A Lyapunov functional for a stage-structured predator–prey model with nonlinear predation rate

We consider the dynamics of a general stage-structured predator–prey model which generalizes several known predator–prey, SEIR, and virus dynamics models, assuming that the intrinsic growth rate of the prey, the predation rate, and the removal functions are given in an unspecified form. Using the Lyapunov method, we derive sufficient conditions for the local stability of the equilibria together with estimations of their respective domains of attraction, while observing that in several particular but important situations these conditions yield global stability results. The biological significance of these conditions is discussed and the existence of the positive steady state is also investigated.     

Dissipative Nonlinear Evolution Equations and Chaos

In this article we have studied the nonlinear interaction between ellipticity and dissipation in a set of model equations (1.1) and established the relation between this interaction and chaos. In addition to theoretical investigations, extensive numerical simulations with these equations have been made, and different routes to chaos have been found. The numerical studies have revealed the chaotic nature of the solutions.     

Volume contents

Volume Contents

Volume contents     

Translations and Associated Dirichlet Polyhedra in Complex Hyperbolic Space

We study a nonidentity transvection (i.e. (strictly) hyperbolic isometry) or nonidentity Heisenberg translation f of complex hyperbolic space H ⁿ and a Dirichlet polyhedron P of the cyclic group f. We have four main results: (a) If z & in H ⁿ and the axis of a nonidentity transvection are not complex collinear, then, roughly speaking, any two distinct 'naturally arising' geodesics passing through z are not complex collinear. (b) If g is also a transvection or Heisenberg translation of H ⁿ and z & in H ⁿ such that f(z)=g(z) and f ^–1(z)=g ^–1(z), then f=g. (c) We classify all this kind of polyhedra up to congruence in H ⁿ. (d) We obtain an equivalent condition for P to be cospinal (which means that the complex spines of the two sides of P coincide) in terms of the distance of the spines of the two sides of P.     

Determining optimal lot size for a two-warehouse system with deterioration and shortages using net present value

In this paper, we develop a deterministic inventory model for deteriorating items with two warehouses by minimizing the net present value of the total cost. Deterioration rates of items in the two warehouses may be different. In addition, we allow for shortages and complete backlogging. We then prove that the optimal replenishment policy not only exists but also is unique under some condition. Further, the result reveals that the reorder interval based on the average total cost, if it exists, must be longer than that derived using net present value. Finally, we use Yang’s [H.L. Yang, European Journal of Operational Research 157 (2004) 344–356] numerical example to illustrate the model and conclude the paper with suggestions for possible future research.     

Graft interpenetrating polymer networks of polyurethane and epoxy. I. mechanical behavior

Polyurethanes (PU) based on poly(butylene adipate) [PU(PBA)] and poly(oxypropylene) [PU(PPG)] polyols have bean introduced into the diglycidyl ether of bisphenol A (epoxy) to form interpenetrating polymer networks (IPNs) with a PU-grafted epoxy structure (graft-IPNs). The tensile strength in both PU(PPG)/epoxy and PU(PBA)/epoxy systems increases with increasing PU content. Maximum values emerge at PU/epoxy ratios between 19/81 and 27/73. This is explained as a result of the presence of the graft structure, which leads to more intimate interpenetration between the PU and epoxy in the graft-IPNs. Dynamic mechanical analysis (DMA) indicates that the PU introduced can be incorporated in either the α or β transition domain of the epoxy. The tensile strength of the resulting graft-IPNs shows a significant improvement as the PU is incorporated in the α transition domain of the epoxy. It is also noted that suitable amounts of PU incorporated in both the α and β transition domains of epoxy can increase the tensile strength of the IPNs, while excessive amounts of PU introduced into both α or β transition domains tend to decrease the tensile strength of the graft-IPNs.     

