Exact solution to a parametric linear programming problem

In this paper, we present a cubically convergent method for finding the largest eigenvalue of a nonnegative irreducible tensor. A cubically convergent method is used to solve an equivalent system of nonlinear equations which is transformed by the tensor eigenvalue problem. Due to particular structure of tensor, Chebyshev’s direction is added to the method with a few extra computation. Two rules are designed such that the descendant property of the search directions is ensured. The global convergence is proved by using the line search technique. Numerical results indicate that the proposed method is competitive and efficient on some test problems.     

Numerical simulations for tumor and cellular immune system interactions in lung cancer treatment

We investigate a new mathematical model that describes lung cancer regression in patients treated by chemotherapy and radiotherapy. The model is composed of nonlinear integro-differential equations derived from the so-called kinetic theory for active particles and a new sink function is investigated according to clinical data from carcinoma planoepitheliale. The model equations are solved numerically and the data are utilized in order to find their unknown parameters. The results of the numerical experiments show a good correlation between the predicted and clinical data and illustrate that the mathematical model has potential to describe lung cancer regression.     

Two positivity preserving flux limited,second‐order numerical methods for a haptotaxis model

Two numerical methods for a one‐dimensional haptotaxis model, which exploit the use of van Leer flux limiter, are developed and analyzed. Sufficient conditions time step size and flux limiting are given for such formulation to ensure the non‐negativity of the discrete solution and second‐order accuracy in space. Another advantage is that we avoid solving large nonlinear systems of algebraic equations. The discrete preservation of total conservation of cell density, concentration, and logarithmic density is also verified for the numerical solution. Numerical results concerning accuracy, convergence rate, positivity, and conservation properties are presented and discussed. Similar approach could be applied efficiently in the corresponding two‐ and three‐dimensional problems. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013     

Vibrational Assignment of N-Phenylphthalimide and 15N-Phenylphthalimide

Abstract

The i.r. spectra of N-phenylphthalimide and ¹⁵N-phenylphthalimide have been measured in 4000–100 cm^?1 frequency range as KBr and polyethylene pellets and as chloroform solutions. The Raman spectra (4000–50) cm^?1 of microcrystalline powder of the of the same compounds have also been investigated.

A detailed assignment of most of the observed frequencies has been proposed on the basis of the group vibrational concept, isotopic shift data and analogies with the spectra of related molecules. Some literature data have been discussed and some frequencies are reassigned.     

Solid-state linear polarized IR-spectroscopy of croconic and rhodizonic acids

The applications of linear-polarized IR-spectroscopy to oriented colloid suspensions in a nematic host are demonstrated with croconic and rhodizonic acids. The experimental IR vibrational assignments of the solid-state of both neutral compounds are presented. Assignments are supported by theoretical quantum chemical calculations and vibrational analysis at the DFT level of theoretical approximation with the 6-311++G^** basis set.      

The aggregation of the merocyanine dyes, depending of the type of the counterions

Counterions affect on the substructures formation in the case of the merocyanine dye, 1-methyl-4-[2-(4-hydroxyphenyl)ethenyl)]piridinium] hydrogensquarate both in gas and condense phase. Spectroscopically and structural elucidation of these aggregates have been performed, using solid-state conventional and linear-polarized IR-spectroscopy of oriented colloids as a nematic liquid crystal suspension, UV-vis spectroscopy, HPLC tandem ESI mass spectrometry, (1)H and (13)C NMR, TGV and DSC. Quantum chemical DFT calculations have been carried out as well. Experimental and theoretical data are compared with analogous ones of corresponding iodide salt of dye studied.     

Ethyl esters of coumarin-3-phosphonic acid and 1,2-benzoxaphosphorine-3-carboxylic acid: crystal structure,spectroscopic and theoretical elucidation

IR-spectroscopic characterization of the coumarin-3-phosphonic acid and 1,2-benzoxaphosphorine-3-carboxylic acid ethyl esters has been carried out by means of linear-polarized IR (IR-LD) spectroscopy of oriented colloid suspensions in a nematic host. Quantum chemical DFT calculations at the B3LYP level of theory and 6-311++G** basis set were performed. The electronic structure and vibrational properties of both compounds are discussed. The spectroscopic data for 2-benzoxaphosphorine-3-carboxylic acid ethyl ester are in accordance with the crystal structure determined by single crystal X-ray diffraction. The compound C₁₃H₁₅O₅P crystallizes in the noncentrosymmetric space group P2₁2₁2₁, and its structure consists of a 3D network formed by short contacts of the type P=O···HC_(Ar) with distances of 3.420 and 2.467 Å. The geometry of the PO₃C fragment exhibits a pseudo T _d symmetry.     

Crystal structure and spectroscopic properties of ammonium hydrogensquarate squaric acid monohydrate

The structure of ammonium hydrogensquarate squaric acid monohydrate has been determined by single crystal X-ray diffraction. The compound crystallizes in the monoclinic space group C2/c and exhibits a 3D network with molecules linked by intermolecular interactions with participation of the H₂Sq, HSq^?, NH₄ ⁺, and H₂O species. The HSq^? anion and the neutral H₂Sq form a strong head-to-tail dimer through O–H···O hydrogen bonding with lengths of 2.587 and 2.494 Å (protected space between numeral and unit). The layers are connected by ammonium cations and water molecules in a plane through the O···N (2.950, 2.978, 3.036 Å) and O···O (2.953, 2.781 Å) bonds. Another such layer is connected to the NH₄ ⁺ cation in the adjacent plane through bifurcated N–H···O hydrogen-bonding to form a double layer (NH···O bond lengths are 3.036, 2.978, 2.857, 2.909, 2.958, and 2.742 Å, respectively). The IR-band assignment of the compound was achieved using the polarized IR-spectroscopy of oriented colloids in a nematic host. Theoretical ab initio calculations were performed and achieved with a view to explain the IR-bands of the H₂Sq.HSq^? motif.     

Synthesis,spectroscopic analysis and structure deduction of gold(III), palladium(II) and platinum(II) complexes with the tripeptide glycyl-<Emphasis Type="SmallCaps">l</Emphasis>-phenylalanyl-glycine

The coordination behaviour of the tripeptide glycyl-l-phenylalanyl-glycine (H-Gly-Phe-Gly-OH) with Au(III), Pd(II), and Pt(II) in both solution and in the solid state has been investigated experimentally. In addition, quantum chemical calculations have been carried out with a view to obtain the structures and spectroscopic properties of the ligand and its complexes. Both in solution and in the solid state the tripeptide interacts in a tetradentate manner with the Au(III) and Pd(II) ions through the NH₂, two deprotonated amide N atoms and the COO⁻group, forming [Au(H-Gly-Phe-Gly-OH)H₋₂)] × H₂O and [Pd(H-Gly-l-Phe-Gly-OH)H₋₂)]Na × H₂O complexes. The MN₃O chromophores are calculated to be near planar. Interaction with cisplatin leads to the formation of a mononuclear complex with tridentate coordination of the ligand by NH₂ and two N- atoms from the deprotonated amide groups ([Pt(H-Gly-l-Phe-Gly-OH)H₋₂)NH₃] × 2H₂O). The fourth coordination position of the Pt(II) is occupied by an NH₃ ligand. The PtN₄ chromophore is flat with a deviation from planarity of 0.3°. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.