Search results for "Multiplicative function"
showing 10 items of 35 documents
Selmer's Multiplicative Algorithm
2011
Abstract.The behavior of the multiplicative acceleration of Selmer's algorithm is widely unknown and no general result on convergence has been detected yet. Solely for its 2-dimensional, periodic expansions, there exist some results on convergence and approximation due to Fritz Schweiger. In this paper we show that periodic expansions of any dimension do in fact converge and that the coordinates of the limit points are rational functions of the largest eigenvalue of the periodicity matrix.
Symmetry-assisted adversaries for quantum state generation
2011
We introduce a new quantum adversary method to prove lower bounds on the query complexity of the quantum state generation problem. This problem encompasses both, the computation of partial or total functions and the preparation of target quantum states. There has been hope for quite some time that quantum state generation might be a route to tackle the $backslash$sc Graph Isomorphism problem. We show that for the related problem of $backslash$sc Index Erasure our method leads to a lower bound of $backslash Omega(backslash sqrt N)$ which matches an upper bound obtained via reduction to quantum search on $N$ elements. This closes an open problem first raised by Shi [FOCS'02]. Our approach is …
Inversion formulae for the integral transform on a locally compact zero-dimensional group
2009
Abstract Generalized inversion formulae for multiplicative integral transform with a kernel defined by characters of a locally compact zero-dimensional abelian group are obtained using a Kurzweil-Henstock type integral.
Arithmetic visibility estimates for OECD countries with three government levels
2003
The importance of fiscal visibility has been well known for a long time but attempts to quantify it by taking the internal structure of every type of revenue and expenditure in a fiscal system into consideration are recent. Indicators used until now rest on structural parameters combined in a multiplicative way with a 0 estimate always resulting in at least one of such factors being null. An alternative way to measure fiscal visibility consists of combining parametric values in an additive instead of a multiplicative form. Calculations can then show estimates which are much more sensitive to the initial values. The aim of this contribution is to present new additive indicators that are appl…
Approximate solution of the Fokker-Planck-Kolmogorov equation
2002
The aim of this paper is to present a thorough investigation of approximate techniques for estimating the stationary and non-stationary probability density function (PDF) of the response of nonlinear systems subjected to (additive and/or multiplicative) Gaussian white noise excitations. Attention is focused on the general scheme of weighted residuals for the approximate solution of the Fokker-Planck-Kolmogorov (FPK) equation. It is shown that the main drawbacks of closure schemes, such as negative values of the PDF in some regions, may be overcome by rewriting the FPK equation in terms of log-probability density function (log-PDF). The criteria for selecting the set of weighting functions i…
Direct evaluation of jumps for nonlinear systems under external and multiplicative impulses
2015
In this paper the problem of the response evaluation of nonlinear systems under multiplicative impulsive input is treated. Such systems exhibit a jump at each impulse occurrence, whose value cannot be predicted through the classical differential calculus. In this context here the correct jump evaluation of nonlinear systems is obtained in closed form for two general classes of nonlinear multiplicative functions. Analysis has been performed to show the different typical behaviors of the response, which in some cases could diverge or converge to zero instantaneously, depending on the amplitude of the Dirac's delta.
FINITE-SIZE CORRECTIONS TO CORRELATION FUNCTION AND SUSCEPTIBILITY IN 2D ISING MODEL
2006
Transfer matrix calculations of the critical two-point correlation function in 2D Ising model on a finite-size [Formula: see text] lattice with periodic boundaries along 〈11〉 direction are extended to L = 21. A refined analysis of the correlation function in 〈10〉 crystallographic direction at the distance r = L indicates the existence of a nontrivial finite-size correction of a very small amplitude with correction-to-scaling exponent ω < 2 in agreement with our foregoing study for L ≤ 20. Here we provide an additional evidence and show that amplitude a of the multiplicative correction term 1 + aL-ωis about -3.5·10-8if ω = 1/4 (the expected value). We calculate also the susceptibility for…
Multiplicative Loops of Quasifields Having Complex Numbers as Kernel
2017
We determine the multiplicative loops of locally compact connected 4-dimensional quasifields Q having the field of complex numbers as their kernel. In particular, we turn our attention to multiplicative loops which have either a normal subloop of dimension one or which contain a subgroup isomorphic to $$Spin_3({\mathbb {R}})$$ . Although the 4-dimensional semifields Q are known, their multiplicative loops have interesting Lie groups generated by left or right translations. We determine explicitly the quasifields Q which coordinatize locally compact translation planes of dimension 8 admitting an at least 16-dimensional Lie group as automorphism group.
Power Corrections to Event Shapes with Mass-Dependent Operators
2013
We introduce an operator depending on the "transverse velocity'' r that describes the effect of hadron masses on the leading 1/Q power correction to event-shape observables. Here, Q is the scale of the hard collision. This work builds on earlier studies of mass effects by Salam and Wicke [J. High Energy Phys. 05 (2001) 061] and of operators by Lee and Sterman [Phys. Rev. D 75, 014022 (2007)]. Despite the fact that different event shapes have different hadron mass dependence, we provide a simple method to identify universality classes of event shapes whose power corrections depend on a common nonperturbative parameter. We also develop an operator basis to show that at a fixed value of Q, the…
Normalizability, Synchronicity, and Relative Exactness for Vector Fields in C2
2004
In this paper, we study the necessary and su.cient condition under which an orbitally normalizable vector field of saddle or saddle-node type in C2 is analytically conjugate to its formal normal form (i.e., normalizable) by a transformation fixing the leaves of the foliation locally. First, we express this condition in terms of the relative exactness of a certain 1-form derived from comparing the time-form of the vector field with the time-form of the normal form. Then we show that this condition is equivalent to a synchronicity condition: the vanishing of the integral of this 1-form along certain asymptotic cycles de.ned by the vector field. This can be seen as a generalization of the clas…