Probabilistic evolution theory for explicit autonomous ordinary differential equations: recursion of squarified telescope matrices and optimal space extension

Probabilistic evolution theory facilitates the solution of initial value problem of explicit autonomous ordinary differential equations with second degree multinomial right hand side functions. Its formulation has components we call telescope matrices. The matrices grow in size very rapidly and has many zeroes and repeating structures. In order to avoid the computational complexity coming from telescope matrices, squarified telescope matrices are utilized. Their calculation is through a recursion. This recursion has been used in several works by the authors and their colleagues but its proof was not given. This work gives the proof of the recursion and all the surrounding details. A second purpose of this work is to provide a method for most facilitative (optimal) space extension. Space extension is needed for using probabilistic evolution theory when degree of multinomiality of the right hand side functions is more than two. For this purpose, an approach using method of exhaustion (brute-force) is proposed.     

Helical chirality of 1-phenacyl-1,10-phenanthrolinium bromides

Evidence for non-coplanarity of the pyridine and pyridinium rings in a series of 1-phenacyl-1,10-phenanthrolinium bromides was gleaned from ¹H-NMR data recorded in DMSO-d ₆ solution. The X-ray structure of 1-(4-chlorophenacyl)-1,10-phenanthrolinium bromide, as representative of this series, was determined in order to establish whether such a molecular distortion occurs in the solid state. The title compound crystallizes in the space group C2/c as a sesquihydrate of formula C₂₀H₁₄BrClN₂O·1.5H₂O with a = 35.7348(3) Å, b = 5.3468(1) Å, c = 21.7312(2) Å, = 116.4076(4)° and Z = 8. In the crystal, the helical chirality is manifested as a pronounced twist in the phenanthrolinium moiety, with the pyridine and pyridinium rings inclined at 6.8(2)°. This distortion is attributed to intramolecular hydrogen bonding of type C–H···N involving the methylene group and the uncharged nitrogen atom of the phenanthrolinium moiety. In the crystal, the cations surround an intricate array of water molecules and bromide ions held together by O–H···Br^– hydrogen bonds and comprising infinite chains ···Br^–···H–O–H···Br^–···, cross-linked by water molecules.     

Phase shift analysis of modulated photocurrent: A new approach to determining the energy scale

One of the major problems of the method of phase shift analysis of modulated photocurrent for studying the density of states in the energy gap of amorphous semiconductors has been the determination of the energy scale corresponding to this DOS profile. This study presents a new way of dealing with this problem. This new method is especially useful in the case where the DOS profile lacks a characteristic peak. A computer analysis is used to confirm the validity of this method and to demonstrate how it can be used.     

On Saint-Venant's problem for elastic dielectrics

The equilibrium theory of linear piezoelectricity is considered. Saint-Venant's problem for a homogeneous and anisotropic piezoelectric cylinder is studied.     

Synthesis and structure elucidation of bromination products from dibromohomobenzonorbornadienes: high temperature bromination--part 17

The electrophilic addition of bromine to dibromohomobenzonorbornadiene derivatives at -45 +/- 5 degrees C led to the formation of the rearranged and non-rearranged tetrabromides in a ratio of 6:4. However, high-temperature bromination of the same system in CCl4 at 77 degrees C produced only non-rearranged products. The formation mechanism of the isomers and the role of the substituent on the rearrangement is discussed. The structure elucidation of the isomeric tetrabromides was achieved from NMR spectral data. The agreement between the calculated dihedral angles and the measured coupling constants is especially excellent. The gamma-gauche effect is discussed.     

CO-releasing properties and anticancer activities of manganese complexes with imidazole/benzimidazole ligands

Carbon monoxide (CO) is an important signaling molecule which plays significant roles in the pathogenesis of cancer. CO is produced by enzymatic degradation of heme in mammals. Heme oxygenase 1 (HO-1) catalyzes the breakdown of heme into CO, ferrous iron, and biliverdin. CO induces HO-1 and inhibits cell proliferation. Cancer cells exposed to several stress factors (hypoxia, reactive oxygen species, cis-platin, and oxidative stress), and HO-1 displays cytoprotective role against oxidative stress and inhibits apoptosis, metastases, angiogenesis, and cell proliferation processes. Therefore, metal containing CO-releasing molecules (CORMs) have been designed as an effective cancer treatment strategy. CORMs are responsible for releasing controlled amounts of CO to cells and tissues. Thus, we synthesized [Mn(CO)₃(bpy)L]X manganese containing CORMs [bpy = 2,2′-bipyridine, X = hexafluorophosphate (PF₆), trifluoromethanesulfonate (OTf), L = imidazole, methylimidazole, benzimidazole, N-benzylbenzimidazole, N-(4-chlorobenzyl)benzimidazole] to release CO in human invasive ductal breast (MCF-7) cell line. In vitro experiments indicated that the compounds inhibited cell proliferation and exhibited cytotoxic effect on breast cancer cells. Moreover, side groups of the compounds enhanced the anticancer effects in MCF-7 cell line. These manganese containing CORMs gave promising results and may be used as a drug template for effective treatment of invasive ductal breast carcinoma.     

The Scaled Hermite–Weber Basis Still Highly Competitive

The effectiveness of the usual harmonic oscillator basis is demonstrated on a wide class of Schrödinger Hamiltonians with various spectral properties. More specifically, it is shown numerically that an appropriately scaled Hermite–Weber basis yields extremely accurate results not only for the energy eigenvalues which differ slighly from the harmonic oscillator levels, but also for the states which reflect a purely anharmonic character.     

Determination of novocaine in pharmaceutical preparations with novocaine(+)-selective membrane electrodes

Liquid-membrane ion-selective electrodes made with the ion-association complexes of novocaine with tetraphenylborate or dipicrylamine are proposed for use in the determination of novocaine by direct potentiometry or by potentiometric titration with sodium tetraphenylborate. The titration method is preferred, and the mean relative error for 4-12 mg of novocaine hydrochloride is 0.5%.     

Electrochemically controlled solid-phase microextraction (EC-SPME) based on overoxidized sulfonated polypyrrole

A method for the extraction and selective determination of cations is proposed using electro-synthesized overoxidized sulfonated polypyrrole film. The polymer film is used for the selective extraction of trace levels of nickel and cadmium ions by solid-phase microextraction (SPME). The cation uptake and release properties of the overoxidized sulfonated polypyrrole film electrode were examined under both open circuit and controlled potential conditions for prospective applications in electrochemically controlled solid-phase microextraction. Increased extraction efficiency and selectivity toward cations were achieved in high saline content of water. Simple preparation of film coatings on a platinum wire was possible using a constant potential method. Applied positive and negative potentials facilitated the extraction and desorption of cations, respectively. Nickel and cadmium ions were desorbed into sample aliquot and determined by electrothermal atomic absorption spectrometry (ETAAS). The cation uptake and release mechanism is affected both by the cation exchange at the negative sulfonate and carboxylate moiety on the film and the altered solution pH occurring at the counter electrode caused by the applied potential. The method was validated using a standard reference material and tested for the determination of cadmium ion in commercial table salt samples.     

The syntheses of some novel (naphthalen-1-yl-selenyl)acetic acid derivatives

Some new (naphthalen-1-yl-selenyl)acetic acids derivatives 7a-d have been synthesized by two different methods, using naphthylselenols or naphthylselenocyanates. The structures of the products were investigated by spectroscopic methods.