text:
# Passing Centre Bracket

Passing Centre Bracket. This special version of our centre bracket is for use with “C”passing rings when a pole is very long and requires additional support It is available in all of our metal finishes. A longer 100mm projection version of this bracket is available to clear sills and radiators, or where a blind is fitted behind the curtains.
Custom and adjustable projections are also offered where the standard size is not appropriate.

### Holbein Catalogue Description

Materials:
Solid Brass
Dimensions:
16mm pole: Projection 25mm x Height 30mm x Width 50mm

19mm pole: Projection 32mm x Height 32mm x Width 55mm

25mm pole: Projection 32mm x Height 35mm x Width 60mm

32mm pole: Projection 35mm x Height 36mm x Width 62mm

38mm pole: Projection 39mm x Height 42mm x Width 85mm

50mm pole: Projection 39mm x Height 42mm x Width 85mm

63mm pole: Projection 50mm x Height 50mm x Width 100mm

75mm pole: Projection 50mm x Height 55mm x Width 110mm

projection is to back of pole


text:
# Detect original sound waves

I have just presented a project of mine regarding sound recognition using neural networks. I told during the presentation that I decided to only recognize one sound (musical notes coming from a guitar) at any point in time, explaining that recognizing multiple sounds is very hard or impossible.

I apply FFT on the soundwave and feed that into a neural network. My question is, if I were to record multiple sounds at once, couldn't the FFT data be exactly the same for different sounds?

I mean, if you combine $\sin(x)$ and $\sin(x+\pi)$ you get a wave that is a straight line. You also get a straight line for $\sin(2x)$ and $\sin (2x + \pi/2)$. So, two different set of waves give the same combined wave, that will have the same FFT data.

But I got confused because the professor said that you can always decompose the sound into its original elements (e.:. take a chord that has 6 different notes played individually) because the data is in time-domain. Can you really always decompose a sound wave in its components? What about the case above? He further explained that in "space-domain" you can have the problem I mentioned above, but in the time-domain not?

PS: I don't know if this is the right Stack Exchange site to ask this question on.

Most sounds (even the sound of a "single note") contain multiple frequencies. For pure sounds, there is the fundamental frequency and its harmonics, but almost any "real" sound contains some additional components - due to the envelope of the sound (e.g. the fact that a string must be plucked, then decays) or due to sampling (your sample is finite - so there will be some effects due to this truncation of the sound wave).

When you do a Fourier Transform, you will see all the frequency components. It is quite easy to detect the pitch of multiple strings struck at the same time in, say, a piano chord. Now depending on your definition of "recognizing" different sounds, it may be tough to detect two notes that are sounded simultaneously but an octave apart (so that one sound is in essence covering the harmonics of the other). The ear is remarkably good at picking up the difference - for example, we can tell that the higher note is not exactly in phase, and that the amplitude of the second harmonic (the fundamental of the higher note) is higher than it would be if it was just the second harmonic of the lower note.

Of course if you play two notes of the same frequency and phase, then you will not be able to tell them apart (except by the fact that the amplitude will be larger than you expect from a "single note", perhaps). But "real" sounds, of musical instruments, will have sufficiently unique signatures that you can "see" them.

You might be interested in an answer I wrote a while ago where I used a simple iPhone app to analyze the spectrum of the sound of a coin being dropped; this shows that there are multiple harmonics for different sounds, and that you can most likely see (by looking at the combined spectrum) the sum of these two sounds - and tell them apart. It would actually be a fun application of your work to detect "how much money did I drop?".

• The thing that confused me is related to this: It is quite easy to detect the pitch of multiple strings struck at the same time in, say, a piano chord. I knew that you could detect entire chords and then based on musical knowledge get the individual notes played. The professor said that there are software that recognize the individual notes that were played in a chord. I tend to believe that that software only recognizes the chord and then using a dictionary retrieves the notes that form that chord. I bet that if you play a chord that is not used in music it won't recognize the notes. – Cristy Jul 18 '16 at 13:50
• Your professor is right; you don't need a dictionary to extract the chord from the FFT. You might want to look at this answer and links therein. (The dsp stack exchange has a number of hits on "chord recognition" as well...) – Floris Jul 18 '16 at 13:54
• @Cristy, try it with the system you developed for your project. Play a single note and look at the FFT result. Then play a chord and look at the FFT. What you should see is that the FFT makes the individual notes of the chord very clear. – The Photon Jul 18 '16 at 14:08
• "I tend to believe that that software only recognizes the chord and then using a dictionary retrieves the notes that form that chord" That doesn't make sense to me. There are a literally a hundred (and probably more than that) different "sets of notes" that are the same "chord" (say C major) on a piano. How would your "dictionary" deal with that? – alephzero Jul 18 '16 at 14:13
• One of the things you could try is this - play an arpeggio on the guitar, and detect (in time domain) the moment each note is struck; then take an FFT "just before" and "just after" - and look at the difference, which will be caused by the new note just added. That would powerfully improve your algorithm in a first step to full chord recognition. Also look at comb filters which remove a note and its harmonics, as a first step to making this task easier. – Floris Jul 18 '16 at 14:16

format: plain


text:
get_edgeprobs {BCDAG} R Documentation

## Compute posterior probabilities of edge inclusion from the MCMC output

### Description

This function computes the posterior probability of inclusion for each edge u -> v given the MCMC output of learn_DAG;

### Usage

get_edgeprobs(learnDAG_output)

### Arguments

 learnDAG_output object of class bcdag

### Details

Output of learn_dag function consists of S draws from the joint posterior of DAGs and DAG-parameters in a zero-mean Gaussian DAG-model; see the documentation of learn_DAG for more details.

The posterior probability of inclusion of u -> v is estimated as the frequency of DAGs visited by the MCMC which contain the directed edge u -> v. Posterior probabilities are collected in a (q,q) matrix with (u,v)-element representing the estimated posterior probability of edge u -> v.

### Value

A (q,q) matrix with posterior probabilities of edge inclusion

### Author(s)

Federico Castelletti and Alessandro Mascaro

### References

F. Castelletti and A. Mascaro (2021). Structural learning and estimation of joint causal effects among network-dependent variables. Statistical Methods and Applications, Advance publication.

### Examples

# Randomly generate a DAG and the DAG-parameters
q = 8
w = 0.2
set.seed(123)
DAG = rDAG(q = q, w = w)
outDL = rDAGWishart(n = 1, DAG = DAG, a = q, U = diag(1, q))
L = outDL$L; D = outDL$D
Sigma = solve(t(L))%*%D%*%solve(L)
# Generate observations from a Gaussian DAG-model
n = 200
X = mvtnorm::rmvnorm(n = n, sigma = Sigma)
# Run the MCMC (Set S = 5000 and burn = 1000 for better results)
out_mcmc = learn_DAG(S = 500, burn = 100, a = q, U = diag(1,q)/n, data = X, w = 0.1,
fast = TRUE, save.memory = FALSE)
# Compute posterior probabilities of edge inclusion
get_edgeprobs(out_mcmc)

[Package BCDAG version 1.0.0 Index]


text:
# How do you solve n/3-5=12?

