<Emphasis Type="Italic">SU</Emphasis>(2) invariants of symmetric qubit states

We express the density matrix for the N-qubit symmetric state or spin-j state (j = N/2) in terms of the well-known Fano statistical tensor parameters. Employing the multi-axial representation, where the spin-j density matrix is shown to be characterized by j(2j + 1) axes and 2j real scalars, we enumerate the number of invariants constructed out of these axes and scalars. We calculate these invariants explicitly in the particular case of the pure and mixed spin-1 state.     

Synthesis and Characterization of Some Bromosubstituted Symmetrical Dipyridyl Ditellurides and X-Ray Structure of 2,2′-Dipyridyl Ditelluride

Organotellurium compounds are proving important precursors for the generation of semiconducting materials. However, synthetic methods for their preparation involve cumbersome manipulations and require controlled experimental conditions. We wish to report a convenient method recently developed for the synthesis of this interesting class of ditellurides. The title compounds were prepared by the reaction of ditelluride anion Te₂ ^2? with 2-bromopyridine (Scheme 1). The ditelluride anion was generated in situ by the reaction of tellurium metal with sodium borohydride in 2-ethoxyethanol. The compounds prepared were characterized by elemental analysis and through various spectroscopic techniques viz; IR, NMR (¹H, ¹³C), mass spectral analysis, crystal structure of 2,2′-dipyridyl ditelluride is reported.

Synthesis and Characterization of Some Bromosubstituted Symmetrical Dipyridyl Ditellurides and X-Ray Structure of 2,2′-Dipyridyl Ditelluride

All authors

K. K. Bhasin, Harish Kumar, Veena Trehan & Jaspreet Singh

https://doi.org/10.1080/10426500590904825

Published online:

01 February 2007

SCHEME 1 Preparation of bromosubstituted symmetrical dipyridyl ditellurides.     

85.

Self-assembly of azo molecules to mesogenic phasmid-like materials through inter-molecular hydrogen bonding     

Veena Prasad  Shin-Woong Kang  Sanjay K. Varshney  N.G. Nagaveni 《Liquid crystals》2013,40(2):121-128

A series of acid-functionalised new azo compounds was synthesised and characterised. The constituent molecules self-organise to form dimers through inter-molecular hydrogen bonding, resulting in phasmid-like compounds. This was once considered to be a promising molecular architecture to form biaxial nematic phases. The mesomorphic properties of these new azo compounds were studied using polarising optical microscopy, differential scanning calorimetry and X-ray diffraction. Investigations revealed that these compounds form nematic and columnar mesophases. A few more compounds were synthesised by replacing the??N=N- linkage in these compounds with??CH=N- and??COO- to study the effect of different linkages on the mesomorphic properties in such molecular systems. All were found to be liquid crystalline. The compounds with a??N=N- linkage are more conducive to mesomorphism and are thermally very stable. The effect of number of alkoxy chains on the mesomorphic properties of this system was also studied. To the best of our knowledge, at present, only a handful of phasmid-like mesogenic compounds, formed by the intermolecular hydrogen bonding, are known.     

86.

Microstructural and mechanical properties of porous biocomposite scaffolds based on polyvinyl alcohol,nano-hydroxyapatite and cellulose nanocrystals     

Anuj Kumar  Yuvraj Singh Negi  Veena Choudhary  Nishi Kant Bhardwaj 《Cellulose (London, England)》2014,21(5):3409-3426

