Thermolysis of Imidates: A New Method for the Generation of Carbonyl Ylides

Thermolysis of dimethyl 2‐[(3‐oxo‐3H‐isoindol‐1‐yl)oxy]malonate ( 8 ) promotes a [1,4]‐H shift in the imidic ? N?C? O? CH? fragment of the starting molecule, which leads to a reactive carbonyl ylide. This carbonyl ylide can be trapped by the C?N bond of imidates and imines, as well as the C?O bond of benzaldehyde. The corresponding cycloadducts 11, 14 , and 16 are formed regioselectively in good yields (60–95%) and with high stereoselectivity. In the case of 11 , the minor cycloadduct in solution undergoes an isomerization to give the more stable stereoisomer. The structures of two cycloadducts, i.e., 11a and 14a , have been established by X‐ray crystallography.     

Instability of axially symmetric equilibrium figures of a rotating, viscous, incompressible liquid

We prove that axially symmetric equilibrium figures of a uniformly rotating, viscous, incompressible liquid are unstable if the second variation of the energy functional takes negative values. Biblipgraphy: 14 titles. Dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya Published in Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 277–297.     

The Stokes Problem in a Ball and in the Exterior of a Ball

We analyze the formula for the solution to the Stokes problem in a ball and in the exterior of a ball which was derived in the previous paper by the author published in 2002. The main result is pointwise estimates for the kernels of potentials in this formula. Bibliography: 4 titles.     

On a certain nonstationary problem in a dihedral angle. II

An existence theorem is obtained for the initial-boundary value problem, considered in the previous paper, in the case of a positive parameter h in the boundary condition.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademiya Nauk SSSR, Vol. 188, pp. 178–185, 1991.     

Estimates of Solutions of the Second Initial Boundary-Value Problem for the Stokes System in the Spaces of Functions Having Hölder Continuous Derivatives with Respect to Spatial Variables

It is known that the solutions of parabolic initial boundary-value problems can be estimates in the Hölder norms with respect to the spatial variables for any fixed positive value of time in terms of similar norms of the data. We obtain estimate of this type for the solutions of nonstationary Stokes equations with stresses prescribed on the boundary. Bibliography: 12 titles.     

On the stability of uniformly rotating liquid in a weak magnetic field

We analyze the simplest free boundary problem of magnetohydrodynamics governing the evolution of an isolated mass of a viscous incompressible liquid in the presence of the magnetic field. The motion of the liquid is governed by the Navier–Stokes equations, and for the magnetic field we have the Maxwell equations with an excluded displacement current. The magnetic field should be determined not only in the domain filled with the liquid, but also in the surrounding vacuum region. On the free boundary of the liquid standard jump conditions for the magnetic field are prescribed, as well as kinematic and dynamic boundary conditions, where the magnetic stress tensor is taken into account. We prove that the solution corresponding to a rigid rotation of the fluid and to zero magnetic field is stable if the functional of potential energy has a positive second variation. Bibliography: 11 titles.     

Rationale of underwriters’ pricing conduct on competitive insurance market

Underwriters’ desire to show a good annual review is known to be a rationale of the aggressive pricing conduct. On the competitive insurance market, it impacts the global insurance processes and can lead to the competition-originated underwriting cycles. Applying Lundberg’s model of the annual probability mechanism of insurance, we model the influence of a price reduction on migration and consequently on the company’s annual expansion, revenue and solvency.     

On a theorem due to Crouzeix and Ferland

In this article we introduce the notions of Kuhn-Tucker and Fritz John pseudoconvex nonlinear programming problems with inequality constraints. We derive several properties of these problems. We prove that the problem with quasiconvex data is (second-order) Kuhn-Tucker pseudoconvex if and only if every (second-order) Kuhn-Tucker stationary point is a global minimizer. We obtain respective results for Fritz John pseudoconvex problems. For the first-order case we consider Fréchet differentiable functions and locally Lipschitz ones, for the second-order case Fréchet and twice directionally differentiable functions.