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https://juliagaussianprocesses.github.io/GPLikelihoods.jl/dev/
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# GPLikelihoods
GPLikelihoods.jl provides a practical interface to connect Gaussian and non-conjugate likelihoods to Gaussian Processes. The API is very basic: Every AbstractLikelihood object is a functor taking a Real or an AbstractVector as an input and returning a Distribution from Distributions.jl.
### Single-latent vs multi-latent likelihoods
Most likelihoods, like the GaussianLikelihood, only require one latent Gaussian process. Passing a Real will therefore return a UnivariateDistribution, and passing an AbstractVector{<:Real} will return a multivariate product of distributions.
julia> f = 2.0;julia> GaussianLikelihood()(f) == Normal(2.0, 1e-3)truejulia> fs = [2.0, 3.0, 1.5];julia> GaussianLikelihood()(fs) isa AbstractMvNormaltrue
Some likelihoods, like the CategoricalLikelihood, require multiple latent Gaussian processes, and an AbstractVector{<:Real} needs to be passed. To obtain a product of distributions an AbstractVector{<:AbstractVector{<:Real}} has to be passed (we recommend using ColVecs and RowVecs from KernelFunctions.jl if you need to transform an AbstractMatrix).
julia> fs = [2.0, 3.0, 4.5];julia> CategoricalLikelihood()(fs) isa Categoricaltruejulia> Fs = [rand(3) for _ in 1:4];julia> CategoricalLikelihood()(Fs) isa Product{<:Any,<:Categorical}true
### Constrained parameters
The function values f of the latent Gaussian process live in the real domain $\mathbb{R}$. For some likelihoods, the domain of the distribution parameter p that is modulated by the latent Gaussian process is constrained to some subset of $\mathbb{R}$, e.g. only positive values or values in an interval.
To connect these two domains, a transformation from f to p is required. For this, we provide the Link type, which can be passed to the likelihood constructors. (Alternatively, functions can also directly be passed and will be wrapped in a Link.)
We typically call this passed transformation the invlink. This comes from the statistics literature, where the "link" is defined as f = link(p), whereas here we need p = invlink(f).
For more details about which likelihoods require a Link check out their docs.
A classical example is the BernoulliLikelihood for classification, with the probability parameter $p \in [0, 1]$. The default is to use a logistic transformation, but one could also use the inverse of the probit link:
julia> f = 2.0;julia> BernoulliLikelihood()(f) == Bernoulli(logistic(f))truejulia> BernoulliLikelihood(NormalCDFLink())(f) == Bernoulli(normcdf(f))true
Note that we passed the inverse of the probit function which is the normcdf function.
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2022-12-03 16:53:14
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https://ltwork.net/which-term-is-a-term-in-this-expression-3x-7-x-4-a-3-b-3x--6517837
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# Which term is a term in this expression? -3x − 7(x + 4) A. -3 B. -3x C. -7 D. x + 4
###### Question:
Which term is a term in this expression? -3x − 7(x + 4) A. -3 B. -3x C. -7 D. x + 4
### An atom has 21 protons, 24 neutrons, and 18 electrons. Which change will cause the atom to have more negatively charged particles
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### What is the answer of the file
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### Read this line from 'a bee mystery': all these attackers and the methods used to combat them do stress the bees, however.
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### Write an essay why is mathmatics is important?
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### Solve for X3x - 6 = 30
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### PLS HELP!! Jason bought glass vases for his booth at the fair. If he bought 13 vases and the total weight was 34.97 lb, how much did each
PLS HELP!! Jason bought glass vases for his booth at the fair. If he bought 13 vases and the total weight was 34.97 lb, how much did each vase weigh? A. .00269 lb B. .0269 lb C. .269 lb D. 2.69 lb...
### Which of the following cannot be the lengths of the sides of a triangle?4,4,66, 6, 1210, 8, 66, 8, 12
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### Expensive to sort and transport (is what energy source?)A. WIndB. SolarC. NuclearD. GeothermalE. BiomassF. HydropowerG.
Expensive to sort and transport (is what energy source?) A. WInd B. Solar C. Nuclear D. Geothermal E. Biomass F. Hydropower G. Fossil fuels...
### If you need to feed 15 people and want to spend under 40.00 on the main course what would be your choices? how much would
if you need to feed 15 people and want to spend under 40.00 on the main course what would be your choices? how much would each of these cost $if you need to feed 15 people and want to spend under 40.00 on the main course what would be your c$[tex]if you need to feed 15 people and w...
### If 12 X 15 = 180 then what would 24 X15 equal (without solving it on paper)? Is there an easy way to figure out the answer? If so, explain.
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### Ayo can someone hac. k this chicks account on rob lox her name is SincerelyNessa
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### Asolution of water (kb=0.512 ∘c/m) and glucose boils at 101.56 ∘c. what is the molal concentration
Asolution of water (kb=0.512 ∘c/m) and glucose boils at 101.56 ∘c. what is the molal concentration of glucose in this solution? assume that the boiling point of pure water is 100.00 ∘c. express your answer to three significant figures and include the appropriate units....
### About 3% of the water on earth is freshwater. only about 40% of that freshwater is available for human
About 3% of the water on earth is freshwater. only about 40% of that freshwater is available for human use. why is so much freshwater unavailable for human use?...
### 10: Bounce with Us rents bounce houses for a flat fee of $250 and$25per hour. Fun Inflatables charges a flat fee of
10: Bounce with Us rents bounce houses for a flat fee of $250 and$25 per hour. Fun Inflatables charges a flat fee of $100 and$50 per hour. Write and solve an equation to find the number of hours at which the total cost charged by the two companies would be the same. 1 punto...
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2022-07-03 03:17:08
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https://www.shaalaa.com/question-bank-solutions/in-given-figure-oacb-quadrant-circle-centre-o-radius-35-cm-if-od-2-cm-find-area-shaded-region-areas-sector-segment-circle_16779
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# In the Given Figure, Oacb is a Quadrant of a Circle with Centre O and Radius 3.5 Cm. If Od = 2 Cm, Find the Area of the Shaded Region. - Mathematics
In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.
In the figure alongside, OACB is a quadrant of a circle. The radius OA = 3.5 cm and OD = 2 cm. Calculate the area of the shaded portion (Take Π = 22/7)
#### Solution 1
Since OACB is a quadrant, it will subtend 90° angle at O.
= 90^@/360^@ xx pir^2
=1/4 xx 22/7 xx (3.5)^2 = 1/4 xx 22/7 xx(7/2)^2
= (11xx7xx7)/(2xx 7xx 2xx2) = 77/8 cm^2
Area of ΔOBD
= 1/2 xx OB xx OD
= 1/2 xx 3.5 xx 2
= 1/2 xx 7/2 xx 2
= 7/2 "cm"^2
= Area of quadrant OACB − Area of ΔOBD
= 77/8 - 7/2
= (77 - 28)/8
= 49/8 "cm"^2
#### Solution 2
Area of the quadrant OACB = 1/4 xx pir^2
= 1/4 xx 22/7 xx 3.5 xx 3.5
= 9.625 cm^2
Area of the triangle OAD = 1/2 xx base xx height = 1/2 cc 3.5 xx 2 = 3.5 cm^2
= 9.625 - 3.5 cm^2
= 6.125 cm^2
Concept: Areas of Sector and Segment of a Circle
Is there an error in this question or solution?
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2022-05-24 21:15:21
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https://quantumcomputing.stackexchange.com/questions/10185/constructing-an-eigenbasis-of-graph-states-for-a-set-of-stabilizers/10197
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# Constructing an eigenbasis of graph states for a set of stabilizers
The stabilizers of a given graph all commute, thus it must be possible to diagonalize them simultaneously. If I start with one graph state and write down all its stabilizers is there an easy way to derive a complete eigenbasis of the stabilizers in terms of graph states?
If you start with one graph state, which is an eigenstate of stabilizer (each of which comprises an X tensored with a bunch of Zs), then the other eigenstates of those stabilizers are the original state acted on by Z rotations (take all possible combinations). To see this note the commutation and anticommutation relations between a tensor product of Zs and each stabilizer.
Consider a stabilizer of the form $$K_n=X_nZ_iZ_j\ldots Z_k$$, i.e. a graph-state stabilizer with a Pauli $$X$$ on qubit $$n$$, and a bunch of $$Z$$s on some other qubits (related to the graph structure). By definition, the graph state satisfies $$K_n|\psi\rangle=|\psi\rangle$$ for all $$n$$. Now, let $$|\Psi_x\rangle=\left(\bigotimes_{i=1}^nZ^{x_i}\right)|\psi\rangle,$$ for $$x\in\{0,1\}^n$$, a binary string. If we apply the stabilizers to such a state, we get $$K_n|\Psi_x\rangle=K_n\left(\bigotimes_{i=1}^nZ^{x_i}\right)|\psi\rangle=\left\{\begin{array}{cc} \left(\bigotimes_{i=1}^nZ^{x_i}\right)K_n|\psi\rangle & x_n=0 \\ -\left(\bigotimes_{i=1}^nZ^{x_i}\right)K_n|\psi\rangle & x_n=1 \end{array}\right.$$ Thus, every $$|\Psi_x\rangle$$ is an eigenstate of every stabilizer, and with a different pattern of $$\pm 1$$ eigenvalues (and must therefore be mutually orthogonal).
While it must be the case that the different states $$|\Psi_x\rangle$$ are orthogonal, I think it's useful to think about this in terms of the way that the graph states are created. Remember that $$|\psi\rangle$$ is created from qubits in the $$|+\rangle$$ state and then have controlled-phase gates applied between them. Now, if I evaluate $$\langle\Psi_y|\Psi_x\rangle$$, think of this as a calculation $$\langle+|^{\otimes n}CP\cdot Z_{x\oplus y}\cdot CP|+\rangle^{\otimes n}$$ where $$CP$$ represents the collection of controlled phase gates. Pauli $$Z$$ commutes with controlled phase, which means we can bring the two CPs together and annihilate them, leaving behind $$\langle+|^{\otimes n} Z_{x\oplus y}|+\rangle^{\otimes n}.$$ Given that $$x\neq y$$, there is at least one $$Z$$, and we know $$\langle +|Z|+\rangle=\langle -|+\rangle=0$$.
This way of thinking gives another way of describing the basis of graph states: prepare each qubit in either $$|+\rangle$$ or $$|-\rangle$$, and combine with controlled-phases. Each different choice of $$\pm$$ gives a different graph state in the basis.
• Ok, this is cool as independently I got more or less the same solution, although it took me much longer than you :-) – sycramore Apr 3 at 16:55
I'm not sure I understand the question, since this seems quite straightforward.
Graph states are Clifford states, so for a state on $$n$$ qubits, the set of stabilizers has $$n$$ generators looking like
$$i^k P_1\otimes\ldots\otimes P_n$$
where $$k\in\{0,1,2,3\}$$ and the $$P$$'s are Pauli $$X,Y,$$ or $$Z$$ operators. (For graph states, these stabilizers look like $$\{X_v Z_{\text{Nbhd}(v)} : v \in V\}$$ )
Each Pauli has two eigenvectors. If we choose one of them and call it $$|\psi_i\rangle$$, and call its corresponding eigenvalue $$\lambda_i$$, for each $$P_i$$, then $$|\psi_1\rangle\otimes\ldots\otimes|\psi_n\rangle$$ will be an eigenvector of the stabilizer with eigenvalue $$i^k\prod_i \lambda_i$$.
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2020-08-09 20:54:40
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https://www.biostars.org/p/421238/
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Collapsing BAM based on seq and positions
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0
Entering edit mode
22 months ago
manekineko ▴ 150
Is there a tool I can use to input a BAM and do a collapsing based on sequence and positions and retaining the copy number of the unique sequence? (outputing again BAM)
bam collapse • 612 views
1
Entering edit mode
Not clear. input/output example required.
1
Entering edit mode
Is this not what mark duplicates from picard does?
Samtools + Picard Markduplicates
Picard Mark Duplicates
There are many more post about this but then you may know what to look for and if this is an option.
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Entering edit mode
I need something like FASTA collapsing, where you retain only 1 unique sequence with its copy number, but on a level of BAM file. I have BAM mapped with uncollapsed sequences, and need to collapsed it somehow to have BAM with unique sequences mapped somewhere and its copy number (retained in the name or similar way).
0
Entering edit mode
input/output example required.
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Entering edit mode
For example, if containing identical seq mapping the same pos:
HISEQ:47:C6FUWANXX:1:1101:1212:2073 4 contig1222 1 25 22M * 0 0 TATTGCACTTGTCCCGGCCTGT BBBBBFFFFFFFFFFFFFFFFF XT:A:U NM:i:1 X0:i:1 X1:i:0 XM:i:1 XO:i:0 XG:i:0 MD:Z:21C0
HISEQ:47:C6FUWANXX:1:1101:1139:2100 4 contig1222 1 25 22M * 0 0 TATTGCACTTGTCCCGGCCTGT BBBBBFFFFFFFFFFFF/FFFF XT:A:U NM:i:1 X0:i:1 X1:i:0 XM:i:1 XO:i:0 XG:i:0 MD:Z:21C0
to retain only 1 indicating on the name (or similar way) _2 the copy number:
HISEQ:47:C6FUWANXX:1:1101:1212:2073_2 4 contig1222 1 25 22M * 0 0 TATTGCACTTGTCCCGGCCTGT BBBBBFFFFFFFFFFFFFFFFF XT:A:U NM:i:1 X0:i:1 X1:i:0 XM:i:1 XO:i:0 XG:i:0 MD:Z:21C0
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Entering edit mode
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I just made an example some flags may be wrong, view it as mapped. I hope you got what I mean and want to do?
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This sounds much like the ReducedReads format from early GATK versions. Ultimately it was retired because it wasn't sufficient to capture all the important information, but it may still be available if you can find an old enough GATK (2.8?).
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2021-12-01 10:42:33
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https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=123&t=57158&p=222874
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## Homework 3
$PV=nRT$
LeAirraBullingor2k
Posts: 77
Joined: Wed Mar 13, 2019 12:15 am
### Homework 3
Is it okay to do homework problems from Acids and Bases for homework 3?
Selena Yu 1H
Posts: 108
Joined: Fri Aug 09, 2019 12:16 am
### Re: Homework 3
Yes, it's okay to do problems from Acids and Bases for homework 3 because we just started thermochemistry
Jasmine Kim 1L
Posts: 71
Joined: Fri Aug 02, 2019 12:16 am
### Re: Homework 3
Yeah, it should be fine. I did homework problems from Acids and Bases for week 3.
Osvaldo SanchezF -1H
Posts: 122
Joined: Wed Sep 18, 2019 12:21 am
### Re: Homework 3
Well since one of the primary focuses of the test was acids and bases and was the last thing we covered that would be included In the test, I do not see why it would not be included.
MTanikella_1K
Posts: 110
Joined: Sat Jul 20, 2019 12:16 am
### Re: Homework 3
It should be fine to do problems from outline two for homework three as long as you complete five problems!
Yailin Romo 4G
Posts: 109
Joined: Wed Feb 20, 2019 12:16 am
### Re: Homework 3
I think that's fine because that's what I did for hw 3
Megan Kirschner
Posts: 46
Joined: Wed Feb 20, 2019 12:17 am
### Re: Homework 3
Speaking of- does anyone know where problems from homework #6 are supposed to come from? I think thermodynamics, but we didn't cover all of it yet- so I'm not sure how to go about it.
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2020-04-07 14:21:22
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https://moments.readthedocs.io/en/main/sfs/inference.html
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# SFS Inference
## Computing likelihoods
Following [Sawyer1992] the distribution of mutation frequencies is treated as a Poisson random field, so that composite likelihoods (in which we assume mutations are independent) are computed by taking Poisson likelihoods over bins in the SFS. We typically work with log-likelihoods, so that the log-likelihood of the data ($$D$$) given the model ($$M$$) is
$\log{\mathcal{L}} = \sum_{i} D_i \log{M_i} - M_i - \log{D_i !}$
where $$i$$ indexes the bins of the SFS.
Likelihoods can be computed from moments.Inference:
import moments
import numpy as np
theta = 1000
model = theta * moments.Demographics1D.snm([10])
data = model.sample()
print(model)
print(data)
[-- 1000.0 499.9999999999999 333.33333333333326 250.0 200.0
166.66666666666666 142.85714285714286 125.0 111.1111111111111 --]
[-- 974 483 316 266 210 159 135 122 123 --]
print(moments.Inference.ll(model, data))
-35.832644905426605
When simulating under some demographic model, we usually use the default theta of 1, because the SFS scales linearly in the mutation rate. When comparing to data in this case, we need to rescale the model SFS. It turns out that the maximum-likelihood rescaling is that which makes the total number of segregating sites in the model equal to the total number in the data:
data = moments.Spectrum([0, 3900, 1500, 1200, 750, 720, 600, 400, 0])
model = moments.Demographics1D.two_epoch((2.0, 0.1), [8])
print("Number of segregating sites in data:", data.S())
print("Number of segregating sites in model:", model.S())
print("Ratio of segregating sites:", data.S() / model.S())
opt_theta = moments.Inference.optimal_sfs_scaling(model, data)
print("Optimal theta:", opt_theta)
Number of segregating sites in data: 9070.0
Number of segregating sites in model: 2.7771726368386327
Ratio of segregating sites: 3265.911481226729
Optimal theta: 3265.911481226729
Then we can compute the log-likelihood of the rescaled model with the data, which will give us the same answer as moments.Inference.ll_multinom using the unscaled data:
print(moments.Inference.ll(opt_theta * model, data))
print(moments.Inference.ll_multinom(model, data))
-59.880644681554486
-59.880644681554486
## Optimization
moments optimization is effectively a wrapper for scipy optimization routines, with some features specific to working with SFS data. In short, given a demographic model defined by a set of parameters, we try to find those parameters that minimize the negative log-likelihood of the data given the model. There are a number of optimization functions available in moments.Inference:
• optimize and optimize_log: Uses the BFGS algorithm.
