Improved bounds for some nonstandard problems in generalized heat conduction

We consider the Maxwell-Cattaneo system of equations for generalized heat conduction where the temperature and heat flux satisfy a nonstandard auxiliary condition which prescribes a combination of their values initially and at a later time. We obtain L₂ bounds for the temperature and heat flux by means of Lagrange identities. These bounds extend the range of validity for the parameter in the nonstandard condition under a constraint on the coefficients in the differential equations.     

Sur les grands quotients partiels du développement en fraction continue

In this paper we obtain some metrics results about large partial quotients in the continued fraction expansion.     

Maximizing revenue in the airline industry under one-way pricing

The paper describes a methodology that has been implemented in a major British airline to find the optimal price to charge for airline tickets under one-way pricing. An analytical model has been developed to describe the buying behaviour of customers for flights over the selling period. Using this model and a standard analytical method for constrained optimization, we can find an expression for the optimal price structure for a flight. The expected number of bookings made on each day of the selling period and in each fare class given these prices can then be easily calculated. A simulation model is used to find the confidence ranges on the numbers of bookings and these ranges can be used to regulate the sale of tickets. A procedure to update the price structure based on the remaining capacity has also been developed.     

Depth profile analysis of polyimide film treated by potassium hydroxide

The structural change in the depth direction of a polyimide (UPILEX‐S) film treated in alkaline solution, which was a representative surface treatment used to form a seed layer for plating and to improve the adhesive strength, was analyzed by means of micro Fourier transform infrared attenuated total reflection (FTIR‐ATR) line analysis with gradient shaving preparation. The polyimide film was treated with KOH. The imide ring opened through the alkaline treatment, and the amide structure and carboxylic acid salt were formed. The attainment depth of this structural change was almost proportional to the treatment time, and it reached about 8 μm after a 30‐min treatment. The degree of structural change through the alkaline treatment was almost constant after it reached a considerably degraded stage, and the chemically changed region penetrated into the inner part of the film from the surface. An intermediate layer before the final degraded stage appeared in the treated layer, and its thickness increased with the treatment time. The region that was changed chemically by the alkaline treatment progressed to the inner part simultaneously and continuously as the treatment time increased. The combined use of gradient shaving preparation and micro FTIR‐ATR line analysis was found to be extremely effective for the depth profiling of organic materials. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2071–2078, 2003     

Dynamic mechanical thermal analysis transitions of partially and fully substituted cellulose fatty esters

The main transitions of cellulose fatty esters with different degrees of substitution (DSs) were investigated with dynamic mechanical thermal analysis. Two distinct main relaxations were observed in partially substituted cellulose esters (PSCEs). They were attributed to the glass‐transition temperature and to the chain local motion of the aliphatic substituents. The temperatures of both transitions decreased when DS or the number of carbon atoms (n) of the acyl substituent increased. Conversely, all the transitions of fully substituted cellulose esters occurred within a narrow temperature range, and they did not vary significantly with n. This phenomenon was explained by the formation of a crystalline phase of the fatty substituents. The presence of few residual OH groups in PSCEs was responsible for a large increase in the storage bending modulus, and it eliminated the effect of n on damping. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 281–288, 2003     

Properties of the Central Points in Linear Programming Problems

In this paper we list several useful properties of central points in linear programming problems. We study the logarithmic barrier function, the analytic center and the central path, relating the proximity measures and scaled Euclidean distances defined for the primal and primal–dual problems. We study the Newton centering steps, and show how large the short steps used in path following algorithms can actually be, and what variation can be ensured for the barrier function in each iteration of such methods. We relate the primal and primal–dual Newton centering steps and propose a primal-only path following algorithm for linear programming.     

Exact Solutions of Extended Boussinesq Equations

The problem addressed in this paper is the verification of numerical solutions of nonlinear dispersive wave equations such as Boussinesq-like system of equations. A practical verification tool for numerical results is to compare the numerical solution to an exact solution if available. In this work, we derive some exact solitary wave solutions and several invariants of motion for a wide range of Boussinesq-like equations using Maple software. The exact solitary wave solutions can be used to specify initial data for the incident waves in the Boussinesq numerical model and for the verification of the associated computed solution. The invariants of motions can be used as verification tools for the conservation properties of the numerical model.     

On the Representation of Band-Dominant Functions on the Sphere Using Finitely Many Bits

A band-dominant function on the Euclidean sphere embedded in R ^q+1 is the restriction to this sphere of an entire function of q+1 complex variables having a finite exponential type in each of its variables. We develop a method to represent such a function using finitely many bits, using the values of the function at scattered sites on the sphere. The number of bits required in our representation is asymptotically the same as the metric entropy of the class of such functions with respect to any of the L ^p norms on the sphere.     

Duality Principles in Frame Theory

Duality principles in Gabor theory such as the Ron–Shen duality principle and the Wexler–Raz biorthogonality relations play a fundamental role for analyzing Gabor systems. In this article we present a general approach to derive duality principles in abstract frame theory. For each sequence in a separable Hilbert space we define a corresponding sequence dependent only on two orthonormal bases. Then we characterize exactly properties of the first sequence in terms of the associated one, which yields duality relations for the abstract frame setting. In the last part we apply our results to Gabor systems.     

Nonlocality of Reaction-Diffusion Equations Induced by Delay: Biological Modeling and Nonlinear Dynamics

We present a short survey on the biological modeling, dynamics analysis, and numerical simulation of nonlocal spatial effects, induced by time delays, in diffusion models for a single species confined to either a finite or an infinite domain. The nonlocality, a weighted average in space, arises when account is taken of the fact that individuals have been at different points in space at previous times. We discuss and compare two existing approaches to correctly derive the spatial averaging kernels, and we summarize some of the recent developments in both qualitative and numerical analysis of the nonlinear dynamics, including the existence, uniqueness (up to a translation), and stability of traveling wave fronts and periodic spatio-temporal patterns of the model equations in unbounded domains and the linear stability, boundedness, global convergence of solutions and bifurcations of the model equations in finite domains.