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.     

Viscosity solutions to a Cauchy problem of a phase-field model for solid-solid phase transitions

We investigate a partial differential equation which models solid-solid phase transitions. This model is for martensitic phase transitions driven by configurational force and its counterpart is for interface motion by mean curvature. Mathematically, this equation is a second-order nonlinear degenerate parabolic equation. And in multidimensional case, its principal part cannot be written into divergence form . We prove the existence and uniqueness of viscosity solution to a Cauchy problem for this model.     

Nonlinear second order evolution inclusions with noncoercive viscosity term

In this paper we deal with a second order nonlinear evolution inclusion, with a nonmonotone, noncoercive viscosity term. Using a parabolic regularization (approximation) of the problem and a priori bounds that permit passing to the limit, we prove that the problem has a solution.     

拟变分包含与不动点问题公共解的迭代算法

By introducing the resolvent operator associated with a maximal monotone mapping, the author obtains a strong convergence theorem of a generalized iterative algorithm for a class of quasi-variational inclusion problems, which extends and unifies some recent results.     

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.     

Shallow water model for lakes with friction and penetration

We deduce a shallow water model, describ‐ ing the motion of the fluid in a lake, assuming inflow–outflow effects across the bottom. This model arises from the asymptotic analysis of the 3D dimensional Navier–Stokes equations. We prove the global in time existence result for this model in a bounded domain taking the nonlinear slip/friction boundary conditions to describe the inflows and outflows of the porous coast and the rivers. The solvability is shown in the class of solutions with L_p‐bounded vorticity for any given p∈(1,∞]. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Hybrid variable neighbourhood approaches to university exam timetabling

In this paper, we investigate variable neighbourhood search (VNS) approaches for the university examination timetabling problem. In addition to a basic VNS method, we introduce variants of the technique with different initialisation methods including a biased VNS and its hybridisation with a Genetic Algorithm. A number of different neighbourhood structures are analysed. It is demonstrated that the proposed technique is able to produce high quality solutions across a wide range of benchmark problem instances. In particular, we demonstrate that the Genetic Algorithm, which intelligently selects appropriate neighbourhoods to use within the biased VNS, produces the best known results in the literature, in terms of solution quality, on some of the benchmark instances. However, it requires relatively large amount of computational time. Possible extensions to this overall approach are also discussed.