Traveling plane wave solutions of delayed lattice differential systems in competitive Lotka-Volterra type

99學年度楊定揮教師升等代表著作 100學年度研究獎補助論文[[abstract]]In this work we consider the existence of traveling plane wave solutions of systems of delayed lattice differential equations in competitive Lotka-Volterra type. Employing iterative method coupled with the explicit construction of upper and lower solutions in the theory of weak quasi-monotone dynamical systems, we obtain a speed, c *, and show the existence of traveling plane wave solutions connecting two different equilibria when the wave speeds are large than c *.[[incitationindex]]SCI[[booktype]]紙

Existence and Multiplicity of Traveling Waves in a Lattice Dynamical System

AbstractThis work proves the existence and multiplicity results of monotonic traveling wave solutions for some lattice differential equations by using the monotone iteration method. Our results include the model of cellular neural networks (CNN). In addition to the monotonic traveling wave solutions, non-monotonic and oscillating traveling wave solutions in the delay type of CNN are also obtained

An Application of Nash-Moser Theorem to Smooth Solutions of One-Dimensional Compressible Euler Equation with Gravity

We study one-dimensional motions of polytropic gas governed by the compressible Euler equations. The problem on the half space under a constant gravity gives an equilibrium which has free boundary touching the vacuum and the linearized approximation at this equilibrium gives time periodic solutions. But it is not easy to justify the existence of long-time true solutions for which this time periodic solution is the first approximation. The situation is in contrast to the problem of free motions without gravity. The reason is that the usual iteration method for quasilinear hyperbolic problem cannot be used because of the loss of regularities which causes from the touch with the vacuum. Interestingly, the equation can be transformed to a nonlinear wave equation on a higher dimensional space, for which the space dimension, being larger than 4, is related to the adiabatic exponent of the original one-dimensional problem. We try to find a family of solutions expanded by a small parameter. Applying the Nash-Moser theory, we justify this expansion.The application of the Nash-Moser theory is necessary for the sake of conquest of the trouble with loss of regularities, and the justification of the applicability requires a very delicate analysis of the problem

Travelling wave solutions for Kolmogorov-type delayed lattice reaction–diffusion systems

[[abstract]]This work investigates the existence and non-existence of travelling wave solutions for Kolmogorov-type delayed lattice reaction–diffusion systems. Employing the cross iterative technique coupled with the explicit construction of upper and lower solutions in the theory of quasimonotone dynamical systems, we can find two threshold speeds c∗ and c∗ with c∗≥c∗>0. If the wave speed is greater than c∗, then we establish the existence of travelling wave solutions connecting two different equilibria. On the other hand, if the wave speed is smaller than c∗, we further prove the non-existence result of travelling wave solutions. Finally, several ecological examples including one-species, two-species and three-species models with various functional responses and time delays are presented to illustrate the analytical results.[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SCI[[ispeerreviewed]]Y[[booktype]]紙本[[countrycodes]]GB

Infectious Alopecia in a Dog Breeder After Renal Transplantation

Tinea capitis rarely occurs in renal transplant recipients. We report this living-related renal transplant patient receiving cyclosporine-based therapy who initially presented with severe exfoliation of the scalp with yellowish-white scales and marked hair loss. The lesions extended to the frontal area and both cheeks, resulting in several skin ulcers with perifocal erythematous inflammatory changes, and palpable cervical lymph nodes. A biopsy of a skin lesion revealed fungal infection and culture yielded Microsporum canis. The patient mentioned an outbreak of ringworm in her breeding dogs during this period. After adequate treatment of the patient and her infected animals with griseofulvin and disinfection of the environment, her skin lesions resolved dramatically, with regrowth of hair

Reduced Ca2+ transport across sarcolemma but enhanced spontaneous activity in cardiomyocytes isolated from left atrium-pulmonary veins tissue of myopathic hamster

<p>Abstract</p> <p>Background</p> <p>Several lines of evidence point to a particularly important role of the left atrium (LA) in initiating and maintaining atrial fibrillation (AF). This role may be related to the location of pulmonary veins (PVs) in the LA. The aim of the present study was to investigate the action potential (AP) and ionic currents in LA-PV cardiomyocytes isolated from Bio14.6 myopathic Syrian hamsters (36-57 week-old) versus age-matched F1B healthy control hamsters.</p> <p>Methods and Results</p> <p>Whole-cell patch-clamp techniques were used to record AP in current-clamp mode and ionic currents in voltage-clamp mode. The results obtained show that in both healthy and myopathic LA-PV tissue spontaneously discharging cardiomyocytes can be found, but they are more numerous in myopathic (9/29) than in healthy hamsters (4/42, p < 0.05 by χ²analysis). Myopathic myocytes have shorter AP duration (APD) with smaller I_Ca,Land I_NCXthan the healthy control. The currents I_TO, I_K, I_K1and I_Ca,Tare not significantly different in myopathic versus healthy cells.</p> <p>Conclusions</p> <p>Our results indicate that in myopathic Syrian hamsters LA-PV cardiomyocytes are more prone to automatic rhythms. Also, they show altered electrophysiologic properties, which may be due to abnormal Ca²⁺channels and may account for contractile dysfunction.</p