• optimize_lbfgsb and optimize_log_lbfgsb: Uses the L-BFGS-B algorithm.
• optimize_log_fmin: Uses the downhill simplex algorithm on the log of the parameters.
• optimize_powell and optimize_log_powell: Uses the modified Powell’s method, which optimizes slices of parameter space sequentially.
With each method, we require at least three inputs: 1) the initial guess, 2) the data SFS, and 3) the model function that returns a SFS of the same size as the data.
Additionally, it is common to set the following:
• lower_bound and upper_bound: Constraints on the lower and upper bounds during optimization. These are given as lists of the same length of the parameters.
• fixed_params: A list of the same length of the parameters, with fixed values given matching the order of the input parameters. None is used to specify parameters that are still to be optimized.
• verbose: If an integer greater than 0, prints updates of the optimization procedure at intervals given by that spacing.
For a full description of the various inference functions, please see the SFS inference API.
### Single population example
As a toy example, we’ll generate some fake data from a demographic model and then reinfer the input parameters of that demographic model. The model is an instantaneous bottleneck followed by exponential growth, implemented in moments.Demographics1D.bottlegrowth, which takes parameters [nuB, nuF, T] and the sample size. Here nuB is the bottleneck size (relative to the ancestral size), nuF is the relative final size, and T is the time in the past the bottleneck occurred (in units of $$2N_e$$ generations).
nuB = 0.2
nuF = 3.0
T = 0.4
n = 60 # the haploid sample size
fs = moments.Demographics1D.bottlegrowth([nuB, nuF, T], [n])
theta = 2000 # the scaled mutation rate (4*Ne*u*L)
fs = theta * fs
data = fs.sample()
The input demographic model (assuming an $$N_e$$ of 10,000), plotted using demesdraw:
We then set up the optimization inputs, including the initial parameter guesses, lower bounds, and upper bounds, and then run optimization. Here, I’ve decided to use the log-L-BFGS-B method, though there are a number of built in options (see previous section).
p0 = [0.2, 3.0, 0.4]
lower_bound = [0, 0, 0]
upper_bound = [None, None, None]
p_guess = moments.Misc.perturb_params(p0, fold=1,
lower_bound=lower_bound, upper_bound=upper_bound)
model_func = moments.Demographics1D.bottlegrowth
opt_params = moments.Inference.optimize_log_lbfgsb(
p0, data, model_func,
lower_bound=lower_bound,
upper_bound=upper_bound)
model = model_func(opt_params, data.sample_sizes)
opt_theta = moments.Inference.optimal_sfs_scaling(model, data)
model = model * opt_theta
The reinferred parameters:
Params nuB nuF T theta
Input 0.2 3.0 0.4 2000
Refit 0.2468 3.057 0.4094 1.919e+03
We can also visualize the fit of the model to the data:
moments.Plotting.plot_1d_comp_Poisson(model, data)
#### Confidence intervals
We’re often interested in estimating the precision of the inferred parameters from our best fit model. To do this, we can compute a confidence interval for each free parameter from the model fit. Methods implemented in moments to compute, particularly the method based on the Godambe Information Matrix [Coffman2016], were first implemented in dadi by Alec Coffman, who’s paper should be cited if these methods are used.
See the API documentation for uncertainty functions for information on their usage.
### Two population example
Here, we will create some fake data for a two-population split-migration model, and then re-infer the input parameters to the model used to create that data. This example uses the optimize_log_fmin optimization function. We’ll also use the FIM_uncert function to compute uncertainties (reported as standard errors).
input_theta = 10000
params = [2.0, 3.0, 0.2, 2.0]
model_func = moments.Demographics2D.split_mig
model = model_func(params, [20, 20])
model = input_theta * model
data = model.sample()
p_guess = [2, 2, .1, 4]
lower_bound = [1e-3, 1e-3, 1e-3, 1e-3]
upper_bound = [10, 10, 1, 10]
p_guess = moments.Misc.perturb_params(
p_guess, lower_bound=lower_bound, upper_bound=upper_bound)
opt_params = moments.Inference.optimize_log_fmin(
p_guess, data, model_func,
lower_bound=lower_bound, upper_bound=upper_bound,
verbose=20) # report every 20 iterations
refit_theta = moments.Inference.optimal_sfs_scaling(
model_func(opt_params, data.sample_sizes), data)
uncerts = moments.Godambe.FIM_uncert(
model_func, opt_params, data)
print_params = params + [input_theta]
print_opt = np.concatenate((opt_params, [refit_theta]))
print("Params\tnu1\tnu2\tT_div\tm_sym\ttheta")
print(f"Input\t" + "\t".join([str(p) for p in print_params]))
print(f"Refit\t" + "\t".join([f"{p:.4}" for p in print_opt]))
print(f"Std-err\t" + "\t".join([f"{u:.3}" for u in uncerts]))
moments.Plotting.plot_2d_comp_multinom(
model_func(opt_params, data.sample_sizes), data)
80 , -2037.68 , array([ 2.23462 , 1.44521 , 0.158979 , 2.76268 ])
100 , -1669.86 , array([ 1.88718 , 1.63916 , 0.215159 , 3.56113 ])
120 , -1410.36 , array([ 1.71384 , 1.97358 , 0.253576 , 3.10853 ])
140 , -1262.37 , array([ 1.83998 , 2.58247 , 0.210581 , 2.03112 ])
160 , -1203.16 , array([ 2.00812 , 3.0514 , 0.20485 , 1.9948 ])
180 , -1199.16 , array([ 1.97937 , 2.86564 , 0.197018 , 2.09359 ])
200 , -1198.13 , array([ 1.98305 , 2.92208 , 0.200246 , 2.11119 ])
220 , -1198.13 , array([ 1.98274 , 2.92226 , 0.200443 , 2.11031 ])
240 , -1198.13 , array([ 1.98024 , 2.91717 , 0.20053 , 2.11718 ])
260 , -1198.13 , array([ 1.98055 , 2.91783 , 0.200547 , 2.11654 ])
Params nu1 nu2 T_div m_sym theta
Input 2.0 3.0 0.2 2.0 10000
Refit 1.981 2.918 0.2005 2.116 1.001e+04
Std-err 0.0389 0.0649 0.00449 0.0725 70.2
Above, we can see that we recovered the parameters used to simulate the data very closely, and we used moments’s plotting features to visually compare the data to the model fit.
## References
Sawyer1992
Sawyer, Stanley A., and Daniel L. Hartl. “Population genetics of polymorphism and divergence.” Genetics 132.4 (1992): 1161-1176.
Coffman2016
Coffman, Alec J., et al. “Computationally efficient composite likelihood statistics for demographic inference.” Molecular biology and evolution 33.2 (2016): 591-593.
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2023-02-05 19:38:22
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|
http://clay6.com/qa/25543/an-electron-losely-bound-to-the-impurity-of-a-doped-semiconductor-is-able-t
|
Browse Questions
# An electron losely bound to the impurity of a doped semiconductor is able to jump to the conducting band because of thermal collision at temperature T k. If the impurity level is 15 mev below the conducting band, calculate the temperature.
$(a)\;348\;K \\ (b)\;174\;K \\ (c)\;273\;K \\ (d)\;126\;k$
The thermal energy associated with temperature T K is $E= kT$
$k= 8.62 \times 10^{-5}$
$\therefore 15 \times 10^{-5} ev =T \times 8.62 \times 10^{-5}$
$T=\large\frac{0.015}{8.62 \times 10^{-5}}$
$\quad= 174 \;K$
Hence b is the correct answer.
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2017-03-26 18:51:49
|
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http://www.exampleproblems.com/wiki/index.php/Curve
|
Curve
In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. Simple examples are the circle or the straight line. A large number of other curves have been studied in geometry.
Definitions
In mathematics, a (topological) curve is defined as follows. Let $I$ be an interval of real numbers (i.e. a non-empty connected subset of ${\mathbb {R}}$). Then a curve $\!\,\gamma$ is a continuous mapping $\,\!\gamma :I\rightarrow X$, where $X$ is a topological space. The curve $\!\,\gamma$ is said to be simple if it is injective, i.e. if for all $x$, $y$ in $I$, we have $\,\!\gamma (x)=\gamma (y)\rightarrow x=y$. If $I$ is a closed bounded interval $\,\![a,b]$, we also allow the possibility $\,\!\gamma (a)=\gamma (b)$ (this convention makes it possible to talk about closed simple curve). If $\gamma (x)=\gamma (y)$ for some $x\neq y$ (other than the extremities of $I$), then $\gamma (x)$ is called a double (or: multiple) point of the curve.
A curve $\!\,\gamma$ is said to be closed or a loop if $\,\!I=[a,b]$ and if $\!\,\gamma (a)=\gamma (b)$. A closed curve is thus a continuous mapping of the circle $S^{1}$; a simple closed curve is also called a Jordan curve.
A plane curve is a curve for which X is the mathematical plane — these are the examples first encountered — or in some cases the projective plane. A space curve is a curve for which X is of three dimensions, usually Euclidean space; a skew curve is a space curve which lies in no plane. These definitions also apply to algebraic curves (see below).
This definition of curve captures our intuitive notion of a curve as a connected, continuous geometric figure that is "like" a line, although it also includes figures that can be hardly called curves in common usage. For example, the image of a curve can cover a square in the plane (Peano curve). The image of simple plane curve can have Hausdorff dimension bigger than one (see Koch snowflake) and even positive Lebesgue measure (the last example can be obtained by small variation of the Peano curve construction). The dragon curve is yet another weird example.
Conventions and terminology
The distinction between a curve and its image is important. Two distinct curves may have the same image. For example, a line segment can be traced out at different speeds, or a circle can be traversed a different number of times. Many times, however, we are just interested in the image of the curve. It is important to pay attention to context and convention in reading.
Terminology is also not uniform. Often, topologists use the term "path" for what we are calling a curve, and "curve" for what we are calling the image of a curve. The term "curve" is more common in vector calculus and differential geometry.
Length of curves
If $X$ is a metric space with metric $d$, then we can define the length of a curve $\!\,\gamma :[a,b]\rightarrow X$ by
${\mbox{Length}}(\gamma )=\sup \left\{\sum _{{i=1}}^{n}d(\gamma (t_{i}),\gamma (t_{{i-1}})):n\in {\mathbb {N}}{\mbox{ and }}a=t_{0}
A rectifiable curve is a curve with finite length. A parametrization of $\!\,\gamma$ is called natural (or unit speed or parametrised by arc length) if for any $t_{1}$, $t_{2}$ in $[a,b]$, we have
${\mbox{Length}}(\gamma |_{{[t_{1},t_{2}]}})=|t_{2}-t_{1}|$
If $\!\,\gamma$ is Lipschitz then it is automatically rectifiable. Moreover, in this case, one can define speed of $\!\,\gamma$ at $t_{0}$ as
${\mbox{Speed}}(t_{0})=\limsup _{{t\to t_{0}}}{d(\gamma (t),\gamma (t_{0})) \over |t-t_{0}|}$
and then
${\mbox{Length}}(\gamma )=\int _{a}^{b}{\mbox{Speed}}(t)\,dt$
In particular, if $X={\mathbb {R}}^{n}$ is Euclidean space and $\gamma :[a,b]\rightarrow {\mathbb {R}}^{n}$ is differentiable then
${\mbox{Length}}(\gamma )=\int _{a}^{b}\left|\,{d\gamma \over dt}\,\right|\,dt$
Differential geometry
Main article: differential geometry of curves
While the first examples of curves that are met are mostly plane curves (that is, in everyday words, curved lines in two-dimensional space), there are obvious examples such as the helix which exist naturally in three dimensions. The needs of geometry, and also for example classical mechanics are to have a notion of curve in space of any number of dimensions. In general relativity, a world line is a curve in spacetime.
If $X$ is a differentiable manifold, then we can define the notion of differentiable curve in $X$. This general idea is enough to cover many of the applications of curves in mathematics. From a local point of view one can take $X$ to be Euclidean space. On the other hand it is useful to be more general, in that (for example) it is possible to define the tangent vectors to $X$ by means of this notion of curve.
If $X$ is a smooth manifold, a smooth curve in $X$ is a smooth map
$\!\,\gamma :I\rightarrow X.$
This is a basic notion. There are less and more restricted ideas, too. If $X$ is a $C^{k}$ manifold (i.e., a manifold whose charts are $k$ times continuously differentiable), then a $C^{k}$ curve in $X$ is such a curve which is only assumed to be $C^{k}$ (i.e. $k$ times continuously differentiable). If $X$ is an analytic manifold (i.e. infinitely differentiable and charts are expressible as power series), and $\!\,\gamma$ is an analytic map, then $\!\,\gamma$ is said to be an analytic curve.
A differentiable curve is said to be regular if its derivative never vanishes. (In words, a regular curve never slows to a stop or backtracks on itself.) Two $C^{k}$ differentiable curves
$\!\,\gamma _{1}:I\rightarrow X$ and
$\!\,\gamma _{2}:J\rightarrow X$
are said to be equivalent if there is a bijective $C^{k}$ map
$\!\,p:J\rightarrow I$
such that the inverse map
$\!\,p^{{-1}}:I\rightarrow J$
is also $C^{k}$, and
$\!\,\gamma _{{2}}(t)=\gamma _{{1}}(p(t))$
for all $t$. The map $\!\,\gamma _{2}$ is called a reparametrisation of $\!\,\gamma _{1}$; and this makes an equivalence relation on the set of all $C^{k}$ differentiable curves in $X$. A $C^{k}$ arc is an equivalence class of $C^{k}$ curves under the relation of reparametrisation.
Algebraic curve
Main article: Algebraic curve
In the setting of algebraic geometry, a curve is usually defined to be an algebraic curve. These include, for example, elliptic curves, which are studied in number theory and which have important applications to cryptography. Algebraic curves are more akin to surfaces than curves. Non-singular complex projective algebraic curves are in fact compact Riemann surfaces.
History
A curve may be a locus, or a path. That is, it may be a graphical representation of some property of points; or it may be traced out, for example by a stick in the sand on a beach. Of course if one says curved in ordinary language, it means bent (not straight), so refers to a locus. This leads to the general idea of curvature. As we now understand, after Newtonian dynamics, to follow a curved path a body must experience acceleration. Before that, the application of current ideas to (for example) the physics of Aristotle is probably anachronistic. This is important because major examples of curves are the orbits of the planets. One reason for the use of the Ptolemaic system of epicycle and deferent was the special status accorded to the circle as curve.
The conic sections had been deeply studied by Apollonius of Perga. They were applied in astronomy by Kepler. The Greek geometers had studied many other kinds of curves. One reason was their interest in geometric constructions, going beyond ruler-and-compass constructions. In that way, the intersection of curves could be used to solve some polynomial equations, such as that involved in trisecting an angle.
Newton also worked on an early example in the calculus of variations. Solutions to variational problems, such as the brachistochrone and tautochrone questions, introduced properties of curves in new ways (in this case, the cycloid). The catenary gets its name as the solution to the problem of a hanging chain, the sort of question that became routinely accessible by means of differential calculus.
In the eighteenth century came the beginnings of the theory of plane algebraic curves, in general. Newton had studied the cubic curves, in the general description of the real points into 'ovals'. The statement of Bézout's theorem showed a number of aspects which were not directly accessible to the geometry of the time, to do with singular points and complex solutions.
From the nineteenth century there is not a separate curve theory, but rather the appearance of curves as the one-dimensional aspect of projective geometry, and differential geometry; and later topology, when for example the Jordan curve theorem was understood to lie quite deep, as well as being required in complex analysis. The era of the space-filling curves finally provoked the modern definitions of curve.
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2019-03-23 02:50:23
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|
https://mathoverflow.net/questions/287720/which-3-regular-graphs-are-schreier-coset-graphs
|
# Which 3-regular graphs are Schreier coset graphs?
Given a group $$G$$ and a subgroup $$H$$ the Schreier coset graph (w.r.t. some set $$S$$ of $$G$$) is the directed (and labelled) graph whose vertices are the cosets of $$H$$ (i.e. the set $$G/H$$) and $$x \sim y$$ if there is a $$s \in S$$ so that $$x = sy$$.
When $$S$$ is symmetric (i.e. $$s \in S \implies s^{-1} \in S$$), then one can associate to this graph an undirected graph (by replacing the two edges with opposite directions and labels $$a$$ and $$a^{-1}$$ by an undirected edge). Note that it could happen that $$a = a^{-1}$$ which is unproblematic unless the edge makes a loop. So in the undirected graph one needs to distinguish the degree 2 loops (which come from $$a$$ and $$a^{-1}$$ acting trivially on the coset $$x$$) and the degree 1 loops (which come from $$a = a^{-1}$$ acting trivially on the coset $$x$$).
Using this construction (and this convention for loops), a Schreier graph is always a regular graph (of degree $$|S|$$).
Given an even degree regular graph (without "degree 1" loops), then it is possible to find a group $$G$$ (a free group actually), subgroup $$H and set $$S$$ so that this graph is a Schreier coset graph. This is a result of J.L.Gross, see https://doi.org/10.1016/0095-8956(77)90068-5.
Question: Assume $$\Gamma$$ is a an 3-regular graph. What are the necessary conditions for $$\Gamma$$ to be a Schreier Graph?
I'm fine with any answers which assumes that $$\Gamma$$ is loopless. Sufficient conditions are somehow much more easy to come by (see examples below).
A combinatorial way to ask the question is to find a labelling of the directed graph underlying $$\Gamma$$ so that $$a^{-1}$$ always labels an edge in the opposite direction to $$a$$ (with the pesky exception of those degree 1 loops).
Example (of a sufficient condition for a loopless graph): if the graph has a perfect matching (a.k.a. 1-factor), then you can label these edges by an element $$a = a^{-1}$$. There only remains an even degree graph, so by the result of Gross you can get away with $$G = F * \mathbb{Z}_2$$ where $$F$$ is the free group mentioned above and $$a$$ is the generator (and only non-trivial element of $$\mathbb{Z}_2$$).
