Search results for "Linear equation"
showing 10 items of 102 documents
New Developments in Quantum Algorithms
2010
In this survey, we describe two recent developments in quantum algorithms. The first new development is a quantum algorithm for evaluating a Boolean formula consisting of AND and OR gates of size N in time O(\sqrt{N}). This provides quantum speedups for any problem that can be expressed via Boolean formulas. This result can be also extended to span problems, a generalization of Boolean formulas. This provides an optimal quantum algorithm for any Boolean function in the black-box query model. The second new development is a quantum algorithm for solving systems of linear equations. In contrast with traditional algorithms that run in time O(N^{2.37...}) where N is the size of the system, the …
Linear Waves in Electrical Transmission Lines
1996
Nowadays, linear transmission lines provide vital links in virtually all communications and computer systems, and the parallel-wire line is still widely used today in open-wire form, in coaxial cables and microstrips. The standard twoconductor transmission line is an important familiar system, that is able to support the propagation of transverse electromagnetic modes and is of great interest in many practical situations. We have all often studied this electrical circuit or variation of it in elementary electronics, physics, or mathematics courses (Ramo et al. 1965, Davidson 1978, Badlock and Bridgeman 1981). In fact, the study of linear transmission lines is an old problem: in their simple…
An efficient analytical approach for obtaining a five parameters model of photovoltaic modules using only reference data
2013
Exploiting the equivalent one-diode circuit of a photovoltaic (PV) module, this paper proposes a novel and fully analytical model to predict the electrical performance upon solar irradiance intensity and PV module temperature. The model refers essentially to an equivalent circuit governed by five parameters and the extraction of them permits to describe the current–voltage curve of the PV panel and consequently permits to assess the energy output of PV modules. The proposed model extracts the five characteristic parameters using only exact analytical relationship and tabular data always available such as short-circuit current, open circuit voltage and the Maximum Power Point (MPP). The diff…
Stability of the equilibrium state of the equation system of a viscous barotropic gas in the model of atmosphere
2006
We consider the system of equations of viscous gas motion whose pressure is related to the density by the law $p = h \varrho^\gamma$ with 1<γ <2, in a domain defined by two levels of geopotential. Under the force due to geopotential and the Coriolis force, we prove the stability of the equilibrium state in a suitable Sobolev space. Keywords: Viscous barotropic gas, Equilibrium state, Coriolis force Mathematics Subject Classification (2000): 35Q35, 76N15
Heat exchangers and linear image processing theory
1989
Abstract This paper shows that the transient analysis of some heat exchangers can be derived easily with the linear equations of image processing theory. Partial differential equations of the cross-flow, parallelflow and rotary heat exchangers are considered together with the corresponding discrete models for linear image processing. Some numerical examples show that the nature of the heat and/or mass transfer problems is similar to those of image processing.
Dynamical equivalence of impulsive quasilinear equations
2015
Abstract Using Green type map we can find sufficient conditions under which an impulsive quasilinear equation is dynamically equivalent to its corresponding linear equation. This result extends Grobman Hartman theorem for equations without ordinary dichotomy.
Beyond second-order convergence in simulations of binary neutron stars in full general relativity
2014
Despite the recent rapid progress in numerical relativity, a convergence order less than the second has so far plagued codes solving the Einstein-Euler system of equations. We report simulations of the inspiral of binary neutron stars in quasi-circular orbits computed with a new code employing high-order, high-resolution shock-capturing, finite-differencing schemes that, for the first time, go beyond the second-order barrier. In particular, without any tuning or alignment, we measure a convergence order above three both in the phase and in the amplitude of the gravitational waves. Because the new code is able to calculate waveforms with very small phase errors already at modest resolutions,…
An HLLC Riemann solver for resistive relativistic magnetohydrodynamics
2017
We present a new approximate Riemann solver for the augmented system of equations of resistive relativistic magnetohydrodynamics (RRMHD) that belongs to the family of Harten-Lax-van Leer contact wave (HLLC) solvers. In HLLC solvers, the solution is approximated by two constant states flanked by two shocks separated by a contact wave. The accuracy of the new approximate solver is calibrated through one- and two-dimensional test problems.
Integral Reduction with Kira 2.0 and Finite Field Methods
2021
We present the new version 2.0 of the Feynman integral reduction program Kira and describe the new features. The primary new feature is the reconstruction of the final coefficients in integration-by-parts reductions by means of finite field methods with the help of FireFly. This procedure can be parallelized on computer clusters with MPI. Furthermore, the support for user-provided systems of equations has been significantly improved. This mode provides the flexibility to integrate Kira into projects that employ specialized reduction formulas, direct reduction of amplitudes, or to problems involving linear system of equations not limited to relations among standard Feynman integrals. We show…
Decomposition of one-loop QCD amplitudes into primitive amplitudes based on shuffle relations
2013
We present the decomposition of QCD partial amplitudes into primitive amplitudes at one-loop level and tree level for arbitrary numbers of quarks and gluons. Our method is based on shuffle relations. This method is purely combinatorial and does not require the inversion of a system of linear equations.