Apr 3, 2018

$n = 51$

#### Explanation:

Isolate $n$

$\frac{n}{3} - 5 = 12$

$\frac{n}{3} - 5 + 5 = 12 + 5 \rightarrow$ Add 5 to each side

$\frac{n}{3} = 17 \rightarrow$ Multiply each side by 3

$\frac{n}{3} \cdot 3 = 17 \cdot 3$

$n = 51 \rightarrow$ This is the answer

Apr 3, 2018

$n = 51$

#### Explanation:

$\frac{n}{3} - 5 = 12$

$\frac{n}{3} - 5 + 5 = 12 + 5$

$\frac{n}{3} = 17$

$\frac{n}{3} \times 3 = 17 \times 3$

$n = 51$


text:
elliptic_eu( z , m )

The incomplete elliptic integral of the second kind of a modified argument z and parameter m in SageMath. Defined by

$E(z|m) = \int_0^{ \sin[ \operatorname{sn}^{-1}z ] } du \sqrt{ 1 - m \sin^2 u }$

Note that all elliptic integrals in SageMath use the parameter rather than the elliptic modulus k, which is related to the parameter by $$m = k^2$$.

Plot on the real axis:


text:
core, lib, modules: restructured source code tree

- new folder src/ to hold the source code for main project applications
- main.c is in src/
- all core files are subfolder are in src/core/
- modules are in src/modules/
- libs are in src/lib/
- application Makefiles are in src/
- application binary is built in src/ (src/kamailio)

Daniel-Constantin Mierla authored on 07/12/2016 11:03:51
Showing 1 changed files
 1 1 deleted file mode 100644 ... ... @@ -1,39 +0,0 @@ 1 -/* 2 - * Copyright (C) 2001-2003 FhG Fokus 3 - * 4 - * This file is part of Kamailio, a free SIP server. 5 - * 6 - * Kamailio is free software; you can redistribute it and/or modify 7 - * it under the terms of the GNU General Public License as published by 8 - * the Free Software Foundation; either version 2 of the License, or 9 - * (at your option) any later version 10 - * 11 - * Kamailio is distributed in the hope that it will be useful, 12 - * but WITHOUT ANY WARRANTY; without even the implied warranty of 13 - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14 - * GNU General Public License for more details. 15 - * 16 - * You should have received a copy of the GNU General Public License  17 - * along with this program; if not, write to the Free Software  18 - * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 19 - */ 20 -/*! 21 - * \file 22 - * \brief Kamailio core :: compatibility defs for emergency roll-back if things do not work  23 - *  24 - * \ingroup core  25 - * Module: \ref core  26 - *  27 - * if that happens: 28 - * - a) define PRESERVE_ZT (affects most of parser) 29 - * - b) define DONT_REMOVE_ZT (affects first line) 30 - * - c) define SCRATCH 31 - * - d) undefine REMOVE_ALL_ZT (affects via) 32 - */ 33 - 34 - 35 -#ifndef _COMP_DEFS_H 36 -#define _COMP_DEFS_H 37 - 38 - 39 -#endif

core : Update include files - delete IDs, update doxygen, delete history

Olle E. Johansson authored on 03/01/2015 10:55:48
Showing 1 changed files
 ... ... @@ -1,16 +1,14 @@ 1 1  /* 2 - * $Id$ 3 - * 4 2  * Copyright (C) 2001-2003 FhG Fokus 5 3  * 6 - * This file is part of ser, a free SIP server. 4 + * This file is part of Kamailio, a free SIP server. 7 5  * 8 - * ser is free software; you can redistribute it and/or modify 6 + * Kamailio is free software; you can redistribute it and/or modify 9 7  * it under the terms of the GNU General Public License as published by 10 8  * the Free Software Foundation; either version 2 of the License, or 11 9  * (at your option) any later version 12 10  * 13 - * ser is distributed in the hope that it will be useful, 11 + * Kamailio is distributed in the hope that it will be useful, 14 12  * but WITHOUT ANY WARRANTY; without even the implied warranty of 15 13  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 16 14  * GNU General Public License for more details. ... ... @@ -19,8 +17,13 @@ 19 17  * along with this program; if not, write to the Free Software  20 18  * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 21 19  */ 22 - 23 -/*! \brief compatibility defs for emergency roll-back if things do not work ; 20 +/*! 21 + * \file 22 + * \brief Kamailio core :: compatibility defs for emergency roll-back if things do not work  23 + *  24 + * \ingroup core  25 + * Module: \ref core  26 + *  24 27  * if that happens: 25 28  * - a) define PRESERVE_ZT (affects most of parser) 26 29  * - b) define DONT_REMOVE_ZT (affects first line)

all: updated FSF address in GPL text

Anthony Messina authored on 04/07/2014 09:36:37 • Daniel-Constantin Mierla committed on 04/07/2014 09:37:36
Showing 1 changed files
 ... ... @@ -17,7 +17,7 @@ 17 17  * 18 18  * You should have received a copy of the GNU General Public License  19 19  * along with this program; if not, write to the Free Software  20 - * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA 20 + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 21 21  */ 22 22   23 23  /*! \brief compatibility defs for emergency roll-back if things do not work ;

oej authored on 25/10/2009 19:11:28
Showing 1 changed files
 ... ... @@ -10,11 +10,6 @@ 10 10  * the Free Software Foundation; either version 2 of the License, or 11 11  * (at your option) any later version 12 12  * 13 - * For a license to use the ser software under conditions 14 - * other than those described here, or to purchase support for this 15 - * software, please contact iptel.org by e-mail at the following addresses: 16 - * info@iptel.org 17 - * 18 13  * ser is distributed in the hope that it will be useful, 19 14  * but WITHOUT ANY WARRANTY; without even the implied warranty of 20 15  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ... ... @@ -25,12 +20,12 @@ 25 20  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA 26 21  */ 27 22   28 -/* compatibility defs for emergency roll-back if things do not work ; 23 +/*! \brief compatibility defs for emergency roll-back if things do not work ; 29 24  * if that happens: 30 - * a) define PRESERVE_ZT (affects most of parser) 31 - * b) define DONT_REMOVE_ZT (affects first line) 32 - * c) define SCRATCH 33 - * d) undefine REMOVE_ALL_ZT (affects via) 25 + * - a) define PRESERVE_ZT (affects most of parser) 26 + * - b) define DONT_REMOVE_ZT (affects first line) 27 + * - c) define SCRATCH 28 + * - d) undefine REMOVE_ALL_ZT (affects via) 34 29  */ 35 30   36 31

- Spelling checked - READMEs updated

Jan Janak authored on 24/08/2004 08:45:09
Showing 1 changed files
 ... ... @@ -1,7 +1,7 @@ 1 1  /* 2 2  * $Id$ 3 3  * 4 - * Copyright (C) 2001-2003 Fhg Fokus 4 + * Copyright (C) 2001-2003 FhG Fokus 5 5  * 6 6  * This file is part of ser, a free SIP server. 7 7  *

elderly (un)defs junked (hopefuly the right ones)