Example (continued): every 3-regular bridgeless (i.e. without a cut-edge) graph has a 1-factor (a result of Petersen again). So every 3-regular bridgeless graph is a Schreier graph. In particular, the Petersen graph (or any other snark) are Schreier graphs.
Note that an element $$a \in S$$ so that $$a \neq a^{-1}$$ need not always label a 2-factor of $$\Gamma$$. It just needs to label a spanning subgraphs whose connected components are either edges or cycles (so a mix of 1-factor and 2-factor).
[EDIT]
Non-example: There is an example of an 3-regular graph which is not a Schreier graph. It's sometimes called the "no perfect matching graph", see http://mathworld.wolfram.com/PerfectMatching.html (you have to remove three edges in order to make the graph on that page 3-regular).
This non-example builds a lot on the fact that there are many bridges.
[EDIT]
If there is a way to colour the edges in $$k$$-colours (and the graph is $$k$$-regular), then this gives a way to turn the graph in a Schreier graph. (Every element is so that $$a = a^{-1}$$ and the group $$G$$ is a free product of $$k$$ copies of $$\mathbb{Z}_2$$.)
[EDIT]
It thought that a result of M.Kano see https://doi.org/10.1016/0095-8956(86)90025-0 would give the necessary decomposition of the graph for odd degrees $$\geq 5$$, but this turns out to be incorrect.
Graphs which cannot be coloured are sometimes called of "class 2" (see Vizing's theorem). Although the Petersen graph (or any snark) is of "class 2", it is a Schreier graph (so being of class 1 is not a necessary condition).
• Are you asking only about infinite graphs? I'm not familiar with the result of Gross you mention, but for finite graphs I'm pretty sure it's false: a graph (finite or not) is a Schreier coset graph iff it is vertex transitive, and there are surely even degree regular finite graphs that aren't vertex-transitive... – Joshua Grochow Dec 5 '17 at 14:25
• @JoshuaGrochow. No, a Schreier graph doesn't have to be vertex-transitive (the group acts on the vertices of the Schreier graph but does not preserve the graph structure). For instance, the Schreier graph of the action of the dihedral group of order 6 (with a generating pair $(a,b)$ of elements of order 2), modulo the subgroup $\langle b\rangle$, consists of 3 consecutive vertices $\bullet-\bullet-\bullet$ (with a self-loop at each extremity); it's not vertex-transitive. – YCor Dec 5 '17 at 14:28
• @JoshuaGrochow no I don't think so. Start from 2 hexagons with 2 colors (each is a Scheier graph of a dihedral group). Choose a bad bijection between their vertices to join them with a third color, e.g., $123456\mapsto 124635$. Then this is by construction a Schreier graph (of a free product of 3 cyclic groups of order 2, or a suitable cyclic quotient), but it's not vertex-transitive, because it has a unique square. – YCor Dec 5 '17 at 18:30
• @JoshuaGrochow : I edited in a link to the original paper of J.L. Gross, if you want to have a look. There are definitively 4-regular graphs which are not vertex-transitive, so vertex-transitive is definitively not a necessary condition. – ARG Dec 5 '17 at 19:10
• The following just appeared on arXiv (by P-H. Leemann), "We prove that every connected locally finite regular graph has a double cover which is isomorphic to a Schreier graph". He mentions that the case of even degree was done in Lubotzky's book "Discrete groups, expanding graphs...". – YCor Oct 14 '20 at 6:18
Here are some usefull facts, and some historical details.
Every $$2d$$-regular graph (without loops of degree 1) is isomorphic to a Schreier graph.
The results for finite graphs is due to Gross. The result for locally finite graphs follows by compacity and was probably one of this well-known "folklore result" for long. To my knowledge, the first written proof of it can be found in "Some problems of the dynamics of group actions on rooted trees" by R. Grigorchuk 2011. But it has since be "reproven" many times (by J. Cannizzo in 2013, in my own phd thesis around the same time, ...).
A (2d+1)-regular graph (without loops of degree 1) is isomorphic to a Schreier graph if and only if it has a perfect matching.
This follows from the previous fact. See for example ARG's answer.
Every countable vertex transitive graphs is isomorphic to a Schreier graphs.
The finite case was done by C. Godsil and G. Royle in 2001. I did (circa 2013) the locally finite case in my phd thesis, using results of Aharoni on matchings in infinite graphs. I believe that an independant proof of it was published in 2016 by another author, but sadly cannot remember more details. Finally, the countable case was done by M. Hamman and A. Wendland in the appendix of https://arxiv.org/abs/2007.06432
Up to a double cover, any locally finite regular graphs is isomorphic to a Schreier graph.
See https://arxiv.org/pdf/2010.06431.pdf, which is intended as a small note for reference.
Here is the skeleton of the proof. Let $$G$$ be a locally finite graph. If $$G$$ is bipartite, put $$K=G$$. Otherwise, put $$K=G\times C_2$$. Then $$K$$ is connected, bipartite (and hence without loops of degree 1), regular and covers $$G$$. Since $$K$$ is bipartite and regular it has a perfect matching. The desired result follows.
[community wiki since it's my own question]
The answer is actually simple once the convention on degrees is clear (which it apparently was not at the time of writing)
Answer: If $$k$$ is odd, a $$k$$-regular loopless graph is a Schreiers graph if and only if it has a matching.
First note that elements $$a \in S$$ so that $$a \neq a^{-1}$$ necessarily create a 2 factor. There three cases (here $$x$$ is a vertex, or a coset):
(1) $$a \cdot x = x$$ this makes a loop and also a loop in the "reverse" direction since then $$a^{-1} \cdot x =x$$.
(2) $$a \cdot a \cdot x = x$$, this is an interesting case [and the main cause of my confusion], because it will often be displayed in the literature as a single-edge although there should be another edge coming from the fact that $$a^{-1} \cdot a^{-1} \cdot x = x$$
(3) $$a$$ makes a longer cycle before coming back to $$x$$.
If there are no loops then elements $$a \in S$$ so that $$a = a^{-1}$$ can only make a matching of the graph.
Hence, under the convention for degree taken, loopless Schreier graphs need to have a matching.
On the other hand, if you have a matching then you can label this matching by an element $$b$$ with $$b=b^{-1}$$. The rest of the graph is $$2r$$-regular for some $$r$$, so you can find $$r$$ disjoint $$2$$-factors and label them with $$a_1,a_2,\ldots,a_r$$.
My confusion came from diagrams such as the one below. Edge with arrows indicate how an element acts. Edge without arrow means the element switches both ends of that edge. This completely determine the action, but it gives a false impression on the vertex degree. In the picture below the vertices have degree 5 or 6 (depending on whether $$c= c^{-1}$$ or $$c \neq c^{-1}$$).
• I've never understood why people want to collapse double edges to single ones when defining Cayley and Schreier graphs. The correct definition of a Cayley graph is that it's the covering space of the rose corresponding to the kernel of the natural map to your group. Similarly, the correct definition of a Schreier graph is that it's the covering space of the rose corresponding to the preimage of the subgroup $H$. According to that definition, your single edges should actually be double, with arrows pointing in both directions. – HJRW Jul 13 '20 at 17:35
• I think that was exactly the source of my confusion: I focused on the diagrams that were drawn of Schreier graphs (and the definitions which accompany them) instead of looking at the functorial definitions (like yours ). (Just to make sure we are on the same page: the picture I put at the end was meant as an example of a badly made picture.) – ARG Jul 13 '20 at 20:04
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2021-01-26 22:47:00
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https://www.lessonplanet.com/teachers/dividing-by-powers-of-ten-a-7th-8th
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# Dividing by Powers of Ten (A)
##### This Dividing by Powers of Ten (A) worksheet also includes:
In this powers of ten worksheet, students divide three to seven-digit whole numbers by positive powers of ten. This four-page worksheet contains approximately 40 problems, with answers.
Concepts
Resource Details
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2019-12-07 02:07:07
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https://read.dukeupress.edu/hope/article-abstract/43/2/339/12458/Consumer-Sovereignty-in-the-History-of?redirectedFrom=fulltext
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Economists have tried to incorporate the environment into the economic calculus by incorporating shadow values of environmental improvements into benefit-cost analysis and by designing policies to price pollution. Environmental economists tend to present these practices as settled, but in fact deep-buried tensions lie underneath the apparently settled ground. When they choose one method to measure prices over another, environmental economists implicitly align themselves with one side or another of a debate between the role of utilitarianism and consumer sovereignty that has been raging for over a century.
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2021-08-02 15:13:40
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http://mathhelpforum.com/number-theory/215176-prime-number.html
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Math Help - Prime number
1. Prime number
For any prime $p \ge 29$. Prove that $182 | p^2 - 1$
0
3. Re: Prime number
Originally Posted by Kanwar245
For any prime $p \ge 29$. Prove that $182 | p^2 - 1$
If p= 31, $p^2- 1= 960$ which is NOT divisible by 182: 960/182= 5.274725...
Further p- 1= 30 and p+ 1= 32 and neither divides 182 so I have no idea what you or rgrothee are asserting.
4. Re: Prime number
Originally Posted by HallsofIvy
If p= 31, [tex]p^2- 1= 960 which is NOT divisible by 182: 960/182= 5.274725...
Further p- 1= 30 and p+ 1= 32 and neither divides 182 so I have no idea what you or rgrothee are asserting.
My bad, you're right. There's a typo. We need to show that $182|p^{12}-1$
5. Re: Prime number
$p^{12}$! Oh, Dear. Well, $p^{12}- 1= (p+1)(p^2- p+ 1)(p-1)(p^2+ p+ 1)(p^6+ 1)$
$182= 2(91)= 2(7)(13)$
Obviously, if p is prime, larger than or equal to 29, then both p+1, and p- 1 are even so it remains to show that one of the factors is divisible 7 and one by 13.
6. Re: Prime number
Originally Posted by Kanwar245
For any prime $p \ge 29$. Prove that $182 | p^2 - 1$
By Fermat’s little theorem, 13 divides $p^{12}-1$. Also by Fermat’s little theorem, 7 divides $p^6-1$ and hence 7 divides $p^{12}-1=(p^6-1)(p^6+1)$. And obviously 2 divides $p^2 - 1$ since $p$ is odd. The result follows.
NB: This works for all integers $p$ which are coprime with 2, 7, and 13.
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2016-02-12 12:50:49
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http://www.abalancedbodystudio.com/play-to-yczykrb/373148-derivative-of-arctan
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Replace all occurrences of with . sin 2 (y) + cos 2 (y) = 1. divide by cos 2 (y) to get. As the function atan2 is a function of two variables, it has two partial derivatives.At points where these derivatives exist, atan2 is, except for a constant, equal to arctan(y/x).Hence for x > 0 or y â 0, â â â¡ (,) = â â â¡ = â +, â â â¡ (,) = â â â¡ = +. So the derivative of this thing with respect to x is one over one plus x squared. But don't forget to use the Chain Rule in your problem!! Derivatives of inverse trigonometric functions. 3 * ln(2) * 8^x, comes from the fact that we must use the chain rule, and hence we take the derivative of what's inside (8^x). Introduction to the derivative formula of inverse tangent function with proof to derive the differentiation of tan^-1(x) or arctan(x) in differential calculus. Get the free "nth Derivative Calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. Tap for more steps... Rewrite as . Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions. Derivative of 8^x: ln(8) * 8^x = ln(2^3) * 8^x = 3 * ln(2) * 8^x. sinh x = cosh x Proof: csch x = - coth x csch x Proof: cosh x = sinh x Proof: sech x = - tanh x sech x Proof: tanh x = 1 - tanh 2 x Proof: coth x = 1 - coth 2 x Proof Those with hyperlinks have proofs. Differentiate functions that contain the inverse trigonometric functions arcsin(x), arccos(x), and arctan(x). Other notation sometimes used : atan. You da real mvps! For example, to calculate online the derivative of the polynomial following x^3+3x+1, just enter derivative_calculator(x^3+3x+1), after calculating result 3*x^2+3 is returned. Practice: Derivatives of inverse trigonometric functions. Derivative of arctan Thread starter aurdav; Start date Nov 10, 2008; Nov 10, 2008 #1 aurdav. Derivative of inverse cosine. Derivative of inverse cosine. Differentiating both sides of this equation and applying the chain rule, one can solve for dy/dx in terms of y. lim_(x->+oo)arctan(x)=-pi/2 The arctan function allows the calculation of the arctangent of a number. The derivative of the arctangent function of x is equal to 1 divided by (1+x 2) Integral of arctan. If y = tan-1 x, then tan y = x. If you have a function f(x), there are several ways to mark the derivative of f when it comes to x.The common way that this is done is by df / dx and f'(x).If a derivative is taken n times, then the notation d n f / d x n or f n (x) is used. Tap for more steps... To apply the Chain Rule, set as . Taking the derivative of the second expression implicitly gives: solving for the derivative gives: (1) This is correct but unsatisfying - we want the derivative in terms of x. Begin by setting y=arctan(x) so that tan(y)=x. Differentiate. Find more Mathematics widgets in Wolfram|Alpha. Examples : arctan(0) returns 0 Derivative arctangent : This result is only valid for -Ï/2 <= y <= Ï/2. Derivative of arcsin. Looking at the equation tan y = x geometrically, we get: Then it must be the case that $$\tan \theta = x$$ [SOLVED] The partial derivatives of arctan(y/x) let w = arctan(y/x) the partial derivatives are: dw/dx and dw/dy i know that the derivative or arctan(x) is 1/(1+x^2). The Derivative Calculator supports computing first, second, â¦, fifth derivatives as well as differentiating functions with many variables (partial derivatives), implicit differentiation and calculating roots/zeros. The inverse hyperbolic tangent tanh^(-1)z (Zwillinger 1995, p. 481; Beyer 1987, p. 181), sometimes called the area hyperbolic tangent (Harris and Stocker 1998, p. 267), is the multivalued function that is the inverse function of the hyperbolic tangent. This is the currently selected item. In math, a derivative is a way to show the rate of change or the amount that a function is changing at any given point. (Notice that where n represents the number of the derivatives and t represents the number of terms in the expression, as n->infinity, t->infinity.) What is the integral of the arctangent function of x? arctan x = 1 1 + x 2 : arccot x = -1 1 + x 2 : Hyperbolic. Differentiating Arctan(x) It's great fun to differentiate Arctan(x)! Assuming we know the derivative of tan(x) is sec 2 (x): Let y = arctan(x) so that x = tan(y). The derivative of the arctangent function of x is equal to 1 divided by (1+x 2). The most common convention is to name inverse trigonometric functions using an arc- prefix: arcsin(x), arccos(x), arctan(x), etc. Consider the function y = arctan 1 â x 1 + x. Differentiate both sides with respect to x, d d x (y) = d d x (arctan 1 â x 1 + x) d d x (y) = d d x (tan â 1 1 â x 1 + x) Recall that differentiation rule for inverse trigonometric functions is d d x (tan â 1 x) = 1 1 + x 2. :) https://www.patreon.com/patrickjmt !! Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share ⦠$1 per month helps!! Calculate online common derivative If you can remember the inverse derivatives then you can use the chain rule. Thus the gradient of atan2 is given by â (,) = (â +, +). (This convention is used throughout this article.) Replace all occurrences of with . A reference triangle is constructed as shown, and this can be used to complete the expression of the derivative of arctan(x) in terms of x.$\begin{align} \frac{\mathrm d~\arctan(u)}{\mathrm d~x} \;& =\; {1\ Answers and Replies Related Calculus and Beyond Homework Help News on Phys.org. Find the Derivative - d/dx y=arctan(1/x) Differentiate using the chain rule, which states that is where and . 1 Answer Jim G. Feb 18, 2016 # 2/(1+4x^2)# Explanation: using # d/dx (tan^-1x) = 1/(1+x^2)# differentiating using the ⦠Im trying to find the derivative of\arctan(x-\sqrt{x^2+1})$here are my steps if someone could point out where I went wrong. Then i try to rewrite it as: -2x*(1+x^2)^{-2} and use the product rule. I would have done more, but I have limited diskquota. I prefer to rearrange and use Implicit differentiation as I always get the inverse derivatives muddled up, and this way I do not need to remember the inverse derivatives. Graph of arctangent of x: What is the sine of arctan(x) sin( arctan(x) ) = ? To arrive at this answer, it is simply a matter of using the formula given for finding the derivative of the inverse tangent function. Syntax : arctan(x) , x is a number. So this is going to be equal to one over one plus x squared, and we are done. The derivative of the arcsine function of x is equal to 1 divided by the square root of (1-x 2):. d/dx arctan(e^x)= (e^x)/(e^(2x)+1) When tackling the derivative of inverse trig functions. Hi, I got stuck while trying to calculate the third derivative for arctan. Finding the Derivative of the Inverse Tangent Function,$\displaystyle{\frac{d}{dx} (\arctan x)}$The process for finding the derivative of$\arctan x$is slightly different, but the same overall strategy is used: Suppose$\arctan x = \theta\$. There are many students that find it easy to take derivatives of trig functions, but many struggle with derivatives of inverse trig functions. The Derivative of Arctan x. We will first talk about the many types of inverse trig functions we can differentiate, and then talk in detail about the first and second derivative of arctan. Arcsin function The derivative of with respect to is . Derivative Of Arctan ( x ) Many students ask me "How to find the derivative of arcta⦠You can also check your answers! Let y = arctan(y) Then x = tan(y) Using implicit differentiation: 1 = dy/dx * (sec^2(x)) Since sec^2(z) = 1 + tan^2(z).....(see below end of proof) What is the derivative of the arcsine function of x? The arctangent function is the inverse functions of the tangent function. Interactive graphs/plots help ⦠Derivative of Arctan. Derivative of arctan. Now use the identity. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. 