An Intuitive Approach to Geometric Continuity for Parametric Curves and Surfaces (Extended Abstract)

The notion of geometric continuity is extended to an arbitrary order for curves and surfaces, and an intuitive development of constraints equations is presented that are necessary for it. The constraints result from a direct application of the univariate chain rule for curves, and the bivariate chain rule for surfaces. The constraints provide for the introduction of quantities known as shape parameters. The approach taken is important for several reasons: First, it generalizes geometric continuity to arbitrary order for both curves and surfaces. Second, it shows the fundamental connection between geometric continuity of curves and geometric continuity of surfaces. Third, due to the chain rule derivation, constraints of any order can be determined more easily than derivations based exclusively on geometric measures

The Seasonal Cycle and the Business Cycle

Almost all recent research on macroeconomic fluctuations has worked with seasonally adjusted or annual data. This paper takes a different approach by treating seasonal fluctuations as worthy of study in their own right. We document the quantitative importance of seasonal fluctuations, and we present estimates of the seasonal patterns in a set of standard macroeconomic variables. Our results show that seasonal fluctuations are an important source of variation in all macroeconomic quantity variables but small or entirely absent in both real and nominal price variables. The timing of the seasonal fluctuations consists of increases in the second and fourth quarter, a large decrease in the first quarter, and a mild decrease in the third quarter. The paper demonstrates that, with respect to each of several major stylized facts about business cycles, the seasonal cycle displays the same characteristics as the business cycle, in some cases even more dramatically than the business cycle. That is, we find that at seasonal frequencies as well as at business cycle frequencies, output movements across broadly defined sectors move together, the timing of production and sales coincide closely, labor productivity is procyclical, nominal money and real output are highly correlated, and prices vary less than quantities. There is a "seasonal business cycle" in the United States economy, and its characteristics mirror closely those of the conventional business cycle.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100965/1/ECON040.pd

The Worldwide Change in the Behavior of Interest Rates and Prices in 1914

This paper evaluates the role of the destruction of the gold standard and the founding of the Federal Reserve, both of which occurred in 1914, in contributing to observed changes in the behavior of interest rates and prices after 1914. The paper presents a model of policy coordination in which the introduction of the Fed stabilizes interest rates, even if the gold standard remains intact, and it offers empirical evidence that the dismantling of the gold standard did not play a crucial role in precipitating the changes in interest rate behavior.

The Worldwide Change in the Behavior of Interest Rates and Prices in 1914

This paper evaluates the role of the destruction of the gold standard and the founding of the Federal Reserve, both of which occurred in 1914, in contributing to observed changes in the behavior of interest rates and prices after 1914. The paper presents a model of policy coordination in which the introduction of the Fed stabilizes interest rates, even if the gold standard remains intact, and it offers empirical evidence that the dismantling of the gold standard did not play a crucial role in precipitating the changes in interest rate behavior.Center for Research on Economic and Social Theory, Department of Economics, University of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/100954/1/ECON039.pd

Bulk and Interfacial Shear Thinning of Immiscible Polymers

Nonequilibrium molecular dynamics simulations are used to study the shear thinning behavior of immiscible symmetric polymer blends. The phase separated polymers are subjected to a simple shear flow imposed by moving a wall parallel to the fluid-fluid interface. The viscosity begins to shear thin at much lower rates in the bulk than at the interface. The entire shear rate dependence of the interfacial viscosity is consistent with a shorter effective chain length $s^*$ that also describes the width of the interface. This $s^*$ is independent of chain length $N$ and is a function only of the degree of immiscibility of the two polymers. Changes in polymer conformation are studied as a function of position and shear rate.Shear thinning correlates more closely with a decrease in the component of the radius of gyration along the velocity gradient than with elongation along the flow. At the interface, this contraction of chains is independent of $N$ and consistent with the bulk behavior for chains of length $s^*$. The distribution of conformational changes along chains is also studied. Central regions begin to stretch at a shear rate that decreases with increasing $N$, while shear induced changes at the ends of chains are independent of $N$.Comment: 8 pages, 8 figure

Statistical mechanics of permanent random atomic and molecular networks: Structure and heterogeneity of the amorphous solid state