In this study, in situ synthesis of polyvinyl alcohol (PVA)/nano-hydroxyapatite (n-HA)/cellulose nanocrystals (CNC) organic–inorganic biocomposite porous scaffolds is reported. The effect of the CNC content on the properties of the biocomposite scaffold was investigated and characterized using field-emission scanning electron microscopy, Fourier-transform infrared spectroscopy (FTIR), X-ray diffraction (XRD) analysis, porosity and compressive strength measurements, thermal studies, and in vitro biomineralization and degradation studies. The morphological study showed highly porous structures with good pore interconnectivity in which n-HA was homogeneously dispersed. XRD analysis showed a decrease in the crystalline fraction and crystallite size of nano-hydroxyapatite with introduction of PVA and with increasing content of CNC. It was observed that the porosity decreased to some extent with increasing CNC content, while increases in the compressive strength (from 0.85 to 2.09 MPa) and elastic modulus (from 4.68 to 16.01 MPa) were found as the CNC content was increased. In vitro biomineralization study revealed the formation of apatite on PVA/n-HA/CNC biocomposite scaffolds when soaked for 7 and 14 days in simulated body fluid (SBF) solution. The obtained porous scaffolds offering good mechanical performance may provide a promising alternative scaffolding matrix for use in the field of bone tissue engineering.     

87.

Starting and stopping rules for simulations using a priori information     

Veena G. Adlakha  George S. Fishman 《European Journal of Operational Research》1982,10(4):379-394

This paper proposes a method of interval estimation (based on the autoregressive method) that exploits a priori information about activity level (traffic intensity) and data skewness in a queueing simulation. The method relies on two rules: One determines when to start collecting data during a run and the other determines when to stop collection. The rules are designed to use the a priori information in a way that mitigates the effects of the initial conditions in the simulation and ensures representative congested behavior in the collected data.Experiments with a simulation of the M/M//c queue, with c = 1, 2, 4 and = 0.7, 0.8, 0.9, 0.95 produce favorable results. For = 0.7, 0.8, 0.9, the coverage rates for interval estimates are close to the specified theoretical coverage rates and are higher than those reported in the literature for other methods of interval estimation. The sample sizes to obtain the coverage rates are moderate and are insensitive to variation in the number of servers and the activity level. Experiments with a fixed truncation starting rule and a fixed sample-size stopping rule clearly demonstrate the effectiveness of the proposed method. It is anticipated that a priori information also exists in more complex simulations, and that such information can be used in an analogous way to achieve desired coverage levels.     

88.

Optimal rules with polynomial precision for Hilbert spaces possessing reproducing kernel functions     

Dr. M. M. Chawla  Dr. Veena Kaul 《Numerische Mathematik》1975,25(4):379-382

     

89.

Optimal rules with polynomial precision for Hilbert spaces possessing reproducing kernel functions     

Chawla  M. M.  Kaul  Veena 《Numerische Mathematik》1974,22(3):207-218

Numerische Mathematik - Optimal linear rules with polynomial precision, based on preassigned abscissas, are considered over a Hilbert space possessing a reproducing kernel function; the weights are...     

90.

Optimal rules for numerical integration round the unit circle     

M. M. Chawla  Veena Kaul 《BIT Numerical Mathematics》1973,13(2):145-152

The construction of optimal linear rules of numerical approximation by Davis' method has already been discussed for functions analytic in circles and in certain ellipses. In the present paper, introducing an appropriate Hilbert space, we discuss optimal linear rules for functions analytic in a circular annulus. We then consider the construction of optimal rules for numerical integration round the unit circleC ₁ : z=1. In Theorem 2 we obtain explicitly a family of optimal rules forc ₁ f(z)dz, withf analytic onC ₁; interestingly, in general, the optimal nodes do not lie onC ₁. For functionsf(1/2(z +z ^–1)), Theorem 2 gives a family of optimal quadrature formulas for integration over [–1,1].     

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Self-assembly of azo molecules to mesogenic phasmid-like materials through inter-molecular hydrogen bonding

A series of acid-functionalised new azo compounds was synthesised and characterised. The constituent molecules self-organise to form dimers through inter-molecular hydrogen bonding, resulting in phasmid-like compounds. This was once considered to be a promising molecular architecture to form biaxial nematic phases. The mesomorphic properties of these new azo compounds were studied using polarising optical microscopy, differential scanning calorimetry and X-ray diffraction. Investigations revealed that these compounds form nematic and columnar mesophases. A few more compounds were synthesised by replacing the??N=N- linkage in these compounds with??CH=N- and??COO- to study the effect of different linkages on the mesomorphic properties in such molecular systems. All were found to be liquid crystalline. The compounds with a??N=N- linkage are more conducive to mesomorphism and are thermally very stable. The effect of number of alkoxy chains on the mesomorphic properties of this system was also studied. To the best of our knowledge, at present, only a handful of phasmid-like mesogenic compounds, formed by the intermolecular hydrogen bonding, are known.     

