On the Number of 5‐Cycles in a Tournament

We find a formula for the number of directed 5‐cycles in a tournament in terms of its edge scores and use the formula to find upper and lower bounds on the number of 5‐cycles in any n‐tournament. In particular, we show that the maximum number of 5‐cycles is asymptotically equal to , the expected number 5‐cycles in a random tournament (), with equality (up to order of magnitude) for almost all tournaments.     

Consumer memory and price fluctuations in commodity markets: An integrodifferential model

A model for the dynamics of price adjustment in a single commodity market is developed. Nonlinearities in both supply and demand functions are considered explicitly, as are delays due to production lags and storage policies, to yield a nonlinear integrodifferential equation. Conditions for the local stability of the equilibrium price are derived in terms of the elasticities of supply and demand, the supply and demand relaxation times, and the equilibrium production-storage delay. The destabilizing effect of consumer memory on the equilibrium price is analyzed, and the ensuing Hopf bifurcations are described.     

Noise and stability in differential delay equations

We study the stability of linear stochastic differential delay equations in the presence of additive or multiplicative white and colored noise. Using a stochastic analog of the second Liapunov method, sufficient conditions for mean square and stochastic stability are derived.     

Effect of biaxial orientation on dielectric and breakdown properties of poly(ethylene terephthalate)/poly(vinylidene fluoride‐co‐tetrafluoroethylene) multilayer films

Polymer films with enhanced dielectric and breakdown properties are essential for the production of high energy density polymer film capacitors. By capitalizing on the synergistic effects of forced assembly nanolayer coextrusion and biaxial orientation, polymer multilayer films using poly(ethylene terephthalate) (PET) and a poly(vinylidene fluoride‐co‐tetrafluoroethylene) [P(VDF‐TFE)] copolymer were produced. These films exhibited breakdown fields, under a divergent field using needle/plane electrodes, as high as 1000 kV mm^?1. The energy densities of these same materials, under a uniform electric field measured using plane/plane electrodes, were as high as 16 J cm^?3. The confined morphologies of both PET and P(VDF‐TFE) were correlated to the observed breakdown properties and damage zones. On‐edge P(VDF‐TFE) crystals induced from solid‐state biaxial stretching enhanced the effective P(VDF‐TFE) layer dielectric constant and therefore increased the dielectric contrast between the PET and P(VDF‐TFE) layers. This resulted in additional charge buildup at the layer interface producing larger tree diameters and branches and ultimately increasing the breakdown and energy storage properties. In addition to energy storage and breakdown properties, the hysteresis behavior of these materials was also evaluated. By varying the morphology of the P(VDF‐TFE) layer, the low‐field dielectric loss (or ion migration behavior) could be manipulated, which in turn also changed the observed hysteresis behavior. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 882–896     

Confined crystallization of PVDF and a PVDF‐TFE copolymer in nanolayered films

Layer‐multiplying coextrusion was used in conjunction with isothermal recrystallization to study the confined crystallization of polyvinylidene fluoride (PVDF) and polyvinylidene fluoride‐tetrafluoroethylene (PVDF‐TFE) using polycarbonate (PC) and polysulfone (PSF) as confining materials. Three layered systems were produced (PC/PVDF, PSF/PVDF, and PC/PVDF‐TFE) with layer thicknesses ranging from 525 to 28 nm. The crystal morphology was affected by both layer thickness and recrystallization temperature. Specifically, increased recrystallization temperature and decreased layer thickness facilitated the formation of high aspect ratio in‐plane crystals in both PVDF based polymers. On the other side of the spectrum, thicker layers and lower recrystallization temperatures produced on‐edge PVDF crystals and isotropic PVDF‐TFE crystals. The morphology was correlated with oxygen permeability, which decreased by almost two orders of magnitude compared with the bulk. A variety of crystal structures were obtained and explained with nucleation and diffusion theory. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Noise-induced global asymptotic stability

We prove analytically that additive and parametric (multiplicative) Gaussian distributed white noise, interpreted in either the Itô or Stratonovich formalism, induces global asymptotic stability in two prototypical dynamical systems designated as supercritical (the Landau equation) and subcritical, respectively. In both systems without noise, variation of a parameter leads to a switching between a single, globally stable steady state and multiple, locally stable steady states. With additive noise this switching is mirrored in the behavior of the extrema of probability densities at the same value of the parameter. However, parametric noise causes a noise-amplitude-dependent shift (postponement) in the parameter value at which the switching occurs. It is shown analytically that the density converges to a Dirac delta function when the solution of the Fokker-Planck equation is no longer normalizable.     

NAA characterization of the new Bovine Liver SRM

The National Institute of Standards and Technology (NIST) is preparing a freeze-dried powdered bovine liver tissue Standard Reference Material (SRM) to replace SRM 1577b Bovine Liver as the stock of this material was exhausted during 2006. Like the original SRM 1577 issued in 1972, this renewal focuses on the key elements for diagnostic, nutritional, and toxicological measurements that are important to medical, veterinary, and environmental sciences investigations. NIST’s approach for value assignment included extensive characterization by neutron activation analysis (NAA). Difficulties in the determination of some elements present at very low levels were overcome by use of radiochemical separations. Twentyone elements were characterized in SRM 1577c by NAA. The previous materials, SRM 1577 and 1577b, served as quality control.