Symmetric bi-derivations on prime and semi-prime rings

Summary LetR be a ring. A bi-additive symmetric mappingD(.,.): R × R R is called a symmetric bi-derivation if, for any fixedy R, a mappingx D(x, y) is a derivation. The purpose of this paper is to prove some results concerning symmetric bi-derivations on prime and semi-prime rings. We prove that the existence of a nonzero symmetric bi-derivationD(.,.): R × R R, whereR is a prime ring of characteristic not two, with the propertyD(x, x)x = xD(x, x), x R, forcesR to be commutative. A theorem in the spirit of a classical result first proved by E. Posner, which states that, ifR is a prime ring of characteristic not two andD ₁,D ₂ are nonzero derivations onR, then the mappingx D ₁(D ₂ (x)) cannot be a derivation, is also presented.     

Some remarks on derivations in Banach algebras and related results

Summary In the first section of this paper we consider some functional equations which are closely connected to derivations (i.e. additive mappings with the propertyD(ab) = aD(b) + D(a)b) on Banach algebras. IfD is a derivation on some algebraA, then the equationD(a) = – aD(a ^–1 )a holds for all invertible elementsa A. It seems natural to ask whether this functional equation characterizes derivations among all additive mappings. It is too much to expect an affirmative answer to this question in arbitrary algebras, since it may happen that even in normed algebras the group of all invertible elements contains only scalar multiples of the identity. We try to answer the question above in Banach algebras, since in Banach algebras invertible elements exist in abundance. In the second section of the paper we prove some results concerning representability of quadratic forms by bilinear forms.     

Thermal decomposition of N2H6GeF6 · H2O,isolation and characterization of intermediates

The thermal behaviour of N₂H₆GeF₆ · H₂O was investigated by TG, DTG and DTA measurements. The decomposition proceeded in three steps, in which anhydrous N₂H₆GeF₆ and N₂H₅GeF₅; were isolated and characterized by chemical analysis and vibrational spectroscopy. The X-ray powder photographs of the intermediates were indexed, namely, for N₂H₆GeF₆ on the basis of a monoclinic cell with a = 8.86(9), b = 9.29(2), c =7.40(0) Å, β = 85° and for N₂H₅GeF₅ on the basis of an ortrhorhombic cell with a = 8.43(5),b = 9.19(9), c = 7.43(6) Å.     

The stability of the exponential equation

We generalize the well-known Baker's superstability result for exponential mappings with values in the field of complex numbers to the case of an arbitrary commutative complex semisimple Banach algebra. It was shown by Ger that the superstability phenomenon disappears if we formulate the stability question for exponential complex-valued functions in a more natural way. We improve his result by showing that the maximal possible distance of an -approximately exponential function to the set of all exponential functions tends to zero as tends to zero. In order to get this result we have to prove a stability theorem for real-valued functions additive modulo the set of all integers .

     

Volumetric properties of ethanol–water mixtures under high temperatures and pressures

The densities of ethanol and ethanol–water mixtures were measured with a vibrating tube densimeter at 25.0, 50.0 and 75.0 °C in the pressure range from 0.10 to 40.00 MPa. Densities were correlated using an empirical model. Partial molar volumes, excess molar volumes, isothermal compressibilities, cubic expansion coefficients and internal pressures were calculated from obtained densities. This study reports the dependence of densities, partial molar volumes, excess molar volumes, isothermal compressibilities, cubic expansion coefficients and internal pressures on composition, temperature and pressure.     

