Sign changes of certain arithmetical function at prime powers

Czechoslovak Mathematical Journal - We examine an arithmetical function defined by recursion relations on the sequence {f(pk)}k∈? and obtain sufficient condition(s) for the sequence to...     

Parametric modeling of protein–DNA binding kinetics: A discrete event based simulation approach

To understand the stochastic behavior of biological systems, we adopt an “in silico” stochastic event based simulation methodology that can determine the temporal dynamics of different molecules. The main requirement for this technique is the event execution time models for the different biological functions of the system. This paper presents a parametric model to determine the execution time of one such biological function: protein–DNA binding. This biological function is modeled as a combination of microlevel biological events using a coarse-grained probability measure to estimate the stochastic parameters of the function. Our model considers the actual binding mechanism along with some approximated protein and DNA structural information. We use a collision theory based approach to transform the thermal and concentration gradients of this biological function into their corresponding probability measure. This information theoretic approach significantly removes the complexity of the classical protein sliding along the DNA model, improves the speed of computation and can bypass the speed-stability paradox. This model can produce acceptable estimates of DNA–protein binding time necessary for our event based stochastic system simulator where the higher order (more than second order statistics) uncertainties can be ignored. The results show good correspondence with available experimental estimates. The model depends very little on experimentally generated rate constants and brings the important biological parameters and functions into consideration. We also present some “in silico” results showing the effects of protein–DNA binding on gene expression in prokaryotic cells.     

Koplienko Trace Formula

Koplienko (Sib Math J 25(5): 735–743, 1984) gave a trace formula for perturbations of self-adjoint operators by operators of Hilbert–Schmidt class ${\mathcal{B}_2(\mathcal{H})}$ . Recently Gesztesy et?al. (Basics Z Mat Fiz Anal Geom 4(1):63–107, 2008) gave an alternative proof of the trace formula when the operators involved are bounded. In this article, we give a still another proof and extend the formula for unbounded case by reducing the problem to a finite dimensional one as in the proof of Krein trace formula by Voiculescu (On a Trace Formula of M. G. Krein. Operator Theory: Advances and Applications, vol. 24, pp. 329–332. Birkhauser, Basel, 1987), Sinha and Mohapatra (Proc Indian Acad Sci (Math Sci) 104(4):819–853, 1994).     

Differentiation of Operator Functions and Perturbation Bounds

Given a smooth real function f on the positive half line consider the induced map on the set of positive Hilbert space operators. Let f ^(k<) /E5> be the k ^th derivative of the real function f and >E5>D ^k f the k ^th Fréchet derivative of the operator map f. We identify large classes of functions for which , for k= 1,2,... . This reduction of a noncommutative problem to a commutative one makes it easy to obtain perturbation bounds for several operator maps. Our techniques serve to illustrate the use of a formalism for “quantum analysis” that is like the one recently developed by M. Suzuki. Received: 4 April 1997 / Accepted: 28 May 1997     

Kinetics of Oxidation of Phosphinic, Phenylphosphinic and Phosphorous Acid by Benzyltrimethylammonium Chlorobromate

The oxidation of lower phosphorus oxyacids by benzyltrimethylammonium chlorobromate (BTMACB) proceeds by a mechanism involving a hydride-ion transfer from oxyacids to the oxidant in the rate-determining step.     

Field-cooled measurements of harmonic generation in magnetization of high-T c superconductors

We present measurements of harmonic generation in the magnetization of sintered pellets of YBa₂Cu₃O₇ and Bi_1.7Pb_0.3Sr₂Ca₂Cu₃O₁₀ as a function of DC field. The DC field is applied in the field-cooled mode. Measurements are made at 77 K for various values of the AC field amplitude. A comparison is made with calculations done within the critical state model.     

Kinetics and mechanism of the oxidation of neutralized α-hydroxy acids by tris(pyridine-2-carboxylato)manganese(III)

The kinetics of oxidation of the neutralized -hydroxy acids: lactic, -hydroxyisobutyric, mandelic, benzilic and atrolactic acids by tris(pyridine-2-carboxylato)manganese(III) have been studied. The reactions were carried out in a Na(pic)-picH [Na(pic) = sodium salt of pyridine-2-carboxylic acid and picH = pyridine-2-carboxylic acid] buffer medium in the 4.89–6.10pH range. The oxidation rate was found to be independent of pH, and rate follows the order: benzilate > mandelate >atrolactate>lactate > -hydroxy isobutyrate. The oxidation products are MeCHO, Me2CO, PhCHO, Ph2CO and PhCOMe for the respective reactions. A mechanism is proposed involving intermediate formation of hepta-coordinated MnIII complexes in a fast step. The complexes then decompose to give free radicals and MnII in the rate determining step. The free radicals subsequently react with another molecule of the MnIII species to give the respective carbonyl compounds in a fast step.     

Relative reactivities of 1,2-dicarbonyl compounds towards permanganate in ethanoic acid medium. Mechanism of the oxidation processes

The oxidative behaviour of the 1,2-dicarbonyl compounds, viz., glyoxal, biacetyl and benzil, towards permanganate in ethanoic acid medium in the presence of HClO₄ has been investigated. The reaction is first order with respect to MnO^– ₄, substrate, as well as H⁺. The rate decreases with an increase in ionic strength. Different thermodynamic parameters have been evaluated. The protonated dialdehyde or diketone reacts with permanganate ion to form an intermediate ester which decomposes in a slow step to produce the corresponding carboxylic acid via C—C bond cleavage.     

Experimental Determination of Third Derivative of the Gibbs Free Energy, <Emphasis Type=Italic>G</Emphasis> II: Differential Pressure Perturbation Calorimetry

We have been evaluating third derivative quantities of the Gibbs free energy, G, by graphically differentiating the second derivatives that are accessible experimentally, and demonstrated their power in elucidating the mixing schemes in aqueous solutions. Here we determine directly one of the third derivatives of G, the partial molar entropy-volume cross fluctuation density of 2-butoxyethanol (BE) in the BE–H₂O system, ^SV δ _BE . The difference of the heats of compression were directly determined using two identical cells and applying the same pressure change to both cells concurrently. Both cells are filled with sample solutions having a small appropriate difference in mole fraction. The results indicated that this method is feasible with the prior knowledge of the thermal expansivity of the solution to within a few per cent accuracy. If the volumes of the two cells are identical within the order of 0.01%, the method provides the required results to within 0.1% without the thermal expansivity data. This success opens a possibility of evaluating the fourth derivative graphically, which is expected to provide much more detailed information about the molecular processes in aqueous solutions.     

A Thermally Induced Low-temperature Intramolecular Redox Reaction of bis(pyridine)silver(I) Permanganate and its hemipyridine Solvate

Among the known three pyridine complexes of silver permanganate, i.e. [Agpy₂]MnO₄ (1), [Agpy_2.25]MnO₄ or 7[Agpy₂]MnO₄[Agpy₄]MnO₄ (2) and [Agpy₂]MnO₄0.5py (3), compounds (1) and (2) were studied by means of thermal analysis and TG-MS methods. Presuming identical structural motifs for the Agpy₂MnO₄ blocks in (1) as it has been found in its solvate (3) by single-crystal diffraction, α-C–H...O–Mn H-bonded structures are responsible for a thermally induced low-temperature intramolecular redox reaction observed for the first time between the [Agpy₂]⁺ cation and permanganate anion.