Differential as a harmonic morphism with respect to Cheeger–Gromoll-type metrics

We investigate horizontal conformality of a differential of a map between Riemannian manifolds, where the tangent bundles are equipped with Cheeger–Gromoll-type metrics. As a corollary, we characterize the differential of a map as a harmonic morphism.     

Fekete-Szegö problem for close-to-convex functions with respect to a certain convex function dependent on a real parameter

Given α ∈ [0, 1], let h _α (z):= z/(1 - αz), z ∈ D:= {z ∈ D: |z| < 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to h _α if there exists δ ∈ (-π/2, π/2) such that Re{e^iδ zf′(z)/h _α (z)} > 0, z ∈ D. For the class ? (h _α ) of all close-to-convex functions with respect to h _α , the Fekete-Szegö problem is studied.     

Remarks on a parameter estimation for von Mises–Fisher distributions

We point out an error in the proof of the main result of the paper of Tanabe et al. (Comput Stat 22:145–157, 2007) concerning a parameter estimation for von Mises–Fisher distributions, we correct the proof of the main result and we present a short alternative proof.     

Cartan–Eilenberg complexes with respect to cotorsion pairs

Let ${(\mathcal{A}, \mathcal{B})}$ be a cotorsion pair in R-Mod. We introduce and study the notion of Cartan–Eilenberg- ${\mathcal{A}}$ complexes. Specifically, we establish some relationships between Cartan–Eilenberg- ${\mathcal{A}}$ complexes and DG- ${\mathcal{A}}$ complexes. Using these relationships, some applications are given.     

Leray–Hopf solutions to a viscoelastoplastic fluid model with nonsmooth stress–strain relation

We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba–Jaumann derivative. Moreover, the stress tensor obeys a nonlinear and nonsmooth dissipation law as well as stress diffusion. We prove the existence of global-in-time weak solutions satisfying an energy inequality under general Dirichlet conditions for the velocity field and Neumann conditions for the stress tensor.     

Periodic solutions to a delayed predator–prey model with Hassell–Varley type functional response

In this paper, a delayed predator–prey model with Hassell–Varley type functional responses is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions to it by applying the coincidence degree theorem. It is interesting that the result is based on the delay, which is different from the previous work (the results are delay-independent). Furthermore, the simulation shows that some conditions are sharp.     

On solutions to a FitzHugh–Rinzel type model

Ricerche di Matematica - A ternary autonomous dynamical system of FitzHugh–Rinzel type is analyzed. The system, at start, is reduced to a nonlinear integro differential equation. The...     

On the conditional expectation with respect to a sequence of independent σ-fields

Summary In the paper we characterize those sequences of random variables which are conditional expectations of a p-integrable random variable with respect to a given sequence of independent -fields.     

Pattern dynamics in a Gierer–Meinhardt model with a saturating term

Gierer–Meinhardt system is a typical mathematical model to describe chemical and biological phenomena. In this paper, the Gierer–Meinhardt model with a saturating term is considered. By the linear stability analysis, we find the parameter area where possible Turing instability can occur. Then the multiple scales method is applied to obtain the amplitude equations at the critical value of Turing bifurcation, which help us to derive parameter space more specific where certain patterns such as spot-like pattern, stripe-like pattern and the coexistence pattern will emerge. Furthermore, the numerical simulations provide an indication of the wealth of patterns that the system can exhibit and the two-dimensional Fourier transform by the image processing interface of GUI from Matlab enables us to gain intensive understanding of these patterns. Besides, the interesting patterns including labyrinthine-like patterns are also numerically observed. All the results obtained reveal the mechanism of morphogenetic processes in adult mesenchymal cells. The patterns obtained corresponding to the patterns induced by morphogens in the vascular mesenchymal cells may play a role in atherosclerotic vascular calcification.     

Stability of a predator–prey model with refuge effect

We consider a predator–prey model, where some prey are completely free from predation within a temporal or spacial refuge. The most common type of spacial refuge, that we investigate here, takes the form where a constant proportion of the prey population is protected. The model is a modification of the classical Nicholson–Bailey host-parasitoid model. In this paper, we study the effect of the presence of refuge on the stability and bifurcation of the system. Moreover, we provide a detailed analysis of the Neimark–Sacker bifurcation of the model.