Thermomechanical behavior of underfill/solder mask/substrate interface under thermal cycling

With the increasing application of flip-chip technology in the microelectronics industry, the adhesion strength of interfaces in flip-chip microelectronic structures has become an important issue for manufacturing and operation. In this paper we present an experimental investigation of the adhesive strength of underfill material to solder mask coated FR-4 substrate under thermal cycling. The effects of the number of thermal cycles on interfacial strength were investigated by using the button shear test. The relationship between interfacial strength and the thickness of solder mask was also examined. Furthermore, the morphologies of fracture surfaces of the test specimens were analyzed by scanning electron microscopy. The results of this study show that the interfacial strength of the underfill/solder mask/substrate joint was significantly reduced by thermal fatigue. Finally, the degradation behavior and possible mechanisms were then determined on the basis of these observations.     

Effect of aniline formaldehyde resin on the conjugation length and structure of doped polyaniline: Spectral studies

A DBSA (n‐dodecylbenzene sulfate)‐complexed aniline formaldehyde [AF(DBSA)_1.0] was successfully synthesized with excess aniline (compared with formaldehyde) in the presence of n‐dodecylbenzene sulfonic acid (HDBSA), which was complexed with aniline monomer before polymerization. The resin was carefully characterized with ¹H and ¹³C NMR, electron spectroscopy for chemical analysis, and Fourier transform infrared and was demonstrated to be a polymer in which anilines were all complexed with HDBSA and became anilinium salts. A drastic decrease of the maximum absorption wavelength (ultraviolet–visible spectra) of DBSA‐doped polyaniline [PANI(DBSA)_0.5] was found when AF(DBSA)_1.0 was mixed, and this resulted from the reduced conjugation length. A similar effect on PANI(DBSA)_0.5 was found when free HDBSAs were mixed with PANI(DBSA)_0.5. Visual inspection with an optical microscope revealed that PANI(DBSA)_0.5/AF(DBSA)_1.0 gave uniform morphologies in various compositions, showing possible miscibility for this system. X‐ray diffraction patterns of PANI(DBSA)_0.5/AF(DBSA)_1.0 showed that the layered structure of PANI(DBSA)_0.5 was still present but became shorter in the polyblend because of the presence of AF(DBSA)_1.0. Solid‐state ¹³C NMR spectra revealed that the reduced conjugation length was derived from the interaction of alkyl groups between HDBSA, complexed DBSA, and dopant DBSAs. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3116–3125, 2005     

Synthesis of electroluminescent copoly(aryl ether)s containing alternate 1,4‐distyrylbenzene derivatives and aromatic 1,3,4‐oxadiazole or 3,3″‐terphenyldicarbonitrile segments

New copoly(aryl ether)s ( P1 – P3 ) containing alternate 2,5‐dihexyloxy‐1,4‐di(m‐ethoxystyryl)benzene ( P1 , P2 ) or 2,5‐dihexyloxy‐1,4‐distyrylbenzene ( P3 ) chromophores and aromatic 1,3,4‐oxadiazole ( P1 ) or 3,3″‐terphenyldicarbonitrile ( P2 , P3 ) segments were prepared by Horner reaction ( P1 and P2 ) or nucleophilic displacement reaction ( P3 ). They are basically amorphous materials with 5% weight‐loss temperature above 410 °C. Their absorption, photoluminescence spectra, and quantum yields are dependent on the composition of the isolated fluorophores. The emissions are exclusively dominated by 1,4‐distyrylbenzene segments via excitation energy transfer from electron‐transporting 1,3,4‐oxadiazole ( P1 ) or 3,3″‐terphenyldicarbonitrile ( P2 , P3 ) chromophores. The HOMO and LUMO energy levels have been estimated from their cyclic voltammograms, and the observations confirm that oxidation and reduction start from the emitting 1,4‐distyrylbenzene and electron‐transporting segments, respectively, indicating that both carriers affinity can be enhanced simultaneously. Among the two‐layer PLED devices (ITO/PEDOT/ P1 – P3 /Al), P1 exhibits the best performance with a turn‐on field of 4 × 10⁵ V/cm and a maximum luminance of 225 cd/m². However, P2 emits green–yellow light (555 nm), owing to the excimer emission. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5009–5022, 2005