On quadratic bond-order decomposition within molecular orbital space

A simple method of analysing and localization of canonical molecular orbitals for particular chemical bond using the MO-resolved bond-order decomposition scheme is presented. An alternative definition of classical bond order orbitals is provided and links to communication theory of the chemical bond are outlined and briefly discussed. The introduced procedure of decomposition of quadratic bond orders allows one to analyse two- as well as three- center chemical bonds within the framework of the same theory.     

Modified PZT ceramics as a material that can be used in micromechatronics

Results on investigations of the PZT type ceramics with the following chemical composition: Pb_0.94Sr_0.06(Zr_0.50 Ti_0.50)_0.99 Cr_0.01O₃ (PSZTC) which belongs to a group of multicomponent ceramic materials obtained on basis of the PZT type solid solution, are presented in this work. Ceramics PSZTC was obtained by a free sintering method under the following conditions: T _sint = 1250 °C and t _sint = 2 h. Ceramic compacts of specimens for the sintering process were made from the ceramic mass consisting of a mixture of the synthesized PSZTC powder and 3% polyvinyl alcohol while wet. The PSZTC ceramic specimens were subjected to poling by two methods: low temperature and high temperature. On the basis of the examinations made it has been found that the ceramics obtained belongs to ferroelectric-hard materials and that is why it may be used to build resonators, filters and ultrasonic transducers.     

Effect of Basic Amino Acids on Nickel Ion Reduction at a Mercury Electrode

In a 0.02 M borax solution (pH 8.5), basic amino acids (arginine, lysine, and ornithine) react with Ni²⁺ to form a mono‐ligand complex that is reduced at a mercury electrode at about ?0.85 V vs. Ag|AgCl|KCl (3 M). At a long time scale (staircase voltammetry; scan rate<50 mV s^?1), the complex reduction is a catalytic (EC′) process, the rate‐determining step being the regeneration of the reducible species by the reaction of the amino acid with free Ni²⁺. At a short time scale (differential pulse voltammetry or higher scan rate staircase voltammetry), the reaction rate is controlled by the diffusion of the complex. Although the same kind of complexation occurs with either basic amino acids or glycine, the last one does not induce a similar process. The peculiar effect of basic amino acids is due to the side chain that causes the ligand molecule to adopt a favorable orientation at the electrode surface. The differential pulse voltammetry peak current is proportional to the total amino acid concentration over the concentration range from 2 to 100 μM. Hence a voltammetric method for arginine determination in nutritional supplements was developed and validated using HPLC as reference method.     

Darwin and mass-velocity relativistic corrections in the non-Born-Oppenheimer calculations of pure vibrational states of H2

The Darwin and mass-velocity relativistic corrections have been calculated for all pure vibrational states of the H2 using the perturbation theory and very accurate variational wave functions obtained without assuming the Born-Oppenheimer (BO) approximation. Expansions in terms of explicitly correlated Gaussians with premultipliers in the form of even powers of the internuclear distance were used for the wave functions. With the inclusion of the two relativistic corrections to the non-BO energies the transition energies for the highest states agree more with the experimental results.     

PPh4]3[W(CN)7(O2)].4H2O as the representative of the [M(L)7(LL)] class for nine-coordinate complexes

The photoinduced dissociation of a W-CN bond in [W(CN)8]4- in an aqueous solution under ambient conditions, in conjunction with the uptake of molecular oxygen, affords the W(VI) mixed-ligand complex anion [W(CN)(7)(eta2-O2)]3-, conveniently isolable as its [PPh4+] salt. Although research into the chemistry of cyanomolybdates and cyanotungstates has been pursued with great interest and vigor over several decades, there is a paucity of structurally characterized cyano-peroxo complexes of Mo and W. The side-on coordination mode of the peroxo moiety in [W(CN)7(eta2-O2)]3- has been ascertained with X-ray crystal structure determination [d(O-O) = 1.41 A; peroxo bite angle: 41.0 degrees ] and corroborated with vibrational spectroscopy [nu(O-O) = 915 cm(-1)]. The complex ion exhibits trapezoidal tridecahedral geometry and represents the new class of nine-coordinate complexes with one bidentate and seven monodentate ligands. Cyclic voltammetry shows a reversible redox behavior of [W(CN)7(eta2-O2)]3- in CH3CN with its standard reduction potential equal to 1.130 V. Generally, interest in atmospheric oxygen derives from the versatility of this molecule as a ligand and oxidant and extends to the physicochemical features it imparts to transition metals such as copper and iron in biological oxygen carriers.     

Selfadjointness of Integral and Matrix Operators

Criteria for selfadjointness of integral operators, includingmatrix operators, based on our earlier domination results areestablished. The range of applicability is elucidated by carefullychosen examples, not covered by previously known criteria.     

Smoothing arithmetic error terms: the case of the Euler φ function

In many cases known methods of detecting oscillations of arithmetic error terms involve certain smoothing pro‐cedures. Usually an application of the smoothing operator does not change significantly the order of magnitude of the error under consideration. This is so for instance in the case of the classical error terms known in the prime number theory. The main purpose of this paper is to show that the situation for primes is not general. Considering the error term in the asymptotic formula for the Euler totient function we show that just one application of an integral smoothing operator changes situation dramatically: the order of magnitude of drops from x to √x (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Equations of motion from field equations and a gauge-invariant variational principle for the motion of charged particles

New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is proposed. It differs from the standard, gauge-dependent, first-order Lagrangian by boundary terms only. A new method of deriving equations of motion from field equations is developed. When applied to classical electrodynamics, this method enables us to obtain unambiguously the above, second-order Lagrangian from the general energy-momentum conservation principle.     

On unstable and unoptimal prediction

We consider the notion of prediction functions (or predictors) studied before in the context of randomness and stochasticity by Ko, and later by Ambos‐Spies and others. Predictor is a total computable function which tries to predict bits of some infinite binary sequence. The prediction error is defined as the limit of the number of incorrect answers divided by the number of answers given so far. We discuss indefiniteness of prediction errors for weak 1‐generics and show that this phenomenon affects certain c.e. sequences as well. On the other hand, a notion of optimal predictor is considered. It is shown that there is a sequence for which increasingly better predictors exist but for which no predictor is optimal.