Phase morphology of iPP/aPS/SEP blends

Supermolecular structure and phase morphology of the ternary isotactic polypropylene/atactic polystyrene/poly(styrene-b-ethylene-co-propylene) (iPP/aPS/SEP) compression molded blends with 100/0, 90/10, 70/30, and 50/50 iPP/aPS weight ratios and with different amounts of added SEP compatibilizer were studied by optical microscopy (OM), scanning electron microscopy (SEM), transmission electron microscopy (TEM), small-angle X-ray scattering (SAXS) and wide-angle X-ray diffraction (WAXD). SEP significantly reduced the size of dispersed aPS particles that enabled better spherulitization in the iPP matrix. Furthermore, iPP spherulites in ternary blends with 90/10 iPP/aPS weight ratio became larger in comparison with the pure iPP. TEM revealed that the SEP formed continuous interface layer around the dispersed aPS particles even when only 2.5 wt.% of SEP was added. Particle size distribution was distinctly bimodal. When the SEP content was increased to 10 wt.%, joining together smaller and bigger aPS and SEP particles formed dispersed aggregates. Additionally, both amorphous components (aPS and SEP) influenced crystallization process of iPP matrix and so modified, to some extent, its final supermolecular structure. SEP compatibilizer did not significantly affect crystallite orientation. The increase of crystallite sizes, which was more affected by the addition of aPS than by the addition of SEP, seemed to be influenced by the solidification effect rather than by the phase morphology of the blends.     

Local dissipation and coupling properties of cellular oscillators: a case study on calcium oscillations

Synchronised signal transduction between cells is crucial, since it assures fast and immutable information processing, which is vital for flawless functioning of living organisms. The question arises how to recognise the ability of a cell to be easily coupled with other cells. In the present paper, we investigate the system properties that determine best coupling abilities and assure the most efficient signal transduction between cells. A case study is done for intercellular calcium oscillations. For a particular diffusion-like coupled system of cellular oscillators, we determined the minimal gap-junctional permeability that is necessary for synchronisation of initially asynchronous oscillators. Our results show that dissipation is a crucial system property that determines the coupling ability of cellular oscillators. We found that low dissipation assures synchronisation of coupled cells already at very low gap-junctional permeability, whereas highly dissipative oscillators require much higher gap-junctional permeability in order to synchronise. The results are discussed in the sense of their biological importance for systems where the synchronous responses of cells were recognised to be indispensable for appropriate physiological functioning of the tissue.     

The Additive Influence of Propane-1,2-Diol on SDS Micellar Structure and Properties

Micellar systems are colloids with significant properties for pharmaceutical and food applications. They can be used to formulate thermodynamically stable mixtures to solubilize hydrophobic food-related substances. Furthermore, micellar formation is a complex process in which a variety of intermolecular interactions determine the course of formation and most important are the hydrophobic and hydrophilic interactions between surfactant–solvent and solvent–solvent. Glycols are organic compounds that belong to the group of alcohols. Among them, propane-1,2-diol (PG) is a substance commonly used as a food additive or ingredient in many cosmetic and hygiene products. The nature of the additive influences the micellar structure and properties of sodium dodecyl sulfate (SDS). When increasing the mass fraction of propane-1,2-diol in binary mixtures, the c.m.c. values decrease because propane-1,2-diol is a polar solvent, which gives it the ability to form hydrogen bonds, decreasing the cohesivity of water and reducing the dielectric constant of the aqueous phase. The values of ΔGm0 are negative in all mixed solvents according to the reduction in solvophobic interactions and increase in electrostatic interaction. With the rising concentration of cosolvent, the equilibrium between cosolvent in bulk solution and in the formed micelles is on the side of micelles, leading to the formation of micelles at a lower concentration with a small change in micellar size. According to the ¹H NMR, with the addition of propylene glycol, there is a slight shift of SDS peaks towards lower ppm regions in comparison to the D₂O peak. The shift is more evident with the increase in the amount of added propane-1,2-diol in comparison to the NMR spectra of pure SDS. Addition of propane-1,2-diol causes the upfield shift of the protons associated with hydrophilic groups, causing the shielding effect. This signifies that the alcohol is linked with the polar head groups of SDS due to its proximity to the SDS molecules.     

Mathematical modeling of the relation between myosin phosphorylation and stress development in smooth muscles

In this paper the 4-state latch bridge model proposed by Rembold and Murphy is expanded; first by incorporation of the analytical expression of Ca2+ dependent MLCK activation from the work of Kato et al. and second, by inclusion of the myosin dephosphorylation based on the Michaelis-Menten kinetics. The analysis of the proposed model and the comparison with the original model results as well as with the experimental data is presented. The model is able to predict the steady-state isometric stress and the myosin phosphorylation in dependence on steady cytosolic [Ca2+] as well as the temporal evolution of the system in dependence on the input Ca2+ signal in the form of biphasic transient, whereby our model results are in several aspects in better agreement with experimental observations.