Studies on amine hydrothiocyanates. IV. Thermal decomposition studies using TG

The thermal decomposition of piperidine hydrothiocyanate, piperazine hydrothiocyanate, and the dihydrothiocyanates of ethylenediamine and 1,3-diaminopropane has been studied using TG. Piperidine hydrothiocyanate decomposes in a single step while the dihydrothiocyanates follow more complicated decomposition patterns yielding H₂S and half of the organic moiety first. The second step involves the loss of H₂S and the remainder of the organic moiety. In each case, complex polymeric materials result. Piperazine hydrothiocyanate also decomposes in two steps, the first involving the loss of half of the piperazine and the second involving the loss of piperazine and H₂S. Kinetic parameters have been determined for all these reactions.     

Mode of complement activation by acidic heteroglycans from the leaves of Artemisia princeps PAMP.

The mode of action of the anti-complementary acidic heteroglycans, AAF-IIb-2 and IIb-3 which consisted of rhamnogalacturonan core and arabinogalactan moieties, purified from the leaves of Artemisia princeps PAMP (Japanese name = Gaiyo) were investigated. The anti-complementary activities of AAF-IIb-2 and IIb-3 were reduced partially in the absence of Ca2+ ions. A marked consumption of C4 was observed to have occurred when serum was incubated with both polysaccharides in the presence of Ca2+ ions. AAF-IIb-2 showed more potent C4 consumption than IIb-3. After the incubation of the serum with AAF-IIb-2 in the absence of Ca2+ ions, a cleavage of C3 in the serum was detected by immunoelectrophoresis. AAF-IIb-2 showed more significant consumption of the complement than IIb-3 when rabbit erythrocytes were used in the assay system in the absence of Ca2+ ions. These results indicate that AAF-IIb-2 activates the complement via both the alternative and classical pathways, whereas IIb-3 mainly activates the complement via the classical pathway. The absorption of serum with Protein A-Sepharose results in a decrease of the activity of AAF-IIb-2 and IIb-3. However, the decrease of the activity was restored by the replacement of the immunoglobulin G (IgG) fraction after its recovery from the Protein A-Sepharose. These results suggest that IgG dependent mechanisms are both involved in the anti-complementary activity of AAF-IIb-2 and IIb-3.     

Hilbert重级数定理的一个改进

The object of this note is to prove the followingTheorem Let{a_n}and{b_n}be sequences of real numbers such that0<∑∑a_n~2<+∞and0<∑b_n~2<+∞.Then we have the inequalitysum from m=1 to∞sum from n=1 to∞a_mb_n/m+n<{sum from n=1 to∞(π-θ/n~(1/2)a_n~2}~1/2{sum from n=1 to∞(π-θ/n~(1/2)b_n~2}~1/2 (1)whereθ=3/2~(1/2)-1=1.121320343.     

On the connection of the superposition and homogeneous-solutions methods in wave propagation problems in a semi-infinite rigidly-clamped elastic layer

The process of harmonic wave propagation is investigated in a semi-infinite rigidly-clamped elastic layer. An analytic solution of the problem is obtained by the superposition method. The wave field expansion in the form of a normal mode series for a corresponding infinite waveguide is established. According to residue theory, the explicit form of the expansion coefficients is established with physical requirements of the radiation conditions taken into account.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 3–10, 1988.     

Affine-scaling for linear programs with free variables

The affine-scaling modification of Karmarkar's algorithm is extended to solve problems with free variables. This extended primal algorithm is used to prove two important results. First the geometrically elegant feasibility algorithm proposed by Chandru and Kochar is the same algorithm as the one obtained by appending a single column of residuals to the constraint matrix. Second the dual algorithm as first described by Adler et al., is the same as the extended primal algorithm applied to the dual.     

Design of neutral, mono- or di-cationic water-soluble trihydrazidophosphoradamantanes

The versatile behavior of a trihydrazidophosphoradamantane allowing the synthesis of a variety of neutral, mono- or di-cationic water-soluble molecules of potential interest for biphasic catalysis is reported.     

Piecewise-linearized methods for oscillators with limit cycles

A piecewise linearization method based on the linearization of nonlinear ordinary differential equations in small intervals, that provides piecewise analytical solutions in each interval and smooth solutions everywhere, is developed for the study of the limit cycles of smooth and non-smooth, conservative and non-conservative, nonlinear oscillators. It is shown that this method provides nonlinear maps for the displacement and velocity which depend on the previous values through the nonlinearity and its partial derivatives with respect to time, displacement and velocity, and yields non-standard finite difference formulae. It is also shown by means of five examples that the piecewise linearization method presented here is more robust and yields more accurate (in terms of displacement, energy and frequency) solutions than the harmonic balance procedure, the method of slowly varying amplitude and phase, and other non-standard finite difference equations.     

Continuum Limit of the Volterra Model, Separation of Variables and Non-Standard Realizations of the Virasoro Poisson Bracket

The classical Volterra model, equipped with the Faddeev-Takhtajan Poisson bracket provides a lattice version of the Virasoro algebra. The Volterra model being integrable, we can express the dynamical variables in terms of the so-called separated variables. Taking the continuum limit of these formulae, we obtain the Virasoro generators written as determinants of infinite matrices, the elements of which are constructed with a set of points lying on an infinite genus Riemann surface. The coordinates of these points are separated variables for an infinite set of Poisson commuting quantities including L ₀. The scaling limit of the eigenvector can also be calculated explicitly, so that the associated Schroedinger equation is in fact exactly solvable.