Lack of dissipativity is not symplecticness

We show that, when numerically integrating Hamiltonian problems, nondissipative numerical methods do not in general share the advantages possessed by symplectic integrators. Here a numerical method is called nondissipative if, when applied with a small stepsize to the test equationdy/dt = img src="/content/j040852nn584g078/xxlarge955.gif" alt="lambda" align="BASELINE" BORDER="0">y, mg src="/content/j040852nn584g078/xxlarge955.gif" alt="lambda" align="BASELINE" BORDER="0"> real, has amplification factors of unit modulus. We construct a fourth order, nondissipative, explicit Runge-Kutta-Nyström procedure with small error constants. Numerical experiments show that this scheme does not perform efficiently in the numerical integration of Hamiltonian problems.This research has been supported by project DGICYT PB92-254.     

Thermodynamic properties of the spin-Peierls transition in CuGeO3

We present an investigation of the spin-Peierls transition atT _SP=14.5 K in polycrystalline CuGeO₃ through specific-heat and thermal-expansion measurements. Clear second-order phase-transition anomalies are found in both properties atT _SP, although only a small entropy of Smg src="/content/v01k5l8g84314342/xxlarge8776.gif" alt="ap" align="MIDDLE" BORDER="0">0.1 Rmg src="/content/v01k5l8g84314342/xxlarge8467.gif" alt="ell" align="BASELINE" BORDER="0">n2 is released at the transition. Most of the entropy is released atT _SP<T<150 K, where the temperature dependence of the magnetic contribution to the specific heat as well as the thermal expansion exhibit extrema atT ^*mg src="/content/v01k5l8g84314342/xxlarge8776.gif" alt="ap" align="MIDDLE" BORDER="0">40 K. These are caused by one-dimensional antiferromagnetic fluctuations along the Cu chains, possibly accompanied by structural fluctuations. Using Ehrenfest's relation, a hydrostatic pressure coefficient (mg src="/content/v01k5l8g84314342/xxlarge8706.gif" alt="part" align="MIDDLE" BORDER="0">T _SP/mg src="/content/v01k5l8g84314342/xxlarge8706.gif" alt="part" align="MIDDLE" BORDER="0">_p)_{pmg src="/content/v01k5l8g84314342/xxlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0">0} mg src="/content/v01k5l8g84314342/xxlarge8776.gif" alt="ap" align="MIDDLE" BORDER="0"> (0.45&amp;plusmn;0.06) K/kbar is derived.     

On input/output stabilization of singular integrodifferential systems

In this paper we consider a class of systems described by singular integrodifferential equations. This type of systems appear, for example, in the modeling of certain aeroelastic control problems. We study these systems in frequency domain framework and show the existence of finite-dimensional stabilizing controllers. An algorithmic procedure is outlined for the construction of such controllers. In order to illustrate the numerical aspects of this algorithm, we present an example involving the classical Theodorsen model of an airfoil, which fits in the class of systems considered here.This work was supported in part by the National Science Foundation under Grants DMS-8907019 and MSS-9203418.     

Pattern transfer and photoluminescence damage assessment of deep-submicrometer features etched by photon-induced cryoetching

We present a study of pattern-transfer and etch-induced damage in photon-induced cryoetching. Features with effective radii as small as mg src="/content/p22r02h202665621/xxlarge8776.gif" alt="ap" align="MIDDLE" BORDER="0"> 100 nm have been formed in both bulk and layered GaAs/AlGaAs materials. A measurement of the photoluminescence of etch-defined deep- submicrometer structures material suggests that this form of etching results in minimal process-induced damage. Modeling of the luminescence vs feature size for these features shows that the luminescence is limited only by carrier diffusion and non-radiative surface recombination.     

The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2mg alt="urn:x-wiley:09425616:media:MALQ19960420133:tex2gif-sup-1" loading="lazy" class="section_image" src="/cms/asset/8a8423e8-cbcf-4f3b-b48e-d1ff7cdfbd39/tex2gif-sup-1.gif"> and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25.     