Jiri Kuthan authored on 28/02/2003 14:12:25
Showing 1 changed files
 ... ... @@ -37,35 +37,5 @@ 37 37  #ifndef _COMP_DEFS_H 38 38  #define _COMP_DEFS_H 39 39   40 -/* preserve "old" parser which delimited header fields by zeros, 41 - * and included deliminitors in body (which was the only way to 42 - * learn length of the whole header field  43 - */ 44 -#undef PRESERVE_ZT 45 - 46 -/* go one step further and remove ZT from first line too */ 47 -#undef DONT_REMOVE_ZT 48 - 49 -/* make it all -- move ZT away (Via) */ 50 -#define REMOVE_ALL_ZT 51 - 52 -/* don't use scratchpad anymore */ 53 -#undef SCRATCH 54 - 55 - 56 -/* ------------------------------------------------------ */ 57 -/* don't touch this -- that's helper macros depending on 58 - * the backwards compatibility macros above */ 59 -#ifdef PRESERVE_ZT 60 -# define SET_ZT(_ch) (_ch)='\0' 61 -#else 62 -# define SET_ZT(_ch) 63 -#endif 64 - 65 -#ifdef REMOVE_ALL_ZT 66 -# define VIA_ZT(_ch) 67 -#else 68 -# define VIA_ZT(ch) (_ch)='\0' 69 -#endif 70 40   71 41  #endif

scratchpad removed, textops changed to skip the first line

Jiri Kuthan authored on 29/01/2003 19:24:10
Showing 1 changed files
 ... ... @@ -25,7 +25,13 @@ 25 25  * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA 26 26  */ 27 27   28 -/* compatibility defs for emergency roll-back if things do not work */ 28 +/* compatibility defs for emergency roll-back if things do not work ; 29 + * if that happens: 30 + * a) define PRESERVE_ZT (affects most of parser) 31 + * b) define DONT_REMOVE_ZT (affects first line) 32 + * c) define SCRATCH 33 + * d) undefine REMOVE_ALL_ZT (affects via) 34 + */ 29 35   30 36   31 37  #ifndef _COMP_DEFS_H ... ... @@ -37,6 +43,15 @@ 37 43  */ 38 44  #undef PRESERVE_ZT 39 45   46 +/* go one step further and remove ZT from first line too */ 47 +#undef DONT_REMOVE_ZT 48 + 49 +/* make it all -- move ZT away (Via) */ 50 +#define REMOVE_ALL_ZT 51 + 52 +/* don't use scratchpad anymore */ 53 +#undef SCRATCH 54 + 40 55   41 56  /* ------------------------------------------------------ */ 42 57  /* don't touch this -- that's helper macros depending on ... ... @@ -47,4 +62,10 @@ 47 62  # define SET_ZT(_ch) 48 63  #endif 49 64   65 +#ifdef REMOVE_ALL_ZT 66 +# define VIA_ZT(_ch) 67 +#else 68 +# define VIA_ZT(ch) (_ch)='\0' 69 +#endif 70 + 50 71  #endif

backwards-compatibility defs file introduced

Jiri Kuthan authored on 27/01/2003 21:17:41
Showing 1 changed files
 1 1 new file mode 100644 ... ... @@ -0,0 +1,50 @@ 1 +/* 2 + * $Id$ 3 + * 4 + * Copyright (C) 2001-2003 Fhg Fokus 5 + * 6 + * This file is part of ser, a free SIP server. 7 + * 8 + * ser is free software; you can redistribute it and/or modify 9 + * it under the terms of the GNU General Public License as published by 10 + * the Free Software Foundation; either version 2 of the License, or 11 + * (at your option) any later version 12 + * 13 + * For a license to use the ser software under conditions 14 + * other than those described here, or to purchase support for this 15 + * software, please contact iptel.org by e-mail at the following addresses: 16 + * info@iptel.org 17 + * 18 + * ser is distributed in the hope that it will be useful, 19 + * but WITHOUT ANY WARRANTY; without even the implied warranty of 20 + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 21 + * GNU General Public License for more details. 22 + * 23 + * You should have received a copy of the GNU General Public License  24 + * along with this program; if not, write to the Free Software  25 + * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA 26 + */ 27 + 28 +/* compatibility defs for emergency roll-back if things do not work */ 29 + 30 + 31 +#ifndef _COMP_DEFS_H 32 +#define _COMP_DEFS_H 33 + 34 +/* preserve "old" parser which delimited header fields by zeros, 35 + * and included deliminitors in body (which was the only way to 36 + * learn length of the whole header field  37 + */ 38 +#undef PRESERVE_ZT 39 + 40 + 41 +/* ------------------------------------------------------ */ 42 +/* don't touch this -- that's helper macros depending on 43 + * the backwards compatibility macros above */ 44 +#ifdef PRESERVE_ZT 45 +# define SET_ZT(_ch) (_ch)='\0' 46 +#else 47 +# define SET_ZT(_ch) 48 +#endif 49 + 50 +#endif


text:
# MCMC-recover

0th

Percentile

##### Compare MCMC estimates to "true" parameter values

Plots comparing MCMC estimates to "true" parameter values. Before fitting a model to real data it is useful to simulate data according to the model using known (fixed) parameter values and to check that these "true" parameter values are (approximately) recovered by fitting the model to the simulated data. See the Plot Descriptions section, below, for details on the available plots.

##### Usage
mcmc_recover_intervals(x, true, batch = rep(1, length(true)),
facet_args = list(), ..., prob = 0.5, prob_outer = 0.9,
point_est = c("median", "mean", "none"), size = 4, alpha = 1)mcmc_recover_scatter(x, true, batch = rep(1, length(true)),
facet_args = list(), ..., point_est = c("median", "mean"), size = 3,
alpha = 1)mcmc_recover_hist(x, true, facet_args = list(), ..., binwidth = NULL,
breaks = NULL)
##### Arguments
x

A 3-D array, matrix, list of matrices, or data frame of MCMC draws. The MCMC-overview page provides details on how to specify each these allowed inputs.

true

A numeric vector of "true" values of the parameters in x. There should be one value in true for each parameter included in x and the order of the parameters in true should be the same as the order of the parameters in x.

batch

Optionally, a vector-like object (numeric, character, integer, factor) used to split the parameters into batches. If batch is specified, it must have the same length as true and be in the same order as true. Parameters in the same batch will be grouped together in the same facet in the plot (see the Examples section, below). The default is to group all parameters together into a single batch. Changing the default is most useful when parameters are on very different scales, in which case batch can be used to group them into batches within which it makes sense to use the same $y$-axis.

facet_args

A named list of arguments (other than facets) passed to facet_wrap or facet_grid to control faceting.

...

Currently unused.

prob

The probability mass to include in the inner interval. The default is 0.5 (50% interval).

prob_outer

The probability mass to include in the outer interval. The default is 0.9 (90% interval).

point_est

The point estimate to show. Either "median" (the default), "mean", or "none".

size, alpha

Passed to geom_point to control the appearance of plotted points.

binwidth

Passed to geom_histogram to override the default binwidth.

breaks

Passed to geom_histogram as an alternative to binwidth.

##### Value

A ggplot object that can be further customized using the ggplot2 package.

##### Plot Descriptions

mcmc_recover_intervals

Central intervals and point estimates computed from MCMC draws, with "true" values plotted using a different shape.

mcmc_recover_scatter

Scatterplot of posterior means (or medians) against "true" values.

mcmc_recover_hist

Histograms of the draws for each parameter with the "true" value overlaid as a vertical line.

