Ergodic stationary distribution and practical application of a hybrid stochastic cholera transmission model with waning vaccine-induced immunity under nonlinear regime switching

Considering the effect of stochasticity including white noise and colored noise, this paper aims to study a hybrid stochastic cholera epidemic model with waning vaccine-induced immunity and nonlinear telegraph perturbations. First, we derive a critical value ${?}_0^C$ related to the basic reproduction number ${?}_0$ of the deterministic model. The key aim of this paper is to generalize the θ-stochastic criterion method proposed by the recent work (Han et al. in Chaos Solit Fract 140:110238, 2020) to eliminate nonlinear telegraph perturbations. Next, via constructing several θ-stochastic Lyapunov functions and using the generalized method, we further prove that the stochastic model have a unique ergodic stationary distribution under ${?}_0^C>1$. Results show that the prevention and control of cholera epidemic depend on low transmission rate and small telegraph perturbations. Finally, the corresponding numerical simulations are performed to illustrate our analytical results and a practical application on the Somalia cholera outbreak is shown at the end of this paper.     

Dynamic Modeling of the Feed Drive System of a CNC Metal Cutting Machine

Studying the vibrational behavior of feed drive systems is important for enhancing the structural performance of computer numerical control (CNC) machines. The preload on the screw and nut position have a great influence on the vibration characteristics of the feed drive as two very important operational conditions. Rotational acceleration of the screw also affects the performance of the CNC feed drive when machining small parts. This paper investigates the influence of preload and nut position on the vibration characteristics of the feed drive system of a CNC metal cutting machine in order to be able to eliminate an observed resonance occurred at high rotational speeds of the screw, corresponding to high feed rates. Additionally, rational structural parameters of the feed drive system are selected in order to increase the rotational acceleration for improving the performance of the CNC machine. Experiments and analyses showed that by selecting specific parameters of feed drive system and simultaneously applying a certain value of preload, a 97% increase in rotational acceleration and 30% time reduction considering the vibration resistance at high rotational speeds can be achieved.     

Dynamic Interactions in Synthetic Receptors: A Guest Exchange Saturation Transfer Study

The accumulated knowledge regarding molecular architectures is based on established, reliable, and accessible analytical tools that provide robust structural and functional information on assemblies. However, both the dynamicity and low population of noncovalently interacting moieties within studied molecular systems limit the efficiency and accuracy of traditional methods. Herein, the use of a saturation transfer-based NMR approach to study the dynamic binding characteristics of an anion to a series of synthetic receptors derived from bambusuril macrocycles is demonstrated. The exchange rates of BF₄⁻ are mediated by the side chains on the receptor (100 s⁻¹<k_ex<5000 s⁻¹), which play a critical role in receptor-anion binding dynamics. The signal amplification obtained with this approach allows for the identification of different types of intermolecular interactions between the receptor and the anion, something that could not have been detected by techniques hitherto used to study molecular assemblies. These findings, which are supported by a computational molecular dynamic study, demonstrate the uniqueness and added value of this NMR method.     

Validation of quartz crystal rheometry in the megahertz frequency regime

The utility of the quartz crystal microbalance (QCM) as a high‐frequency rheometer operating at 15 MHz was demonstrated. High‐frequency data obtained from a series of rubbery materials were compared with results obtained from traditional dynamic mechanical analysis (DMA) at much lower frequencies. The high‐frequency data enable meaningful shift factors to be obtained at temperatures much further above glass‐transition temperature (T _g) than would otherwise be possible, giving a more complete picture of the temperature dependence of the viscoelastic properties. The QCM can also be used to quantify mass uptake and changes in viscoelastic properties during sample oxidation. The viscoelastic response spanning the full range of behaviors from the rubber to glassy regimes was found to fit well with a six‐element model consisting of three power‐law springpot elements. One of these elements is particularly sensitive to the behavior in the transition regime where the phase angle is maximized. The value of this quantity is obtained from the maximum phase angle, which can be obtained from a temperature sweep at fixed frequency, proving a means for more detailed frequency‐dependent rheometric information to be obtained from a fixed‐frequency measurement at a range of temperatures. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1246–1254     

Reducing the computational cost of NMR crystallography of organic powders at natural isotopic abundance with the help of 13C-13C dipolar couplings

Structure determination of functional organic compounds remains a formidable challenge when the sample exists as a powder. Nuclear magnetic resonance crystallography approaches based on the comparison of experimental and Density Functional Theory (DFT)-computed ¹H chemical shifts have already demonstrated great potential for structure determination of organic powders, but limitations still persist. In this study, we discuss the possibility of using ¹³C-¹³C dipolar couplings quantified on powdered theophylline at natural isotopic abundance with the help of dynamic nuclear polarization, to realize a DFT-free, rapid screening of a pool of structures predicted by ab initio random structure search. We show that although ¹³C-¹³C dipolar couplings can identify structures possessing long range structural motifs and unit cell parameters close to those of the true structure, it must be complemented with other data to recover information about the presence and the chemical nature of the supramolecular interactions.     