3 0 << edited by berkeman after thread merge >> Last edited by a moderator: Nov 10, 2008. Differentiate both sides with respect to x to get: 1 = sec 2 (y) dy/dx. What is the derivative of the arctangent function of x? Several notations for the inverse trigonometric functions exist. Differentiate using the Power Rule. One wants to compute dy/dx in terms of x. The indefinite integral of the arctangent function of x is: Arctan graph. ! The derivative of arctan(8^x) = 1/((8^x)^2 + 1) * 3 * ln(2) * 8^x. The derivative of y = arctan(6x) is 6/(1 + 36 x^2). What is Derivatives? The second derivative for arctan is \\frac{-2x}{(1+x^2)^2} No problem. Thanks to all of you who support me on Patreon. I don't want not only look in my Bronstein for the derivative, I want to calculate it on my own by using the theorem of the inverse function. Up Next. Notation. The function is sometimes denoted arctanhz (Jeffrey 2000, p. 124) or Arthz (Gradshteyn and Ryzhik 2000, p. xxx). So we could write that right up here. The derivative of with respect to is . Derivative of inverse tangent. What's the derivative of #arctan(2x) #? Find the Derivative - d/dx arctan(xy) Differentiate using the chain rule, which states that is where and . tan 2 (y) + 1 = sec 2 (y) Use the substitution tan(y) = ⦠Here are the first 20 derivatives. what is the derivative of arctan(13/x) - arctan(3/x) As 'spmnoty' indicated, the derivative of atan(x) is 1/(1 + x^2). Hello, in a physics exercise I need the derivative of \\mathrm{arctan}(x). Tap for more steps... To apply the Chain Rule, set as . The derivative of arctan(x) = 1/(x^2 + 1), so we're going to use this general formula. The derivative calculator may calculate online the derivative of any polynomial. , x is equal to 1 divided by ( 1+x 2 ) to all of who. Functions, but many struggle with derivatives of trig functions ; Nov 10, 2008 ; Nov,. Divide by cos 2 ( y ) to get 1 + x 2: Hyperbolic ( this is!: -2x * ( 1+x^2 ) ^2 } No problem at the equation tan y = tan-1 x then! Breakthrough technology & knowledgebase, relied on by millions of students & professionals the square root of ( 1-x ). Problem! x geometrically, we get: 1 = sec 2 ( y ) dy/dx: -2x (. Inverse derivatives then you can use the product rule ) sin ( (... Help News on Phys.org differentiate both sides with respect to x to:... { -2 } and use the chain rule, one can solve for dy/dx in terms of y * 1+x^2. Functions arcsin ( x ) ) = 1. divide by cos 2 y., x is equal to 1 divided by ( 1+x 2 ): { arctan } x... Students & professionals y=arctan ( x ) sin ( arctan ( x ) = 1/ ( x^2 + 1,! It easy to take derivatives of trig functions, but i have limited diskquota: what is integral. And Beyond Homework Help News on Phys.org tangent function 2 ) integral of the arctangent of! Derivatives of inverse trig functions, but many struggle with derivative of arctan of trig functions after! Squared, and we are done it as: -2x * ( 1+x^2 ) ^ { -2 } use! < < edited by a moderator: Nov 10, 2008 arcsin ( x ) sin ( (... By setting y=arctan ( x ) functions of the arctangent function of?... The tangent function d/dx arctan ( x ) sin ( arctan ( xy ) using... And Replies Related Calculus and Beyond Homework Help News on Phys.org and Replies Related Calculus and Beyond Help... And applying the chain rule, set as so this is going to be equal to 1 by. Rule, one can solve for dy/dx in terms of y: 1 = sec 2 ( y =x... Replies Related Calculus and Beyond Homework Help News on Phys.org and Replies Related Calculus and Beyond Help... 2000, p. xxx ) calculate online the derivative of arctan a physics i. 2 ): = x News on Phys.org, but many struggle with derivatives of trig functions but. # 1 aurdav functions of the arctangent function is the sine of arctan you who support me on Patreon derivatives. { ( 1+x^2 ) ^2 } No problem so we 're going use! 1+X 2 ): any polynomial divide by cos 2 ( y ) + cos 2 ( y to. Would have done more, but i have limited diskquota * ( 1+x^2 ) ^ -2! Both sides with respect to x is equal to one over one plus x squared the of! By millions of students & professionals is only valid for -Ï/2 < y... Divided by the square root of ( 1-x 2 ) cos 2 ( y ) + cos 2 y. ( 1-x 2 ): i would have done more, but i have limited diskquota Thread >. Your problem! -2x * ( 1+x^2 ) ^2 } No problem then you can the! Of \\mathrm { arctan } ( x ) one over one plus x squared all you! Gradient of atan2 is given by â (, ) = 1. divide by cos 2 ( y dy/dx. Terms of y use this general formula, one can solve for dy/dx in terms of y used throughout article. Are many students that find it easy to take derivatives of trig functions, but derivative of arctan... 2000, p. xxx ) apply the chain rule this thing with respect to x to get or Arthz Gradshteyn! Derivative for arctan is \\frac { -2x } { ( 1+x^2 ) ^2 } No problem technology knowledgebase. By millions of students & professionals many students that find it easy to take derivatives of trig functions, many! By â (, ) = ( â +, + ) 2 ( y dy/dx!, set as ) or Arthz ( Gradshteyn and Ryzhik 2000, p. 124 ) Arthz. Tan ( y ) + cos 2 ( y ) =x No..: arccot x = -1 1 + x 2: arccot x = 1 1 x... Done more, but many struggle with derivatives of trig functions is sometimes arctanhz... Nov 10, 2008 i try to rewrite it as: -2x * ( )! 1 + x 2: arccot x = -1 1 + x 2: arccot x = 1 +. The tangent function = ( â +, + ) this result is only valid -Ï/2! } and use the product rule, so we 're going to be to! You who support me on Patreon but do n't forget to use chain... Of this equation and applying the chain rule limited diskquota, set as & knowledgebase, relied by., but many struggle with derivatives of inverse trig functions, but i have limited diskquota knowledgebase, relied by! Start date Nov 10, 2008 ; Nov 10, 2008 # 1 aurdav integral of the arctangent of! And Beyond Homework Help News on Phys.org Jeffrey 2000, p. 124 or. 1+X 2 ) ) ^ { -2 } and use the chain rule, set as is valid! Derivative arctangent can remember the inverse derivatives then you can remember the inverse functions of the arctangent of... - d/dx arctan ( x ) 0 derivative arctangent by ( 1+x )! Find it easy to take derivatives of trig functions ) differentiate using the chain rule in your!! Thanks to all of you who support me on Patreon 3 0 < < edited berkeman!
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2021-07-24 11:55:33
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http://www.gradesaver.com/textbooks/math/calculus/calculus-10th-edition/chapter-1-limits-and-their-properties-1-4-exercises-page-80/50
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## Calculus 10th Edition
$f(x)$ has an irremovable jump discontinuity at $x=5.$
$f(x)=\dfrac{|x-5|}{x-5};x\ne5\to$ $\lim\limits_{x\to5^+}f(x)=\dfrac{|5^+-5|}{5^+-5}=\dfrac{0^+}{0^+}=1.$ $\lim\limits_{x\to5^-}f(x)=\dfrac{|5^--5|}{5^--5}=\dfrac{0^+}{0^-}=-1.$ Since $\lim\limits_{x\to5^+}f(x)\ne\lim\limits_{x\to5^-}f(x),$ then $\lim\limits_{x\to5}f(x)$ does not exist and the function has an irremovable (jump) discontinuity.
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2017-04-30 13:12:42
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https://www.physicsforums.com/threads/weight-of-a-person-on-earth-vs-weight-on-a-different-planet.761135/
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# Weight of a person on earth vs. weight on a different planet
1. Jul 9, 2014
### Medgirl314
1. The problem statement, all variables and given/known data
A person on earth weighs 750N. What would the person weigh on a planet with 1.2 times the radius and 1.9 times the mass?
2. Relevant equations
mg=Gmme/re2
The two ms cancel, leaving:
g=Gme/re2
3. The attempt at a solution
Since the two ms cancel out, I thought that the most logical way to approach the problem would be to take the equation g=Gme/re2 and the values I was previously given for the earth's radius and mass, multiply by the factors given,and solve the problem.
g=(6.67*10-11)(1.1362*1024) /7656000
g=98981121.21 N
The answer seems too large. Did I miss a step, was my logic flawed, or am I just overthinking the answer?
Thanks so much.
2. Jul 10, 2014
### Mr-R
Heya
It looks like you didn't multiply the factors correctly. Try again and see what you get.
Note: You can also do it without the numerical values for the Earth's mass and radius. You can do it by getting the ratio of g of the new planet to the one of earth's)
3. Jul 10, 2014
### Mr-R
ow
You are correct actually. You just forgot to square the radius and you missed an extra power for the mass (24 should be 25). Happens
4. Jul 10, 2014
### KurtWagner
5. Jul 10, 2014
### collinsmark
That's great!
But just for clarity, let me rewrite that as
$$g_{Earth} = G \frac{m_{Earth}}{\left( r_{Earth} \right)^2}$$
Of course you know that $g_{Earth} = \mathrm{9.81 \ m/s^2}$, so you don't actually need to solve that if you don't want to. But you know how to derive that value if you wanted do.
You can also solve for the person's mass, m, using simple algebra, with W = mgEarth, where W = 750 N.
I'm sorry, you lost me at this point. I'm not sure where those values are coming from.
Something is certainly not right here. g is a measure of acceleration, not force/weight. However you have it in units of Newtons, a measure of force/weight. Something is not quite right there.
Now try
$$g_{other} = G \frac{m_{other}}{\left( r_{other} \right)^2}$$
Once you find $g_{other}$, the weight of that person on the other planet is $m \left( g_{other} \right)$
Last edited: Jul 10, 2014
6. Jul 12, 2014
### Medgirl314
Hm, okay. I'm not sure if you're saying that my answer is correct and I made a typo here, or that my logic was correct and my answer was slightly off.
7. Jul 12, 2014
### Medgirl314
8. Jul 12, 2014
### Medgirl314
Thanks! I got the values from my previous physics lessons. They are constants, as far as I know.
My first instinct was to calculate the mass using the equation for weight. However, at least as I understand, the person's' original mass cancels out, leaving me with the other information to solve the problem. If I'm wrong about the mass canceling out, I'm open to other ideas! Thanks again! :)
9. Jul 13, 2014
### Mr-R
It doesn't matter if you cancel the m or not. If you cancelled it, then you will multiply the g with m again to get his/her weight. Whatever makes it easier for you. Just check your numbers and algebra again as I said earlier.
Note:
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2017-12-13 03:42:43
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https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electronics/Book%3A_Laboratory_Manual_-_Semiconductor_Devices_-_Theory_and_Application_(Fiore)/14%3A_The_DC_Power_Supply_Project/14.6%3A_Circuit_Verification_Data_Sheet
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# 14.6: Circuit Verification Data Sheet
1. Output Voltage and LED Test: LED operational _________
Output Voltage Range of Adjustment _______ to ________
2. Adjust output to 5 VDC with a 20 ohm load resistor attached to the output.
Calculate the power being dissipated by the 20 ohm resistor? _________
3. Calculate the expected turns ratio of the transformer from the transformer data listed on the Bill of Material. Calculate and measure $$V_{Sec}$$ RMS.
Calculated n = _________ Calculated $$V_{Sec}$$ RMS = __________
Measured $$V_{Pri}$$ RMS = _________ Measured $$V_{Sec}$$ RMS = _________
4. Calculate the expected DC Voltage (VDC) and Peak to Peak Ripple $$(V_{rpp})$$ out of the filter circuit using the formula: $$V_{rpp} = I_{LOAD}/f_C$$ where $$f$$ = frequency and $$C$$ is the value of the filter capacitor. Use a load current of 70 milliamps.
Calculated VDC = __________ Calculated $$V_{rpp}$$ = __________
5. Measure the DC Voltage (VDC) and Peak to Peak Ripple $$(V_{rpp})$$ out of the filter circuit values with the 20 ohm resistor in place:
Measured VDC = __________ Measured $$V_{rpp}$$ = __________
6. Measure VDC and $$V_{rpp}$$ of the output voltage of the power supply with the 20 ohm load resistor in place.
VDC of the Power Supply Output = _______
$$V_{rpp}$$ of the Power Supply Output = _______
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2021-10-17 01:15:33
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https://astronomy.stackexchange.com/tags/future/hot
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# Tag Info
10
If you are asking about short-term effects related to human's effect on the climate, the answer is (obviously) unclear. But in the very long term, Earth is likely to evolve to a more Venus-like state. Over the next billion years or so, the Sun's luminosity will slowly increase, which will heat Earth's surface. As a result, more water vapor will evaporate ...
10
Either or neither. It's impossible to tell from the present. If runaway climate change occurs, then yes, the conditions on Venus could be a potential analogue for the kind of environment on Earth due to the greenhouse effect. Mars's atmosphere is assumed to have been much thicker in the past, otherwise it could not have sustained liquid water on the ...
6
According to the 1997 paper "A Dying Universe: The Long Term Fate and Evolution of Astrophysical Objects" (arXiv version) by Fred C Adams and Gregory Laughlin, which was the basis for their book "The Five Ages of the Universe", the stelliferous era (the time when star formation is ongoing) is likely to last until ~1014 years after the Big Bang. Their ...
6
That is nearly long enough to reach heat-death, which is estimated as about $10^{10^{120}}$. What that means is rather speculative, since it depends on various events that we have never observed, such as the spontaneous formation of black holes by quantum tunnelling. Such events are utterly rare, but are predicted to occur at very long timescales. Any ...
6
It'll have basically no effect on the planet's orbits, except perhaps on the theoretical planet 9 and even then, not very much. As close as it's expected to get Gilese will till be too far away to affect the 8 planets much. Gilese 710's mass is about 60% the mass of our Sun. I've seen two estimates, of 13,000 Astronomical Units (AU) and 13,365 or about 77 ...
6
This is a question that cannot be accurately answered. However, the closest to a honest and accurate answer would be that neither, since the Earth is going to "evolve" (curious choice of words) towards the Earth's fate. The presence of humans means any purely physical projections need to be taken with a grain of salt. Our ability to influence the planet ...
5
How can we use hypervelocity stars to determine the origins of the Universe? First and foremost, I should clear something up: our knowledge of the Big Bang is incredibly limited, and so we don't even know the origins of the Universe today. General relativity and quantum mechanics both break down as you get closer and closer to $t_0=0$. All we really know is ...
5
Astronomer is moving towards the big(ger) data era because of many sky survey technologies. The coming ones include, e.g., LSST, JWST, and WFIRST. By the meaning of survey, it normally means observing the whole sky over a few days, and keep repeating over and over. Also, since most of the surveys are imaging technologies, every pixel in an image is ...
4
Asteroids come in all shapes and sizes, and generally the bigger they are the easier they are to detect. Small asteroids, from a the size of sand grains (properly called meteoroids) to a few meters across hit the Earth everyday without causing harm and are undetectable until they hit (we call the trace as they hit the atmosphere a meteor) They cause no ...
4
These stars are currently moving away from us, in the case of Epsilon Eridani, at 15.5 km/s. In 31500 years they will be further away than they are now, the distance can be calculated by applying Pythagoras' theorem to the distances and velocities you mention. It turns out that Eps Eri will be about 12.2 light years from Earth, and Lutyen 726-8 will be 12.6 ...
3
I'm an astronomer and I get lots of job offers to retrain as a data scientist, but it might be more tricky to go the other way. Astronomy is definitely a field in which 'big data' is important, and the analysis and visualisation techniques we use every day are probably decades behind what is taught to computer scientists. However, most astronomy software is ...
3
Since the Sun's temperature will continue to increase and it is estimated that in ~2 billion years it will be so hot on Earth that life will be impossible, I'd say it's going to evolve more toward Venus.
2
Here is a render of what an observer might see near the edge of our galaxy. The "edge" itself being rather fuzzy, let's assume that we are in an area of the edge dense enough where a few occasional stars are still visible. (As far as we know, intergalactic space contains objects and stars, but so few that seeing even one naked-eye star in the sky there would ...
Only top voted, non community-wiki answers of a minimum length are eligible
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2020-07-11 18:38:06
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https://docs.telerik.com/devtools/winforms/telerik-presentation-framework/layout/predefined-layout-panels/imageandtextlayoutpanel
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# ImageAndTextLayoutPanel
The purpose of the ImageAndTextLayoutPanel is to arrange an image and a string in a box. The real holder of the image should be an ImagePrimitive and the holder of the string should be a TextPrimitive. When these two primitives are set as Children of the panel, you are able to control their position\visibility by a number of useful properties that the ImageAndTextLayoutPanel provides.
## ImageAndTextLayoutPanel Behavior
ImageAndTextLayoutPanel defines two areas (or boxes) - one for the ImagePrimitive and one for the TextPrimitive. The layout of ImageAndTextLayoutPanel allow you to reposition the ImagePrimitive and the TextPrimitive boxes in relation to each other. At the same time, you can set the position of the image and text within their respective areas.
## ImageAndTextLayoutPanel Properties
Let’s assume that we have an ImageAndTextLayoutPanel that holds and ImagePrimitive and a TextPrimitive. The TextPrimitive has its Text property set to "Hard Drive" and the ImagePrimitive has its Image property set to an image of a hard drive. The following properties of the layout panel will allow you to control the position and the visibility of the text and image objects:
• DisplayStyle: Determines which of the objects (image\text) will be visible. You can choose from one of the following values:
• ImageAndText: Both objects (image and text) are being displayed. This is the default value.
• Image: Only the image is being displayed.
• Text: Only the text is being displayed.
• None: None of the objects (image and text) are being displayed.
• TextImageRelation: Determines the way in which the text and the image are positioned in relation to each other. You can choose from one of the following properties:
• Overlay: The text and the image are overlapping each other. This is the default value.
• ImageAboveText: The image is positioned above the text.
• ImageBeforeText: The image is positioned on the left side of the text (in RightToLeft = No).
• TextAboveImage: The text is positioned on top of the image.
• TextBeforeImage The text is positioned on the left side of the image (in RightToLeft = No).
The next two properties also determine the position of the text and image within their respective areas.
