Uniform Asymptotic Expansions for the Discrete Chebyshev Polynomials

The discrete Chebyshev polynomials t_n(x, N) are orthogonal with respect to a distribution function, which is a step function with jumps one unit at the points x = 0, 1, … , N ? 1, N being a fixed positive integer. By using a double integral representation, we derive two asymptotic expansions for t_n(aN, N + 1) in the double scaling limit, namely, N →∞ and n/N → b, where b ∈ (0, 1) and a ∈ (?∞, ∞). One expansion involves the confluent hypergeometric function and holds uniformly for , and the other involves the Gamma function and holds uniformly for a ∈ (?∞, 0). Both intervals of validity of these two expansions can be extended slightly to include a neighborhood of the origin. Asymptotic expansions for can be obtained via a symmetry relation of t_n(aN, N + 1) with respect to . Asymptotic formulas for small and large zeros of t_n(x, N + 1) are also given.     

Coverage Maximization with Autonomous Agents in Fast Flow Environments

This work examines the cooperative motion of a group of autonomous vehicles in a fast flow environment. The magnitude of the flow velocity is assumed to be greater than the available actuation to each agent. Collectively, the agents wish to maximize total coverage area defined as the set of points reachable by any agent within T time. The reachable set of an agent in a fast flow is characterized using optimal control techniques. Specifically, this work addresses the complementary cases where the static flow field is smooth, and where the flow field is piecewise constant. The latter case arises as a proposed approximation of a smooth flow that remains analytically tractable. Furthermore, the techniques used in the piecewise constant flow case enable treatment for obstacles in the environment. In both cases, a gradient ascent method is derived to maximize the total coverage area in a distributed fashion. Simulations show that such a network is able to maximize the coverage area in a fast flow.     

Suppression of random vibration in flexible structures using a hybrid vibration absorber

A design method is proposed to suppress stationary random vibration in flexible structures using a hybrid vibration absorber (HVA). While the traditional vibration absorber can damp down the vibration mainly at the pre-tuned mode of the primary structure, active damping is generated by the proposed HVA to damp down all resonant modes of interest of the vibrating structure and the spatial average mean square motion of the vibrating structure can be minimized. Only one absorber and one feedback signal are required to achieve global vibration suppression of a flexible structure under stationary random excitation. A special pole-placement controller is designed such that all vibration modes of the flexible structures become critically damped. It is proved analytically that the proposed HVA damps the vibration of the entire structure instead of just the attachment point of the absorber. The proposed optimized HVA is tested on a beam structure and it shows a superior performance on global suppression of broadband vibration in comparison to other published designs of passive and hybrid vibration absorbers.     

A Simple,Convenient, and Efficient Synthetic Route for The Preparation of (Z)‐3,5‐Dichloro‐N‐(3‐(4‐substitutedphenyl)‐4‐phenylthiazole‐2(3H)‐ylide)benzamide Heterocyclic Compounds from Aroyl Thiourea Derivatives via S‐cyclization Mechanism

A series of variously substituted 1,3‐thiazole heterocyclic compounds ( 3a – 3d ) were prepared by base‐catalyzed S‐cyclization of corresponding 2,4‐dichloro‐N‐{[(4‐substitutedphenyl)amino]carbonothioyl}benzamide ( 2a – 2d ) with acetophenone in the presence of bromine. The structure of all compounds was established by IR, ¹H‐NMR, ¹³C‐NMR, elemental analysis, and X‐ray crystallographic analysis.     

A visualization system for observing plastic foaming processes under shear stress

Previous studies offered theories to explain shear-induced bubble nucleation and growth phenomena in plastic foaming processes, but empirical verification was limited due to difficulty in observing these processes in situ under an easily adjustable and uniform shear flow. This study presents a novel visualization system that successfully achieved this goal. The system allows easy control of the critical experimental parameters: applied shear strain, shear strain rate, temperature, pressure, pressure drop rate, plastic material and blowing agent. From a foaming visualization study of polystyrene, it was observed that cell nucleation rate and maximum cell density increased with the applied shear strain, which was due to the decreased local system pressure, detachment and growth of microvoids, and elongation of bubbles. This foaming visualization system provides a direct and effective way to investigate the mechanisms of bubble nucleation and growth under dynamic conditions that simulates industrial plastic foaming processes.     