Other MCMC: MCMC-combos, MCMC-diagnostics, MCMC-distributions, MCMC-intervals, MCMC-nuts, MCMC-overview, MCMC-parcoord, MCMC-scatterplots, MCMC-traces

##### Aliases
• MCMC-recover
• mcmc_recover_intervals
• mcmc_recover_scatter
• mcmc_recover_hist
##### Examples
# NOT RUN {
library(rstanarm)
alpha <- 1; beta <- rnorm(10, 0, 3); sigma <- 2
X <- matrix(rnorm(1000), 100, 10)
y <- rnorm(100, mean = c(alpha + X %*% beta), sd = sigma)
fit <- stan_glm(y ~ ., data = data.frame(y, X))
draws <- as.matrix(fit)
print(colnames(draws))
true <- c(alpha, beta, sigma)

mcmc_recover_intervals(draws, true)

# put the coefficients on X into the same batch
mcmc_recover_intervals(draws, true, batch = c(1, rep(2, 10), 1))
# equivalent
mcmc_recover_intervals(draws, true, batch = grepl("X", colnames(draws)))
# same but facets stacked vertically
mcmc_recover_intervals(draws, true,
batch = grepl("X", colnames(draws)),
facet_args = list(ncol = 1),
size = 3)

# each parameter in its own facet
mcmc_recover_intervals(draws, true, batch = 1:ncol(draws))
# same but in a different order
mcmc_recover_intervals(draws, true, batch = c(1, 3, 4, 2, 5:12))
# present as bias by centering with true values
mcmc_recover_intervals(sweep(draws, 2, true), rep(0, ncol(draws))) + hline_0()

# scatterplot of posterior means vs true values
mcmc_recover_scatter(draws, true, point_est = "mean")

# histograms of parameter draws with true value added as vertical line
color_scheme_set("brightblue")
mcmc_recover_hist(draws[, 1:4], true[1:4])
# }
# NOT RUN {
# }

Documentation reproduced from package bayesplot, version 1.6.0, License: GPL (>= 3)

### Community examples

Looks like there are no examples yet.


text:
Q

# A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be 1.5 s. The radius of the disc is 15 cm.

Q .14.23 A circular disc of mass $\inline 10\; kg$ is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be $\inline 1.5 \; s.$ The radius of the disc is $\inline 15 \; cm$. Determine the torsional spring constant of the wire. (Torsional spring constant $\inline a$ is defined by the relation$\inline J=-a\; \theta$, where J is the restoring couple and θ the angle of twist).

Views

$\inline J=-a\; \theta$

Moment of Inertia of the disc about the axis passing through its centre and perpendicular to it is

$I=\frac{MR^{2}}{2}$

$\\J=I\frac{\mathrm{d}^{2}\theta }{\mathrm{d} t^{2}}\\ -a\theta =\frac{MR^{2}}{2}\frac{\mathrm{d}^{2}\theta }{\mathrm{d} t^{2}}\\ \frac{\mathrm{d}^{2}\theta }{\mathrm{d} t^{2}}=-\frac{2a}{MR^{2}}\theta$

The period of Torsional oscillations would be

$\\T=2\pi \sqrt{\frac{MR^{2}}{2a}}\\ a=\frac{2\pi ^{2}MR^{2}}{T^{2}}\\ a=\frac{2\pi ^{2}\times 10\times (0.15)^{2}}{(1.5)^{2}}\\ a=1.97\ N\ m\ rad^{-1}$

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text:
# Bowling Average Calculator

Created by Luis Fernando
Reviewed by Hanna Pamuła, PhD candidate and Steven Wooding
Last updated: Jan 28, 2022

With this bowling average calculator, you'll evaluate your cricket performance or your favorite player's bowling skills. The main objective of the fielding team in this sport is to minimize the number of runs scored by the batting team. To achieve this goal, bowlers are a fundamental part. Due to the importance of bowling in this sport, some cricket statistical measures of how well bowlers perform exist. Bowling average is one the most important ones.

⚠ Using only the term "bowling average" may be confusing. In this article, we're talking about the statistic used in cricket🏏 and not in bowling sport🎳. We'll mainly use "bowling average" instead of "cricket bowling average" for practical purposes.

Do you have an interest in knowing how to calculate the bowling average in cricket on your own? Do you want to have an idea of what is a good bowling average?

We believe our bowling average calculator can help you to answer these questions and calculate this metric quickly and reliably, so you get a sense of the performance of yourself or your favorite player.

## What is bowling average?

Bowling average is a measure of the performance of a cricket bowler. It compares the runs conceded by a bowler to the wickets taken by himself.

The lower this number is, the better the performance of the player.

## How to calculate bowling average in cricket with this calculator?

To use this calculator, all you need to do is:

1. Take the total number of runs the bowler conceded.
2. The total number of wickets the bowler took.
3. Input these numbers in the calculator, and our tool will assess the bowler's performance in a flash using the following formula:
$\quad\ \ \footnotesize \text{bowling average}=\frac{\text{runs conceded}}{\text{wickets taken}}$

## Common bowling average values

The bowling average of a cricket bowler is usually between 20 and 50. The following is a frequent interpretation of the findings that can give you an idea of what is a good bowling average:

• Under 20: extraordinary bowling skills
• 20 to 25: excellent bowling skills
• 25 to 30: good bowling skills
• 30 to 35: average bowling skills
• 35 to 40: below average bowling skills
• Above 40: minimal bowling skills

A higher bowling average doesn't mean we're in front of a bad player, but it suggests that this cricketer is selected more probably for batting roles.

The best test cricket bowling average 🧐🧐🧐
To have an idea of how extraordinary a bowling average under 20 is, the lowest test cricket bowling average (for players who bowled at least 600 balls in the test cricket modality) is 10.74. It belongs to the English cricketer George Lohman.

## Some other helpful cricket statistics and tools

There are more cricket statistics beyond bowling average. We have developed calculators we think can be valuable for you, no matter you're a professional or amateur cricket player (or simply a fan):

• Batting Average: this is the equivalent statistic in batting. It compares the total number of runs the batsman scored to the overall number of times the batsman was out. Contrary to what we'd encounter with the bowling average calculator, a higher batting average indicates better performance.
• Net Run Rate: another cricket statistic used in performance assessment. Unlike bowling and batting averages, net run rate measures team's performance instead of individual performance.
• Duckworth Lewis: this calculator will help you decide which cricket team won a match if it can't be completed. It can also help the batting team set a target score if the match is interrupted and a second part is left.
• Cricket Follow-On: a calculator used for strategy purposes that will help you determine whether you should force your opponent to bat again or keep the traditional sequence. "Follow-on" is a critical decision assigned to the captain, so it would be a good idea you make efforts to become the leader of your team and have the opportunity to use this great calculator.

## FAQ

### How to calculate bowling average in cricket?

Divide the number of runs the bowler conceded by the number of wickets he took. With this procedure, calculating the bowling average in cricket becomes an easy task.

### What is a good bowling average?

They usually consider that a bowling average under 30 is a good result in cricket.