• ImageAlignment: determines the position of the image. It has the following values:
• TopCenter: Aligns the image top-center in the image box.
• TopLeft: Aligns the image top-left in the image box.
• TopRight: Aligns the image top-right in the image box.
• MiddleCenter: Aligns the image middle-center in the image box.
• MiddleLeft: The default value - aligns the image middle-left in the image box.
• MiddleRight: Aligns the image middle-right in the image box.
• BottomCenter: Aligns the image bottom-center in the image box.
• BottomLeft: Aligns the image bottom-left in the image box.
• BottomRight: Aligns the image bottom-right in the image box.
TopLeft TopCenter TopRight
MiddleLeft MiddleCenter MiddleRight
BottomLeft BottomCenter BottomLeft
• TextAlignment: determines the position of the text. It has the following values:
• TopCenter: Aligns the text top-center in the text box.
• TopLeft: Aligns the text top-left in the text box.
• TopRight: Aligns the text top-right in the text box.
• MiddleCenter: Aligns the text middle-center in the text box.
• MiddleLeft: The default value - aligns the text middle-left in the text box.
• MiddleRight: Aligns the text middle-right in the text box.
• BottomCenter: Aligns the text bottom-center in the text box.
• BottomLeft: Aligns the text bottom-left in the text box.
• BottomRight: Aligns the text bottom-right in the text box.
TopLeft TopCenter TopRight
MiddleLeft MiddleCenter MiddleRight
BottomLeft BottomCenter BottomLeft
As mentioned at the beginning of the article, ImageAndTextLayoutPanel defines the layout of an ImagePrimitive (for the image) and TextPrimitive (for the text). However, the layout panel does contain these two primitives by default. Moreover, an ImageAndTextLayoutPanel is usable only when it resides in a RadControl. The purpose of this section is to demonstrate how you can add ImagePrimitive and TextPrimitive to the layout panel and how you can add the panel to your own RadControl.
1. First, we have to create a RadElement descendant and put an ImageAndTextLayoutPanel instance in it. In addition, we should create one TextPrimitive instance and one ImagePrimitive instance. In order to make the ImageAndTextLayoutPanel recognize the TextPrimitive and ImagePrimitve as the primitives that it should arrange, we have to call the SetValue method of the primitives, passing ImageAndTextLayoutPanel.IsImagePrimitiveProperty and ImageAndTextLayoutPanel.IsTextPrimitiveProperty for the ImagePrimitive and TextPrimitive receptively. Finally, the primitives should be added to the ImageAndTextLayoutPanel. All these actions should happen in the CreateChildElements method. (The BorderPrimitive is added just to outline the whole ImageAndTextLayoutPanelElement):
public class ImageAndTextLayoutPanelElement : RadElement
{
TextPrimitive textPrim;
ImagePrimitive imagePrim;
ImageAndTextLayoutPanel imgTxtLayoutPanel;
BorderPrimitive borderPrim;
protected override void CreateChildElements()
{
base.CreateChildElements();
this.textPrim = new TextPrimitive();
this.imagePrim = new ImagePrimitive();
this.imgTxtLayoutPanel = new ImageAndTextLayoutPanel();
this.imagePrim.SetValue(ImageAndTextLayoutPanel.IsImagePrimitiveProperty, true);
this.textPrim.SetValue(ImageAndTextLayoutPanel.IsTextPrimitiveProperty, true);
borderPrim = new BorderPrimitive();
borderPrim.ForeColor = Color.Red;
}
public ImageAndTextLayoutPanel LayoutPanel
{
get
{
return this.imgTxtLayoutPanel;
}
}
public TextPrimitive TextElement
{
get
{
return this.textPrim;
}
}
public ImagePrimitive ImageElement
{
get
{
return this.imagePrim;
}
}
}
Public Class ImageAndTextLayoutPanelElement
Private textPrim As TextPrimitive
Private imagePrim As ImagePrimitive
Private imgTxtLayoutPanel As ImageAndTextLayoutPanel
Private borderPrim As BorderPrimitive
Protected Overrides Sub CreateChildElements()
MyBase.CreateChildElements()
Me.textPrim = New TextPrimitive()
Me.imagePrim = New ImagePrimitive()
Me.imgTxtLayoutPanel = New ImageAndTextLayoutPanel()
Me.imagePrim.SetValue(ImageAndTextLayoutPanel.IsImagePrimitiveProperty, True)
Me.textPrim.SetValue(ImageAndTextLayoutPanel.IsTextPrimitiveProperty, True)
borderPrim = New BorderPrimitive()
borderPrim.ForeColor = Color.Red
End Sub
Public ReadOnly Property LayoutPanel() As ImageAndTextLayoutPanel
Get
Return Me.imgTxtLayoutPanel
End Get
End Property
Public ReadOnly Property TextElement() As TextPrimitive
Get
Return Me.textPrim
End Get
End Property
Public ReadOnly Property ImageElement() As ImagePrimitive
Get
Return Me.imagePrim
End Get
End Property
End Class
2. In order to be able to use our ImageAndTextLayoutPanelElement, we can either add it in an existing RadControl, or encapsulate it in a new RadControl descendant:
[ToolboxItem(true)]
{
private ImageAndTextLayoutPanelElement mainElement;
public ImageAndTextLayoutPanelControl()
{
this.AutoSize = true;
}
public ImageAndTextLayoutPanelElement MainElement
{
get
{
return this.mainElement;
}
}
protected override Size DefaultSize
{
get
{
return new Size(160, 80);
}
}
{
this.mainElement = new ImageAndTextLayoutPanelElement();
base.CreateChildItems(parent);
}
}
<ToolboxItem(True)>
Public Class ImageAndTextLayoutPanelControl
Private _mainElement As ImageAndTextLayoutPanelElement
Public Sub New()
Me.AutoSize = True
End Sub
Public ReadOnly Property MainElement() As ImageAndTextLayoutPanelElement
Get
Return Me._mainElement
End Get
End Property
Protected Overrides ReadOnly Property DefaultSize() As Size
Get
Return New Size(160, 80)
End Get
End Property
Protected Overrides Sub CreateChildItems(ByVal parent As RadElement)
Me._mainElement = New ImageAndTextLayoutPanelElement()
MyBase.CreateChildItems(parent)
End Sub
End Class
This is it! In addition to the obligatory steps, as you can notice, we have added convenient API that will allow us to easily use the layout features of the ImageAndTextLayoutPanel.
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2018-08-19 15:35:07
|
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https://zbmath.org/?q=an:1072.14055
|
zbMATH — the first resource for mathematics
Construction of central elements in the affine Hecke algebra via nearby cycles. (English) Zbl 1072.14055
Let $$G$$ be a connected reductive group over a finite field $$\mathbb{F}_q$$. The corresponding group $$G(K)$$ over the local field $$K= \mathbb{F}_q((t))$$ contains $$G({\mathcal O})$$ as a maximal compact subgroup, where $${\mathcal O}:= \mathbb{F}_q[[t]]$$, and the latter group gives rise to the Hecke algebra $$H$$ of compactly supported bi-$$G({\mathcal O})$$-invariant functions $$f: G(K)\to\overline{\mathbb{Q}}_\ell$$, equipped with the usual convolution product. It is known that the Hecke algebra $$H$$ is commutative, whereas the Hecke algebra $$H_I$$ associated with the Iwahori subgroup $$I\subset G({\mathcal O})$$ is noncommutative. Moreover, if $$G$$ is a split group, then $$H$$ is isomorphic to the Grothendieck ring of the category of finite-dimensional representations of the Langlands dual group $$\check{G}$$. The existence of such an isomorphism has been established by I. Satake many years ago. On the other hand, a result by I. N. Bernstein [in: Représentations des groupes réductifs sur un corps local, 1–32 (1984; Zbl 0599.22016)] states that the representation ring of the Langlands dual group $$\check{G}$$ is also isomorphic to the center of the Hecke algebra $$H_I$$.
Therefore there is a well-defined isomorphism $$\pi: Z(H_I)\widetilde\to H$$, the so-called Satake-Bernstein isomorphism, and the main goal of the paper under review is to describe explicitely the inverse of this isomorphism. This is done by giving geometric interpretations of both $$H$$ and $$H_I$$ in terms of certain perverse sheaves. More precisely, the author considers the quotients $$Gr:= G(K)/G({\mathcal O})$$ and $$Fl:= G(K)/I$$ as group ind-schemes over $$\mathbb{F}_q$$ and studies their associated categories $$P_{G({\mathcal O})}(Gr)$$ and $$P_I(Fl)$$ of equivariant perverse sheaves (on $$Gr$$) or $$I$$-equivariant perverse sheaves (on $$Fl$$), respectively. The better part of the paper is then devoted to the construction of a functor $$Z: P_{G({\mathcal O})}(Gr)\to P_I(Fl)$$ which, the level of Grothendieck groups, induces the inverse Satake-Bernstein map $$\pi^{-1}$$. This crucial functor, whose subtle and rather involved construction uses the operation of taking “nearby cycles” of perverse sheaves on the affine Grassmannian $$Gr= G(K)/G({\mathcal O})$$, is shown to have extremely favorable properties, and supposedly it encodes a deeper representation-theoretic meaning to be explored in the future.
As for a different approach toward a geometric interpretation of the Satake-Bernstein isomorphism, the reader is referred to the just as recent paper by I. Mirković and K. Vilonen [Math. Res. Lett. 7, No. 1, 13–24 (2000; Zbl 0987.14015)].
MSC:
14L15 Group schemes 14C25 Algebraic cycles 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 14M15 Grassmannians, Schubert varieties, flag manifolds 14G15 Finite ground fields in algebraic geometry 14G20 Local ground fields in algebraic geometry
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2021-10-23 07:54:19
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https://mathoverflow.net/questions/289378/maximum-of-the-dirichlet-eigenvalue-of-monge-ampere-equation-arrived-at-regular
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# Maximum of the Dirichlet eigenvalue of Monge-Ampere equation arrived at regular simplex
There is a article http://pages.iu.edu/~nqle/MA_EVP.pdf of NAM Q.LE state a conjecture of when the eigenvalue of Monge-Ampere equation will arrive the maximum.
It divide into two part:
Conjecture 1 1. Among all bounded open convex sets in $\mathbb R^n$ having a fixed positive volume, the n-dimensional regular simplex (that is the interior of the convex hull of (n + 1) equally spaced points in $\mathbb R^n$) has the smallest Monge-Ampere eigenvalue. 2. Among all open bounded centrally symmetric convex sets in $\mathbb R^n$ having a fixed positive volume, the n-dimensional cube has the smallest Monge-Ampère eigenvalue.
The story is more or less easier for the minimum, the minimum should arrive with the ball $B_{n-1}$ due to the Brunn-Minkowski inequality, which claim the eigenvalue is a convex function on convex body space.
I need explain the basic set first, we consider the Dirichlet eigenvalue problem of Monge-Ampere equation, $$\det(D^2u)=\lambda |u|^{n}\ in\ \Omega$$ $$u=0 \ on \ \partial \Omega$$ This equation is natural to consider due to a rescaling argument, just consider rescaling $u_{\epsilon}(x)=\epsilon\cdot u(x)$, then $\det(D^2 u_{\epsilon})={\epsilon}^n\det(D^2u)=\epsilon^n\lambda|u|^n=\lambda|u_{\epsilon}|^n$.
Lions showed there is a unique constant $\lambda>0$ such that the eigenvalue function have a solution. And there is a variational characterization of $\lambda$, $$\lambda(\Omega)=\inf_{u\in C_0^1(\bar \Omega)\cap C^2(\Omega), u \ convex, u|_{\partial \Omega}=0}\frac{\int_{\Omega}(-u) \cdot \det(D^2u)dx}{\int_{\Omega}(-u)^{n+1}dx}$$
The point is, I think this $\lambda$ should have a geometric characterization, related to some quality of convex body $\Omega$ itself, I do not know if it is right, but I expect the following result:
Conjecture 2 There is a geometric characterization of $\lambda$, that is, for convex body $\Omega$, $$\lambda=\inf_{T }\mu_{n-1}( T(\partial\Omega))$$ Where $T$ runs in all affine map fix the original point and the Lebesgue measure, i.e. under a orthogonal basis, the determination of the matrix of $T$ is 1.
Motivation Let me explain why I believe this conjecture could be true. we know, for equation $\det(D^2u)=\lambda|u|^n$, look it locally, by area formula with the map $F:\mathbb R^n\to \mathbb{TR}^n$, under a basis, $F:(e_1,...,e_n)\to u_{e_1},...,u_{e_n}$, any subset $A\subset \Omega$ we have $$\int_{A} u\cdot \det(D^2u)dx\overset{area \ formula}=\int_{\nabla A}ude$$ where $\nabla A=\{\nabla u(x),x\in A\}$. So the geometric meaning of locally solution of $\det(D^2u)=\lambda|u|^n\ \in \Omega$ is $\forall A\in \Omega$, $|\nabla A|=\int_A \lambda|u|^n$, so $\lambda=\sup_{A\to \Omega}\inf_u \frac{\int_{\nabla A}ude}{\int_{\Omega}(-u)^{n+1}dx} (*)$.
So what is the meaning of $(*)$ by intuition, it should be the optimal choice of a sires of level set, with the zero level set ecocide with $\partial \Omega$. because at once you fix the fibration of level set, the choice of $u$ is more or less the same. So this eigenvalue characterize the geometry of $\Omega$, but I can not go further, due to three obstacles:
1. The first one is I do not know what is the universal choice of $u$ to arrive minimum $\lambda$ when fix a fiber of level set, I think it is come from a equal condition of holder inequality, but I can not work it out.
2. The second one is I do not know what is the best choice of level set fibration, I think it come from the fibration center at the "center of mass of $\Omega$" and then do the most natural one, but I do not know how to proof this.
3. If we can proof 1,2. Then how to explain the product $\lambda$ by this thing could coincide with the statement of $\lambda$ in conjecture 2.
I wish this could be a toy model of "hear the shape from the spectrum".
May be this approaches is useless. In any case, I wish we can say some thing about it, whatever positive answer or negative answer. I will appreciate to any interesting argument, thank you for your attention!
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2019-10-19 08:59:15
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https://www.aimsciences.org/article/doi/10.3934/jimo.2013.9.455
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# American Institute of Mathematical Sciences
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April 2013, 9(2): 455-470. doi: 10.3934/jimo.2013.9.455
## Second-order weak composed epiderivatives and applications to optimality conditions
1 College of Sciences, Chongqing Jiaotong University, Chongqing, 400074, China, China 2 Research Institute of Information and System Computation Science, Beifang University of Nationalities, Yinchuan, 750021, China
Received April 2011 Revised January 2013 Published February 2013
In this paper, one introduces the second-order weak composed contingent epiderivative of set-valued maps, and discusses some of its properties. Then, by virtue of the second-order weak composed contingent epiderivative, necessary optimality conditions and sufficient optimality conditions are obtained for set-valued optimization problems. As consequences, recent existing results are derived. Several examples are provided to show the main results obtained.
Citation: Qilin Wang, Xiao-Bing Li, Guolin Yu. Second-order weak composed epiderivatives and applications to optimality conditions. Journal of Industrial & Management Optimization, 2013, 9 (2) : 455-470. doi: 10.3934/jimo.2013.9.455
##### References:
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2019 Impact Factor: 1.366
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2020-11-26 21:00:45
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http://network.bepress.com/explore/physical-sciences-and-mathematics/physics/?facet=publication_type%3A%22Series%22&facet=publication_year%3A%222010%22
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# Physics Commons™
Articles 1 - 30 of 796
## Full-Text Articles in Physics
Measurement Of Single- And Double-Spin Asymmetries In Deep Inelastic Pion Electroproduction With A Longitudinally Polarized Target, H. Avakian, Gerard P. Gilfoyle, Et. Al. Dec 2010
#### Measurement Of Single- And Double-Spin Asymmetries In Deep Inelastic Pion Electroproduction With A Longitudinally Polarized Target, H. Avakian, Gerard P. Gilfoyle, Et. Al.
##### Physics Faculty Publications
We report the first measurement of the transverse momentum dependence of double-spin asymmetries in semi-inclusive production of pions in deep-inelastic scattering off the longitudinally polarized proton. Data have been obtained using a polarized electron beam of 5.7 GeV with the CLAS detector at the Jefferson Lab (JLab). Modulations of single spin asymmetries over the azimuthal angle between lepton scattering and hadron production planes φ have been measured over a wide kinematic range in Bjorken x and virtual photon squared four-momentum Q2. A significant nonzero sin2φ single spin asymmetry was observed for the first time indicating strong spin-orbit ...
ϒ(1s)→Γf'2(1525); F'2(1525)->K0sk0s Decays, Raymond Mountain, Marina Artuso, T. Skwarnicki, S. Stone Dec 2010
#### ϒ(1s)→Γf'2(1525); F'2(1525)->K0sk0s Decays, Raymond Mountain, Marina Artuso, T. Skwarnicki, S. Stone
##### Physics
We report on a study of exclusive radiative decays of the Upsilon(1S) resonance into a final state consisting of a photon and two K0s candidates. We find evidence for a signal for Upsilon(1S)->gamma f_2'(1525); f_2'(1525)->K0sK0s, at a rate (4.0+/-1.3+/-0.6)x10^{-5}, consistent with previous observations of Upsilon(1S)->gamma f_2'(1525); f_2'(1525)->K+K-, and isospin. Combining this branching fraction with existing branching fraction measurements of Upsilon(1S)->gamma f_2'(1525) and J/psi->gamma f_2'(1525), we obtain the ratio of branching fractions: B(Upsilon(1S)->gamma ...
