An alternate linear algorithm for the minimum flow problem

We present an alternate linear algorithm for finding the minimum flow in (s, t)-planar networks using a new concept of minimal removable sets developed here. The iterative nature of the algorithm facilitates the adjustment of solutions for systems in developmental stages. The minimum flow algorithm presented here requires O(|V|) time, where V denotes the set of vertices. The minimum flow problem arises in many transportation and communication systems.     

Absolute points for multiple assignment problems

An algorithm is presented to solve multiple assignment problems in which a cost is incurred only when an assignment is made at a given cell. The proposed method recursively searches for single/group absolute points to identify cells that must be loaded in any optimal solution. Unlike other methods, the first solution is the optimal solution. The algorithm provides the user with both an insight into the problem and the ability to critically analyse the data. It is easy to apply and can provide an effective tool for practitioners to solve problems of any size.     

Shape resonances in slow electron scattering by aromatic molecules. I. Anthraquinone derivatives

A series of anthraquinone (C(14)O(2)H(8)) derivatives has been studied by means of electron capture negative ion mass spectrometry (ECNI-MS), photoelectron spectroscopy (PES), and AM1 quantum chemical calculations. Mean lifetimes of molecular negative ions M(-.) (MNI) have been measured. The mechanism of long-lived MNI formation in the epithermal energy region of incident electrons has been investigated. A simple model of a molecule (a spherical potential well with the repulsive centrifugal term) has been applied for the analysis of the energy dependence of cross sections at the first stage of the electron capture process. It has been shown that a temporary resonance of MNI at the energy approximately 0.5 eV corresponds to a shape resonance with lifetime 1-2.10(-13) s in the f-partial wave (l = 3) of the incident electron. The next resonant state of MNI at the energy approximately 1.7 eV has been associated with the electron excited Feshbach resonance (whose parent state is a triplet npi* transition). In all cases the initial electron state of the MNI relaxes into the ground state by means of a radiationless transition, and the final state of the MNI is a nuclear excited resonance with a lifetime measurable on the mass spectrometry timescale. Copyright 1999 John Wiley & Sons, Ltd.     

Synthesis, characterization, crystal and molecular structure analysis of N-(2,4-dimethylphenyl)-6-methyl-4-(3-nitrophenyl)-2-oxo-1,2,3,4-tetrahydropyrimidine-5-carboxamide

A novel dihydropyrimidine (DHPM) derivative bearing a carbamoyl moiety was synthesized by an efficient three-component Biginelli reaction and was characterized spectroscopically and finally confirmed by X-ray diffraction studies. The title compound C₂₀H₂₀N₄O₄ crystallizes in the monoclinic space group P2₁/c with cell parameters a=12.8970(12) Å, b=13.6210(11) Å, c=11.8420(13) Å, β=115.860(3)°, Z=4 and V=1872.0(3) Å³. The conformation of the dihydropyrimidine ring is unusual; it is planar instead of the usual boat-like conformation. The 3-nitrophenyl ring is orthogonal to the 3,4-DHPM ring. The carbonyl group is in an anti-clinal conformation.     

Analysis of a shielded TE011 mode composite dielectric resonator for stable frequency reference

Analysis of a TE₀₁₁ mode composite sapphire-rutile dielectric resonator has been carried out to study the temperature variation of resonance frequency, close to the Cs atomic clock hyperfine frequency of 9.192 GHz. The complementary behavior of dielectric permittivity with temperature of the composite has been exploited to obtain the desired turning point in the resonant frequency. The frequency of the composite structure is found to be independent of the shield diameter beyond four times the puck diameter.     

Electrospray ionization multiple-stage tandem mass spectrometric analysis of diglycosyldiacylglycerol glycolipids from the bacteria Bacillus pumilus

Electrospray ionization (ESI) combined with multiple-stage tandem mass spectrometry (MS(n)) was used to directly analyze the glycolipid mixture from bacteria Bacillus pumilus without preliminary separation. Full scan ESI-MS revealed the composition of picomole quantities of glycerolglycolipid species containing C(14)-C(19) fatty acids, some of which were monounsaturated. Two main components were identified from their molecular masses and fragmentation pathways. The fragmentation pathway of the known compound compared with the investigated compound verified the proposed structure as 1(3)-acyl-2-pentadecanoyl-3(1)-O-[beta-D-glucopyranosyl-(1-->6)-O-beta-D-glucopyranosyl]-sn-glycerols. A comparison of the multiple tandem mass spectra of the different alkali-metal cation adducts indicates that the intensity of fragments and the dissociation pathways are dependent on the alkali-metal type. The basic structures of glycerolglycolipids were reflected clearly from the fragmentation patterns of the sodium cations. The intense fragments of the sugar residue from the precursor ions were obtained from the lithiated adduct ions. ESI-MS(n) spectra of [M + K](+) ions did not provide as much fragmentation as [M + Na](+) and [M + Li](+) adducts, but their spectra allow the position of glycerol acylation to be determined. On the basis of MS(2) spectra of [M + K](+) ions, it was established that all components have a C(15:0) fatty acid at the sn-2 position of the glycerol backbone and C(14)-C(19) acids at the sn-1 position of the glycerol backbone. Copyright 1999 John Wiley & Sons, Ltd.     

