On the number of vertices of given degree in a random graph

This note can be treated as a supplement to a paper written by Bollobas which was devoted to the vertices of a given degree in a random graph. We determine some values of the edge probability p for which the number of vertices of a given degree of a random graph G ∈ ??(n, p) asymptotically has a normal distribution.     

Structure and stereochemistry of lactames and cyclic imides: Part VI. The structure of reaction products of 2-methylglutarimide with phenyllithium

On the basis of spectral and X-ray analyses it is established that the reaction of phenyllithium with substituted glutarimide derivatives results in the open-chain amidoketone, which can be cyclised upon the dehydration.     

EPR study of the dinitrogen tetroxide dissociation in organic solvents

The dinitrogen tetroxide homolytical dissociation constants K _DIS are determined in organic solvents. The values are the highest in non-donor and the lowest in n-donor solvents. The variations of K _DIS with solvent are interpreted in terms of electron donor-acceptor interactions between dinitrogen tetroxide and electron donor molecules.     

On the fundamentals of extended thermodynamics (ET) of a one-dimensional rarefied gas

Extended thermodynamics (ET) of degreer for a one-dimensional rarefied gas based, by definition, on a finite set A^r={a⁰, a²,..., a^r} of the firstr–1(3r) direct internal moments of the one-point distribution functionf is carefully investigated. With the aid of the second axiom of thermodynamics, the new representation forf, depending in a local and nonlinear way onA ^r , is explicitly derived. It is demonstrated that in ET of degreer an infinite sequence {b^r+1, b^r+2,...} ofhigher order Hermite coefficients, which normally drops out of Grad's proposition forf fashioned by mathematical apparatus such as the Hermite polynomials, cannot be considered negligible in the case when nonlinear constitutive functions are established. Using Ma's kinetic equation corresponding to a one-dimensional rarefied gas as well as the generalized representation forf, collision productions in the nonconservative moment equations are then calculated for a special choice of the rate of collisions between particles.     

Ion transport across model lipid membranes containing light-harvesting complex II: an effect of light

The effect of light on proton transport across lipid membranes of small unilamellar liposomes containing incorporated major light-harvesting pigment-protein complex of Photosystem II (LHCII) has been studied with the application of pH-sensitive dyes entrapped inside vesicles. Proton permeability coefficient for LHCII-modified membranes was found to be about twice as high as in the case of the control pure lipid vesicles. Illumination of the samples with light absorbed by the LHCII-bound photosynthetic pigments considerably affects the kinetics of proton transport: it increases the rate and decreases the steady-state level of proton gradient across the membranes. The effect was interpreted in terms of heat-induced conformational changes of LHCII molecular structures that affect proton buffering capacity of this protein. Both the control and the LHCII-modified lipid membranes have been found to be practically impermeable to Ca(++) ions, as demonstrated by fluorescence of liposome-entrapped calcium-sensitive probe calcium crimson. The slight differences in the proton transport across the LHCII-containing membranes under the presence of Ca(++) suggest calcium binding to this antenna protein.     

On stability of the Cauchy equation on semigroups

Summary We say that Hyers's theorem holds for the class of all complex-valued functions defined on a semigroup (S, +) (not necessarily commutative) if for anyf:S such that the set {f(x + y) – f(x) – f(y): x, y S} is bounded, there exists an additive functiona:S for which the functionf – a is bounded.Recently L. Székelyhidi (C. R. Math. Rep. Acad. Sci. Canada8 (1986) has proved that the validity of Hyers's theorem for the class of complex-valued functions onS implies its validity for functions mappingS into a semi-reflexive locally convex linear topological spaceX. We improve this result by assuming sequential completeness of the spaceX instead of its semi-reflexiveness. Our assumption onX is essentially weaker than that of Székelyhidi. Theorem.Suppose that Hyers's theorem holds for the class of all complex-valued functions on a semigroup (S, +) and let X be a sequentially complete locally convex linear topological (Hausdorff) space. If F: S X is a function for which the mapping (x, y) F(x + y) – F(x) – F(y) is bounded, then there exists an additive function A : S X such that F — A is bounded.     

Possible role of hydrolytic enzymes (Sap,Kex2) in <Emphasis Type="Italic">Candida albicans</Emphasis> response to aromatic compounds bearing a sulfone moiety

Hydrolytic enzymes e.g., Saps and Kex2 are, due to their role in Candida virulence, considered important targets for new synthetic inhibitors. MICTI and MICPI values indicate that disruption of SAP1-3 significantly increases the resistance of Candida mutants to β-ketosulfone (1). Contrariwise, sap123Δ showed sensitive phenotype to halogenated methylphenyl sulfone (2). Anticandidal potency of 2 differed in the Candida cells of kex2Δ. Sulfone is the most effective agent against the Candida albicans kex2Δ double mutant (MICTI of 0.5 µg mL^?1). Up-regulation of KEX2 mediated the resistance of sap4-6Δ towards 2. Both sulfones tested reduced the adhesion of the wild type cells significantly (P ≤ 0.05). Contrariwise, sap123Δ showed significantly enhanced adhesion capability when 1 was used (P ≤ 0.05). Both sulfones had weak fungicidal effect on mature C. albicans biofilms. It was shown that the uptake of IP correlates with the membrane perturbations caused by 1 in the blastoconidial cells. Sulfones were found to disturb the basic developmental phases of biofilm growth: adhesion and morphogenesis. Altered KEX2 levels for 1 can be caused by the compensatory mechanism for the maintenance of cell wall integrity and morphogenesis. KEX2 decreases the antifungal activity of sulfones. Sulfones affecting the crucial virulence factors of Candida can even eliminate these fungal infections.     

Counting signed swallowtails of polynomial selfmaps of {\mathbb {R}^3}

For a generic \({f \in C^\infty({\mathbb {R}}^3,{\mathbb {R}}^3)}\), there is a discrete set of swallowtail critical points. At any swallowtail point p there exists a well-oriented coordinate system centred at p, and a coordinate system centred at f(p), such that locally f has the form \({f_\pm(x, y, z) = (\pm xy+x^2 z+x^4, y, z)}\), so one may associate with p a sign \({I(f, p) \in \{\pm 1\}}\). We shall show how to compute the number of swallowtail points having the positive/negative sign, in the case where \({f : {\mathbb {R}}^3 \rightarrow {\mathbb {R}}^3}\) is a polynomial mapping, in terms of signatures of quadratic forms.