2,200 research outputs found

    The influence of Galactic aberration on precession parameters determined from VLBI observations

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    The influence of proper motions of sources due to Galactic aberration on precession models based on VLBI data is determined. Comparisons of the linear trends in the coordinates of the celestial pole obtained with and without taking into account Galactic aberration indicate that this effect can reach 20 μ\muas per century, which is important for modern precession models. It is also shown that correcting for Galactic aberration influences the derived parameters of low-frequency nutation terms. It is therefore necessary to correct for Galactic aberration in the reduction of modern astrometric observations

    Higher order approximation of isochrons

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    Phase reduction is a commonly used techinque for analyzing stable oscillators, particularly in studies concerning synchronization and phase lock of a network of oscillators. In a widely used numerical approach for obtaining phase reduction of a single oscillator, one needs to obtain the gradient of the phase function, which essentially provides a linear approximation of isochrons. In this paper, we extend the method for obtaining partial derivatives of the phase function to arbitrary order, providing higher order approximations of isochrons. In particular, our method in order 2 can be applied to the study of dynamics of a stable oscillator subjected to stochastic perturbations, a topic that will be discussed in a future paper. We use the Stuart-Landau oscillator to illustrate the method in order 2

    Recognizing Graph Theoretic Properties with Polynomial Ideals

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    Many hard combinatorial problems can be modeled by a system of polynomial equations. N. Alon coined the term polynomial method to describe the use of nonlinear polynomials when solving combinatorial problems. We continue the exploration of the polynomial method and show how the algorithmic theory of polynomial ideals can be used to detect k-colorability, unique Hamiltonicity, and automorphism rigidity of graphs. Our techniques are diverse and involve Nullstellensatz certificates, linear algebra over finite fields, Groebner bases, toric algebra, convex programming, and real algebraic geometry.Comment: 20 pages, 3 figure

    Squeezed States and Helmholtz Spectra

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    The 'classical interpretation' of the wave function psi(x) reveals an interesting operational aspect of the Helmholtz spectra. It is shown that the traditional Sturm-Liouville problem contains the simplest key to predict the squeezing effect for charged particle states.Comment: 10 pages, Latex, 3 gzip-compressed figures in figh.tar.g

    The power of negations in cryptography

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    The study of monotonicity and negation complexity for Bool-ean functions has been prevalent in complexity theory as well as in computational learning theory, but little attention has been given to it in the cryptographic context. Recently, Goldreich and Izsak (2012) have initiated a study of whether cryptographic primitives can be monotone, and showed that one-way functions can be monotone (assuming they exist), but a pseudorandom generator cannot. In this paper, we start by filling in the picture and proving that many other basic cryptographic primitives cannot be monotone. We then initiate a quantitative study of the power of negations, asking how many negations are required. We provide several lower bounds, some of them tight, for various cryptographic primitives and building blocks including one-way permutations, pseudorandom functions, small-bias generators, hard-core predicates, error-correcting codes, and randomness extractors. Among our results, we highlight the following. Unlike one-way functions, one-way permutations cannot be monotone. We prove that pseudorandom functions require logn − O(1) negations (which is optimal up to the additive term). We prove that error-correcting codes with optimal distance parameters require logn − O(1) negations (again, optimal up to the additive term). We prove a general result for monotone functions, showing a lower bound on the depth of any circuit with t negations on the bottom that computes a monotone function f in terms of the monotone circuit depth of f. This result addresses a question posed by Koroth and Sarma (2014) in the context of the circuit complexity of the Clique problem

    Resistive superconducting fault current limiter coil design using multistrand MgB2 wire

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    Resistive superconducting fault current limiters (SFCLs) offer the advantages of low weight and compact structure. Magnesium diboride (MgB2) in simple round wire form has been previously tested and shown to be suitable as a low-cost resistive SFCL. The primary objective of this work was to design a resistive SFCL for an 11-kV substation using multiple MgB2 wire strands. This paper will look into the options for the coil design. Two types of low-inductance solenoidal coils, namely, the series-connected coil and the parallel-connected coil, were theoretically examined and compared. This paper also reports the experimental results of two multistrand MgB 2 prototype coils used as a resistive SFCL. This paper demonstrates the potential of SFCL coils using multistrand MgB2 wire for distribution network levels.</p

    Resistive Superconducting Fault Current Limiter AC Loss Measurements and Analysis

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    Resistive superconducting fault current limiters (SFCLs) offer the advantages of low weight and compact structure. Multistrand magnesium diboride (MgB2) wire can be used in the SFCL coil design to increase the transport current capacity. A monofilament 0.36-mm MgB2 wire with a stainless-steel sheath was used to build three SFCL coils with 3 strands, 16 (9+7) strands, and 50 (28+22) strands of the MgB2 wire. The quench current level and ac losses in the MgB2 wire are critical design parameters for a resistive SFCL. The experimental results showed that the measured quench current densities reduced as the strand number increased and the ac losses increased as the strand number increased. An axisymmetric 2-D finite-element (FE) model therefore was built to analyze the current distribution and the ac losses in the coil. The multistranded coil FE model showed that proximity effect can modify the current distribution in the strands. This not only reduces the current carrying ability but also increases the ac losses nonlinearly. The FE model confirmed the issues highlighted by the experimental testing. Finally, a winding method for the multistrand coil has been proposed to reduce the impact of these effects.</p

    f-Oscillators and Nonlinear Coherent States

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    The notion of f-oscillators generalizing q-oscillators is introduced. For classical and quantum cases, an interpretation of the f-oscillator is provided as corresponding to a special nonlinearity of vibration for which the frequency of oscillation depends on the energy. The f-coherent states (nonlinear coherent states) generalizing q-coherent states are constructed. Applied to quantum optics, photon distribution function, photon number means, and dispersions are calculated for the f-coherent states as well as the Wigner function and Q-function. As an example, it is shown how this nonlinearity may affect the Planck distribution formula.Comment: Latex, 32 pages, accepted by Physica Script
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