### What is the importance of bowling average and other cricket statistics?

These cricket statistics objectively try to predict the performance of a player or team in a future game. Although they help predict others' performance, you can also use them to assess your cricket skills and improve them in time.

Luis Fernando
Runs conceded
Wickets taken
Bowling average
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text:
SCIENCE CHINA Information Sciences, Volume 59, Issue 3: 032104(2016) https://doi.org/10.1007/s11432-015-5420-9

## Salient object detection via region contrast and graph regularization

• AcceptedJun 24, 2015
• PublishedJan 18, 2016
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### Abstract

Detection of salient objects in an image is now gaining increasing research interest in computer vision community. In this study, a novel region-contrast based saliency detection solution involving three phases is proposed. First, a color-based super-pixels segmentation approach is used to decompose the image into regions. Second, three high-level saliency measures which could effectively characterize the salient regions are evaluated and integrated in an effective manner to produce the initial saliency map. Finally, we construct a pairwise graphical model to encourage that adjacent image regions with similar features take continuous saliency values, thus producing the more perceptually consistent saliency map. We extensively evaluate the proposed method on three public benchmark datasets, and show it can produce promising results when compared to 14 state-of-the-art salient object detection approaches.

### Funded by

International Scientific and Technological Cooperation Projects of China(2015DFG12650)

National Natural Science Foundation of China(61573048)

National Natural Science Foundation of China(51475017)

Beijing Municipal Natural Science Foundation(4142033)

### Acknowledgment

Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant Nos. 61573048, 51475017), Beijing Municipal Natural Science Foundation (Grant No. 4142033), and International Scientific and Technological Cooperation Projects of China (Grant No. 2015DFG12650).

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text:
# Hexagon A

Calculate area of regular hexagon inscribed in circle with radius r=9 cm.

Result

S =  210.4 cm2

#### Solution:

$S_1 = \dfrac{1}{2} r^2 \sin 60 ^\circ \ \\ S_1 = \dfrac{1}{2} 9^2 \sin 60 ^\circ \ \\ S_1 = 35.074 \ cm^2 \ \\ S = 6S_1 = 210.4 \ cm^2$

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text:
# Equivalence between the eigenvalue problem of non-commutative harmonic oscillators and existence of holomorphic solutions of Heun differential equations, eigenstates degeneration, and the rabi model

Masato Wakayama

2 被引用数 (Scopus)

## 抄録

The initial aim of the present paper is to provide a complete description of the eigenvalue problem for the non-commutative harmonic oscillator (NcHO), which is defined by a (two-by-two) matrix-valued self-adjoint parity-preserving ordinary differential operator [28], in terms of Heun's ordinary differential equations, the second-order Fuchsian differential equations with four regular singularities in a complex domain. This description has been achieved for odd eigenfunctions in Ochiai [25] nicely but missing up to now for the even parity which is more important from the viewpoint of determination of the ground state of the NcHO. As a by-product of this study examining the monodromy data (characteristic exponents, etc.) of the Heun equation, we prove that the multiplicity of the eigenvalue of the NcHO is at most two. Moreover, we give a condition for the existence of a finite-type eigenfunction (i.e., given by essentially a finite sum of Hermite functions) for the eigenvalue problem and an explicit example of such eigenvalues, from which one finds that doubly degenerate eigenstates of the NcHO actually exist even in the same parity Also, we determine the possible shape of (so-called) Heun polynomial solutions of the Heun equations, which are obtained by the eigenvalue problem.

本文言語 英語 759-794 36 International Mathematics Research Notices 2016 3 https://doi.org/10.1093/imrn/rnv145 出版済み - 2016

• 数学 (全般)

## フィンガープリント

「Equivalence between the eigenvalue problem of non-commutative harmonic oscillators and existence of holomorphic solutions of Heun differential equations, eigenstates degeneration, and the rabi model」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。


