Paddling mode of forward flight in insects

By analyzing high-speed video of the fruit fly, we discover a swimminglike mode of forward flight characterized by paddling wing motions. We develop a new aerodynamic analysis procedure to show that these insects generate drag-based thrust by slicing their wings forward at low angle of attack and pushing backwards at a higher angle. Reduced-order models and simulations reveal that the law for flight speed is determined by these wing motions but is insensitive to material properties of the fluid. Thus, paddling is as effective in air as in water and represents a common strategy for propulsion through aquatic and aerial environments.     

Intracavity ionization and pulse formation in femtosecond enhancement cavities

We experimentally and numerically investigate the intracavity ionization of a dilute gas target by an ultrashort pulse inside a femtosecond enhancement cavity. Numerical simulations detail how the dynamic ionization of the gas target limits the achievable peak intensity of the evolving intracavity pulse beyond that of linear cavity losses, setting a constraint on the strength of the nonlinear interaction that can be sustained in such optical cavities. Experimental measurements combined with numerical simulations predict ionization levels in a femtosecond enhancement cavity for the first time. We demonstrate how the resonant response of the femtosecond enhancement cavity can itself be used as a sensitive probe of optical nonlinearities at high intensities.     

Noninvasive observation of cervical spinal cord activity in children by functional MRI during cold thermal stimulation

Functional magnetic resonance imaging (fMRI) is a non-invasive neuroimaging tool that indirectly identifies areas of neural activity in the brain and more recently has been applied to the adult spinal cord (spinal fMRI). Spinal fMRI could clearly benefit pediatric populations as well. The purpose of this work was to characterize the response observed with spinal fMRI in the brainstem and cervical (C) spinal cord of awake, healthy children during thermal stimulation (17°C and 27°C) applied to the right hand. Functional MRI detected neuronal activity in the expected region of the spinal cord (C6 and C7) as well as in the brainstem and thalamus. The observed magnitudes of signal change of the responses to 17°C and 27°C were similar; however, the spatial distribution of active pixels was greater during 17°C stimulation. The results of this study indicate that fMRI can be used to assess activity in the spinal cords of children, with good sensitivity and reliability.     

A delay-dependent model with HIV drug resistance during therapy

The use of combination antiretroviral therapy has proven remarkably effective in controlling HIV disease progression and prolonging survival. However, the emergence of drug resistance can occur. It is necessary that we gain a greater understanding of the evolution of drug resistance. Here, we consider an HIV viral dynamical model with general form of target cell density, drug resistance and intracellular delay incorporating antiretroviral therapy. The model includes two strains: wild-type and drug-resistant. The basic reproductive ratio for each strain is obtained for the existence of steady states. Qualitative analysis of the model such as the well-posedness of the solutions and the equilibrium stability is provided. Global asymptotic stability of the disease-free and drug-resistant steady states is shown by constructing Lyapunov functions. Furthermore, sufficient conditions related to the properties of the target cell density are obtained for the local asymptotic stability of the positive steady state. Numerical simulations are conducted to study the impact of target cell density and intracellular delay focusing on the stability of the positive steady state. The occurrence of Hopf bifurcation of periodic solutions is shown to depend on the target cell density.     

Enhanced Karush–Kuhn–Tucker Conditions for Mathematical Programs with Equilibrium Constraints

In this paper, we study necessary optimality conditions for nonsmooth mathematical programs with equilibrium constraints. We first show that, unlike the smooth case, the mathematical program with equilibrium constraints linear independent constraint qualification is not a constraint qualification for the strong stationary condition when the objective function is nonsmooth. We then focus on the study of the enhanced version of the Mordukhovich stationary condition, which is a weaker optimality condition than the strong stationary condition. We introduce the quasi-normality and several other new constraint qualifications and show that the enhanced Mordukhovich stationary condition holds under them. Finally, we prove that quasi-normality with regularity implies the existence of a local error bound.     

Boundary of Anosov dynamics and evolution equations for surfaces

We show that a compact surface of genus greater than one, without focal points and a finite number of bubbles (“good” shaped regions of positive curvature) is in the closure of Anosov metrics. Compact surfaces of nonpositive curvature and genus greater than one are in the closure of Anosov metrics, by Hamilton's work about the Ricci flow. We generalize this fact to the above surfaces without focal points admitting regions of positive curvature using a “magnetic” version of the Ricci flow, the so‐called Ricci Yang‐Mills flow.     

Two-Way Tables: Issues at the Heart of Statistics and Probability for Students and Teachers

Some problems exist at the intersection of statistics and probability, creating a dilemma in relation to the best approach to assist student understanding. Such is the case with problems presented in two-way tables representing conditional information. The difficulty can be confounded if the context within which the problem is set is one where students have preconceived opinions on the direction of the potential association present. This article considers school students’ responses to two problems of association, with data presented in 2 × 2 tables. A hierarchical rubric is presented to document students’ understandings. Teachers’ pedagogical content knowledge is also considered in relation to the same two problems. Findings include a surprising relationship of outcomes for students across the problem contexts and some concern about teachers’ pedagogical content knowledge in this area of the curriculum.     

Solving semi-infinite programs by smoothing projected gradient method

In this paper, we study a semi-infinite programming (SIP) problem with a convex set constraint. Using the value function of the lower level problem, we reformulate SIP problem as a nonsmooth optimization problem. Using the theory of nonsmooth Lagrange multiplier rules and Danskin’s theorem, we present constraint qualifications and necessary optimality conditions. We propose a new numerical method for solving the problem. The novelty of our numerical method is to use the integral entropy function to approximate the value function and then solve SIP by the smoothing projected gradient method. Moreover we study the relationships between the approximating problems and the original SIP problem. We derive error bounds between the integral entropy function and the value function, and between locally optimal solutions of the smoothing problem and those for the original problem. Using certain second order sufficient conditions, we derive some estimates for locally optimal solutions of problem. Numerical experiments show that the algorithm is efficient for solving SIP.     

Hydrolytic stability and high Tg of polyimides derived from the novel 4,9‐bis[4‐(3,4‐dicarboxyphenoxy)phenyl]‐diamantane dianhydride

This work reports the synthesis and characterization of diamantane‐based polyimides obtained from 4,9‐bis[4(3,4‐dicarboxyphenoxy)phenyl]diamantane dianhydride and various aromatic diamines. Interestingly, the diamantane‐based polyimides were very stable to hydrolysis. This novel polyimide exhibits a low dielectric constant (2.65–2.77), low moisture absorption (<0.67%), good solubility, high T_g and unusually high thermal stability. Dynamic mechanical analysis (DMA) reveals that the diamantane‐based polyimides have high T_g ranging from 281 to 379 °C. The high‐temperature β₁ subglass transition around 285 °C was observed in polyimide 6a derived from 2,2′‐bis(trifluoromethyl)benzidine. This class of novel diamantane‐based polyimide is very promising for electronic applications, because of its good mechanical properties, good thermal stability, low dielectric constant, excellent hydrolytic resistance, and low moisture absorption. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 1673–1684, 2009