scholarly journals On a nonlinear relation for computing the overpartition function

2021 ◽  
Vol 71 (3) ◽  
pp. 535-542
Author(s):  
Mircea Merca
Keyword(s):  
Recurrence Relation ◽  
High Precision ◽  
Convergent Series ◽  
New Method ◽  
Large Integer ◽  
Fast Computation ◽  
Real Numbers ◽  
Integer Arithmetic ◽  
Nonlinear Relation ◽  
Very High

Abstract In 1939, H. S. Zuckerman provided a Hardy-Ramanujan-Rademacher-type convergent series that can be used to compute an isolated value of the overpartition function p (n). Computing p (n) by this method requires arithmetic with very high-precision approximate real numbers and it is complicated. In this paper, we provide a formula to compute the values of p (n) that requires only the values of p (k) with k ≤ n/2. This formula is combined with a known linear homogeneous recurrence relation for the overpartition function p (n) to obtain a simple and fast computation of the value of p (n). This new method uses only (large) integer arithmetic and it is simpler to program.

scholarly journals Distinct partitions and overpartitions

2021 ◽  
Vol 38 (1) ◽  
pp. 149-158
Author(s):  
MIRCEA MERCA ◽  
Keyword(s):  
Partition Function ◽  
Recurrence Relation ◽  
Recurrence Relations ◽  
Convergent Series ◽  
The Other ◽  
Large Integer ◽  
Linear Recurrence ◽  
Fast Computation ◽  
Real Numbers ◽  
Very High

In 1963, Peter Hagis, Jr. provided a Hardy-Ramanujan-Rademacher-type convergent series that can be used to compute an isolated value of the partition function $Q(n)$ which counts partitions of $n$ into distinct parts. Computing $Q(n)$ by this method requires arithmetic with very high-precision approximate real numbers and it is complicated. In this paper, we investigate new connections between partitions into distinct parts and overpartitions and obtain a surprising recurrence relation for the number of partitions of $n$ into distinct parts. By particularization of this relation, we derive two different linear recurrence relations for the partition function $Q(n)$. One of them involves the thrice square numbers and the other involves the generalized octagonal numbers. The recurrence relation involving the thrice square numbers provide a simple and fast computation of the value of $Q(n)$. This method uses only (large) integer arithmetic and it is simpler to program. Infinite families of linear inequalities involving partitions into distinct parts and overpartitions are introduced in this context.

scholarly journals Analysis of Moving Chord Inclination Angles when Determining Curvature of Track Axis

2021 ◽  
pp. 92-103
Author(s):  
Wladyslaw Koc
Keyword(s):  
High Precision ◽  
Horizontal Plane ◽  
Vertical Plane ◽  
New Method ◽  
Turning Angle ◽  
Circular Arc ◽  
Inclination Angles ◽  
The Difference ◽  
Chord Method ◽  
Very High

The analysis presented in the paper explains computational issues related to the use of a new method of determining the curvature of the track axis – the so-called moving chord method. It indicates the versatility of this method – it may be used both in a horizontal and vertical plane. It also draws attention to its very high precision, as evidenced by the exemplary geometric cases under consideration. The focus here is on the computational foundations of the discussed method regarding the angles of inclination of the moving chord. It was found that for a circular arc in the horizontal plane, the inclination angles of the moving chord depend on the track turning angle, while the difference in inclination angles depends only on the radius of the arc. In the case of a circular arc in the vertical plane, the moving chord inclination angles are much smaller than in the horizontal plane, which is connected with the range of the applied radii of the arcs. As in the horizontal plane, the radius of the vertical curve is the only factor that determines the discrepancy in the inclination angles of the moving chord.

scholarly journals Stellar magnetic imaging from spectropolarimetric data

1996 ◽  
Vol 176 ◽  
pp. 53-60 ◽  
Author(s):  
J.-F. Donati
Keyword(s):  
Small Amplitude ◽  
High Accuracy ◽  
Spectral Lines ◽  
New Method ◽  
Doppler Imaging ◽  
Magnetic Imaging ◽  
Active Stars ◽  
Surface Fields ◽  
Very High

In this paper, I will review the capabilities of magnetic imaging (also called Zeeman-Doppler imaging) to reconstruct spot distributions of surface fields from sets of rotationnally modulated Zeeman signatures in circularly polarised spectral lines. I will then outline a new method to measure small amplitude magnetic signals (typically 0.1% for cool active stars) with very high accuracy. Finally, I will present and comment new magnetic images reconstructed from data collected in 1993 December at the Anglo-Australian Telescope (AAT).

scholarly journals Separate Universe calibration of the dependence of halo bias on cosmic web anisotropy

2020 ◽  
Vol 499 (3) ◽  
pp. 4418-4431 ◽  
Author(s):  
Sujatha Ramakrishnan ◽  
Aseem Paranjape
Keyword(s):  
Dark Matter ◽  
High Precision ◽  
Gaussian Distribution ◽  
Initial Perturbation ◽  
Analytical Framework ◽  
Web Environment ◽  
Wide Range ◽  
Galaxy Assembly ◽  
Very High ◽  
Good Agreement