text:
No matter how you change the angle they make, their tips form a parallelogram. Angles BAC and DCA are congruent by the Alternate Interior Angles … Parallelogram and its Theorems. …, Volume of a cube is 343cm³ . One group of sponsors will donate a total of $25 for each hour she dances. sides of a ] … Another group of sponsors ∠ABE and ∠CDE are alt. Do term limits seem to have more a... A family smoothie recipe calls for strawberry juice and apple juice. Construct a diagonal from A to C with a straightedge. #1 in the Review Queue above, had you write the converses of each of these: Opposite Sides Theorem Converse: If the opposite sides of a quadrilateral are congruent, then the ﬁgure is a parallelogram. Whenever we have parallelogram we can prove that the opposite sides of a parallelogram are congruent by first proving that two triangles which are made by joining the opposite sides are equal. Which is relatively better: a score of 72 on a psychology test or a score of 48 on an economics test? Proving the parallelogram diagonal theorem given: abcd is a parallelogram. Please i need help asap i will mark brainliest, View a few ads and unblock the answer on the site. If it is, what kind of parallelogram is it? To prove: ar (ΔABD) = ar (ΔCDB). Use transformations, triangle congruency criteria, and line and angle relationship to prove parallelogram properties. AB ≅ CD 4). Draw the diagonal BD, and we will show that ΔABD and ΔCDB are congruent. Escribir 1. AC is splitting DB into two segments of equal length. Hablar Contesta las preguntas. THEOREM: If a quadrilateral has diagonals which bisect each other, then it is a parallelogram. Proof: Diagonals of a parallelogram. triangular park of dimensions (4ab + 3bc) meters ,(3ab+2bc)meters and (ab - bc) meters. So you should try the other option: proving the triangles congruent with ASA. Conversely, if the diagonals in a quadrilateral bisect each other, then it is a parallelogram. In AOE and COF; OE = OF: Given – (1) ∠AOE = ∠COF: Vertical angles are equal – (2) AO=CO: The diagonals of the parallelogram intersect at the midpoint – (3) 0000031251 00000 n 0000156537 00000 n Special Parallelograms - Rhombus and Rectangle Proofs This video uses the two column method to prove two theorems. 6.3. The diagonal of a parallelogram separates it into two congruent triangles. Share . from parallelogram HEJG, so you need only one more pair of congruent sides or angles to use SAS (Side-Angle-Side) or ASA (Angle-Side-Angle). *, The value of 25x³ y² z for x=1, y=2 and z=3 is, The area of a parallelogram is 150 cm² and one of its altitude is 10 cm. Proving the Parallelogram Diagram Theorem Given: ABCD is a Parallelogram. ¿Cuándo van tú y tus amigos(as) a la ca... A = (2,3), how long is it? Diagonals AC and BD intersect at E. We have to prove that AE is congruent to CE and BE is congruent to DE i.e diagonals of parallelogram bisect each other. Proving a Parallelogram Theorem #5. if the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram. The first is to use congruent triangles to show the corresponding angles are congruent, the other is to use theAlternate Interior Angles Theoremand apply it twice. Both pairs of opposite sides are parallel. ¿A qué hora vas a la escuela? (Proof of theorem appears further down page.) ... Rectangles are parallelograms with congruent diagonals theorem If a parallelogram has congruent diagonals, then it is a rectangle. Let the straight lines AB, CD be equal and parallel, and let the straight lines AC, BD join their extremities that are on the same side; then AC, BD are themselves equal and parallel. THEOREM: If a quadrilateral is a parallelogram, it has diagonals which form 2 congruent triangles. The area of a trapezium is 384cm². Angles Se… Visit us at - www.risingpearl.comLike us at - www.facebook.com/risingpearlfansFriends,This is a Math video. Square. The lateral surface area of a hollow cylinder is 1320 cm².The radius of it‘s base is 7cm. In ΔACD and ΔBEC. Plus de 6000 vidéos et des dizaines de milliers d'exercices interactifs sont disponibles du niveau primaire au … ii) Find the area of the square park. Now let's go the other way around. Use the reciprocal property to solve for x: 2 / 5 = 38 / x, HELLLLP BEST ANSWER GETS BRAINALIST!!!!! Describe how instructional notes in both the alphabetic index and the tabular list guide coders when selecting ICD-10-CM codes... . will make a one-time donation of$100 regardless of how long she dances. Definition 2: A rectangle is a quadrilateral where all four angles are the same size. Think about the end of the proof. By using the definitions and theorems of parallelograms, we can prove the following. If one pair of opposite sides of a quadrilateral are both parallel and congruent, then it’s a parallelogram (neither the reverse of the definition nor the converse of a property). Definition: A square is a parallelogram with four congruent sides and four right angles. The electrons sp... Jose has a mask collection. sides of a ] AD = BC [Opp. The second angle pair you’d need for ASA consists of angle DHG and angle FJE. diagonals ac, bd intersect at e. prove: ae = ce and be = de assemble the proof by dragging tiles to … interior angles-- def. Find the length of the other diagonal and determine if the baseball diamond is a parallelogram. i) Find the distance covered by Shikha around the triangular park ? THEOREM. THANK YOU :), 50 points Please solve for real or be reported. asked Sep 22, 2018 in Class IX Maths by muskan15 ( -3,443 points) quadrilaterals Shikha jogs around a AD=BC (∵Opposite sides of parallelogram are equal) ∠DAC=∠BCE (∵Alternate angles) ∠ADC=∠CBE (∵Alternate angles) By ASA rule, ΔACD≅ΔBEC. Parallelogram Theorem 1:Diagonals of a parallelogram are equal then it is a rectangle. The proposition proves that if two sides of a quadrilateral are equal and parallel, then the figure is a parallelogram. He keeps some in a display case and the rest on the wall. 4 9 Find the length of e Given a parallelogram ABCD. What is the gear ratio of this gear tra... 50 points Please answer honestly or be reported, if the answer is none of the above, please say so. AB = DC [Opp. Consecutive Angles Add UP to 180° Since the opposite angles are equal and the lines are parallel to each other, parallelograms have other properties. Theorem and the Parallelogram Diagonals Theorem. 4). ∠BAE≌∠DCE--alt. Charles can walk 1/2 of a mile in 9 minutes. … For the other opposite angles, we can prove that the angles are equal by drawing another diagonal line and proving that the triangles are congruent. Gear "A" has 24 teeth while "B" has 8 and C has 16. (Hint: Use the Midpoint formula.) THEOREM: If a quadrilateral has one set of opposite sides which are … interior angles theorem, This site is using cookies under cookie policy. Theorem 4: If one pair of opposite sides in a four sided figure are both opposite and parallel, then the figure is a parallelogram. (Definition 14. You can specify conditions of storing and accessing cookies in your browser, Proving the Parallelogram Diagonal Theorem, Given ABCD is a parralelogam, Diagnals AC and BD intersect at E, quick iii) Find the area of the rectangular park. ΔABE ≅ ΔCDE                                5). Proving the Parallelogram Diagonal Theorem Given: ABCD is a parallelogram. ABCD is a parallelogram                 1). 0000104960 00000 n There are five ways in which you can prove that a quadrilateral is a parallelogram. What number of hours should she dance if she wishes to raise at least $500? Theorem 3: A quadrilateral is a parallelogram if and only if the diagonals bisect each other. interior angles, 6. Def. B = (4,6),C=(-4,-5)D=(4,-1)Determine the followingBC =+-=( )+ ( )= ().... What are the advantages and disadvantages of having so many levels of subnational governments in the United States? You can use these and other theorems in this lesson to prove 0000003720 00000 n The converses of the theorems are stated below. Special Parallelograms: Rhombus, Rectangles This video lesson discusses the properties of the special parallelograms: rectangle and rhombus. 2. proving the parallelogram side theorem edgenuity answers. Proving a Quadrilateral is a Parallelogram To prove a quadrilateral is a parallelogram, prove any of the following conditions: 1. Converse of the Alternate Interior Angles Theorem Quadrilateral PARL is a parallelogram Definition of a Parallelogram Now that you know opposite sides are parallel, you can say that quadrilateral PARL is a parallelogram according to the definition of a parallelogram. The speed of the electrons does not change. Theorem 2: If the opposite sides in a quadrilateral are the same length, then the figure is a parallelogram. By CPCT (Corresponding Parts of Congruent triangles) AE=EC and DE=EB. ∠BAE and ∠DCE are alternate 3). 3 7 (Answer the questions.) This proves that opposite angles in any parallelogram are equal. 3). AD=BC (∵Opposite sides of parallelogram are equal), By CPCT(Corresponding Parts of Congruent triangles), Hence, AE is conruent to CE and BE is congruent to DE, 4. of interior alternate angles. 3) In a parallelogram, opposite angles are equal. 0000031251 00000 n Prove a quadrilateral is a parallelogram using the converses of the theorems from the previous section. So they are bisecting each other. Prove J… The subscriptoin renews automaticaly until you cancel. Both pairs of opposite sides are congruent. ∠ABE and ∠CDE are alternate 2). In a parallelogram, the diagonals bisect each other. 2) If each pair of opposite sides of a quadrilateral is equal then it is a parallelogram. Question sent to expert. The perimeter of a stage is 116 feet. Proof: Opposite angles of a parallelogram. https://tutors.com/.../proving-a-quadrilateral-is-a-parallelogram Theorem 3: A quadrilateral is a parallelogram if and only if the diagonals bisect each other. parallelogram theorem ; THEOREM – 1 A diagonal of parallelogram divides it into two triangles of equal area. 323. Write an equivalent expression for n × a using only addition.... A pink crayon is made with 12\text{ mL}12 mL12, start text, space, m, L, end text of red wax for every 5\text{ mL}5 mL5, start text, space, m, L, end... What happens to the speed of the electrons when the resistance is decreased? 11/03/2020 By . Consider the following figure: Proof: In $$\Delta AEB$$ and … Theorem 3. Parallelograms Apply properties of parallelograms to solve … Def. …. So let me see. Prove a quadrilateral is a parallelogram using the converses of the theorems from the previous section. The gear train on the left is made up of the three gears. There are two ways to go about this. The straight lines which join the extremities on the same side of two equal and parallel straight lines, are themselves equal and parallel. 4) If in a quadrilateral, each pair of opposite angles is equal then it is a parallelogram. PROVING A THEOREM Prove the Parallelogram Diagonals Converse Theorem 7.10 ) Given Diagonals \overline{JL} and \overline{\mathrm{KM}} bisect each other. Parallelogram side theorem, 5). Designed by … of interior alternate angles. Theorem 3. The platform swings back and forth, higher and higher, until it goes over the top and According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD. Proving that a figure is a parallelogram if and only if opposite sides are congruent. Consider the following figure: Proof: In $$\Delta AEB$$ and … Hence, AE is conruent to CE and BE is congruent to DE. You will receive an answer to the email. THEOREM – 1: A diagonal of parallelogram divides it into two triangles of equal area. Same length, then the figure is a parallelogram ) 2 is equal then the shape have. Shown where segment AB is parallel to segment AD a trapezoid are very health conscious she dances a point Statements. Study based question: - Shikha, Neethu and Fabina are friends.They are very conscious! From the previous section and … theorem the definitions and theorems of parallelograms can be! 100 regardless of how long she dances same length, then the we...... Rectangles are parallelograms with congruent diagonals, then it is a rectangle triangles first because it requires less lines! Other then the quadrilateral is a parallelogram, 1 ) and Technology, 08.12.2020.. ) and … theorem www.risingpearl.comLike us at - www.facebook.com/risingpearlfansFriends, This is a.... Video lesson discusses the properties of the following figure: Proof: in \ \Delta! Any of the other diagonal and determine if the diagonals bisect each other score of on. Hypothesis that a figure is a parallelogram is a quadrilateral is a parallelogram the area of special... The only shape you can make is a parallelogram the area of a parallelogram, it has diagonals which each... Which bisect each other, then it is a parallelogram we will that! Is: if a parallelogram straight lines which join the extremities on the wall congruent triangles DE! 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text:
# Quasi-Coherent modules over sheaves of rings (proof question)

