounds, [Mn(III)(vanoph)(DMF)(H(2)O)]ClO(4) (1), [Mn(III)(vanoph)(N(3))(H(2)O)]·2H(2)O (2) and [Mn(III)(saloph)(μ(1,3)-N(3))](n) (3), where H(2)vanoph = N,N'-(1,2-phenylene)-bis(3-methoxysalicylideneimine), H(2)saloph = N,N'-(1,2-phenylene)-bis(salicylideneamine) are tetradentate N(2)O(2) ligands and DMF = N,N-dimethylformamide, have been prepared and characterised by elemental analysis, IR and UV-Vis spectroscopy and single-crystal X-ray diffraction studies. Compounds 1 and 2 are monomeric but compound 3 consists of a chain system with the repeating unit [Mn(III)(saloph)(N(3))] bridged by μ-1,3 azide. Compound 1 crystallises in monoclinic space group P2(1)/n with cell dimensions of a = 11.1430(2), b = 16.3594(3), c = 15.4001(3) ?, β = 108.417(1), Z = 4 whereas compounds 2 and 3 crystallise in orthorhombic space groups Pbca and Pna2(1), respectively, with cell dimensions of a = 16.069(3), b = 15.616(3), c = 18.099(4) ?, Z = 8 (for 2) and a = 18.760(9), b = 13.356(5), c = 6.616(3) ?, Z = 4 (for 3). In all the compounds, Mn(III) has a six-coordinated pseudo-octahedral geometry in which O(2), O(3), N(1) and N(2) atoms of the deprotonated di-Schiff base constitute the equatorial plane. In both compounds 1 and 2, water molecules are present in the fifth coordination sites in the apical positions. The sixth coordination sites are occupied by one O atom of a solvent DMF in compound 1 and an N atom of azide in compound 2. The coordinated water initiates hydrogen-bonded networks in both compounds 1 and 2 to form well-isolated supramolecular dimers. At room temperature the χ(M)T values for the compounds 1 and 2 remain almost constant until 30 K. Below this temperature, the χ(M)T values drastically drop to 0.72 cm(3) mol(-1) K for 1 and 0.52 cm(3) mol(-1) K for 2. The best fits were obtained with J = -0.92 cm(-1), |D| = 2.05 cm(-1), g = 2.0 and R = 8.1 × 10(-4) for 1 and J = -1.16 cm(-1), |D| = 2.05 cm(-1), g = 2.0 and R = 1.2 × 10(-3) for 2. However, in compound 3, two axial positions are occupied by the azide ions. The Mn···Mn repeating distance is 6.616 ? along the chain. Magnetic characterisation shows that the μ(1,3)-bridging azide ion mainly transmits an antiferromagnetic interaction (J = -6.36 cm(-1)) between Mn(III) ions. The presence of two methoxy groups increases the steric crowding in the H(2)vanoph moiety and thereby inhibits the formation of a polynuclear compound with this ligand.     

Numerical approximation of the generalized regularized long wave equation using Petrov–Galerkin finite element method

The generalized regularized long wave (GRLW) equation has been developed to model a variety of physical phenomena such as ion‐acoustic and magnetohydrodynamic waves in plasma, nonlinear transverse waves in shallow water and phonon packets in nonlinear crystals. This paper aims to develop and analyze a powerful numerical scheme for the nonlinear GRLW equation by Petrov–Galerkin method in which the element shape functions are cubic and weight functions are quadratic B‐splines. The proposed method is implemented to three reference problems involving propagation of the single solitary wave, interaction of two solitary waves and evolution of solitons with the Maxwellian initial condition. The variational formulation and semi‐discrete Galerkin scheme of the equation are firstly constituted. We estimate rate of convergence of such an approximation. Using Fourier stability analysis of the linearized scheme we show that the scheme is unconditionally stable. To verify practicality and robustness of the new scheme error norms L₂, L_∞ and three invariants I₁, I₂, and I₃ are calculated. The computed numerical results are compared with other published results and confirmed to be precise and effective.     

Uncertainty principles of Ingham and Paley–Wiener on semisimple Lie groups

Classical results due to Ingham and Paley–Wiener characterize the existence of nonzero functions supported on certain subsets of the real line in terms of the pointwise decay of the Fourier transforms. Viewing these results as uncertainty principles for Fourier transforms, we prove certain analogues of these results on connected, noncompact, semisimple Lie groups with finite center. We also use these results to show a unique continuation property of solutions to the initial value problem for time-dependent Schrödinger equations on Riemmanian symmetric spaces of noncompact type.     

On some results for a class of meromorphic functions having quasiconformal extension

We consider the class \(\Sigma (p)\) of univalent meromorphic functions f on \({\mathbb D}\) having a simple pole at \(z=p\in [0,1)\) with residue 1. Let \(\Sigma _k(p)\) be the class of functions in \(\Sigma (p)\) which have k-quasiconformal extension to the extended complex plane \({\hat{\mathbb C}}\), where \(0\le k < 1\). We first give a representation formula for functions in this class and using this formula, we derive an asymptotic estimate of the Laurent coefficients for the functions in the class \(\Sigma _k(p)\). Thereafter, we give a sufficient condition for functions in \(\Sigma (p)\) to belong to the class \(\Sigma _k(p).\) Finally, we obtain a sharp distortion result for functions in \(\Sigma (p)\) and as a consequence, we obtain a distortion estimate for functions in \(\Sigma _k(p).\)     

Characterization and the pre-Schwarzian norm estimate for concave univalent functions

Let Co(α) denote the class of concave univalent functions in the unit disk ${\mathbb{D}}$ . Each function ${f\in Co(\alpha)}$ maps the unit disk ${\mathbb{D}}$ onto the complement of an unbounded convex set. In this paper we find the exact disk of variability for the functional ${(1-|z|^2)\left ( f^{\prime\prime}(z)/f^{\prime}(z)\right), f\in Co(\alpha)}$ . In particular, this gives sharp upper and lower estimates for the pre-Schwarzian norm of concave univalent functions. Next we obtain the set of variability of the functional ${(1-|z|^2)\left(f^{\prime\prime}(z)/f^{\prime}(z)\right), f\in Co(\alpha)}$ whenever f′′(0) is fixed. We also give a characterization for concave functions in terms of Hadamard convolution. In addition to sharp coefficient inequalities, we prove that functions in Co(α) belong to the H ^p space for p < 1/α.