On variable stepsize Runge-Kutta approximations of a Cauchy problem for the evolution equation

We consider a Cauchy problem for the sectorial evolution equation with generally variable operator in a Banach space. Variable stepsize discretizations of this problem by means of a strongly A(φ)-stable Runge-Kutta method are studied. The stability and error estimates of the discrete solutions are derived for wider families of nonuniform grids than quasiuniform ones (in particular, if the operator in question is constant or Lipschitz-continuous, for arbitrary grids).     

Multinuclear magnetic resonance study of some mesoionic oxatriazoles containing nitrogenous exocyclic groups

¹H,¹³C,¹⁴N and¹⁵N NMR measurements are reported for four mesoionic 1-oxa-2, 3, 4-triazoles containing exocyclic nitrogenous groups. The NMR signal assignments are discussed and compared with those previously published for some corresponding oxatriazoles. The results obtained support the proposed cyclic mesoionic structures for the compounds studied. The questions of possible charge delocalization and valence tautomerism are addressed. Compound with N^– H as a exocyclic group (Fig. 1) is found to be relatively unstable, this is attributed to proton migration in the corresponding non-cyclic form of this molecule.Published in Khimiya Geterotsikiicheskikh Soedinenii, No. 9, pp. 1260–1263, September, 1995.     

Smooth Solutions to Optimal Investment Models with Stochastic Volatilities and Portfolio Constraints

   Abstract. This paper deals with an extension of Merton's optimal investment problem to a multidimensional model with stochastic volatility and portfolio constraints. The classical dynamic programming approach leads to a characterization of the value function as a viscosity solution of the highly nonlinear associated Bellman equation. A logarithmic transformation expresses the value function in terms of the solution to a semilinear parabolic equation with quadratic growth on the derivative term. Using a stochastic control representation and some approximations, we prove the existence of a smooth solution to this semilinear equation. An optimal portfolio is shown to exist, and is expressed in terms of the classical solution to this semilinear equation. This reduction is useful for studying numerical schemes for both the value function and the optimal portfolio. We illustrate our results with several examples of stochastic volatility models popular in the financial literature.     

Symmetries and conservation laws of Navier-Stokes equations

All the symmetries and conservation laws of Navier-Stokes equations are calculated.     

Magnetic Properties of Hf0.8Ta0.2（Fe0.97A0.03）2 （A=Al, Co, Mn） Systems

Moessbauer studies on the effect of substitution with 3% Al, Co, Mn atoms in the intermetallic compound of Hf0.8Ta0.2Fe2 are reported. The Al substitution leads to increase of the FM-AFM transition temperature and to decrease of the AFM-PM transition temperature. The Co substitution leads to disappearance of the FM state, only showing some FM impurity component, while Mn substituted compound indicates coexistence of FM and AFM states at low temperature. The phenomena imply complex itinerant electron properties in these magnetic systems.     

Function spaces over GO-spaces: Part I

We describe the structure of spaces of continuous step functions over GO-spaces. We establish a relation between the Dedekind completion of a GO-space L and properties of the space of continuous functions from L to 2 with finitely many steps. We use the established relation to prove that a countably compact GO-space L has Lindelöf Cp(L) iff the Dedekind remainder of L is Lindelöf and every compact subspace of L is metrizable. Or equivalently, a countably compact GO-space L has Lindelöf Cp(L) iff every compact subspace of L is metrizable and a Gδ-set in L. Other results are obtained.     

Copolymerization of N‐vinylcaprolactam and glycidyl methacrylate: Reactivity ratio and composition control

Free‐radical copolymerizations of N‐vinylcaprolactam (VCL) and glycidyl methacrylate (GMA) were investigated to synthesize temperature‐responsive reactive copolymers with minimized compositional heterogeneity. The average copolymer composition was determined by Fourier transform infrared and nuclear magnetic resonance techniques. The reactivity ratios for VCL and GMA were found to be 0.0365 ± 0.0009 and 6.44 ± 0.36 by the Fineman–Ross method and 0.039 ± 0.006 and 6.75 ± 0.29 by the Kelen–Tudos method, respectively. When prepared by batch polymerization, VCL–GMA copolymers had a highly heterogeneous composition and fractions of different solubilities in water. The use of a gradual feeding technique, which included the sequential addition of more reactive GMA monomer into the reaction, yielded copolymers with much more homogeneous composition. The produced copolymers with 0.9 and 0.11 fractional GMA contents preserved their temperature‐responsive properties and precipitated from aqueous solutions when the temperature exceeded 31 °C. The GMA units in the VCL–GMA copolymers were capable of reacting with amino end‐functionalized poly(ethylene oxide) at room temperature to produce poly(N‐vinylcaprolactam)–poly(ethylene oxide) graft copolymers. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 183–191, 2006