Let $X$ be a scheme with structure sheaf $\mathcal O_X$ and let $\mathcal B$ be a quasi-coherent $\mathcal O_X$-algebra. Let $\mathcal F$ be any sheaf of $\mathcal B$-modules.

In EGA I, § 9, Prop. 9.6.1 it is asserted that then the following holds:

Then $\mathcal F$ is quasi-coherent over $\mathcal B$ if and only if $\mathcal F$ is quasi-coherent over $\mathcal O_ X$.

The proof of the implication $\Rightarrow$ is easy, but the other direction is hard to digest for me: EGA argues as follows: we may work locally on $X$, hence assume $X=Spec(A)$, whence $\mathcal B$ corresponds to a $A$-algebra $B$ and $\mathcal F$ corresponds to a $B$-module $M$ (namely, because $\mathcal B$ and $\mathcal F$ are quasi-coherent over $\mathcal O_X$).

Then it reads without explanation that $M$ is isomorphic to the cokernel of a map

$(*) \quad B^{(I)} \rightarrow B^{(J)}$,

and hence by taking the tilde-construction we see that $\mathcal F$ is quasi-coherent over $\mathcal B$.

Apriori, one should only be able to write $M$ as a cokernel of a map $(*)$ with $B$ replaced by $A$, but tensoring with $B$ doesn't seem to give $M$ as cokernel, but $M\otimes_A B$.

My question is why one may write $M$ as a cokernel of a map $(*)$, as claimed in EGA.

Or any other proof of the desired implication

"$\mathcal F$ quasi-coherent over $\mathcal O_X \Rightarrow \mathcal F$ quasi-coherent over $\mathcal B$"

would be very appreciated.

-
$M$ is already a $B$-module, so you can definitely write $M$ as the cokernel of $(*)$. But then again quasi-coherence is somewhat tautological for modules over rings. –  Zhen Lin Jan 7 '13 at 16:07

By assumption $M$ is a $B$-module, hence any presentation with generators and relations gives an exact sequence $B^{(I)} \to B^{(J)} \to M \to 0$ of $B$-modules. The rest of the EGA proof is quite self-explanatory; if not you can ask further questions.


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# Linear prediction

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 Title: Linear prediction Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Linear prediction

Linear prediction is a mathematical operation where future values of a discrete-time signal are estimated as a linear function of previous samples.

In digital signal processing, linear prediction is often called linear predictive coding (LPC) and can thus be viewed as a subset of filter theory. In system analysis (a subfield of mathematics), linear prediction can be viewed as a part of mathematical modelling or optimization.

## The prediction model

The most common representation is

\widehat{x}(n) = \sum_{i=1}^p a_i x(n-i)\,

where \widehat{x}(n) is the predicted signal value, x(n-i) the previous observed values, and a_i the predictor coefficients. The error generated by this estimate is

e(n) = x(n) - \widehat{x}(n)\,

where x(n) is the true signal value.

These equations are valid for all types of (one-dimensional) linear prediction. The differences are found in the way the parameters a_i are chosen.

For multi-dimensional signals the error metric is often defined as

e(n) = \|x(n) - \widehat{x}(n)\|\,

where \|\cdot\| is a suitable chosen vector norm. Predictions such as \widehat{x}(n) are routinely used within Kalman filters and smoothers [1] to estimate current and past signal values, respectively.

### Estimating the parameters

The most common choice in optimization of parameters a_i is the root mean square criterion which is also called the autocorrelation criterion. In this method we minimize the expected value of the squared error E[e2(n)], which yields the equation

\sum_{i=1}^p a_i R(j-i) = -R(j),

for 1 ≤ jp, where R is the autocorrelation of signal xn, defined as

\ R(i) = E\{x(n)x(n-i)\}\,,

and E is the expected value. In the multi-dimensional case this corresponds to minimizing the L2 norm.

The above equations are called the normal equations or Yule-Walker equations. In matrix form the equations can be equivalently written as

Ra = -r,\,

where the autocorrelation matrix R is a symmetric, p×p Toeplitz matrix with elements ri,j = R(ij), 0≤i,jr is the autocorrelation vector rj = R(j), 0a is the parameter vector.

Another, more general, approach is to minimize the sum of squares of the errors defined in the form

e(n) = x(n) - \widehat{x}(n) = x(n) - \sum_{i=1}^p a_i x(n-i) = - \sum_{i=0}^p a_i x(n-i)

where the optimisation problem searching over all a_i must now be constrained with a_0=-1.

On the other hand, if the mean square prediction error is constrained to be unity and the prediction error equation is included on top of the normal equations, the augmented set of equations is obtained as

\ Ra = [1, 0, ... , 0]^{\mathrm{T}}

where the index i ranges from 0 to p, and R is a (p + 1) × (p + 1) matrix.

Specification of the parameters of the linear predictor is a wide topic and a large number of other approaches have been proposed. In fact, the autocorrelation method is the most common and it is used, for example, for speech coding in the GSM standard.

Solution of the matrix equation Ra = r is computationally a relatively expensive process. The Gauss algorithm for matrix inversion is probably the oldest solution but this approach does not efficiently use the symmetry of R and r. A faster algorithm is the Levinson recursion proposed by Norman Levinson in 1947, which recursively calculates the solution. In particular, the autocorrelation equations above may be more efficiently solved by the Durbin algorithm.[2]

Later, Delsarte et al. proposed an improvement to this algorithm called the split Levinson recursion which requires about half the number of multiplications and divisions. It uses a special symmetrical property of parameter vectors on subsequent recursion levels. That is, calculations for the optimal predictor containing p terms make use of similar calculations for the optimal predictor containing p − 1 terms.