Composition and properties of freeze-dried products of nicotinic acid withβ-cyclodextrin and heptakis (2,6-0-dimethyl)-β-cyclodextrin

The purpose of the study was to examine the formation of inclusion compounds in the freeze-dried products obtained from aqueous solutions of nicotinic acid and mg src="/content/ug1mw776823m9886/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin (mg src="/content/ug1mw776823m9886/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-CD), or heptakis (2,6-0-dimethyl)-mg src="/content/ug1mw776823m9886/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin (DIMEB). The molar ratios used were 1:1 and 2:1. In addition two freezing temperatures (&amp;#x2013;40 and &amp;#x2013;196&amp;deg;C) and different secondary drying temperatures (+50 and +80&amp;deg;C) were used. Freeze-dried products with mg src="/content/ug1mw776823m9886/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-CD obtained after low temperature freezing are of the same crystallographic structure as seen in a pure inclusion compound prepared by coprecipitation. Amorphous products were formed after fast freezing. The molar ratios of included nicotinic acid in the freeze-dried products vary &amp;#x2014; dependent on the preparation conditions &amp;#x2014; between 0.75:1 and 1:1. A factorial design proves that the included drug amount can be increased by enhancement of the amount of nicotinic acid used, by faster freezing, and by the combination of these two factors. The proof of inclusion formation was given by a combination of X-ray diffractography, differential scanning calorimetry, thermogravimetry and thermofractography.The freeze-dried preparations obtained with DIMEB were amorphous mixtures of the two components. No proof for inclusion of the nicotinic acid in the cyclodextrin cavity could be given. Higher (&amp;#x2013;40&amp;deg;C) or lower (&amp;#x2013;196&amp;deg;C) freezing temperatures and the running of the secondary drying process could not influence these results. The very low stability constant of the complex and steric reasons are responsible for this behavior.     

K3 et formules de Riemann-Hurwitzp-adiques

The well-known formula of Riemann-Hurwitz gives the change of genuses in ann-fold covering of compact connected Riemann surfaces. In Iwasawa theory, there existp-adic analogues which give the change of certain mg src="/content/n567m35412435821/xxlarge955.gif" alt="lambda" align="BASELINE" BORDER="0">^&amp;plusmn;-invariants in ap-extension ofCM number fields. Using functorial and arithmetical properties ofK ₃, we extend such Riemann-Hurwitzp-adic formulas to non-CM fields, assuming some restrictive hypotheses on the capitulation ofK ₂.

     

Macrocycle opening in crown ethers

Macrocycle opening in derivatives of benzocrown ethers under the action of amines is affected by the nature of the heteroatoms in the macrocycle, the nature of the functional group in the benzene ring of the crown ether, and the length, branching, and number of hydrocarbon radicals at the amine nitrogen atom. A distinguishing feature of this reaction is the template effect of MeNH₃ ⁺, Me₂NH₂ ⁺, Na⁺, and K⁺ ions.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 687&amp;#x2013;692, March, 1996.For Part I see Ref. 1.     

Synthese und Geruch von Tricyclo[6.2.2.02, 7]dodecan-Derivaten

Summary The acetale-ketone9 was synthesized as precursor for the preparation of mg src="/content/m7871j3141t3w137/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-santalol derivatives posessing a bicyclo[2.2.2]octane nucleus. After methylenation of the keto-group the subsequent acidic hydrolysis of the acetal leads via a Prins reaction of the liberated aldehyde with the methylene group to tricyclo[6.2.2.0^{2, 7}]dodecane derivatives. Their olfactory properties are described.

     

Chemical applications of group theory and topology

The following procedure is described for investigating the qualitative dynamics of simple chemical systems: 1) A so-called influence diagram is generated representing the relationships between the reference reactants (phase-determining intermediates); 2) This influence diagram is used to generate a mg src="/content/j806m481q444068p/xxlarge8220.gif" alt="ldquo" align="MIDDLE" BORDER="0">truth tablemg src="/content/j806m481q444068p/xxlarge8221.gif" alt="rdquo" align="MIDDLE" BORDER="0"> indicating possible transitions between state vectors representing the signs of the time derivatives of of the reference reactant concentrations; 3) The truth table is used to determine a state transition diagram representing the flow topology around unstable equilibrium points; 4) The characteristic equation of the adjacency matrix of the influence diagram is solved in order to determine the presence of such unstable equilibrium points. The two types of qualitative dynamics possible for chemical systems containing two reference reactants and one feedback circuit are bifurcation between two attracting regions (bistability) and limit cycle oscillation. However, in two reference reactant systems oscillation requires an additional self-activating loop to generate the unstable equilibrium point required for its realization. Bistability and limit cycle oscillation are also two of the possible types of qualitative dynamics for chemical systems containing three reference reactants. However, chemical systems with three reference reactants and two or more feedback circuits can also contain interlocking limit cycles, which can lead to toroidal oscillations or chaos. The influence diagrams are given for the systems exhibiting these various types of dynamic behavior along with a summary of the important properties of all 729 possible influences for simple chemical systems containing three reference reactants.