Microstructural and mechanical properties of porous biocomposite scaffolds based on polyvinyl alcohol,nano-hydroxyapatite and cellulose nanocrystals

In this study, in situ synthesis of polyvinyl alcohol (PVA)/nano-hydroxyapatite (n-HA)/cellulose nanocrystals (CNC) organic–inorganic biocomposite porous scaffolds is reported. The effect of the CNC content on the properties of the biocomposite scaffold was investigated and characterized using field-emission scanning electron microscopy, Fourier-transform infrared spectroscopy (FTIR), X-ray diffraction (XRD) analysis, porosity and compressive strength measurements, thermal studies, and in vitro biomineralization and degradation studies. The morphological study showed highly porous structures with good pore interconnectivity in which n-HA was homogeneously dispersed. XRD analysis showed a decrease in the crystalline fraction and crystallite size of nano-hydroxyapatite with introduction of PVA and with increasing content of CNC. It was observed that the porosity decreased to some extent with increasing CNC content, while increases in the compressive strength (from 0.85 to 2.09 MPa) and elastic modulus (from 4.68 to 16.01 MPa) were found as the CNC content was increased. In vitro biomineralization study revealed the formation of apatite on PVA/n-HA/CNC biocomposite scaffolds when soaked for 7 and 14 days in simulated body fluid (SBF) solution. The obtained porous scaffolds offering good mechanical performance may provide a promising alternative scaffolding matrix for use in the field of bone tissue engineering.     

Starting and stopping rules for simulations using a priori information

This paper proposes a method of interval estimation (based on the autoregressive method) that exploits a priori information about activity level (traffic intensity) and data skewness in a queueing simulation. The method relies on two rules: One determines when to start collecting data during a run and the other determines when to stop collection. The rules are designed to use the a priori information in a way that mitigates the effects of the initial conditions in the simulation and ensures representative congested behavior in the collected data.Experiments with a simulation of the M/M//c queue, with c = 1, 2, 4 and = 0.7, 0.8, 0.9, 0.95 produce favorable results. For = 0.7, 0.8, 0.9, the coverage rates for interval estimates are close to the specified theoretical coverage rates and are higher than those reported in the literature for other methods of interval estimation. The sample sizes to obtain the coverage rates are moderate and are insensitive to variation in the number of servers and the activity level. Experiments with a fixed truncation starting rule and a fixed sample-size stopping rule clearly demonstrate the effectiveness of the proposed method. It is anticipated that a priori information also exists in more complex simulations, and that such information can be used in an analogous way to achieve desired coverage levels.     

Optimal rules with polynomial precision for Hilbert spaces possessing reproducing kernel functions

Numerische Mathematik - Optimal linear rules with polynomial precision, based on preassigned abscissas, are considered over a Hilbert space possessing a reproducing kernel function; the weights are...     

Optimal rules for numerical integration round the unit circle

The construction of optimal linear rules of numerical approximation by Davis' method has already been discussed for functions analytic in circles and in certain ellipses. In the present paper, introducing an appropriate Hilbert space, we discuss optimal linear rules for functions analytic in a circular annulus. We then consider the construction of optimal rules for numerical integration round the unit circleC ₁ : z=1. In Theorem 2 we obtain explicitly a family of optimal rules forc ₁ f(z)dz, withf analytic onC ₁; interestingly, in general, the optimal nodes do not lie onC ₁. For functionsf(1/2(z +z ^–1)), Theorem 2 gives a family of optimal quadrature formulas for integration over [–1,1].