A general transformation for theta series associated with the quadratic form $$x^2+ky^2$$

Using elementary techniques, we prove a general transformation for theta series associated with the quadratic form \(x^2+ky^2.\) The transformation is then applied to establish several infinite families of identities involving theta series whose Fourier coefficients are interlinked.     

QSDPNAL: a two-phase augmented Lagrangian method for convex quadratic semidefinite programming

In this paper, we present a two-phase augmented Lagrangian method, called QSDPNAL, for solving convex quadratic semidefinite programming (QSDP) problems with constraints consisting of a large number of linear equality and inequality constraints, a simple convex polyhedral set constraint, and a positive semidefinite cone constraint. A first order algorithm which relies on the inexact Schur complement based decomposition technique is developed in QSDPNAL-Phase I with the aim of solving a QSDP problem to moderate accuracy or using it to generate a reasonably good initial point for the second phase. In QSDPNAL-Phase II, we design an augmented Lagrangian method (ALM) wherein the inner subproblem in each iteration is solved via inexact semismooth Newton based algorithms. Simple and implementable stopping criteria are designed for the ALM. Moreover, under mild conditions, we are able to establish the rate of convergence of the proposed algorithm and prove the R-(super)linear convergence of the KKT residual. In the implementation of QSDPNAL, we also develop efficient techniques for solving large scale linear systems of equations under certain subspace constraints. More specifically, simpler and yet better conditioned linear systems are carefully designed to replace the original linear systems and novel shadow sequences are constructed to alleviate the numerical difficulties brought about by the crucial subspace constraints. Extensive numerical results for various large scale QSDPs show that our two-phase algorithm is highly efficient and robust in obtaining accurate solutions. The software reviewed as part of this submission was given the DOI (Digital Object Identifier)  https://doi.org/10.5281/zenodo.1206980.     

Experimental analysis of spectral characteristics of antiresonant guiding photonic crystal fibers

Both numerical and experimental analyses are carried out to investigate the spectral characteristics of antiresonant guiding photonic crystal fibers. The transmission minima were observed at the wavelengths where LP(ml) (m相似文献   

Prolate and Oblate Shape Coexistence in 188Pt

A standard in-beam γ-spectroscopy experiment for ¹⁸⁸Pt is performed via the¹⁷⁶Yb(¹⁸O, 6n) reaction at beam energies of 88 and 95MeV, and the level scheme for ¹⁸⁸Pt is established. Prolate and oblate shape coexistence has been demonstrated to occur in ¹⁸⁸Pt by applying the projected shell model. The rotation alignment of i_13/2 neutrons drives the yrast sequence changingsuddenly from prolate to oblate shape at angular momentum 10h, indicating likely a new type of shape phase transition along the yrast line in ¹⁸⁸Pt.     

Development of an improved divergence‐free‐condition compensated coupled framework to solve flow problems with time‐varying geometries

In this article a coupled version of the improved divergence‐free‐condition compensated method will be proposed to simulate time‐varying geometries by direct forcing immersed boundary method. The proposed method can be seen as a quasi‐multi‐moment framework due to the fact that the momentum equations are discretized by both cell‐centered and cell‐face velocity. For simulating time‐varying geometries, a semi‐implicit iterative method is proposed for calculating the direct forcing terms. Treatments for suppressing spurious force oscillations, calculating drag/lift forces, and evaluating velocity and pressure for freshly cells will also be addressed. In order to show the applicability and accuracy, analytical as well as benchmark problems will be investigated by the present framework and compared with other numerical and experimental results.     

Optical implementation of a constant-time multicomparand bit-parallel magnitude-comparison algorithm using wavelength- and polarization-division multiplexing with application to parallel database processing

We present a word- and bit-parallel magnitude-comparison architecture that permits multiple comparands to be compared with multiple relations in constant time. The proposed magnitude-comparison algorithm uses a novel polarization and wavelength-encoding scheme to achieve a fast, scalable realization. Distinctive features of the proposed architecture include (1) the use of a multiple-wavelength encoding scheme to increase processing parallelism and (2) multiple-comparand word- and bit-parallel comparison with an execution time that is independent of the data or word size.     

New serotonin 5-HT(6) ligands from common feature pharmacophore hypotheses

Serotonin 5-HT6 receptor antagonists are thought to play an important role in the treatment of psychiatry, Alzheimer's disease, and probably obesity. To find novel and potent 5-HT6 antagonists and to provide a new idea for drug design, we used a ligand-based pharmacophore to perform the virtual screening of a commercially available database. A three-dimensional common feature pharmacophore model was developed by using the HipHop program provided in Catalyst software and was used as a query for screening the database. A recursive partitioning (RP) model which can separate active and inactive compounds was used as a filtering system. Finally a sequential virtual screening procedure (SQSP) was conducted, wherein both the common feature pharmacophore and the RP model were used in succession to improve the results. Some of the hits were selected based on druglikeness, ADME properties, structural diversity, and synthetic accessibility for real biological evaluation. The best hit compound showed a significant IC50 value of 9.6 nM and can be used as a lead for further drug development.     

Lower limit of determination values for trace elements in iron certified reference materials by neutron activation analysis with multiple gamma-ray detection

Recycling steel products demands a new technique for determining tramp elements in steel. Tramp elements, As and Sb, in some iron certified reference materials were determined by neutron activation analysis with multiple gamma-ray detection method and reported in MTAA11. In MTAA12, the authors reported the lower limit of determination values (LDL) and the dispersion of this method. The values of the LDLs for As and Sb in high purity iron were 0.002 and 0.0009 μg·g⁻¹. The dispersion is small enough to satisfy the demand from materials science.     

5- And 6-exocyclic products, cis-2,3,5-trisubstituted tetrahydrofurans, and cis-2,3,6-trisubstituted tetrahydropyrans via Prins-type cyclization

Exocyclic products having cis-2,5 and cis-2,6 substitution were synthesized from terminally substituted alkynyl alcohols with various aldehydes via Prins-type cyclization in good yields. It is of interest that synthesized 5- and 6-exocyclic vinyl cations generated as a result of Prins-type cyclization could be trapped as a vinyl triflate in CH2Cl2 to give 3-furanylidenes and 3-pyranylidenes. Those 3-furanylidenes and 3-pyranylidenes underwent hydrolysis to give the corresponding 3-acyl-substituted products having all-cis-configured isomers, such as 2,3,5-trisubstituted tetrahydrofurans and 2,3,6-trisubstituted tetrahydropyrans.     

Ultraviolet cavity ringdown spectra and the S1(n,pi) ring-inversion potential energy function for 2-cyclohexen-1-one-d0 and Its 2,6,6-d3 isotopomer

The cavity ringdown spectra of 2-cyclohexen-1-one (2CHO) and its 2,6,6-d3 isotopomer (2CHO-d3) have been recorded in the spectral region near their S1(n,pi)<--S0 band origins which are at 26,081.3 and 26,075.3 cm-1, respectively. The data allow several of the quantum states of nu39, the ring inversion, to be determined for both the ground and excited electronic states. These were utilized to calculate the one-dimensional potential energy functions which best fit the data. The barriers to inversion for the S0 and S1(n,pi) states were found to be 1,900 +/- 300 and 3,550 +/- 500 cm-1, respectively. Density functional theory calculations predict values of 2,090 and 2,265 cm-1, respectively.