On the study of a third-order mechanical oscillator

In this paper, the study of a third-order mechanical oscillator is presented by demonstrating its equivalence to the well-known R.C. multivibrator with two additional reactive elements. The conditions for the oscillator's possession of periodic solutions are presented. It is also shown that under certain conditions, the study of the given third-order autonomous system can be reduced to the study of an equivalent second-order, non-autonomous system.

Third Polymorph of Phenylacetylene

A third polymorph of phenylacetylene (Z' = 6), which is obtained by quenching the liquid, shows some similarities to the two earlier known forms, and the adoption of a high Z' value in this crystal form is discussed.

Head-on infall of two compact objects: Third post-Newtonian energy flux

Head-on infall of two compact objects with arbitrary mass ratio is investigated using the multipolar post-Minkowskian approximation method. At the third post-Newtonian order the energy flux, in addition to the instantaneous contributions, also includes hereditary contributions consisting of the gravitational-wave tails, tails-of-tails, and the tail-squared terms. The results are given both for infall from infinity and also for infall from a finite distance. These analytical expressions should be useful for the comparison with the high accuracy numerical relativity results within the limit in which post-Newtonian approximations are valid.

Third harmonic generation through shaped superconductors

This paper describes a methodology of obtaining only third harmonic along with the fundamental using shaped superconductors. It also indicates how one can design a nonlinear superconducting resistor with the required current versus resistance variation.

Singularity structure of third-order dynamical systems .2

The singularity structure of the solutions of a general third-order system, with polynomial right-hand sides of degree less than or equal to two, is studied about a movable singular point, An algorithm for transforming the given third-order system to a third-order Briot-Bouquet system is presented, The dominant behavior of a solution of the given system near a movable singularity is used to construct a transformation that changes the given system directly to a third-order Briot-Bouquet system. The results of Horn for the third-order Briot-Bouquet system are exploited to give the complete form of the series solutions of the given third-order system; convergence of these series in a deleted neighborhood of the singularity is ensured, This algorithm is used to study the singularity structure of the solutions of the Lorenz system, the Rikitake system, the three-wave interaction problem, the Rabinovich system, the Lotka-Volterra system, and the May-Leonard system for different sets of parameter values. The proposed approach goes far beyond the ARS algorithm.

Novel phase-transition behavior near liquid/liquid critical points of aqueous solutions: Formation of a third phase at the interface

We report a novel phase behavior in aqueous solutions of simple organic solutes near their liquid/liquid critical points, where a solid-like third phase appears at the liquid/liquid interface. The phenomenon has been found in three different laboratories. It appears in many aqueous systems of organic solutes and becomes enhanced upon the addition of salt to these solutions.

The standard enthalpy and entropy of formation of Rh2O3 - A third-law optimization

The standard Gibbs energy of formation of Rh203 at high temperature has been determined recently with high precision. The new data are significantly different from those given in thermodynamic compilations.Accurate values for enthalpy and entropy of formation at 298.15 K could not be evaluated from the new data,because reliable values for heat capacity of Rh2O3 were not available. In this article, a new measurement of the high temperature heat capacity of Rh2O3 using differential scanning calorimetry (DSC) is presented.The new values for heat capacity also differ significantly from those given in compilations. The information on heat capacity is coupled with standard Gibbs energy of formation to evaluate values for standard enthalpy and entropy of formation at 289.15 K using a multivariate analysis. The results suggest a major revision in thermodynamic data for Rh2O3. For example, it is recommended that the standard entropy of Rh203 at 298.15 K be changed from 106.27 J mol-' K-'given in the compilations of Barin and Knacke et al. to 75.69 J mol-' K". The recommended revision in the standard enthalpy of formation is from -355.64 kJ mol-'to -405.53 kJ mol".

Differentially private stochastic gradient descent algorithm for multiparty classification

We consider the problem of developing privacy-preserving machine learning algorithms in a dis-tributed multiparty setting. Here different parties own different parts of a data set, and the goal is to learn a classifier from the entire data set with-out any party revealing any information about the individual data points it owns. Pathak et al [7]recently proposed a solution to this problem in which each party learns a local classifier from its own data, and a third party then aggregates these classifiers in a privacy-preserving manner using a cryptographic scheme. The generaliza-tion performance of their algorithm is sensitive to the number of parties and the relative frac-tions of data owned by the different parties. In this paper, we describe a new differentially pri-vate algorithm for the multiparty setting that uses a stochastic gradient descent based procedure to directly optimize the overall multiparty ob-jective rather than combining classifiers learned from optimizing local objectives. The algorithm achieves a slightly weaker form of differential privacy than that of [7], but provides improved generalization guarantees that do not depend on the number of parties or the relative sizes of the individual data sets. Experimental results corrob-orate our theoretical findings.

Third order trace formula

In J. Funct. Anal. 257 (2009) 1092-1132, Dykema and Skripka showed the existence of higher order spectral shift functions when the unperturbed self-adjoint operator is bounded and the perturbation is Hilbert-Schmidt. In this article, we give a different proof for the existence of spectral shift function for the third order when the unperturbed operator is self-adjoint (bounded or unbounded, but bounded below).

Counterfactual quantum certificate authorization

We present a multipartite protocol in a counterfactual paradigm. In counterfactual quantum cryptography, secure information is transmitted between two spatially separated parties even when there is no physical travel of particles transferring the information between them. We propose here a tripartite counterfactual quantum protocol for the task of certificate authorization. Here a trusted third party, Alice, authenticates an entity Bob (e.g., a bank) that a client Charlie wishes to securely transact with. The protocol is counterfactual with respect to either Bob or Charlie. We prove its security against a general incoherent attack, where Eve attacks single particles.