Evolution of hypersurfaces in \Bbb RN {\Bbb R}^N by Gaussian curvature

In this paper we first prove short time existence of a classical solution for the problem which describes the evolution by Gaussian curvature of a strictly convex hypersurface in . Then we give a proof of the existence of a viscosity solution for this problem in such a way as to define a generalized motion existing for each time. Received November 24, 1997     

Lyapunov, Opial and Beesack inequalities for one-dimensional p(t)-Laplacian equations

We generalize the classical Lyapunov, Opial and Beesack inequalities for one-dimensional differential equations to nonstandard growth p(t)-Laplacian.     

Physicochemical Characterization of Two Polysulfon-Amides in Dilute Solution

Summary: As one class of high temperature resistant aromatic polymers, polysulfonamides (PSA) are widely used in industry, physicochemical properties and conformation in solution have not been disclosed yet. In this work, the dilute solution behaviour of poly(m-diphenylsulphone terephthal amide) (m-PSA) was investigated by laser light scattering (LLS) and viscometry. The results showed that the m-PSA exists as single chains both in dimethylsulfoxide (DMSO) and dimethylformamide (DMF). The value of radius of gyration to hydrodynamic radius (s/R_h) indicats that the m-PSA has a random coil conformation in solution. Both the persistence length a and the characteristic ratio C_∞ indicate that the m-PSA chain is flexible in solution. The Mark-Houwink equation of m-PSA in DMSO was determined as [η] = 1.62 × 10⁻⁵M, and the exponent of 0.87 supports the assumption that m-PSA forms random coils in DMSO-solution at 25 °C. It was found that the flexibility of the PSA was affected when 4,4'-diphenylsulphone terephthalamide monomer was incorporated in backbone. The PSA random copolymer (r-PSA) with a comonomer ratio of 3:1 (4,4′-diaminodiphenyl- sulfone to 3,3′-diaminodiphenylsulfone) also had a random coil conformation in DMF; the rigidity increased, while the mobility of the chain was maintained.     

VISCOSITY SOLUTIONS OF HJB EQUATIONS ARISING FROM THE VALUATION OF EUROPEAN PASSPORT OPTIONS

The passport option is a call option on the balance of a trading account. The option holder retains the gain from trading, while the issuer is liable for the net loss. In this article, the mathematical foundation for pricing the European passport option is established. The pricing equation which is a fully nonlinear equation is derived using the dynamic programming principle. The comparison principle, uniqueness and convexity preserving of the viscosity solutions of related H J13 equation are proved. A relationship between the passport and lookback options is discussed.     

A unified analysis for the single-machine scheduling problem with controllable and non-controllable variable job processing times

We present a unified analysis for single-machine scheduling problems in which the actual job processing times are controlled by either a linear or a convex resource allocation function and also vary concurrently depending on either the job’s position in the sequence and/or on the total processing time of the already processed jobs. We show that the problem is solvable in O(nlogn)$O(n\log n)$ time by using a weight-matching approach when a convex resource allocation function is in effect. In the case of a linear resource allocation function, we show that the problem can be solved in O(n³)$O(n^3)$ time by using an assignment formulation. Our approach generalizes the solution approach for the corresponding problems with controllable job processing times to incorporate the variability of the job processing times stemming from either the job’s position in the sequence and/or the total processing time of the already processed jobs.     

Vanishing vertical limit of the incompressible combined viscosity and magnetic diffusion magnetohydrodynamic system

In this paper, we consider the incompressible combined viscosity and magnetic diffusion magnetohydrodynamic system with Dirichlet boundary condition in a half space of . We establish the asymptotic expansions of this system by multiscale analysis and obtain the horizontal alone viscosity and magnetic diffusion magnetohydrodynamic equations and the boundary layer equations. And then we study the well‐posedness of the 2 equations. At last, we get the vanishing limit when the vertical viscosity and magnetic diffusion coefficient tends to zero.     

Global well‐posedness for the 2D Boussinesq system with variable viscosity and damping

In this paper, we consider the 2D Boussinesq system with variable kinematic viscosity in the velocity equation and with weak damping effect to instead of the regularity effect for the thermal conductivity. Even if without thermal diffusion in the temperature equation, we establish the global well‐posedness for the 2D Boussinesq system with general initial data.     

Sintering Aerogels

Studies of the densification kinetics and structural evolution of non-crystalline aerogels during sintering are examined in light of theory. In most respects, the theory of viscous sintering is capable of quantitatively accounting for the experimentally observed behavior, as long as the initial pore size distribution is known. Unfortunately, it is difficult to obtain adequate structural information; in particular, measurements using nitrogen desorption and thermoporometry often erroneously indicate the presence of macroporosity. Some authors have claimed that large pores contract more quickly than small pores during sintering; under certain circumstances this is predicted by the theory.