Differential 3ω calorimeter

We have developed a new dynamic calorimeter using the differential 3ω detection method. The differential 3ω calorimeter is capable of measuring dynamic heat capacity of liquid samples. The new calorimeter consists of a Wheatstone bridge made of two identical heater/sensors, and is based on the sensitive null detection method. The balancing is done automatically at all frequencies and is independent of temperature; once a sample is placed on one heater/sensor, a third harmonic signal is produced due to the difference in the two arms of the bridge. The differential 3ω calorimeter provides enhancements over traditional dynamic methods in dynamic range (up to 30 kHz), resolution, and ease of operation.     

CRYSTALLIZATION AND MELTING OF NYLON 610

Differential scanning calorimetry was used to study the crystallization andmelting of nylon 610. For nylon 610 crystallized from the melt state (260℃), the overall rateof bulk crystallization can be described by a simple Avrami equation with Avrami exponentn ≈ 2, independent of crystallization temperature. With the experimentally obtainedT_m~0 (235℃ ～ 255℃) of nylon 610, the fold surface free energy σ_e was determined to be35 ～38 erg/cm~2. The effects of annealing temperature and time on the melting of quenchednylon 610 were also investigated. For nylon 610 quenched at room temperature there isonly one DSC endotherm peak DSC scans on annealed samples exhibited an endothermpeak at approximately 10℃ above the annealing temperature. The size and position of theendothermic peak is strongly related to annealing temperature and time. An additionalthird melting was observed when quenched nylon 610 was annealed at high temperaturefor a sufficiently long residence time. The existence of the third melting peak suggests thatmore than one kind of distribution of lamella thickness may occur when quenched nylon610 is annealed. The implications of these results in terms of crystal thickening mechanismwere discussed.     

Noether's Theorem on Surfaces

In this article we prove a version of Noether's Theorem (of Calculus of Variations) which is valid for a general regular (compact) surface. As a special feature, the Lie group of transformations is allowed to act on the Cartesian product of the surface and the functional space. Additionally, we apply the Theorem to a problem in Classical Differential Geometry of surfaces. The given application is actually an example showing how Noether's Theorem can be used to construct invariant properties of the solutions to variational problems defined on surfaces, or equivalently, of the solutions to the associated Euler-Lagrange equations resulting from them.     

Numerical solution of high-order differential equations by using periodized Shannon wavelets

In this paper, periodized Shannon wavelets are applied as basis functions in solution of the high-order ordinary differential equations and eigenvalue problem. The first periodized Shannon wavelets are defined. The second the connection coefficients of periodized Shannon wavelets are related by a simple variable transformation to the Cattani connection coefficients. Finally, collocation method is used for solving the high-order ordinary differential equations and eigenvalue problem. Some equations are solved in order to find out advantage of such choice of the basis functions.     

Time-delay effects on dynamics of a two-actor conflict model

We present a study of time-delay effects on a two-actor conflict model based on nonlinear differential equations. The state of each actor depends on its own state in isolation, its previous state, its inertia to change, the positive or negative feedback and a time delay in the state of the other actor. We use both theoretical and numerical approaches to characterize the evolution of the system for several values of time delays. We find that, under particular conditions, a time delay leads to the appearance of oscillations in the states of the actors. Besides, phase portraits for the trajectories are presented to illustrate the evolution of the system for different time delays. Finally, we discuss our results in the context of social conflict models.     

Euler–MacLaurin formulas via differential operators

Recently there has been a renewed interest in asymptotic Euler–MacLaurin formulas, because of their applications to spectral theory of differential operators. Using elementary means, we recover such formulas for compactly supported smooth functions on intervals, polygons, and three-dimensional polytopes, where the coefficients in the asymptotic expansion are sums of differential operators involving only derivatives of the function in directions normal to the faces of the polytope. Our formulas apply to wedges of any dimension.     

Determination of Codeine,Dionin and Thebaine by Differential Pulse Polarography

Abstract

The method proposed for determining codeine, dionin and thebaine by differential pulse polarography is based on the reduction (in ammoniacal medium) of the nitroderivatives obtained by dissolving the substances in concentrated nitric acid. The values of the reduction potentials range between -0.45 and -0.69 V. Morphine and heroine do not interfere in the determination of the mentioned alkaloids.     

Simple model for blistering mechanism

A simple model for blistering mechanism is proposed for energies higher than 20 keV. The model assumes that through the nucleation of smaller bubbles, a critical bubble radius is reached. The planar stress results of Jeffery for a semi-infinite plate with a circular hole subject to a uniform inner normal pressure are roughly taken as valid for the three-dimensional case. Under this assumption, the thickness of the blister's cover and critical ion dose for blister formation are calculated from the knowledge of the mean projected range of ions and blister diameter taken from experimental results. The resulting values are in agreement with the experimental values reported. The model can qualitatively explain breakage at the top of the dome-shaped blisters observed in molybdenum at 1100 K.     

On the feedback solutions of differential oligopoly games with hyperbolic demand curve and capacity accumulation

To safeguard analytical tractability and the concavity of objective functions, the vast majority of models belonging to oligopoly theory relies on the restrictive assumption of linear demand functions. Here we lay out the analytical solution of a differential Cournot game with hyperbolic inverse demand, where firms accumulate capacity over time à la Ramsey. The subgame perfect equilibrium is characterized via the Hamilton–Jacobi–Bellman equations solved in closed form both on infinite and on finite horizon setups. To illustrate the applicability of our model and its implications, we analyze the feasibility of horizontal mergers in both static and dynamic settings, and find appropriate conditions for their profitability under both circumstances. Static profitability of a merger implies dynamic profitability of the same merger. It appears that such a demand structure makes mergers more likely to occur than they would on the basis of the standard linear inverse demand.     

Design of robust differential microphone arrays with the Jacobi–Anger expansion

Due to their small size, differential microphone arrays (DMAs) are very attractive. Moreover, they have been effective in combating noise and reverberation. Recently, a new class of DMAs of different orders have been developed with the MacLaurin’s series and the frequency-independent patterns. However, the MacLaurin’s series does not approximate well the exponential function, which appears in the general definition of the beampattern, when the intersensor spacing is not small enough. To circumvent this problem, we propose in this paper to approximate the exponential function with the Jacobi–Anger expansion. Based on this approximation and the frequency-independent Chebyshev patterns, we derive first-, second-, and third-order DMAs. Furthermore, in order to improve the robustness of DMAs against white noise amplification, we propose to use more microphones combined with minimum-norm filters. It is also shown that the Jacobi–Anger expansion is optimal from a mean-squared error perspective. Simulations are carried out to evaluate the performance of the proposed DMAs.