A warm-start dual simplex solution algorithm for the minimum flow networks with postoptimality analyses

This paper presents an algorithm for finding the minimum flow in general (s, t) networks with m directed arcs. The minimum flow problem (MFP) arises in many transportation and communication systems. Here, we construct a linear programming (LP) formulation of MFP and develop a simplex-type algorithm to find a minflow. Unlike other simplex-like algorithms, the algorithm developed here starts with an incomplete Basic Variable Set (BVS) initially and then fills-up the BVS completely while pushing toward an optimal vertex. If this results in pushing too far into infeasibility, the next step pulls the solution back to feasibility. Both phases use the Gauss-Jordan pivoting transformation used in the standard simplex and dual simplex algorithms.

The proposed approach has some common features with Dantzig's self-dual simplex algorithm. We have avoided, however, the need for extra variables (slack and surplus) for equality constraints, as well as an artificial constraint for the self-dual algorithm for initial phase and the dual simplex, respectively. The proposed Push phase takes at most 2m − 1 iterations to complete a tree (this augmentation may not be feasible). An infeasible path to the optimal solution contains at most 2m − 1 iterations; therefore in theory, the algorithm needs a sequence of at most 4m − 2 iterations.

Furthermore, the algorithm developed here makes available the full power of LP perturbation analysis and facilitates introducing network structural changes and side constraints also. It can also detect clerical errors in data entry which may make the problem infeasible or unbounded. It is assumed that the reader is familiar with LP terminology.     

A simple algorithm for the source-induced fixed-charge transportation problem

The fixed-charge problem is a non-linear programming problem of practical interest in business and industry. The source-induced fixed-charge transportation problem (SIFCTP) is a variation of the regular fixed-charge transportation problem (FCTP) in which a fixed cost is incurred for every supply point that is used in the solution, along with a variable cost that is proportional to the amount shipped. This problem is significantly different from the widely studied FCTP, where a fixed cost is incurred upon activation of a route. The introduction of the fixed costs in addition to variable costs results in the objective function being a step function. Therefore, fixed-charge problems are usually solved using sophisticated analytical or computer software. This paper deviates from that approach. It presents a computationally simple algorithm for the solution of source-induced fixed-charge problems. The results of empirical tests of the effectiveness of the proposed algorithm are presented.     

The effect of data scaling on dual prices and sensitivity analysis in linear programs

In many practical situations scaling the data is necessary to solve linear programs. This note explores the relationships in translating the sensitivity analysis between the original and the scaled problems.     

Synthesis,Characterization, Crystal and Molecular Structure Analysis of 2,6-Dimethyl-3-acetyl-5-carbomethoxy-4-(3-nitrophenyl)-1,4-dihydropyridine

Abstract  A novel unsymmetrical dihydropyridine, possessing carboxymethyl and carbomethoxy groups at C(3) and C(5), respectively, has been produced using a modified Hantzsch synthesis, under solvent free conditions, in a domestic microwave oven. The product obtained was characterized by spectroscopic techniques and finally confirmed by X-ray diffraction studies. The title compound C₁₇H₁₈N₂O₅ crystallizes in the monoclinic system in the space group P2₁/c with cell parameters a = 12.860(2) ?, b = 7.4950(6) ?, c = 16.734(3) ?, β = 94.436(3)°, Z = 4 and V = 1608.1(4) ?³. The 1,4-dihydropyridine ring in the structure is in a flattened boat conformation. The molecule possesses a chiral center at C4. The 3-nitrophenyl ring is nearly orthogonal to the 1,4-dihydropyridine ring. The carbonyl groups at C3 and C5 are oriented in −antiperiplanar and +synperiplanar conformations, respectively. The structure exhibits both inter and intramolecular hydrogen bonds of the type N–H···O and C–H···O. Index Abstract  A novel unsymmetrical dihydropyridine, possessing carboxymethyl and carbomethoxy groups at C(3) and C(5) respectively, has been produced using a modified Hantzsch synthesis, under solvent free conditions, in a domestic microwave oven. The product obtained was characterized by spectroscipic techniques and finally confirmed by X-ray diffraction studies. The title compound C₁₇H₁₈N₂O₅ crystallizes in the monoclinic system in the space group P2_1/c with cell parameters a  =  12.860(2) ?, b  =  7.4950(6) ?, c  =  16.734(3) ?, β = 94.436(3)°, Z = 4 and V = 1608.1(4) ?³. The 1,4-dihydropyridine ring in the structure is in a flattened boat conformation. The molecule possesses a chiral center at C(4). The 3-nitrophenyl ring is nearly orthogonal to the 1,4-dihydropyridine ring. The carbonyl groups at C(3) and C(5) are oriented in −antiperiplanar and +synperiplanar conformations respectively. The structure exhibits both inter and intramolecular hydrogen bonds of the type N–H···O and C–H···O.