ABSTRACT We use the Separate Universe technique to calibrate the dependence of linear and quadratic halo bias b1 and b2 on the local cosmic web environment of dark matter haloes. We do this by measuring the response of halo abundances at fixed mass and cosmic web tidal anisotropy α to an infinite wavelength initial perturbation. We augment our measurements with an analytical framework developed in earlier work that exploits the near-lognormal shape of the distribution of α and results in very high precision calibrations. We present convenient fitting functions for the dependence of b1 and b2 on α over a wide range of halo mass for redshifts 0 ≤ z ≤ 1. Our calibration of b2(α) is the first demonstration to date of the dependence of non-linear bias on the local web environment. Motivated by previous results that showed that α is the primary indicator of halo assembly bias for a number of halo properties beyond halo mass, we then extend our analytical framework to accommodate the dependence of b1 and b2 on any such secondary property that has, or can be monotonically transformed to have, a Gaussian distribution. We demonstrate this technique for the specific case of halo concentration, finding good agreement with previous results. Our calibrations will be useful for a variety of halo model analyses focusing on galaxy assembly bias, as well as analytical forecasts of the potential for using α as a segregating variable in multitracer analyses.

scholarly journals Equipartition principle for Wigner matrices

2021 ◽  
Vol 9 ◽  
Author(s):  
Zhigang Bao ◽  
László Erdős ◽  
Kevin Schnelli
Keyword(s):  
High Precision ◽  
Quantum Systems ◽  
Wigner Matrices ◽  
Very High

Abstract We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices.

Influence of Tooth Errors and Truing Principles of Grinding Wheel Abrasion for Machining Arc Enveloping Worm

2013 ◽  
Vol 652-654 ◽  
pp. 2153-2158
Author(s):  
Wu Ji Jiang ◽  
Jing Wei
Keyword(s):  
Mathematical Model ◽  
Case Studies ◽  
High Precision ◽  
High Performance ◽  
New Method ◽  
Grinding Wheel ◽  
Grinding Process ◽  
The Mathematical Model

Controlling the tooth errors induced by the variation of diameter of grinding wheel is the key problem in the process of ZC1 worm grinding. In this paper, the influence of tooth errors by d1, m and z1 as the grinding wheel diameter changes are analyzed based on the mathematical model of the grinding process. A new mathematical model and truing principle for the grinding wheel of ZC1 worm is presented. The shape grinding wheel truing of ZC1 worm is carried out according to the model. The validity and feasibility of the mathematical model is proved by case studies. The mathematical model presented in this paper provides a new method for reducing the tooth errors of ZC1 worm and it can meet the high-performance and high-precision requirements of ZC1 worm grinding.

Formation flying for very high precision astrometry: NEAT and micro-NEAT mission concepts

2014 ◽  
Vol 2 (1) ◽  
pp. 3 ◽  
Author(s):  
Fabien Malbet ◽  
Alexis Brandeker ◽  
Alain Léger ◽  
Bjorn Jakobsson ◽  
Renaud Goullioud ◽  
...  
Keyword(s):  
High Precision ◽  
Formation Flying ◽  
Very High ◽  
Precision Astrometry

A new method for TIMS high precision analysis of Ba and Sr isotopes for cosmochemical studies

2017 ◽  
Vol 32 (7) ◽  
pp. 1388-1399 ◽  
Author(s):  
Elsa Yobregat ◽  
Caroline Fitoussi ◽  
Bernard Bourdon
Keyword(s):  
Mass Spectrometry ◽  
High Resolution ◽  
High Precision ◽  
Thermal Ionization Mass Spectrometry ◽  
New Method ◽  
Ionization Mass ◽  
Sr Isotopes ◽  
Sr Resin ◽  
Thermal Ionization Mass ◽  
Isotope Measurements

A new protocol using Eichron™ Sr-resin for high-resolution Sr and Ba isotope measurements using thermal ionization mass spectrometry for cosmochemical samples.

A HIGHLY ACCURATE BOOTSTRAPPING ALGORITHM FOR WORD SENSE DISAMBIGUATION

2001 ◽  
Vol 10 (01n02) ◽  
pp. 5-21 ◽  
Author(s):  
RADA F. MIHALCEA ◽  
DAN I. MOLDOVAN
Keyword(s):  
High Precision ◽  
Word Sense Disambiguation ◽  
Original Text ◽  
Word Sense ◽  
New Words ◽  
Input Text ◽  
Ambiguous Words ◽  
Sense Disambiguation ◽  
Very High

In this paper, we present a bootstrapping algorithm for Word Sense Disambiguation which succeeds in disambiguating a subset of the words in the input text with very high precision. It uses WordNet and a semantic tagged corpus, for the purpose of identifying the correct sense of the words in a given text. The bootstrapping process initializes a set of ambiguous words with all the nouns and verbs in the text. It then applies various disambiguation procedures and builds a set of disambiguated words: new words are sense tagged based on their relation to the already disambiguated words, and then added to the set. This process allows us to identify, in the original text, a set of words which can be disambiguated with high precision; 55% of the verbs and nouns are disambiguated with an accuracy of 92%.

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