Two-dimensional stability analysis in a HIV model with quadratic logistic growth term

We consider a Human Immunodeficiency Virus (HIV) model with a logistic growth term and continue the analysis of the previous article [6]. We now take the viral diffusion in a two-dimensional environment. The model consists of two ODEs for the concentrations of the target T cells, the infected cells, and a parabolic PDE for the virus particles. We study the stability of the uninfected and infected equilibria, the occurrence of Hopf bifurcation and the stability of the periodic solutions.Comment: To appear on Commun. Pure Appl. Ana

Rigorous derivation of the Kuramoto-Sivashinsky equation in a 2D weakly nonlinear Stefan problem

In this paper we are interested in a rigorous derivation of the Kuramoto-Sivashinsky equation (K--S) in a Free Boundary Problem. As a paradigm, we consider a two-dimensional Stefan problem in a strip, a simplified version of a solid-liquid interface model. Near the instability threshold, we introduce a small parameter $\varepsilon$ and define rescaled variables accordingly. At fixed $\varepsilon$, our method is based on: definition of a suitable linear 1D operator, projection with respect to the longitudinal coordinate only, Lyapunov-Schmidt method. As a solvability condition, we derive a self-consistent parabolic equation for the front. We prove that, starting from the same configuration, the latter remains close to the solution of K--S on a fixed time interval, uniformly in $\varepsilon$ sufficiently small

Double free boundary problem for defaultable corporate bond with credit rating migration risks and their asymptotic behaviors

In this work, a pricing model for a defaultable corporate bond with credit rating migration risk is established. The model turns out to be a free boundary problem with two free boundaries. The latter are the level sets of the solution but of different kinds. One is from the discontinuous second order term, the other from the obstacle. Existence, uniqueness, and regularity of the solution are obtained. We also prove that two free boundaries are $C^\infty$. The asymptotic behavior of the solution is also considered: we show that it converges to a traveling wave solution when time goes to infinity. Moreover, numerical results are presented

Stability analysis and Hopf bifurcation at high Lewis number in a combustion model with free interface

In this paper we analyze the stability of the traveling wave solution for an ignition-temperature, first-order reaction model of thermo-diffusive combustion, in the case of high Lewis numbers (${\rm Le} >1$). The system of two parabolic PDEs is characterized by a free interface at which ignition temperature $\Theta_i$ is reached. We turn the model to a fully nonlinear problem in a fixed domain. When the Lewis number is large, we define a bifurcation parameter $m=\Theta_i/(1-\Theta_i)$ and a perturbation parameter $\varepsilon= 1/{\rm Le}$. The main result is the existence of a critical value $m^c(\varepsilon)$ close to $m^c=6$ at which Hopf bifurcation holds for $\varepsilon$ small enough. Proofs combine spectral analysis and non-standard application of Hurwitz Theorem with asymptotics as $\varepsilon\to 0$

Working time dimensions and well-being : a cross-national study of Finnish and German health care employees

Health care professionals often face irregular working hours and high work pace. We studied associations of the five working time dimensions duration (weekly working hours), timing (shift work and weekend work), on-call work, working time autonomy, and work tempo (deadline and performance pressure) with well-being among health care employees in Finland and Germany. We used data on working time dimensions and indicators of well-being (work-life conflict, poor perceived health, sleep difficulties, and fatigue) from a cohort of 5050 hospital employees (Working Hours in the Finnish Public Sector Study 2015, WHFPS) and 1450 employees in the health care sector in Germany responding to the German BAuA-Working Time Survey in 2015 (BAuA-WTS). Findings from logistic regression analyses showed that high work tempo was associated with increased work-life conflict (WHFPS: odds ratio [OR] = 3.64, 95%CI 3.04-4.36 and BAuA-WTS: OR = 2.29, 95%CI 1.60-3.27), sleep difficulties (OR = 1.75, 95%CI 1.43-2.15 and OR = 1.33, 95%CI 1.03-1.71) and fatigue (OR = 2.13, 95%CI 1.77-2.57 and OR = 1.64, 95%CI 1.29-2.10) in both datasets. Weekend work was associated with increased work-life conflict (OR = 1.48, 95%CI 1.27-1.72 and OR = 1.61, 95%CI 1.12-2.32); and high working time autonomy with decreased work-life conflict (control over the timing of breaks: OR = 0.65, 95%CI 0.55-0.78 and OR = 0.52, 95%CI 0.33-0.81). The associations between other working time dimensions and well-being were less consistent. These results suggest that tight deadlines, performance pressure, weekend work and lack of working time autonomy are linked to impaired well-being among health care employees.Peer reviewe