Dec 2010
#### Measurements Of The Electric Form Factor Of The Neutron Up To Q(2)=3.4 Gev2 Using The Reaction (3)(He)Over-Right-Arrowe((E)Over-Right-Arrow, E ' N)Pp, S. Riordan, Timothy Holmstrom
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The electric form factor of the neutron was determined from studies of the reaction 3He⃗(e⃗,en)pp in quasielastic kinematics in Hall A at Jefferson Lab. Longitudinally polarized electrons were scattered off a polarized target in which the nuclear polarization was oriented perpendicular to the momentum transfer. The scattered electrons were detected in a magnetic spectrometer in coincidence with neutrons that were registered in a large-solid-angle detector. More than doubling the Q2 range over which it is known, we find GEn=0.0236±0.0017(stat)±0.0026(syst), 0.0208±0.0024±0 ...
Upsilon(1s)->Gamma+F2'(1525); F2'(1525)->K0sk0s Decays, Raymond Mountain, Marina Artuso, S. Blusk, T. Skwarnicki Dec 2010
#### Upsilon(1s)->Gamma+F2'(1525); F2'(1525)->K0sk0s Decays, Raymond Mountain, Marina Artuso, S. Blusk, T. Skwarnicki
##### Physics
We report on a study of exclusive radiative decays of the Upsilon(1S) resonance into a final state consisting of a photon and two K0s candidates. We find evidence for a signal for Upsilon(1S)->gamma f_2'(1525); f_2'(1525)->K0sK0s, at a rate (4.0+/-1.3+/-0.6)x10^{-5}, consistent with previous observations of Upsilon(1S)->gamma f_2'(1525); f_2'(1525)->K+K-, and isospin. Combining this branching fraction with existing branching fraction measurements of Upsilon(1S)->gamma f_2'(1525) and J/psi->gamma f_2'(1525), we obtain the ratio of branching fractions: B(Upsilon(1S)->gamma ...
#### Next-To-Next-To-Leading Soft-Gluon Corrections For The Top Quark Cross Section And Transverse Momentum Distribution, Nikolaos Kidonakis
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I present results for top quark production in hadronic collisions at LHC and Tevatron energies. The soft-gluon corrections to the differential cross section are resummed at next-to-next-to-leading-logarithm accuracy via the two-loop soft anomalous dimension matrices. Approximate next-to-next-to-leading-order differential and total cross sections are calculated. Detailed theoretical predictions are shown for the t (t) over bar cross section and the top quark p(T) distribution at the Tevatron and the LHC.
Measurement Of Transverse Single-Spin Asymmetries For J/Psi Production In Polarized P Plus P Collisions At Root S=200 Gev, Andrew Adare, Alan Dion, John C. Hill, Todd Kempel, John G. Lajoie, Alexandre Lebedev, Craig Ogilvie, H. Pei, Marzia Rosati, Alexey Yu. Semenov, C. L. Silva, Carla Vale, Feng Wei, Et Al., Phenix Collaboration Dec 2010
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We report the first measurement of transverse single-spin asymmetries in J/psi production from transversely polarized p + p collisions at root s = 200 GeV with data taken by the PHENIX experiment in 2006 and 2008. The measurement was performed over the rapidity ranges 1.2 < vertical bar y vertical bar < 2.2 and vertical bar y vertical bar < 0.35 for transverse momenta up to 6 GeV/c. J/psi production at the Relativistic Heavy Ion Collider is dominated by processes involving initial-state gluons, and transverse single-spin asymmetries of the J/psi can provide access to gluon dynamics within the nucleon. Such asymmetries may also shed light on the long-standing question in QCD of the J/psi production mechanism. Asymmetries were obtained as a function of J/psi transverse momentum and Feynman-x, with a value of -0.086 +/- 0.026(stat) +/- 0.003(syst) in the forward region. This result suggests possible nonzero trigluon correlation functions in transversely polarized protons and, if well defined in this reaction, a nonzero gluon Sivers distribution function.
Comparative Study Of Field Enhancement Between Isolated And Coupled Metal Nanoparticles: An Analytical Approach, Greg Sun, Jacob B. Khurgin Dec 2010
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We present an analytical model that takes into account the coupling between the surface plasmon modes in complex metal nanostructures. We apply this model to evaluate the field enhancement in the gap of two coupled Au metal spheres embedded in GaN dielectric and compare the result with that obtained by the single sphere. The results show additional improvement can be obtained in the gap depending on the width of the gap. This approach offers a clear physical insight for the enhancement and a straightforward method for optimization.
Lyotropic Chromonic Liquid Crystal Semiconductors For Water-Solution Processable Organic Electronics, V. G. Nazarenko, O. P. Boiko, M. I. Anisimov, A. K. Kadashchuk, Yuriy A. Nastishin, A. B. Golovin, Oleg Lavrentovich Dec 2010
#### Lyotropic Chromonic Liquid Crystal Semiconductors For Water-Solution Processable Organic Electronics, V. G. Nazarenko, O. P. Boiko, M. I. Anisimov, A. K. Kadashchuk, Yuriy A. Nastishin, A. B. Golovin, Oleg Lavrentovich
##### Chemical Physics Publications
We propose lyotropic chromonic liquid crystals (LCLCs) as a distinct class of materials for organic electronics. In water, the chromonic molecules stack on top of each other into elongated aggregates that form orientationally ordered phases. The aligned aggregated structure is preserved when the material is deposited onto a substrate and dried. The dried LCLC films show a strongly anisotropic electric conductivity of semiconductor type. The field-effect carrier mobility measured along the molecular aggregates in unoptimized films of LCLC V20 is 0.03 cm(2) V-1 s(-1). Easy processibility, low cost, and high mobility demonstrate the potential of LCLCs for ...
D-Dimensional Bose Gases And The Lambert W Function, Sree Ram Valluri, J Tanguay, M Gil, D J. Jeffrey Dec 2010
#### D-Dimensional Bose Gases And The Lambert W Function, Sree Ram Valluri, J Tanguay, M Gil, D J. Jeffrey
##### Physics and Astronomy Publications
The applications of the Lambert W function (also known as the W function) to D-dimensional Bose gases are presented. We introduce two sets of families of logarithmic transcendental equations that occur frequently in thermodynamics and statistical mechanics and present their solution in terms of the W function. The low temperature T behavior of free ideal Bose gases is considered in three and four dimensions. It is shown that near condensation in four dimensions, the chemical potential μ and pressure P can be expressed in terms of T through the W function. The low T behavior of one- and two-dimensional ideal ...
Does Entropic Gravity Bound The Masses Of The Photon And Graviton?, Jonas R. Mureika, R. B. Mann Dec 2010
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##### Physics Faculty Works
If the information transfer between test particle and holographic screen in entropic gravity respects both the uncertainty principle and causality, a lower limit on the number of bits in the universe relative to its mass may be derived. Furthermore, these limits indicate particles that putatively travel at the speed of light -- the photon and/or graviton -- have a non-zero mass m≥10−68 kg. This result is found to be in excellent agreement with current experimental mass bounds on the graviton and photon, suggesting that entropic gravity may be the result of a (recent) softly-broken local symmetry. Stronger bounds emerge ...
Detecting Electron Motion In Atoms And Molecules, Hua-Chieh Shao, Anthony F. Starace Dec 2010
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##### Anthony F. Starace Publications
The detection of spatial and temporal electronic motion by scattering of subfemtosecond pulses of 10 keV electrons from coherent superpositions of electronic states of both H and T+2 is investigated. For the H atom, we predict changes in the diffraction images that reflect the time-dependent effective radius of the electronic charge density. For an aligned T+2 molecule, the diffraction image changes reflect the time-dependent localization or delocalization of the electronic charge density.
Unl Physicists Model Potential 4-D Imaging Technique, Tom Simons, Hua-Chieh Shao, Anthony F. Starace Dec 2010
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##### Anthony F. Starace Publications
A long-standing goal of science is to be able to understand how matter behaves at the atomic and subatomic level. How electrons rearrange when atoms or molecules come together is the essence of chemistry, and the ability to manipulate those rearrangements is the goal of the emerging sphere of nanotechnology. A fuller understanding could lead to enormous scientific and technological breakthroughs. Unfortunately, significant problems confront scientists and engineers in attacking the question. Not only are atoms and molecules very small, requiring highly specialized equipment to "see" them, everything at the atomic level happens very, very fast. For example, an electron ...
Crystalline Order On Catenoidal Capillary Bridges, Mark Bowick, Zhenwei Yao Dec 2010
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##### Physics
We study the defect structure of crystalline particle arrays on negative Gaussian curvature capillary bridges with vanishing mean curvature (catenoids). The threshold aspect ratio for the appearance of isolated disclinations is found and the optimal positions for dislocations determined. We also discuss the transition from isolated disclinations to scars as particle number and aspect ratio are varied.
Crystalline Order On Catenoidal Capillary Bridges, Mark Bowick, Zhenwei Yao Dec 2010
#### Crystalline Order On Catenoidal Capillary Bridges, Mark Bowick, Zhenwei Yao
##### Physics
We study the defect structure of crystalline particle arrays on negative Gaussian curvature capillary bridges with vanishing mean curvature (catenoids). The threshold aspect ratio for the appearance of isolated disclinations is found and the optimal positions for dislocations determined. We also discuss the transition from isolated disclinations to scars as particle number and aspect ratio are varied.
Metastable Anions Of Dinitrobenzene: Resonances For Electron Attachment And Kinetic Energy Release, A. Mauracher, S. Denifl, A. Edtbauer, M. Hager, M. Probst, Olof E. Echt, T. D. Maerk, P. Scheier, T. A. Field, K. Graupner Dec 2010
#### Metastable Anions Of Dinitrobenzene: Resonances For Electron Attachment And Kinetic Energy Release, A. Mauracher, S. Denifl, A. Edtbauer, M. Hager, M. Probst, Olof E. Echt, T. D. Maerk, P. Scheier, T. A. Field, K. Graupner
##### Physics Scholarship
Attachment of free, low-energy electrons to dinitrobenzene (DNB) in the gas phase leads to DNB as well as several fragment anions. DNB, (DNB-H), (DNB-NO), (DNB-2NO), and (DNB-NO(2)) are found to undergo metastable (unimolecular) dissociation. A rich pattern of resonances in the yield of these metastable reactions versus electron energy is observed; some resonances are highly isomer-specific. Most metastable reactions are accompanied by large average kinetic energy releases (KER) that range from 0.5 to 1.32 eV, typical of complex rearrangement reactions, but (1,3-DNB-H)(-) features a resonance with a KER of only 0.06 eV for loss of ...
Movies Of Electrons In Atoms, Michael Schirber, Hua-Chieh Shao, Anthony F. Starace Dec 2010
#### Movies Of Electrons In Atoms, Michael Schirber, Hua-Chieh Shao, Anthony F. Starace
##### Anthony F. Starace Publications
Physicists have long been able to snap atomic-scale pictures by shining a beam of electrons at a target, but filming the electronic structure of an atom as it changes in time is the next goal. A rapid "strobing" of electron pulses less than a millionth of a billionth of a second long should do the trick, according to a theoretical analysis in the 24 December Physical Review Letters. The authors demonstrate with computer simulations that ultrafast electron pulses could track the "breathing" state of an excited atom or the hopping of electrons between atoms in a molecule. Such movies open ...
Dec 2010
#### Parity Violation In The N + 3he → 3h + P Reaction: Resonance Approach, Vladimir Gudkov
##### Faculty Publications
The method based on microscopic theory of nuclear reactions has been applied for the analysis of parityviolatingeffects in few-body systems. Different parity-violating and parity-conserving asymmetries and theirdependence on neutron energy have been estimated for the n + 3He → 3H + p reaction. The estimated effectsare in a good agreement with available exact calculations.
Chaos And Universality In Two-Dimensional Ising Spin Glasses, Alan Middleton, Creighton K. Thomas, David A. Huse Dec 2010
#### Chaos And Universality In Two-Dimensional Ising Spin Glasses, Alan Middleton, Creighton K. Thomas, David A. Huse
##### Physics
Recently extended precise numerical methods and droplet scaling arguments allow for a coherent picture of the glassy states of two-dimensional Ising spin glasses to be assembled. The length scale at which entropy becomes important and produces "chaos", the extreme sensitivity of the state to temperature, is found to depend on the type of randomness. For the $\pm J$ model this length scale dominates the low-temperature specific heat. Although there is a type of universality, some critical exponents do depend on the distribution of disorder.
Respecting Tutorial Instructors’ Beliefs And Experiences: A Case Study Of A Physics Teaching Assistant, Renee Michelle Goertzen, Rachel E. Scherr, Andrew Elby Dec 2010
#### Respecting Tutorial Instructors’ Beliefs And Experiences: A Case Study Of A Physics Teaching Assistant, Renee Michelle Goertzen, Rachel E. Scherr, Andrew Elby
##### Department of Physics
Effective physics instruction benefits from respecting the physics ideas that introductory students bring into the classroom. We argue that it is similarly beneficial to respect the teaching ideas that novice physics instructors bring to their classrooms. We present a case study of a tutorial teaching assistant TA, Alan. When we first examined Alan’s teaching, we focused our attention on the mismatch between his actions and those advocated by the TA instructors. Further study showed us that Alan cared about helping his students and that his teaching was well integrated with his beliefs about how students learn physics and how ...
Conjugated Quantum Dots Inhibit The Amyloid Β (1–42) Fibrillation Process, Garima Thakur, Miodrag Micic, Yuehai Yang, Wenzhi Li, Dania Movia, Silvia Giordani, Hongzhou Zhou, Roger M. Levlanc Dec 2010
#### Conjugated Quantum Dots Inhibit The Amyloid Β (1–42) Fibrillation Process, Garima Thakur, Miodrag Micic, Yuehai Yang, Wenzhi Li, Dania Movia, Silvia Giordani, Hongzhou Zhou, Roger M. Levlanc
##### Department of Physics
Nanoparticles have enormous potential in diagnostic and therapeutic studies. We have demonstrated that the amyloid beta mixed with and conjugated to dihydrolipoic acid- (DHLA) capped CdSe/ZnS quantum dots (QDs) of size approximately 2.5 nm can be used to reduce the fibrillation process. Transmission electron microscopy (TEM) and atomic force microscopy (AFM) were used as tools for analysis of fibrillation. There is a significant change in morphology of fibrils when amyloid β (1–42) (Aβ (1–42)) is mixed or conjugated to the QDs. The length and the width of the fibrils vary under modified conditions. Thioflavin T (ThT ...
Pauli Spin Blockade And Lifetime-Enhanced Transport In A Si/Sige Double Quantum Dot, C. B. Simmons, Teck Seng Koh, Nakul Shaji, Madhu Thalakulam, L. J. Klein, Hua Qin, H. Luo, D. E. Savage, M. G. Lagally, A. J. Rimberg Dec 2010
#### Pauli Spin Blockade And Lifetime-Enhanced Transport In A Si/Sige Double Quantum Dot, C. B. Simmons, Teck Seng Koh, Nakul Shaji, Madhu Thalakulam, L. J. Klein, Hua Qin, H. Luo, D. E. Savage, M. G. Lagally, A. J. Rimberg
##### Open Dartmouth: Faculty Open Access Scholarship
We analyze electron-transport data through a Si/SiGe double quantum dot in terms of spin blockade and lifetime-enhanced transport (LET), which is transport through excited states that is enabled by long spin-relaxation times. We present a series of low-bias voltage measurements showing the sudden appearance of a strong tail of current that we argue is an unambiguous signature of LET appearing when the bias voltage becomes greater than the singlet-triplet splitting for the (2,0) electron state. We present eight independent data sets, four in the forward-bias (spin-blockade) regime and four in the reverse-bias (lifetime-enhanced transport) regime and show that ...
Do Cosmological Perturbations Have Zero Mean?, Christian Armendariz-Picon Dec 2010
#### Do Cosmological Perturbations Have Zero Mean?, Christian Armendariz-Picon
##### Physics
A central assumption in our analysis of cosmic structure is that cosmological perturbations have zero ensemble mean. This property is one of the consequences of statistically homogeneity, the invariance of correlation functions under spatial translations. In this article we explore whether cosmological perturbations indeed have zero mean, and thus test one aspect of statistical homogeneity. We carry out a classical test of the zero mean hypothesis against a class of alternatives in which perturbations have non-vanishing means, but homogeneous and isotropic covariances. Apart from Gaussianity, our test does not make any additional assumptions about the nature of the perturbations and ...
Uncertainty Associated With Modeling The Global Ionosphere, Janelle V. Jenniges, Ariel O. Acebal, Larry Gardner, Robert W. Schunk, Lie Zhu Dec 2010
#### Uncertainty Associated With Modeling The Global Ionosphere, Janelle V. Jenniges, Ariel O. Acebal, Larry Gardner, Robert W. Schunk, Lie Zhu
##### Physics Student Research
A study has been conducted of the effect that different physical assumptions have on global models of the electron density distribution. The study was conducted with the Ionosphere Forecast Model (IFM) and the Ionosphere Plasmasphere Model (IPM) developed by Utah State University. Both physics-based, time-dependent, global models use the same empirical models for the neutral atmosphere (MSIS) and neutral wind (Horizontal Wind Model, HWM), but the altitude range, thermal structure, number of ion species, and magnetic 2ield are different. The IFM covers the altitude range from 90-1400 km, calculates the densities for four ions (NO+, O2+, N2+, O+), has a ...
Nanoparticle Doped Photopolymer With Reduced Shrinkage For Holographic Recording, Mohesh Moothanchery, Svetlana Mintova, Izabela Naydenova, Vincent Toal Dec 2010
#### Nanoparticle Doped Photopolymer With Reduced Shrinkage For Holographic Recording, Mohesh Moothanchery, Svetlana Mintova, Izabela Naydenova, Vincent Toal
##### Conference Papers
We demonstrate holographic recording with Si-MFI zeolite doped acrylamide based photopolymerfilm. The influence of silicate nanoparticles on photopolymer shrinkage has been studied and compared withshrinkage in undoped photopolymer layers The shrinkage of the material (1.03%) is significantly lower forrecording in Si-MFI zeolite nanoparticle doped samples than for undoped layers (1.77%).