Polymer chain diffusion in polymer blends: A theoretical interpretation based on a memory function formalism

The diffusion of polymer chains in miscible polymer blends with large dynamic asymmetry—those where the two blend components display very different segmental mobility—is not well understood yet. In the extreme case of the blend system of poly(ethylene oxide) (PEO) and poly(methyl methacrylate)(PMMA), the diffusion coefficient of PEO chains in the blend can change by more than five orders of magnitude while the segmental time scale hardly changes with respect to that of pure PEO. This behavior is not observed in blend systems with small or moderate dynamic asymmetry as, for instance, polyisoprene/poly(vinyl ethylene) blends. These two very different behaviors can be understood and quantitatively explained in a unified way in the framework of a memory function formalism, which takes into account the effect of the collective dynamics on the chain dynamics of a tagged chain. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1239–1245     

Explicit estimates of sums related to the Nyman–Beurling criterion for the Riemann Hypothesis

We give an estimate for sums appearing in the Nyman–Beurling criterion for the Riemann Hypothesis. These sums contain the Möbius function and are related to the imaginary part of the Estermann zeta function. The estimate is remarkably sharp in comparison to other sums containing the Möbius function. The bound is smaller than the trivial bound – essentially the number of terms – by a fixed power of that number. The exponent is made explicit. The methods intensively use tools from the theory of continued fractions and from the theory of Fourier series.     

Synthesis and Characterization of Hydrophilic Trityl Radical TFO for Biomedical and Biophysical Applications

Tetrathiatriarylmethyl (TAM, trityl) radicals have found wide applications as spin probes/labels for EPR spectroscopy and imaging, and as polarizing agents for dynamic nuclear polarization. The high hydrophilicity of TAM radicals is essential for their biomedical applications. However, the synthesis of hydrophilic TAM radicals (e.g., OX063) is extremely challenging and has only been reported in the patent literature, to date. Herein, an efficient synthesis of a highly water-soluble TAM radical bis(8-carboxyl-2,2,6,6-tetramethylbenzo[1,2-d:4,5-d′]bis([1,3]dithiol-4-yl)-mono-(8-carboxyl-2,2,6,6-tetrakis(2-hydroxyethyl)benzo[1,2-d:4,5-d′]bis([1,3]dithiol-4-yl)methyl (TFO), which contains four additional hydroxylethyl groups, relative to the Finland trityl radical CT-03, is reported. Similar to OX063, TFO exhibits excellent properties, including high water solubility in phosphate buffer, low log P, low pK_a, long relaxation times, and negligible binding with bovine serum albumin. On the other hand, TFO has a sharper EPR line and higher O₂ sensitivity than those of OX063. Therefore, in combination with its facile synthesis, TFO should find wide applications in magnetic resonance related fields and this synthetic approach would shed new light on the synthesis of other hydrophilic TAM radicals.     

Going Off the Grid: Iterative Model Selection for Biclustered Matrix Completion

We consider the problem of performing matrix completion with side information on row-by-row and column-by-column similarities. We build upon recent proposals for matrix estimation with smoothness constraints with respect to row and column graphs. We present a novel iterative procedure for directly minimizing an information criterion to select an appropriate amount of row and column smoothing, namely, to perform model selection. We also discuss how to exploit the special structure of the problem to scale up the estimation and model selection procedure via the Hutchinson estimator, combined with a stochastic Quasi-Newton approach. Supplementary material for this article is available online.     

Decay rate for viscoelastic wave equation of variable coefficients with delay and dynamic boundary conditions

In this paper, we consider a viscoelastic wave equation of variable coefficients in the presence of past history with nonlinear damping and delay in the internal feedback and dynamic boundary conditions. Under suitable assumptions, we establish an explicit and general decay rate result without imposing restrictive assumption on the behavior of the relaxation function at infinity by Riemannian geometry method and Lyapunov functional method.