A simple and robust LC-MS/MS method for quantification of free 3-nitrotyrosine in human plasma from patients receiving on-pump CABG surgery

We have developed a simple, sensitive, and robust liquid chromatography-mass spectrometry/mass spectrometry (LC-MS/MS) method to determine free 3-nitrotyrosine concentrations in human plasma of patients receiving on-pump coronary artery bypass grafting surgery. A one-step solid-phase extraction protocol was optimized to enrich the analyte at low nanomolar concentrations. The processed samples were analyzed by LC-MS/MS with a 2.1 × 100 mm Kinetex PFP column and a triple quadrupole mass spectrometer. The method was validated for 3-nitrotyrosine concentrations close to real patient plasma levels. The relative standard deviations or relative errors of the intraday and interday determinations were all within 10%. Limit of detection and limit of quantitation were determined to be 0.034 nM and 0.112 nM, respectively, while lower limit of quantitation was below 0.625 nM. No deterioration of the column performance was noticed after running a large number of patient samples. The results showed that the 3-nitrotyrosine concentrations in coronary sinus plasma samples were elevated after cardiopulmonary bypass (CPB) procedure. The pre-CPB and post-CPB concentrations of 3-nitrotyrosine in patient plasmas were 1.494 ± 0.107 nM and 2.167 ± 0.177 nM (mean ± SEM), respectively. Application of this method to more patients in clinical studies may help validate 3-nitrotyrosine as a meaningful biomarker for nitrosative stress and link patient characteristics, clinical outcomes, and cardioprotective treatments to endogenous nitrosative stress levels.     

Gut microbiota, diet, and heart disease

Modulation of the gut microbiota is an area of growing interest, particularly for its link to improving and maintaining the systemic health of the host. It has been suggested to have potential to reduce risk factors associated with chronic diseases, such as elevated cholesterol levels in coronary heart disease (CHD). Diets of our evolutionary ancestors were largely based on plant foods, high in dietary fiber and fermentable substrate, and our gut microbiota has evolved against a background of such diets. Therapeutic diets that mimic plant-based diets from the early phases of human evolution may result in drug-like cholesterol reductions. In contrast, typical Western diets low in dietary fiber and fermentable substrate, and high in saturated and trans fatty acids, are likely contributors to the increased need for pharmacological agents for cholesterol reduction. The gut microbiota of those consuming a Western diet are likely underutilized and depleted of metabolic fuels, resulting in a less than optimal gut microbial profile. As a result, this diet is mismatched to our archaic gut microbiota and, therefore, to our genome, which has changed relatively little since humans first appeared. While the exact mechanism by which the gut microbiota may modulate cholesterol levels still remains uncertain, end products of bacterial fermentation, particularly the short chain fatty acids (i.e., propionate), have been suggested as potential candidates. While more research is required to clarify the potential link between gut microbiota and CHD risk reduction, consuming a therapeutic diet rich in plant foods, dietary fiber, and fermentable substrate would be a useful strategy for improving systemic health, possibly by altering the gut microbiota.     

Period distribution analysis of some linear maps

This paper discusses period properties of some linear maps which are employed in various applications such as image encryption, public key cryptography and watermarking. Conditions for the bijectiveness of such maps and the existence of a period are presented. Period structure is also given. Then, the recurrence equation theory is adopted to address the period distribution problem. Finally, a framework to solve the problem is proposed with a demonstration of its effectiveness and efficiency into some applications.     

Fixed point theorems and convergence theorems for generalized nonspreading mappings in Banach spaces

In this paper, we first prove a general fixed point theorem for nonlinear mappings in a Banach space. Then we prove a nonlinear mean convergence theorem of Baillon??s type and a weak convergence theorem of Mann??s type for 2-generalized nonspreading mappings in a Banach space.     

The preparation of primary mathematics teachers in Singapore: programs and outcomes from the TEDS-M study

This paper describes five aspects of primary mathematics teacher education in Singapore: (a) the teaching profession in Singapore, (b) the structure of pre-service teacher education programs offered by the National Institute of Education, (c) self-reports of Singapore future primary mathematics teachers about the opportunities to learn mathematics-related contents offered by these programs, based on the Teacher Education and Development Study in Mathematics (TEDS-M) survey, (d) the performance of these future teachers in mathematics content knowledge and mathematics pedagogical content knowledge assessed by the TEDS-M study, and (e) the relationships of opportunities to learn with this performance. The paper concludes with some suggestions about how to improve the quality of initial teacher preparation in the areas of recruitment and training.