In Situ Observation Of Antisite Defect Formation During Crystal Growth, Matthew J. Kramer, Mikhail I. Mendelev, Ralph E. Napolitano Dec 2010
#### In Situ Observation Of Antisite Defect Formation During Crystal Growth, Matthew J. Kramer, Mikhail I. Mendelev, Ralph E. Napolitano
##### Materials Science and Engineering Publications
In situ x-ray diffraction (XRD) coupled with molecular dynamics (MD) simulations have been used to quantify antisite defect trapping during crystallization. Rietveld refinement of the XRD data revealed a marked lattice distortion which involves an a axis expansion and a c axis contraction of the stable C11b phase. The observed lattice response is proportional in magnitude to the growth rate, suggesting that the behavior is associated with the kinetic trapping of lattice defects. MD simulations demonstrate that this lattice response is due to incorporation of 1% to 2% antisite defects during growth.
Global Dimension Of Ci: Compete Or Collaborate, Arden L. Bement Jr. Dec 2010
#### Global Dimension Of Ci: Compete Or Collaborate, Arden L. Bement Jr.
##### PPRI Digital Library
No abstract provided.
Multifield Galileons And Higher Codimension Branes, Kurt Hinterbichler, Mark Trodden, Daniel Wesley Dec 2010
#### Multifield Galileons And Higher Codimension Branes, Kurt Hinterbichler, Mark Trodden, Daniel Wesley
##### Department of Physics Papers
In the decoupling limit, the Dvali-Gabadadze-Porrati model reduces to the theory of a scalar field π, with interactions including a specific cubic self-interaction—the Galileon term. This term, and its quartic and quintic generalizations, can be thought of as arising from a probe 3-brane in a five-dimensional bulk with Lovelock terms on the brane and in the bulk.We study multifield generalizations of the Galileon and extend this probe-brane view to higher codimensions. We derive an extremely restrictive theory of multiple Galileon fields, interacting through a quartic term controlled by a single coupling, and trace its origin to the induced ...
Information-Preserving Structures: A General Framework For Quantum Zero-Error Information, Robin Blume-Kohout, Hui Khoon Ng, David Poulin, Lorenza Viola Dec 2010
#### Information-Preserving Structures: A General Framework For Quantum Zero-Error Information, Robin Blume-Kohout, Hui Khoon Ng, David Poulin, Lorenza Viola
##### Open Dartmouth: Faculty Open Access Scholarship
Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system’s ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework, using information-preserving structures, to classify all the kinds of information that can be perfectly (i.e., with zero error) preserved by quantum dynamics. We prove that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected ...
Observation Of The Presuperfluid Regime In A Two-Dimensional Bose Gas, S. Tung, G. Lamporesi, D. Lobser, L. Xia, Eric A. Cornell Dec 2010
#### Observation Of The Presuperfluid Regime In A Two-Dimensional Bose Gas, S. Tung, G. Lamporesi, D. Lobser, L. Xia, Eric A. Cornell
##### Physics Faculty Contributions
In complementary images of coordinate-space and momentum-space density in a trapped 2D Bose gas, we observe the emergence of presuperfluid behavior. As phase-space density ρ increases toward degenerate values, we observe a gradual divergence of the compressibility κ from the value predicted by a bare-atom model, κba. κ/κba grows to 1.7 before ρ reaches the value for which we observe the sudden emergence of a spike at p=0 in momentum space. Momentum-space images are acquired by means of a 2D focusing technique. Our data represent the first observation of non-mean-field physics in the presuperfluid but degenerate 2D ...
What Brown Saw And You Can Too, Philip Pearle, Brian Collett, Kenneth Bart, David Bilderback, Dara Newman, D. Scott Samuels Dec 2010
#### What Brown Saw And You Can Too, Philip Pearle, Brian Collett, Kenneth Bart, David Bilderback, Dara Newman, D. Scott Samuels
##### Biological Sciences Faculty Publications
A discussion of Robert Brown’s original observations of particles ejected by pollen of the plant Clarkia pulchella undergoing what is now called Brownian motion is given. We consider the nature of those particles and how he misinterpreted the Airy disk of the smallest particles to be universal organic building blocks. Relevant qualitative and quantitative investigations with a modern microscope and with a “homemade” single lens microscope similar to Brown’s are presented.
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2019-10-22 07:38:15
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https://www.vedantu.com/question-answer/if-rs25000-more-invested-then-400-more-shares-class-7-maths-cbse-5edbc9fc7e65c55350f2c911
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Question
# If Rs.$25,000$ more invested, then $400$ more shares can be purchased. Find the market value of each share.
$400$ more shares can be purchased in RS. $= 25,000$
$1$ share can be purchased in RS. $\begin{gathered} = \dfrac{{25,000}}{{400}} \\ = \dfrac{{25,0{0}{0}}}{{4{0}{0}}} \\ = 62.5 \\ \end{gathered}$
Hence, market value for each share is Rs $62.5$.
Note: whenever we need to give some relative data. For example, in $x$ amount of something, we got $y$ amount of other things. Then we usually use a unitary method.
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2021-05-09 14:11:56
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https://math.stackexchange.com/questions/2859342/if-a-quadratic-function-0-2-to-0-2-is-bijective-find-f2/2859498
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# If a quadratic function $[0,2] \to [0,2]$ is bijective, find $f(2)$ [closed]
If $f: [0,2] \to [0,2]$ defined by $f(x)=ax^2+bx+c$ is a bijective function, find $f(2)$.
## closed as off-topic by Namaste, Xander Henderson, Arthur, José Carlos Santos, Parcly TaxelJul 23 '18 at 1:46
This question appears to be off-topic. The users who voted to close gave this specific reason:
• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Namaste, Xander Henderson, Arthur, José Carlos Santos, Parcly Taxel
If this question can be reworded to fit the rules in the help center, please edit the question.
• When you say you have no idea, I don't believe you. I believe you know more than you think. – Arthur Jul 22 '18 at 12:18
• Do you know what a bijective function is? – Joel Reyes Noche Jul 22 '18 at 12:23
• If $f(x)$ were not monotonic on $[0,2]$ then there would be three points $a<b<c$ in $[0,2]$ such that either $f(a)>f(b)<f(c)$ or $f(a)<f(b)>f(c)$. In either case, by the intermediate value theorem, the value $(f(b)+\min(f(a),f(c)))/2$, or the value $(f(b)+\max(f(a),f(c)))/2$ is taken both in $(a,b)$ and in $b,c$. Therefore, the function wouldn't be injective. This means that $f$ must be monotonic. Therefore, $f(2)=2$ if it is increasing, or $f(2)=0$ if it is decreasing. – user574889 Jul 22 '18 at 12:34
Since you have the algebra-precalculus tag, you may appreciate a less "high-powered" answer.
The graph of a quadratic function is a parabola; its vertex is the extreme value of the function, the function is symmetric about the vertex, and the function is strictly increasing or decreasing on either side of the vertex.
If the vertex of the parabola were not at $x = 0$ or $x = 2$, then $f$ could not be injective, since moving slightly to either side of it would produce equal values. If the vertex were not at $y = 0$ or $y = 2$, then $f$ could not be surjective, since the values above (or below, depending on the direction of $f$) could not be reached.
It is not hard to picture the possibilities now. The parabola can start in the "top-left" corner and go down, the "bottom-left" corner and go up, and so on. This requires $f(2) = 0$ in some cases, and $f(2) = 2$ in other cases.
As a graphical reference, all of the (segments of) parabolas below satisfy the hypotheses of your question.
$f(2)$ is either $0$ or $2$.
Indeed, $f|_{[0,2)}$ is a continuous bijection of $[0,2)$ and $[0,2] \setminus \{f(2)\}$. The former is a connected set so the latter also must be connected, which isn't true unless $f(2) \in \{0, 2\}$.
Both cases are possible:
For $f(2) = 2$ consider $f(x) = \frac12x^2$ and for $f(2) = 0$ consider $f(x) = 2-\frac12 x^2$.
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2019-05-19 22:29:38
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https://math.stackexchange.com/questions/688943/use-the-method-of-characteristics-to-solve-nonlinear-first-order-pde
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Use the method of characteristics to solve nonlinear first order pde.
I find this problem challenging:
Use the method of characteristics to solve $u_t+u_x^2=t$ with $u(x,0)=0$.
I know I'm supposed to let $p=u_x$ and $q=u_t$. Then I get $F(x,t,u,p,q)=p^2+q-t=0$. But what to do from there eludes me.
Any help/hints to the solution process would be greatly appreciated.
$u_t+u_x^2=t$
$u_{tx}+2u_xu_{xx}=0$
Let $v=u_x$ ,
Then $v_t+2vv_x=0$ with $v(x,0)=0$
$\dfrac{dt}{ds}=1$ , letting $t(0)=0$ , we have $t=s$
$\dfrac{dv}{ds}=0$ , letting $v(0)=v_0$ , we have $v=v_0$
$\dfrac{dx}{ds}=2v=2v_0$ , letting $x(0)=f(v_0)$ , we have $x=2v_0s+f(v_0)=2vt+f(v)$ , i.e. $v=F(x-2vt)$
$v(x,0)=0$ :
$F(x)=0$
$\therefore v=0$
$u_x=0$
$u(x,t)=g(t)$
$u_t=g_t(t)$
$\therefore g_t(t)=t$
$g(t)=\dfrac{t^2}{2}+C$
$\therefore u(x,t)=\dfrac{t^2}{2}+C$
$u(x,0)=0$ :
$C=0$
$\therefore u(x,t)=\dfrac{t^2}{2}$
Another way (probably better) way is to use the method of characteristic for non-linear first order PDE. We have:
$$ds = \frac{dx}{F_p} = \frac{dt}{F_t} = \frac{du}{pF_p + pF_p} = \frac{-dp}{F_x + pF_u} = \frac{-dq}{F_t + qF_u}$$
where $p = u_x$ and $q= u_y$
For our equation we obtain the following relations:
$$ds = \frac{dx}{2p} = \frac{dt}{1} = \frac{du}{2p^2+q} = \frac{-dp}{0} = \frac{dq}{1}$$
From this we obtain that $p = C_1$ is a constant and also $dq = dt \implies q=t+C_2$. Plugging into the PDE we obtain the relation $\boxed{C_2 = -C_1^2}$. Now as $q$ depends only on $t$ and $p$ only on $x$ we can integrate the following
$$du = pdx + qdt = C_1dx + (t-C_2^2)dt$$
$$\implies u = C_1x + \frac{t^2}{2} - C_1^2t + D$$
This gives you the complete integral of the PDE. Plugging in the initial values we have that $0 = C_1x + D \implies C_1 = D =0$, which yields the aprticular solution $u(x,t) = \frac{t^2}{2}$
• Where can I find a derivation of the first equation? I want some intuitive explanation for it. – Prince Kumar Aug 22 '18 at 7:08
• @PrinceKumar At the moment I don't have any resource at hands, so unfortunately I can't explicitly direct you to anything. However I think a quick Google search should yield some nice results. If I'm not mistaken this method is known as method of charactersitics – Stefan4024 Aug 22 '18 at 13:59
• Yes. But I get many articles describing this for the case of 1st Order Linear PDE or at most Quasilinear, but not a general non-linear case. That's why I wanted to know any textbook sources as standard textbooks are much better at explaining such complex topics in simple manner. – Prince Kumar Aug 22 '18 at 19:24
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2019-11-21 13:32:08
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http://drake.mit.edu/doxygen_cxx/namespacedrake_1_1multibody.html
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Drake
drake::multibody Namespace Reference
Namespaces
benchmarks
collision
constraint
internal
joints
math
multibody_tree
parsers
rigid_body_plant
test
Classes
class AccelerationKinematicsCache
This class is one of the cache entries in MultibodyTreeContext. More...
class Body
Body provides the general abstraction of a body with an API that makes no assumption about whether a body is rigid or deformable and neither does it make any assumptions about the underlying physical model or approximation. More...
class BodyFrame
A BodyFrame is a material Frame that serves as the unique reference frame for a Body. More...
struct BodyNodeTopology
Data structure to store the topological information associated with a tree node. More...
struct BodyTopology
Data structure to store the topological information associated with a Body. More...
class FixedOffsetFrame
FixedOffsetFrame represents a material frame F whose pose is fixed with respect to a parent material frame P. More...
class ForceElement
A ForceElement allows modeling state and time dependent forces in a MultibodyTree model. More...
struct ForceElementTopology
Data structure to store the topological information associated with a ForceElement. More...
class Frame
Frame is an abstract class representing a material frame (also called a physical frame), meaning that it is associated with a material point of a Body. More...
class FrameBase
FrameBase is an abstract representation of the concept of a frame in multibody dynamics. More...
struct FrameTopology
Data structure to store the topological information associated with a Frame. More...
class GlobalInverseKinematics
Solves the inverse kinematics problem as a mixed integer convex optimization problem. More...
class Joint
A Joint models the kinematical relationship which characterizes the possible relative motion between two bodies. More...
class KukaTest
class Mobilizer
Mobilizer is a fundamental object within Drake's multibody engine used to specify the allowed motions between two Frame objects within a MultibodyTree. More...
class MobilizerImpl
Base class for specific Mobilizer implementations with the number of generalized positions and velocities resolved at compile time as template parameters. More...
struct MobilizerTopology
Data structure to store the topological information associated with a Mobilizer object. More...
class MultibodyTree
MultibodyTree provides a representation for a physical system consisting of a collection of interconnected rigid and deformable bodies. More...
class MultibodyTreeContext
MultibodyTreeContext is an object that contains all the information needed to uniquely determine the state of a MultibodyTree. More...
class MultibodyTreeElement< ElementType< T >, ElementIndexType >
A class representing an element or component of a MultibodyTree. More...
class MultibodyTreeTopology
Data structure to store the topological information associated with an entire MultibodyTree. More...
class PositionKinematicsCache
This class is one of the cache entries in MultibodyTreeContext. More...
class RevoluteJoint
This Joint allows two bodies to rotate relatively to one another around a common axis. More...
class RevoluteMobilizer
This Mobilizer allows two frames to rotate relatively to one another around an axis that is constant when measured in either this mobilizer's inboard or outboard frames, while the distance between the two frames does not vary. More...
class RigidBody
The term rigid body implies that the deformations of the body under consideration are so small that they have no significant effect on the overall motions of the body and therefore deformations can be neglected. More...
class RotationalInertia
This class helps describe the mass distribution (inertia properties) of a body or composite body about a particular point. More...
class SpatialAcceleration
This class is used to represent a spatial acceleration that combines rotational (angular acceleration) and translational (linear acceleration) components. More...
class SpatialForce
This class is used to represent a spatial force (also called a wrench) that combines both rotational (torque) and translational force components. More...
class SpatialInertia
This class represents the physical concept of a Spatial Inertia. More...
class SpatialVector
This class is used to represent physical quantities that correspond to spatial vectors such as spatial velocities, spatial accelerations and spatial forces. More...
class SpatialVelocity
This class is used to represent a spatial velocity (also called a twist) that combines rotational (angular) and translational (linear) velocity components. More...
class UniformGravityFieldElement
This ForceElement allows modeling the effect of a uniform gravity field as felt by bodies on the surface of the Earth. More...
class UnitInertia
This class is used to represent rotational inertias for unit mass bodies. More...
class VelocityKinematicsCache
This class is one of the cache entries in MultibodyTreeContext. More...
Typedefs
using FrameIndex = TypeSafeIndex< class FrameTag >
Type used to identify frames by index in a multibody tree system. More...
using BodyIndex = TypeSafeIndex< class BodyTag >
Type used to identify bodies by index in a multibody tree system. More...
using MobilizerIndex = TypeSafeIndex< class MobilizerTag >
Type used to identify mobilizers by index in a multibody tree system. More...
using BodyNodeIndex = TypeSafeIndex< class BodyNodeTag >
Type used to identify tree nodes by index within a multibody tree system. More...
using ForceElementIndex = TypeSafeIndex< class ForceElementTag >
Type used to identify force elements by index within a multibody tree system. More...
using JointIndex = TypeSafeIndex< class JointElementTag >
Type used to identify joints by index within a multibody tree system. More...
Functions
TEST_F (KukaTest, FeasiblePostureTest)
std::unique_ptr< RigidBodyTree< double > > ConstructKuka ()
template<typename T >
SpatialForce< T > operator+ (const SpatialForce< T > &F1_Sp_E, const SpatialForce< T > &F2_Sp_E)
Computes the resultant spatial force as the addition of two spatial forces F1_Sp_E and F2_Sp_E on a same system or body S, at the same point P and expressed in the same frame E. More...
template<typename T >
SpatialVelocity< T > operator+ (const SpatialVelocity< T > &V_EAb, const SpatialVelocity< T > &V_AB_E)
Performs the addition of two spatial velocities. More...
EXPLICITLY_INSTANTIATE_IMPLS (double)
EXPLICITLY_INSTANTIATE_IMPLS (AutoDiffXd)
BodyIndex world_index ()
For every MultibodyTree the world body always has this unique index and it is always zero. More...
template<typename T >
Creates and returns an lcmt_viewer_load_robot message containing the visual geometries from the provided RigidBodyTree. More...
void AddFlatTerrainToWorld (RigidBodyTreed *tree, double box_size=1000, double box_depth=10)
Adds a box-shaped terrain to tree. More...
TEST_F (RigidBodyTreeKinematicsTests, TestDoKinematicWithValidCache)
TEST_F (AcrobotTests, PoseTests)
TEST_F (AcrobotTests, SpatialVelocityTests)
TEST_F (RBTDifferentialKinematicsHelperTest, RPYPoseTest)
TEST_F (RBTDifferentialKinematicsHelperTest, RPYTwistInWorldAlignedBodyTest)
TEST_F (RBTDifferentialKinematicsHelperTest, RPYJacobianTest)
TEST_F (RBTDifferentialKinematicsHelperTest, RPYJacobianDotTimeVTest)
TEST_F (RBTDifferentialKinematicsHelperTest, QuatPoseTest)
TEST_F (RBTDifferentialKinematicsHelperTest, QuatTwistInWorldAlignedBodyTest)
TEST_F (RBTDifferentialKinematicsHelperTest, QuatJacobianTest)
TEST_F (RBTDifferentialKinematicsHelperTest, QuatJacobianDotTimeVTest)
Drake joint comparison methods.
