Optimal transportation and stationary measures for iterated function systems

In this paper we show how ideas, methods and results from optimal transportation can be used to study various aspects of the stationary measures of Iterated Function Systems equipped with a probability distribution. We recover a classical existence and uniqueness result under a contraction-on-average assumption, prove generalised moment bounds from which tail estimates can be deduced, consider the convergence of the empirical measure of an associated Markov chain, and prove in many cases the Lipschitz continuity of the stationary measure when the system is perturbed, with as a consequence a “linear response formula” at almost every parameter of the perturbation.

General Response Formula for CFD Pseudo-Fractional 2D Continuous Linear Systems Described by the Roesser Model

In many engineering problems associated with various physical phenomena, there occurs a necessity of analysis of signals that are described by multidimensional functions of more than one variable such as time t or space coordinates x, y, z. Therefore, in such cases, we should consider dynamical models of two or more dimensions. In this paper, a new two-dimensional (2D) model described by the Roesser type of state-space equations will be considered. In the introduced model, partial differential operators described by the Conformable Fractional Derivative (CFD) definition with respect to the first (horizontal) and second (vertical) variables will be applied. For the model under consideration, the general response formula is derived using the inverse fractional Laplace method. Next, the properties of the solution will be considered. Usefulness of the general response formula will be discussed and illustrated by a numerical example.

Adiabatic currents for interacting fermions on a lattice

We prove an adiabatic theorem for general densities of observables that are sums of local terms in finite systems of interacting fermions, without periodicity assumptions on the Hamiltonian and with error estimates that are uniform in the size of the system. Our result provides an adiabatic expansion to all orders, in particular, also for the initial data that lie in eigenspaces of degenerate eigenvalues. Our proof is based on ideas from [ 10 ], where Bachmann et al. proved an adiabatic theorem for interacting spin systems. As one important application of this adiabatic theorem, we provide the first rigorous derivation of the adiabatic response formula for the current density induced by an adiabatic change of the Hamiltonian of a system of interacting fermions in a ground state, with error estimates uniform in the system size. We also discuss the application to quantum Hall systems.

Analysis of Doppler frequency shift response mechanism based on OFDM system

OFDM system is widely used in mobile communication because of its high spectral efficiency and strong anti-multipath capability. However, in high dynamic scenarios, the Doppler shift between the transmitter and the receiver destroys the orthogonality between the sub-carriers, resulting the interference between the sub-carriers and distortion of the signal, which greatly degrades the system performance. In this paper, a mathematical model of Offset-OFDM system was established and the Doppler response formula of OFDM system in high white channel was derived. Furthermore, we investigated the factors that influence the performance of OFDM. This study laid the foundation for determining OFDM system parameters in high dynamic scenarios.

Dynamics of a Delayed HIV-1 Infection Model with Saturation Incidence Rate and CTL Immune Response

In this paper, we investigate the dynamics of a five-dimensional virus model incorporating saturation incidence rate, CTL immune response and three time delays which represent the latent period, virus production period and immune response delay, respectively. We begin this model by proving the positivity and boundedness of the solutions. Our model admits three possible equilibrium solutions, namely the infection-free equilibrium [Formula: see text], the infectious equilibrium without immune response [Formula: see text] and the infectious equilibrium with immune response [Formula: see text]. Moreover, by analyzing corresponding characteristic equations, the local stability of each of the feasible equilibria and the existence of Hopf bifurcation at the equilibrium point [Formula: see text] are established, respectively. Further, by using fluctuation lemma and suitable Lyapunov functionals, it is shown that [Formula: see text] is globally asymptotically stable when the basic reproductive numbers for viral infection [Formula: see text] is less than unity. When the basic reproductive numbers for immune response [Formula: see text] is less than unity and [Formula: see text] is greater than unity, the equilibrium point [Formula: see text] is globally asymptotically stable. Finally, some numerical simulations are carried out for illustrating the theoretical results.

Research on the Concentration Prediction of Nitrogen in Red Tide Based on an Optimal Grey Verhulst Model

In order to reduce the harm of red tide to marine ecological balance, marine fisheries, aquatic resources, and human health, an optimal Grey Verhulst model is proposed to predict the concentration of nitrogen in seawater, which is the key factor in red tide. The Grey Verhulst model is established according to the existing concentration data series of nitrogen in seawater, which is then optimized based on background value and time response formula to predict the future changes in the nitrogen concentration in seawater. Finally, the accuracy of the model is tested by the posterior test. The results show that the prediction value based on the optimal Grey Verhulst model is in good agreement with the measured nitrogen concentration in seawater, which proves the effectiveness of the optimal Grey Verhulst model in the forecast of red tide.

Topical 5-aminolevulinic acid photodynamic therapy improved refractory acne conglobata and perifolliculitis capitis abscedens et suffodiens rather than hidradenitis suppurativa

Acne conglobata (AC), perifolliculitis capitis abscedens et suffodiens (PCAS) and hidradenitis suppurativa (HS) are uncommon refractory chronic, inflammatory, scarring diseases but cause serious damage to the quality of life. These three diseases are associated with follicular occlusion. Several studies indicated topical 5-aminolevulinic acid photodynamic therapy (ALA-PDT) improved follicular occlusion besides acne treatment. So we attempted to apply ALA-PDT to medicine resistant AC, PCAS and HS. Topical ALA-PDT was applied to 10 patients with AC, seven patients with PCAS and three patients with HS for more than three sessions. All the patients completed the dermatology life quality index (DLQI) questionnaire and were assessed for the efficacy at the baseline and on two weeks after each treatment. Adverse effects were recorded at each visit. The results showed 25.5% (5/20, two cases of AC and three cases of PCAS) of patients achieved excellent improvement after three sessions of PDT and another 60.0% (12/20, eight cases of AC and four cases of PCAS) of patients achieved good improvement. 15.0% (3/20, three cases of HS) got poor response ([Formula: see text] 20% lesions clearance). Another five cases (three cases of AC and two cases of PCAS) also achieved excellent response after 5–7 sessions of PDT. We also found that papular/nodular, cyst/abscess showed higher clearance rate than sinus/fistula (88.5%, 86.1% versus 11.1%). DLQI was reduced after three sessions of PDT in AC and PCAS patients rather than HS patients. 5-ALA-PDT could improve refractory AC and PCAS but could not lead to improvement in late stage of HS. The efficacy increased with more treatment sessions.

Structure, Optical and Formaldehyde Sensing Properties of Co-Precipitated Fe-Doped WO3 Nanomaterials

Co-precipitated undoped and Fe-doped WO3 nanomaterials have been investigated by X-ray diffraction, Raman spectroscopy and scanning electron microscopy in order to study the influence of Fe doping in their structural and morphological properties. The synthesized WO3 nanomaterials have been found to possess monoclinic structure having average crystallite sizes 15–20[Formula: see text]nm. The diffuse reflectance spectroscopy shows the optical bandgap [Formula: see text]2.85[Formula: see text]eV. The 1.8 at.% Fe-doped WO3 exhibits selective high response to formaldehyde over methanol, ethanol, propan-2-ol and acetone. It exhibits the maximum response ([Formula: see text]80%) to formaldehyde at the operating temperature of 225[Formula: see text]C for 50[Formula: see text]ppm concentration in air.