Under sufficient permanent random covalent bonding, a fluid of atoms or small molecules is transformed into an amorphous solid network. Being amorphous, local structural properties in such networks vary across the sample. A natural order parameter, resulting from a statistical-mechanical approach, captures information concerning this heterogeneity via a certain joint probability distribution. This joint probability distribution describes the variations in the positional and orientational localization of the particles, reflecting the random environments experienced by them, as well as further information characterizing the thermal motion of particles. A complete solution, valid in the vicinity of the amorphous solidification transition, is constructed essentially analytically for the amorphous solid order parameter, in the context of the random network model and approach introduced by Goldbart and Zippelius [Europhys. Lett. 27, 599 (1994)]. Knowledge of this order parameter allows us to draw certain conclusions about the stucture and heterogeneity of randomly covalently bonded atomic or molecular network solids in the vicinity of the amorphous solidification transition. Inter alia, the positional aspects of particle localization are established to have precisely the structure obtained perviously in the context of vulcanized media, and results are found for the analogue of the spin glass order parameter describing the orientational freezing of the bonds between particles.Comment: 31 pages, 5 figure

Random solids and random solidification: What can be learned by exploring systems obeying permanent random constraints?

In many interesting physical settings, such as the vulcanization of rubber, the introduction of permanent random constraints between the constituents of a homogeneous fluid can cause a phase transition to a random solid state. In this random solid state, particles are permanently but randomly localized in space, and a rigidity to shear deformations emerges. Owing to the permanence of the random constraints, this phase transition is an equilibrium transition, which confers on it a simplicity (at least relative to the conventional glass transition) in the sense that it is amenable to established techniques of equilibrium statistical mechanics. In this Paper I shall review recent developments in the theory of random solidification for systems obeying permanent random constraints, with the aim of bringing to the fore the similarities and differences between such systems and those exhibiting the conventional glass transition. I shall also report new results, obtained in collaboration with Weiqun Peng, on equilibrium correlations and susceptibilities that signal the approach of the random solidification transition, discussing the physical interpretation and values of these quantities both at the Gaussian level of approximation and, via a renormalization-group approach, beyond.Comment: Paper presented at the "Unifying Concepts in Glass Physics" workshop, International Centre for Theoretical Physics, Trieste, Italy (September 15-18, 1999

ВЫБОР СМЕЩЕНИЯ ПРИ ПОШАГОВОЙ МАРШРУТИЗАЦИИ В БЕСПРОВОДНОЙ СЕТИ

In order to send the frame to the address the authors suggest selecting an adjacent node, taking into account the preferred predetermined weights of those nodes and their current load rates. The adaptive algorithm of alternate path choice is based on logical neural network. Simulation, made by the authors, has shown better values of mean time to execute applications and higher probability of their execution as compared to algorithm of non-alternative choice of neighboring routers. Thus a mean time of execution of application with alternative path choice algorithm DТalt exceeds minimum possible time for the range of change 12 ≤ s ≤ 16 (applications per step) in a changing range 0,3 ≤ DТальт ≤ 1 (steps). The mean time of execution of application with the method of alternative path choice has been reduced as compared to non-alternative path choice by 8% for s = 12, and by 23% – for s = 16.Для передачи кадра по адресу выбор смежного узла предлагается производить с учётом предпочтительных весов этих узлов, определённых заранее, и текущих значений коэффициентов их загрузки. В основе адаптивного  алгоритма альтернативного  смещения лежит логическая нейронная сеть. Моделирование, проведенное авторами, показало лучшие значения среднего времени и вероятности выполнения заявок  в данном варианте по сравнению с алгоритмом безальтернативного выбора искомого узла

The worldwide change in the behavior of interest rates and prices in 1914

This paper evaluates the role of the destruction of the gold standard and the founding of the Federal Reserve, both of which occured in 1914, in contributing to observed changes in the behavior of interest rates and prices after 1914. The paper presents a model of policy coordination in which the introduction of the Fed stabilizes interest rates, even it the gold standard remains intact, and it offers empirical evidence that the dismantling of the gold standard did not play a crucial role in precipitating the changes in interest rate behavior.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27286/1/0000305.pd