Magneto-optics of massive Dirac fermions in bulk Bi2Se3

We report on magneto-optical studies of Bi2Se3, a representative member of the 3D topological insulator family. Its electronic states in bulk are shown to be well described by a simple Dirac-type Hamiltonian for massive particles with only two parameters: the fundamental bandgap and the band velocity. In a magnetic field, this model implies a unique property - spin splitting equal to twice the cyclotron energy: Es = 2Ec. This explains the extensive magneto-transport studies concluding a fortuitous degeneracy of the spin and orbital split Landau levels in this material. The Es = 2Ec match differentiates the massive Dirac electrons in bulk Bi2Se3 from those in quantum electrodynamics, for which Es = Ec always holds.Comment: 5 pages, 3 figures and Supplementary materials, to be published in Physical Review Letter

Childhood craniopharyngioma: greater hypothalamic involvement before surgery is associated with higher homeostasis model insulin resistance index

<p>Abstract</p> <p>Background</p> <p>Obesity seems to be linked to the hypothalamic involvement in craniopharyngioma. We evaluated the pre-surgery relationship between the degree of this involvement on magnetic resonance imaging and insulin resistance, as evaluated by the homeostasis model insulin resistance index (HOMA). As insulin-like growth factor 1, leptin, soluble leptin receptor (sOB-R) and ghrelin may also be involved, we compared their plasma concentrations and their link to weight change.</p> <p>Methods</p> <p>27 children with craniopharyngioma were classified as either grade 0 (n = 7, no hypothalamic involvement), grade 1 (n = 8, compression without involvement), or grade 2 (n = 12, severe involvement).</p> <p>Results</p> <p>Despite having similar body mass indexes (BMI), the grade 2 patients had higher glucose, insulin and HOMA before surgery than the grade 0 (P = 0.02, <0.05 and 0.02 respectively) and 1 patients (P < 0.02 and <0.03 for both insulin and HOMA). The grade 0 (5.8 ± 4.9) and 1 (7.2 ± 5.3) patients gained significantly less weight (kg) during the year after surgery than did the grade 2 (16.3 ± 7.4) patients. The pre-surgery HOMA was positively correlated with these weight changes (P < 0.03).</p> <p>The data for the whole population before and 6–18 months after surgery showed increases in BMI (P < 0.0001), insulin (P < 0.005), and leptin (P = 0.0005), and decreases in sOB-R (P < 0.04) and ghrelin (P < 0.03).</p> <p>Conclusion</p> <p>The hypothalamic involvement by the craniopharyngioma before surgery seems to determine the degree of insulin resistance, regardless of the BMI. The pre-surgery HOMA values were correlated with the post-surgery weight gain. This suggests that obesity should be prevented by reducing inn secretion in those cases with hypothalamic involvement.</p

Abe homotopy classification of topological excitations under the topological influence of vortices

Topological excitations are usually classified by the $n$th homotopy group $\pi_n$. However, for topological excitations that coexist with vortices, there are case in which an element of $\pi_n$ cannot properly describe the charge of a topological excitation due to the influence of the vortices. This is because an element of $\pi_n$ corresponding to the charge of a topological excitation may change when the topological excitation circumnavigates a vortex. This phenomenon is referred to as the action of $\pi_1$ on $\pi_n$. In this paper, we show that topological excitations coexisting with vortices are classified by the Abe homotopy group $\kappa_n$. The $n$th Abe homotopy group $\kappa_n$ is defined as a semi-direct product of $\pi_1$ and $\pi_n$. In this framework, the action of $\pi_1$ on $\pi_n$ is understood as originating from noncommutativity between $\pi_1$ and $\pi_n$. We show that a physical charge of a topological excitation can be described in terms of the conjugacy class of the Abe homotopy group. Moreover, the Abe homotopy group naturally describes vortex-pair creation and annihilation processes, which also influence topological excitations. We calculate the influence of vortices on topological excitations for the case in which the order parameter manifold is $S^n/K$, where $S^n$ is an $n$-dimensional sphere and $K$ is a discrete subgroup of $SO(n+1)$. We show that the influence of vortices on a topological excitation exists only if $n$ is even and $K$ includes a nontrivial element of $O(n)/SO(n)$.Comment: 36 pages, 12 figure