On the solution of a class of the reduced wave equation and the Riccati differential equation

In this paper we present an “iteration” technique for a class of differential equation having the form z^″=λz, where λ is a function in C^∞. We show that we can construct not only the general solution of the reduced wave equation but also the general solution of the Riccati differential equation by using this iteration technique if the given function λ is satisfies the condition

     

Conserved quantities for a class of (1 + n)-dimensional linear evolution equation

A special type of (1 + n)-dimensional linear evolution equation is considered. A class of the equations generated by the Fokker-Planck equation becomes the subcase of the considered equation. Conserved vectors using the partial Lagrangian approach is derived in terms of the coefficients of the discussed equation. Derived results are used for the different models from different sciences. We also discuss the conservation laws of the heat equation on curved manifolds and in different coordinate systems. Potential systems are also obtained for some models. At last conclusion is given.     

New approaches to due date assignment in job shops

In this study, two new approaches for due date assignment in job shops are evaluated. Proposed approaches use statistical prediction techniques for dynamic prediction of job flowtimes in a job shop environment as the job arrives to the shop floor. Primary objective of this research is to compare the performance of the proposed due date assignment model (PDDAM) with several conventional due date assignment models (CDDAM). For this purpose, simulation models are developed and comparisons of the PDDAM and CDDAM are made in terms of the mean absolute percent error (MAPE), mean percent error (MPE) and mean tardiness (MT). Simulation experiments showed that for many test conditions, PDDAM dominates CDDAM. Therefore, case by case findings are summarized in the paper.     

An algorithm for the estimation of a regression function by continuous piecewise linear functions

The problem of the estimation of a regression function by continuous piecewise linear functions is formulated as a nonconvex, nonsmooth optimization problem. Estimates are defined by minimization of the empirical L ₂ risk over a class of functions, which are defined as maxima of minima of linear functions. An algorithm for finding continuous piecewise linear functions is presented. We observe that the objective function in the optimization problem is semismooth, quasidifferentiable and piecewise partially separable. The use of these properties allow us to design an efficient algorithm for approximation of subgradients of the objective function and to apply the discrete gradient method for its minimization. We present computational results with some simulated data and compare the new estimator with a number of existing ones.     

A branch and bound algorithm for class based storage location assignment

Class-based storage implementation decisions have significant impact on the required storage space and the material handling cost in a warehouse. In this paper, a nonlinear integer programming model is proposed to capture the above. Effects of storage area reduction on order picking and storage space cost are incorporated. A branch and bound algorithm is developed to solve the model. Computational experience with randomly generated data sets and an industrial case shows that branch and bound algorithm is computationally more efficient than a baseline dynamic programming algorithm. It is further observed that the class based policy results in lower total cost of order picking and storage space than the dedicated policy.     

Hydrothermal Synthesis and Characterization Properties of C7H12N2[H2PO4]2.1/2H2O

An orthophosphoric hybrid material was successfully prepared by a hydrothermal reaction at 110 °C. A single crystal X-ray structure, thermal behavior, IR, and NMR spectroscopy investigations are given for a new organic cation bis dihydrogenomonophosphate C₇H₁₂N₂[H₂PO₄]₂.1/2H₂O. The latter has been synthesized hydrothermally using 2,4-diaminotoluene (DAT) and orthophosphoric acid. The atomic arrangement can be described as inorganic sheets alternating with inorganic-organic layers. The organic group C₇H₁₂N⁺ ₂ is located between inorganic groups to build multiple hydrogen bonds to ensure the three-dimensional cohesion network. The thermal behavior and IR, NMR and impedance spectroscopy studies are discussed for the powder samples of this compound.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

Highly selective methods for synthesis of internal (α-) vinylboronates through efficient NHC-Cu-catalyzed hydroboration of terminal alkynes. Utility in chemical synthesis and mechanistic basis for selectivity

Cu-catalyzed methods for site-selective hydroboration of terminal alkynes, where the internal or α-vinylboronate is generated predominantly (up to >98%) are presented. Reactions are catalyzed by 1-5 mol % of N-heterocyclic carbene (NHC) complexes of copper, easily prepared from N-aryl-substituted commercially available imidazolinium salts, and proceed in the presence of commercially available bis(pinacolato)diboron [B(2)(pin)(2)] and 1.1 equiv of MeOH at -50 to -15 °C in 3-24 h. Propargyl alcohol and amine and the derived benzyl, tert-butyl, or silyl ethers as well as various amides are particularly effective substrates; also suitable are a wide range of aryl-substituted terminal alkynes, where higher α-selectivity is achieved with substrates that bear an electron-withdrawing substituent. α-Selective Cu-catalyzed hydroborations are amenable to gram-scale procedures (1 mol % catalyst loading). Mechanistic studies are presented, indicating that α selectivity arises from the structural and electronic attributes of the NHC ligands and the alkyne substrates. Consistent with suggested hypotheses, catalytic reactions with a Cu complex, derived from an N-adamantyl-substituted imidazolinium salt, afford high β selectivity with the same class of substrates and under similar conditions.     

Efficient one-pot catalyst-free synthesis of novel coumarin- spiro[indoline-3,4'-pyran] conjugates via three-component domino reaction in aqueous medium

A simple, efficient, eco-friendly and catalyst-free procedure was developed for the construction of novel coumarin-spiro[indoline-3,4'-pyran] conjugates via three-component reactions of various synthetic beta-ketoesters with isatins and malononitrile in aqueous medium. In addition to operational simplicity and absence of tedious separation procedures, being catalyst–free is the prominent advantage of this method.     

Synthesis,spectral properties,in vitro α-glucosidase inhibitory activity and quantum chemical calculations of novel mixed-ligand M(II) complexes containing 1,10-phenanthroline

A series of mixed-ligand M(II) complexes containing 1,10-phenanthroline (phen) and 3-methylpyridine-2-carboxylic acid (3-mpaH) or 6-methylpyridine-2-carboxylic acid (6-mpaH), namely [Co(3-mpa)₂(phen)]·3H₂O ( 1 ), [Hg(6-mpa)₂(phen)]·2H₂O ( 2 ), [Mn(6-mpa)₂(phen)]·2H₂O ( 3 ), [Co(6-mpa)₂(phen)]·H₂O ( 4 ) and [Ni(6-mpa)₂(phen)]·H₂O ( 5 ), were synthesized for the first time. Among them, 1 was obtained as single crystals. The structural characterization for 1 was conducted using X-ray diffraction and that for 2 – 5 using mass spectrometry. The IC₅₀ values for α-glucosidase inhibition of 1 – 5 were obtained as 0.161 to >600 μM. The spectral properties were also investigated using Fourier transform infrared and UV–visible spectra. Furthermore, to investigate the geometrical parameters, spectral and electronic properties and second- and third-order nonlinear optical parameters for 1 – 5 , density functional calculations were applied.