scholarly journals On the mean square of the remainder for the euclidean lattice point counting problem

2017 ◽  
Vol 221 (2) ◽  
pp. 637-659 ◽  
Author(s):  
Dubi Kelmer
Keyword(s):  
Lattice Point ◽  
Mean Square ◽  
Point Counting ◽  
Counting Problem ◽  
Euclidean Lattice ◽  
The Mean

scholarly journals The mean lattice point discrepancy

1995 ◽  
Vol 38 (3) ◽  
pp. 523-531 ◽  
Author(s):  
M. N. Huxley
Keyword(s):  
Root Mean Square ◽  
Lattice Point ◽  
Plane Curve ◽  
Lattice Points ◽  
Mean Square ◽  
Convex Plane ◽  
The Mean

Consider a sufficiently smooth simple closed convex plane curve enclosing the origin, expanding linearly with time. The root mean square of the discrepancy (number of lattice points minus area) from time t = M to t = M + 1 is almost as small as the root mean square discrepancy from time t = 0 to t = M, so the discrepancy has no memory.

scholarly journals The lattice point counting problem on the Heisenberg groups

2015 ◽  
Vol 65 (5) ◽  
pp. 2199-2233 ◽  
Author(s):  
Rahul Garg ◽  
Amos Nevo ◽  
Krystal Taylor
Keyword(s):  
Lattice Point ◽  
Heisenberg Groups ◽  
Point Counting ◽  
Counting Problem

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

The mean-square generalized delayed decision feedback sequence detector

2003 ◽  
Vol 14 (3) ◽  
pp. 265-268 ◽  
Author(s):  
Maurizio Magarini ◽  
Arnaldo Spalvieri ◽  
Guido Tartara
Keyword(s):  
Decision Feedback ◽  
Mean Square ◽  
The Mean

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

scholarly journals Electrical stimulator with mechanomyography-based real-time monitoring, muscle fatigue detection, and safety shut-off: a pilot study

2020 ◽  
Vol 65 (4) ◽  
pp. 461-468
Author(s):  
Jannatul Naeem ◽  
Nur Azah Hamzaid ◽  
Amelia Wong Azman ◽  
Manfred Bijak
Keyword(s):  
Muscle Fatigue ◽  
Real Time ◽  
Isometric Force ◽  
Mean Square ◽  
Clear Indication ◽  
Initial Value ◽  
Cord Injury ◽  
The Mean ◽  
Electrical Stimulator ◽  
Fatigue Detection

AbstractFunctional electrical stimulation (FES) has been used to produce force-related activities on the paralyzed muscle among spinal cord injury (SCI) individuals. Early muscle fatigue is an issue in all FES applications. If not properly monitored, overstimulation can occur, which can lead to muscle damage. A real-time mechanomyography (MMG)-based FES system was implemented on the quadriceps muscles of three individuals with SCI to generate an isometric force on both legs. Three threshold drop levels of MMG-root mean square (MMG-RMS) feature (thr50, thr60, and thr70; representing 50%, 60%, and 70% drop from initial MMG-RMS values, respectively) were used to terminate the stimulation session. The mean stimulation time increased when the MMG-RMS drop threshold increased (thr50: 22.7 s, thr60: 25.7 s, and thr70: 27.3 s), indicating longer sessions when lower performance drop was allowed. Moreover, at thr70, the torque dropped below 50% from the initial value in 14 trials, more than at thr50 and thr60. This is a clear indication of muscle fatigue detection using the MMG-RMS value. The stimulation time at thr70 was significantly longer (p = 0.013) than that at thr50. The results demonstrated that a real-time MMG-based FES monitoring system has the potential to prevent the onset of critical muscle fatigue in individuals with SCI in prolonged FES sessions.

Die Molekülstruktur des N-Chlorsdiwefeloxiddifluoridimids ClNSOF2 / The Molecular Structure of ClNSOF2

1974 ◽  
Vol 29 (6) ◽  
pp. 901-904 ◽  
Author(s):  
O. Oberhammer ◽  
O. Glemser ◽  
H. Klüver
Keyword(s):  
Molecular Structure ◽  
Electron Diffraction ◽  
Geometric Parameters ◽  
Mean Square ◽  
The Mean

The molecular structure of ClNSOF2 was determined by electron diffraction of gases. The following geometric parameters were obtained:Cl-N=1.715(5), S=N=1.484(7), S=O=1.394(3), S-F=1.548(3) Å, ∢ ClNS=114.7 (8), ∢ FSF=92.6(.8), ∢ NSF=111.8(.9) ∢ NSO=117.4 (3.1) and ∢ OSF=108.6 (.8)°. The results for the mean square amplitudes of vibration are given in the paper and an attempt is made to explain differences in corresponding parameters of some related molecules.

scholarly journals Prediction of shallow bit position based on vibration signal monitoring of bit broken rock

2021 ◽  
Vol 17 (1) ◽  
pp. 155014772199170
Author(s):  
Jinping Yu ◽  
Deyong Zou
Keyword(s):  
Acoustic Emission ◽  
Time Domain ◽  
Vibration Signal ◽  
Rock Breaking ◽  
Drill String ◽  
Mean Square ◽  
Drilling Force ◽  
Emission Signal ◽  
Force Signal ◽  
The Mean

The speed of drilling has a great relationship with the rock breaking efficiency of the bit. Based on the above background, the purpose of this article is to predict the position of shallow bit based on the vibration signal monitoring of bit broken rock. In this article, first, the mechanical research of drill string is carried out; the basic changes of the main mechanical parameters such as the axial force, torque, and bending moment of drill string are clarified; and the dynamic equilibrium equation theory of drill string system is analyzed. According to the similarity criterion, the corresponding relationship between drilling process parameters and laboratory test conditions is determined. Then, the position monitoring test system of the vibration bit is established. The acoustic emission signal and the drilling force signal of the different positions of the bit in the process of vibration rock breaking are collected synchronously by the acoustic emission sensor and the piezoelectric force sensor. Then, the denoised acoustic emission signal and drilling force signal are analyzed and processed. The mean value, variance, and mean square value of the signal are calculated in the time domain. The power spectrum of the signal is analyzed in the frequency domain. The signal is decomposed by wavelet in the time and frequency domains, and the wavelet energy coefficients of each frequency band are extracted. Through the wavelet energy coefficient calculated by the model, combined with the mean, variance, and mean square error of time-domain signal, the position of shallow buried bit can be analyzed and predicted. Finally, by fitting the results of indoor experiment and simulation experiment, it can be seen that the stress–strain curve of rock failure is basically the same, and the error is about 3.5%, which verifies the accuracy of the model.

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