Another way of identifying model parameters is to iteratively calculate state estimates using Kalman filters and obtaining maximum likelihood estimates within Expectation–maximization algorithms.

## References

1. ^ Einicke, G.A. (2012). Smoothing, Filtering and Prediction: Estimating the Past, Present and Future. Rijeka, Croatia: Intech.
2. ^ M. A. Ramirez (2008) "A Levinson Algorithm Based on an Isometric Transformation of Durbin's," IEEE Signal Processing Lett., vol. 15, pp. 99-102.


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# Accelerometer

The compass application on your cell phone by one way or another knows which bearing the phone is pointing. Essentially, the stargazing application in your cell-phone knows which part of the sky you are taking a gander at, to show heavenly bodies effectively. Ever considered how they do it? Cell phones and other versatile advance technologies distinguish their direction with the assistance of a little gadget comprised of axis-based movement detecting. This device is an accelerometer.

Accelerometer

## What is an Accelerometer?

An accelerometer is an instrument that estimates legitimate acceleration. Proper quickening is the increasing speed (the pace of progress of speed) of a body in its own prompt rest frame. This is unique in relation to organize acceleration, which is increasing speed in a fixed facilitate framework.

For instance, an accelerometer at rest on the outer surface of the Earth will gauge an increasing speed because of Earth’s gravity. It is straight upwards (by meaning) of $$g \approx 9.81 m/s^{2}$$. On the other hand, accelerometers in free fall (falling toward the focal point of the Earth at a pace of about $$9.81 m/s^{2}$$ will gauge zero.

Accelerometers have numerous utilizations in industry and science. Profoundly delicate accelerometers are in use within inertial route frameworks for aeroplane and rockets. Vibration in pivoting machines is seen by accelerometers. They are used in tablet PCs and computerized cameras so that pictures on screens are constantly shown upstanding. In airborne vehicles, accelerometers help to settle flight.

At the point when at least two accelerometers are facilitated with each other, they can gauge contrasts in legitimate increasing speed. Especially gravity, over their partition in space that is, the inclination of the gravitational field. Gravity gradiometry is helpful on the grounds that total gravity is a frail impact and relies upon the local density of the Earth, which is variable.

Single and multi-axis accelerometers can identify both the magnitude and the direction of the correct speeding up. It is a vector amount and can be in use to detect direction (in light of the fact that the weight changes). It coordinates acceleration, vibration, stun, and falling in a resistive medium. Micromachined microelectromechanical frameworks (MEMS) accelerometers are progressively present in compact electronic gadgets and computer game regulators. It is in use to identify changes in the positions of these gadgets.

### Types of Accelerometer

The three significant kinds of accelerometers are capacitive MEMS accelerometer, piezoresistive accelerometer, and piezoelectric accelerometer.

• Capacitive MEMS Accelerometer-The MEMS represents Micro-Electro-Mechanical-System. MEMS is a creative innovation or fabrication technology. In this kind of accelerometer, the adjustments in capacitance are distinguished rather than an adjustment in obstruction. Most of the cell phones or mobiles utilize this MEMS accelerometer.
• Piezoresistive Accelerometer-  It quantifies the vibrations by changes in resistance. This is the accelerometer that fills in as DC responsive and demonstrates effective while estimating almost no vibrations. For instance, the gravity vector.
• Piezoelectric Accelerometer- In this sort the sensors are made of precious stones or earthenware production like lead zirconate, lead titanate, and so on. This sensor assimilates the vibrations and produces a similar measure of electrical signs.

### Working Principle of Accelerometer

The primary working standard of an accelerometer is that it changes over mechanical energy into electrical energy. At the point when a mass is kept on the sensor which is in reality like a spring, it begins descending. Since it is descending it begins to encounter an acceleration. That speeding up then changes into a measure of the electric sign which is then in use for the estimations of variety in the position of the gadget. An accelerometer can be found with both the structures simple just as computerized structure gadgets. It can be analogue as well as digital form.

### Accelerometer Application

Some applications of the accelerometer are:

• The accelerometer has an ability to detect the vibration from miniature size to an enormous scope. Indeed, even in a large portion of the security establishments, the accelerometer is useful.
• An accelerometer is likewise utilized in games. The wearable gadgets which competitors are utilizing day by day for the training and perceptions contain accelerometers or gyrator.
• The doctors use it to check for pick up in weight and screen body developments. It is additionally present in the gadgets used to check the pulse.
• The piezoelectric accelerometers are utilized at the modern level.
• The most successive accelerometer utilized in aviation is Micro-Electro-Mechanical-sensors (the MEMS innovation) based. The purpose behind utilizing MEMS sensor-based accelerometers is that they can detect the vibrations even on a miniature size and can likewise offer the benefit on a small size.
• It is even utilized for the satellite which is in space, as it can endure high weight, vibration.
• For purposes like gearbox investigation, bearing examination, rotor trim, and equilibrium, an accelerometer assumes a significant job.
• The aircraft are explored utilizing the accelerometer. The aeroplane flight testing is something else that requires an accelerometer. To check the qualities of flight and to affirm the plan of it an exact perception of information is normal. For that, an accelerometer named LCA-5080 is being used.
• An accelerometer is in use for security purposes in workstations for the hard circles. Due to accelerometer sensors, we have scene and picture modes on our telephones. The cell phones continue changing the screen mode in scene or representation mode because of accelerometer applications.

Q.1. What are 6 axis accelerometers?

Answer: A 6 axis accelerometer is a consolidated type of a 3-axis advance digital accelerometer and a 3-axis computerized whirligig. Here gyroscope assists with estimating the precise speed along the x-axis, y-axis, and z-axis. The acceleration and direct speed don’t influence the estimation of the spinner. Henceforth the 6-axis accelerometer is in use for an exact perusing. This sort of accelerometer has an extremely low force utilization since it contains a low force utilization chip named LSM6DS3. It is profoundly delicate to vibration and accompanies a force gracefully controller inside it.

Q.2. What is an XYZ accelerometer?

Answer: A XYZ accelerometer is generally useful in cell phones to identify the movement of the gadget. The XYZ is the course of the axis and is in use by the accelerometer for the data of the situation of the gadget. A wide range of cell phones have alternatives like representation and scene mode. These modes in cell phones change as we turn our gadget as indicated by our inclinations. The estimation of XYZ is in use for the recognition of the situation of the gadget whether we turn it left or right or tilt it on any side.

Q.3. What are accelerometers useful for?
Answer: By estimating the measure of static increasing speed because of gravity, we can discover the point at which the gadget is inclined at concerning the earth. By detecting the measure of dynamic acceleration, we can dissect the manner in which the gadget is moving. From the outset, estimating tilt and increasing speed doesn’t appear to be too energizing. Notwithstanding, engineers have concocted numerous approaches to make truly valuable items with them.

In the computing world, IBM and Apple have as of late began utilizing accelerometers in their workstations to shield hard drives from harm. In the event that you coincidentally drop the PC, the accelerometer identifies the unexpected freefall and switches the hard drive off so the heads don’t crash on the platters. Along these lines, high g accelerometers are the industry-standard method of recognizing vehicle crashes and conveying airbags at the perfect time.

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