An Algorithm for the Single-item Capacitated Lot-Sizing Problem with Concave Production and Holding Costs

We consider a multi-period single-item production scheduling problem with a deterministic, time-varying demand pattern and concave cost functions. Optimal production lot sizes, so as to minimize the total costs of production, set-up, and inventory, are determined subject to dynamic production capacity and no backlogs. The proposed algorithm was tested extensively by solving several randomly generated problems with varying degrees of complexity. The proposed algorithm appears to perform quite reasonably for practical applications.     

Studies in the formation of poly(oxazolidone)s. III. Catalysis and kinetics of the model oxazolidone formation from cyclohexyl isocyanate and phenylglycidyl ether

The reaction of cyclohexyl isocyanate with phenylglycidyl ether was selected as model reaction for the synthesis of cycloaliphatic isocyanate-based poly(2-oxazolidone)s. The selectivity of AlCl₃ and AlCl₃-triphenylphosphine oxide (AlCl₃–TPPO) and AlCl₃-hexamethylphosphoric triamide (AlCl₃–HMPA) complexes was studied for 2-oxazolidone formation. The reaction products were identified by means of the melting point, ¹H-NMR, and IR spectroscopy. The kinetics of the model reaction was studied using AlCl₃-TPPO in o-dichlorobenzene at 120 and 140°C.     

A fluorescence detection scheme for ultra large molecules after gas phase separation

A system was proposed to remove the upper mass limitation of mass spectrometry. In present study, ultra large molecules were separated in the gas phase by mass analyzer after electrospray ionization. Instead of conventional detection with electron multiplier, a laser-induced-fluorescence detection scheme was applied. The instrument sensitivity is independent of molecular weight, but related to the spectroscopic properties of the fluorophores presented by the large biomolecules.     

Practical considerations when using radio frequency-only quadrupole ion guide for atmospheric pressure ionization sources with time-of-flight mass spectrometry

Construction details and performance evaluation of a radio frequency (rf)-only quadrupole ion guide for use with an electrospray ionization time-of-flight mass spectrometer is presented in this paper. Angiotensin III and cytochrome c were used in these experiments to investigate the ion transmission properties of the rf-only quadrupole for different m/z species. In addition, influence of ion kinetic energies along with the characteristic fragmentation due to collision induced dissociation (CID) were studied. These experiments demonstrate that the transmissions of different m/z ions were not only dependent on the frequency and magnitude of the rf waveform, which is similar to a high vacuum rf-only quadrupole ion guide, but also on the pressure inside the quadrupole chamber. For the pressure range tested, low m/z ions are better focused with increasing pressure. As expected, transmission of ions are subject to space charge limitations when significant numbers of ions are focused on the axis of the quadrupole. It is also observed that CID results are related to transverse motion and longitude motion of ions inside the quadrupole region. Consequently, CID is useful for fragmentation of linear peptides and it is not effective (in present configuration) for large bulky proteins. The kinetic energy of ions that enter the repelling region of the TOFMS is ultimately determined by the ensemble effect resulting from the dc bias potential of the quadrupole (the dominant factor), skimmer-2, pressure inside the quadrupole chamber, and jet expansion. While this system is tested with an ESI source, the operational principle and design criteria are directly applicable for improving other atmospheric pressure ionization sources with time-of-flight mass analyzers such as an inductively coupled plasma ion source.     

Barzilai and Borwein’s method for multiobjective optimization problems

The present study is an attempt to extend Barzilai and Borwein’s method for dealing with unconstrained single objective optimization problems to multiobjective ones. As compared with Newton, Quasi-Newton and steepest descent multi-objective optimization methods, Barzilai and Borwein multiobjective optimization (BBMO) method requires simple and quick calculations in that it makes no use of the line search methods like the Armijo rule that necessitates function evaluations at each iteration. It goes without saying that the innovative aspect of the current study is due to the use of no function evaluations in comparison with other multi-objective optimization non-parametric methods (e.g. Newton, Quasi-Newton and steepest descent methods, to name a few) that have been investigated so far. Also, the convergence of the BBMO method for the objective functions assumed to be twice continuously differentiable has been proved. MATLAB software was utilized to implement the BBMO method, and the results were compared with the other methods mentioned earlier. Using some performance assessment, the quality of nondominated frontier of BBMO was analogized to above mentioned methods. In addition, the approximate nondominated frontiers gained from the methods were compared with the exact nondominated frontier for some problems. Also, performance profiles are considered to visualize numerical results presented in tables.     

Effective Potential in Noncommutative BTZ Black Hole

In this paper, we investigated the noncommutative rotating BTZ black hole and showed that such a space-time is not maximally symmetric. We calculated effective potential for the massive and the massless test particle by geodesic equations, also we showed effect of non-commutativity on the minimum mass of BTZ black hole.     

A new iterative method for solving a class of complex symmetric system of linear equations

We present a new stationary iterative method, called Scale-Splitting (SCSP) method, and investigate its convergence properties. The SCSP method naturally results in a simple matrix splitting preconditioner, called SCSP-preconditioner, for the original linear system. Some numerical comparisons are presented between the SCSP-preconditioner and several available block preconditioners, such as PGSOR (Hezari et al. Numer. Linear Algebra Appl. 22, 761–776, 2015) and rotate block triangular preconditioners (Bai Sci. China Math. 56, 2523–2538, 2013), when they are applied to expedite the convergence rate of Krylov subspace iteration methods for solving the original complex system and its block real formulation, respectively. Numerical experiments show that the SCSP-preconditioner can compete with PGSOR-preconditioner and even more effective than the rotate block triangular preconditioners.     

New aspects of quantization of the Jackiw–Pi model: field–antifield formalism and noncommutativity

The so‐called Jackiw–Pi (JP) model for massive vector fields is a three‐dimensional, gauge‐invariant and parity‐preserving model that was discussed in several contexts. In this paper we have discussed its quantum aspects through the introduction of Planck‐scale objects, i.e., via noncommutativity and the well‐known BV quantization. Namely, we have constructed the JP noncommutative space‐time version, we have provided the BV quantization of the commutative JP model and we have discussed its features. The noncommutativity has introduced interesting new objects in JP's Planck‐scale framework.