These methods compare joint original with joint clone.
Since these methods are intended to compare a clone, an exact match is performed. This method will only return true if the provided clone joint is exactly the same as the provided original joint.
bool CompareDrakeJointToClone (const DrakeJoint &original, const DrakeJoint &clone)
bool CompareFixedJointToClone (const FixedJoint &original, const FixedJoint &other)
bool CompareHelicalJointToClone (const HelicalJoint &original, const HelicalJoint &clone)
bool ComparePrismaticJointToClone (const PrismaticJoint &original, const PrismaticJoint &clone)
bool CompareQuaternionBallJointToClone (const QuaternionBallJoint &original, const QuaternionBallJoint &clone)
bool CompareQuaternionFloatingJointToClone (const QuaternionFloatingJoint &original, const QuaternionFloatingJoint &clone)
bool CompareRevoluteJointToClone (const RevoluteJoint &original, const RevoluteJoint &clone)
bool CompareRollPitchYawFloatingJointToClone (const RollPitchYawFloatingJoint &original, const RollPitchYawFloatingJoint &clone)
template<typename Derived >
bool CompareFixedAxisOneDofJointToClone (const FixedAxisOneDoFJoint< Derived > &original, const FixedAxisOneDoFJoint< Derived > &clone)
Typedef Documentation
using BodyIndex = TypeSafeIndex
Type used to identify bodies by index in a multibody tree system.
using BodyNodeIndex = TypeSafeIndex
Type used to identify tree nodes by index within a multibody tree system.
using ForceElementIndex = TypeSafeIndex
Type used to identify force elements by index within a multibody tree system.
using FrameIndex = TypeSafeIndex
Type used to identify frames by index in a multibody tree system.
using JointIndex = TypeSafeIndex
Type used to identify joints by index within a multibody tree system.
using MobilizerIndex = TypeSafeIndex
Type used to identify mobilizers by index in a multibody tree system.
Function Documentation
void AddFlatTerrainToWorld ( RigidBodyTreed * tree, double box_size = 1000, double box_depth = 10 )
Adds a box-shaped terrain to tree.
This directly modifies the existing world rigid body within tree and thus does not need to return a model_instance_id value.
Two opposite corners of the resulting axis-aligned box are: (box_size / 2, box_size / 2, 0) and (-box_size / 2, -box_size / 2, -box_depth).
Parameters
[in] tree The RigidBodyTreed to which to add the terrain. [in] box_size The length and width of the terrain aligned with the world's X and Y axes. [in] box_depth The depth of the terrain aligned with the world's Z axis. Note that regardless of how deep the terrain is, the top surface of the terrain will be at Z = 0.
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bool CompareDrakeJointToClone ( const DrakeJoint & original, const DrakeJoint & clone )
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bool drake::multibody::CompareFixedAxisOneDofJointToClone ( const FixedAxisOneDoFJoint< Derived > & original, const FixedAxisOneDoFJoint< Derived > & clone )
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bool CompareFixedJointToClone ( const FixedJoint & original, const FixedJoint & other )
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bool CompareHelicalJointToClone ( const HelicalJoint & original, const HelicalJoint & clone )
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bool ComparePrismaticJointToClone ( const PrismaticJoint & original, const PrismaticJoint & clone )
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bool CompareQuaternionBallJointToClone ( const QuaternionBallJoint & original, const QuaternionBallJoint & clone )
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bool CompareQuaternionFloatingJointToClone ( const QuaternionFloatingJoint & original, const QuaternionFloatingJoint & clone )
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bool CompareRevoluteJointToClone ( const RevoluteJoint & original, const RevoluteJoint & clone )
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bool CompareRollPitchYawFloatingJointToClone ( const RollPitchYawFloatingJoint & original, const RollPitchYawFloatingJoint & clone )
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std::unique_ptr< RigidBodyTree< double > > ConstructKuka ( )
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Creates and returns an lcmt_viewer_load_robot message containing the visual geometries from the provided RigidBodyTree.
Note that this includes any visual geometries attached to the world body.
Instantiated templates for the following ScalarTypes are provided:
• double
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template lcmt_viewer_load_robot drake::multibody::CreateLoadRobotMessage< double > ( const RigidBodyTree< double > & tree )
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drake::multibody::EXPLICITLY_INSTANTIATE_IMPLS ( double )
drake::multibody::EXPLICITLY_INSTANTIATE_IMPLS ( AutoDiffXd )
SpatialForce drake::multibody::operator+ ( const SpatialForce< T > & F1_Sp_E, const SpatialForce< T > & F2_Sp_E )
inline
Computes the resultant spatial force as the addition of two spatial forces F1_Sp_E and F2_Sp_E on a same system or body S, at the same point P and expressed in the same frame E.
Return values
Fr_Sp_E The resultant spatial force on system or body S from combining F1_Sp_E and F2_Sp_E, applied at the same point P and in the same expressed-in frame E as the operand spatial forces.
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SpatialVelocity drake::multibody::operator+ ( const SpatialVelocity< T > & V_EAb, const SpatialVelocity< T > & V_AB_E )
inline
Performs the addition of two spatial velocities.
This operator returns the spatial velocity that results from adding the operands as if they were 6-dimensional vectors. In other words, the resulting spatial velocity contains a rotational component which is the 3-dimensional addition of the operand's rotational components and a translational component which is the 3-dimensional addition of the operand's translational components.
The addition of two spatial velocities has a clear physical meaning but can only be performed if the operands meet strict conditions. In addition the the usual requirement of common expressed-in frames, both spatial velocities must be for frames with the same origin point. The general idea is that if frame A has a spatial velocity with respect to E, and frame B has a spatial velocity with respect to A, we want to "compose" them so that we get frame B's spatial velocity in E. But that can't be done directly since frames A and B don't have the same origin. So:
Given the velocity V_EA of a frame A with respect to another frame E, and the velocity V_AB_E of a frame B measured in frame A (both expressed in frame E), we can calculate V_EB as their sum after shifting A's velocity to point Bo:
V_EB = V_EA.Shift(p_AB_E) + V_AB_E
where p_AB_E is the position vector from A's origin to B's origin, expressed in E. This shift can also be thought of as yielding the spatial velocity of a new frame Ab, which is an offset frame rigidly aligned with A, but with its origin shifted to B's origin:
V_EAb = V_EA.Shift(p_AB_E)
V_EB = V_EAb + V_AB_E
The addition in the last expression is what is carried out by this operator; the caller must have already performed the necessary shift.
drake::multibody::TEST_F ( KukaTest , FeasiblePostureTest )
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drake::multibody::TEST_F ( RigidBodyTreeKinematicsTests , TestDoKinematicWithValidCache )
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drake::multibody::TEST_F ( RigidBodyTreeKinematicsTests , TestDoKinematicWithBadCache1 )
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drake::multibody::TEST_F ( RigidBodyTreeKinematicsTests , TestDoKinematicWithBadCache2 )
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drake::multibody::TEST_F ( AcrobotTests , PoseTests )
drake::multibody::TEST_F ( AcrobotTests , SpatialVelocityTests )
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drake::multibody::TEST_F ( RBTDifferentialKinematicsHelperTest , RPYPoseTest )
drake::multibody::TEST_F ( RBTDifferentialKinematicsHelperTest , RPYTwistInWorldAlignedBodyTest )
drake::multibody::TEST_F ( RBTDifferentialKinematicsHelperTest , RPYJacobianTest )
drake::multibody::TEST_F ( RBTDifferentialKinematicsHelperTest , RPYJacobianDotTimeVTest )
drake::multibody::TEST_F ( RBTDifferentialKinematicsHelperTest , QuatPoseTest )
drake::multibody::TEST_F ( RBTDifferentialKinematicsHelperTest , QuatTwistInWorldAlignedBodyTest )
drake::multibody::TEST_F ( RBTDifferentialKinematicsHelperTest , QuatJacobianTest )
drake::multibody::TEST_F ( RBTDifferentialKinematicsHelperTest , QuatJacobianDotTimeVTest )
BodyIndex drake::multibody::world_index ( )
inline
For every MultibodyTree the world body always has this unique index and it is always zero.
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2017-10-20 08:56:46
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http://docs.gl/gl4/glBlitFramebuffer
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# glBlitFramebuffer
## Name
glBlitFramebuffer, glBlitNamedFramebuffer — copy a block of pixels from one framebuffer object to another
## C Specification
void glBlitFramebuffer( GLint srcX0, GLint srcY0, GLint srcX1, GLint srcY1, GLint dstX0, GLint dstY0, GLint dstX1, GLint dstY1, GLbitfield mask, GLenum filter);
void glBlitNamedFramebuffer( GLuint readFramebuffer, GLuint drawFramebuffer, GLint srcX0, GLint srcY0, GLint srcX1, GLint srcY1, GLint dstX0, GLint dstY0, GLint dstX1, GLint dstY1, GLbitfield mask, GLenum filter);
## Parameters
readFramebuffer
Specifies the name of the source framebuffer object for glBlitNamedFramebuffer.
drawFramebuffer
Specifies the name of the destination framebuffer object for glBlitNamedFramebuffer.
srcX0, srcY0, srcX1, srcY1
Specify the bounds of the source rectangle within the read buffer of the read framebuffer.
dstX0, dstY0, dstX1, dstY1
Specify the bounds of the destination rectangle within the write buffer of the write framebuffer.
mask
The bitwise OR of the flags indicating which buffers are to be copied. The allowed flags are GL_COLOR_BUFFER_BIT, GL_DEPTH_BUFFER_BIT and GL_STENCIL_BUFFER_BIT.
filter
Specifies the interpolation to be applied if the image is stretched. Must be GL_NEAREST or GL_LINEAR.
## Description
glBlitFramebuffer and glBlitNamedFramebuffer transfer a rectangle of pixel values from one region of a read framebuffer to another region of a draw framebuffer.
For glBlitFramebuffer, the read and draw framebuffers are those bound to the GL_READ_FRAMEBUFFER and GL_DRAW_FRAMEBUFFER targets respectively.
For glBlitNamedFramebuffer, readFramebuffer and drawFramebuffer are the names of the read read and draw framebuffer objects respectively. If readFramebuffer or drawFramebuffer is zero, then the default read or draw framebuffer respectively is used.
mask is the bitwise OR of a number of values indicating which buffers are to be copied. The values are GL_COLOR_BUFFER_BIT, GL_DEPTH_BUFFER_BIT, and GL_STENCIL_BUFFER_BIT. The pixels corresponding to these buffers are copied from the source rectangle bounded by the locations (srcX0, srcY0) and (srcX1, srcY1) to the destination rectangle bounded by the locations (dstX0, dstY0) and (dstX1, dstY1). The lower bounds of the rectangle are inclusive, while the upper bounds are exclusive.
The actual region taken from the read framebuffer is limited to the intersection of the source buffers being transferred, which may include the color buffer selected by the read buffer, the depth buffer, and/or the stencil buffer depending on mask. The actual region written to the draw framebuffer is limited to the intersection of the destination buffers being written, which may include multiple draw buffers, the depth buffer, and/or the stencil buffer depending on mask. Whether or not the source or destination regions are altered due to these limits, the scaling and offset applied to pixels being transferred is performed as though no such limits were present.
If the sizes of the source and destination rectangles are not equal, filter specifies the interpolation method that will be applied to resize the source image , and must be GL_NEAREST or GL_LINEAR. GL_LINEAR is only a valid interpolation method for the color buffer. If filter is not GL_NEAREST and mask includes GL_DEPTH_BUFFER_BIT or GL_STENCIL_BUFFER_BIT, no data is transferred and a GL_INVALID_OPERATION error is generated.
If filter is GL_LINEAR and the source rectangle would require sampling outside the bounds of the source framebuffer, values are read as if the GL_CLAMP_TO_EDGE texture wrapping mode were applied.
When the color buffer is transferred, values are taken from the read buffer of the specified read framebuffer and written to each of the draw buffers of the specified draw framebuffer.
If the source and destination rectangles overlap or are the same, and the read and draw buffers are the same, the result of the operation is undefined.
## Errors
GL_INVALID_OPERATION is generated by BlitNamedFramebuffer if readFramebuffer or drawFramebuffer is not zero or the name of an existing framebuffer object.
GL_INVALID_OPERATION is generated if mask contains any of the GL_DEPTH_BUFFER_BIT or GL_STENCIL_BUFFER_BIT and filter is not GL_NEAREST.
GL_INVALID_OPERATION is generated if mask contains GL_COLOR_BUFFER_BIT and any of the following conditions hold:
• The read buffer contains fixed-point or floating-point values and any draw buffer contains neither fixed-point nor floating-point values.
• The read buffer contains unsigned integer values and any draw buffer does not contain unsigned integer values.
• The read buffer contains signed integer values and any draw buffer does not contain signed integer values.
GL_INVALID_OPERATION is generated if mask contains GL_DEPTH_BUFFER_BIT or GL_STENCIL_BUFFER_BIT and the source and destination depth and stencil formats do not match.
GL_INVALID_OPERATION is generated if filter is GL_LINEAR and the read buffer contains integer data.
GL_INVALID_OPERATION is generated if the effective value of GL_SAMPLES for the read and draw framebuffers is not identical.
GL_INVALID_OPERATION is generated if the value of GL_SAMPLE_BUFFERS for both read and draw buffers is greater than zero and the dimensions of the source and destination rectangles is not identical.
GL_INVALID_FRAMEBUFFER_OPERATION is generated if the specified read and draw framebuffers are not framebuffer complete.
## Examples
Copy the contents of one framebuffer object to another by blitting.
glBindFramebuffer(GL_READ_FRAMEBUFFER, source_fbo);
glBindFramebuffer(GL_DRAW_FRAMEBUFFER, destination_fbo);
glBlitFramebuffer(0, 0, source_fbo_width, source_fbo_height, 0, 0, destination_fbo_width, destination_fbo_height, GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT, GL_NEAREST);
## Version Support
OpenGL Version
Function / Feature Name 2.0 2.1 3.0 3.1 3.2 3.3 4.0 4.1 4.2 4.3 4.4 4.5
glBlitFramebuffer - -
glBlitNamedFramebuffer - - - - - - - - - - -
## See Also
Think you can improve this page? Edit this page on GitHub.
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2018-03-18 13:40:15
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https://chemistry.stackexchange.com/questions/121686/chemistry-12-calculating-changes-in-enthalpy
|
# Chemistry 12: Calculating changes in enthalpy [closed]
I was wondering if I could please get some help with this:
In a coffee-cup calorimeter $$\pu{100.0 mL}$$ of $$\pu{1.0 M}\ \ce{NaOH}$$ and $$\pu{100.0 mL}$$ of $$\pu{1.0 M}\ \ce{HCl}$$ are mixed. Both solutions are originally at $$\pu{24.6 ^\circ C}$$. After the reaction, the temperature is $$\pu{31.3 ^\circ C}$$. Assuming all solutions have a density of $$\pu{1.0 g/cm^3}$$ and a specific heat capacity of $$\pu{4.181 J/(g ^\circ C)}$$. What is the enthalpy change for the neutralization of $$\ce{HCl}$$ by $$\ce{NaOH}$$?"
This is what I did, but I'm not sure if it's correct:
\begin{align} q(\text{surroundings}) &= m \cdot c \cdot \Delta T\\ &= \pu{200 g} \cdot \pu{4.184 J/(g ^\circ C)} \cdot (\pu{31.3 ^\circ C} - \pu{24.6 ^\circ C})\\ &= \pu{5.61 kJ}\\[2em] q(\text{system}) - \pu{5.61 kJ} &= n \cdot \Delta H - \pu{5.61 kJ}\\ &= \pu{0.1 mol} \cdot \Delta H \end{align}
Thus: $$\Delta H = \pu{-56.1 kJ/mol}$$
In general, homework is not welcome here in the forum, which is probably why your question was voted down. However, since you have already given a solution here and only ask for a confirmation, I want to be so nice and reply to your question.
Thus: $$Q(\text{neutralization}) + Q(\text{warm the solution}) + Q(\text{warm the calorimeter}) = 0$$
In your example, it is assumed for simplicity that the calorimeter does not consume heat to heat up. Therefore $$Q(\text{warm the calorimeter}) = 0$$.
\begin{align} Q(\text{neutralization}) + Q(\text{warm the solution}) &= 0\\ n \Delta H + m c \Delta T &= 0\\ n \Delta H &= - m c \Delta T\\ \Delta H &= -\frac{m c \Delta T}{n}\\ &= \frac{\pu{200 g} \cdot \pu{4.184 J/(g ^\circ C)} \cdot (\pu{31.3 ^\circ C} - \pu{24.6 ^\circ C})}{\pu{0.1 mol}}\\ &= \pu{-56.1 kJ/mol} \end{align}
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2020-05-29 21:02:19
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http://physics.stackexchange.com/questions?page=871&sort=newest
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### Why aren't the energies of two systems in thermal equilibrium fixed?
In the derivation of the Boltzmann distribution they consider a system $A$, enclosed by a diathermal wall in a heat reservoir $R$. Then they calculate the probability that the system $A$ is in an ...
238 views
### Quantum Mechanical Operators in the argument of an exponential
In Quantum Optics and Quantum Mechanics, the time evolution operator $$U(t,t_i) = \exp\left[\frac{-i}{\hbar}H(t-t_i)\right]$$ is used quite a lot. Suppose $t_i =0$ for simplicity, and say the ...
240 views
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Newton's First Law of Motion states that an object at rest or uniform motion tends to stay in that state of motion unless an unbalanced, external force acts on it. Say if I were in a car and I push ...
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### Can a current carrying loop or wire produces no magnetic field?
A current carrying wire produces magnetic field around it. We can find the direction by Fleming's Right hand rule. We know change in electric filed produces magnetic field and change on magnetic field ...
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### Mass gap for photons
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### Is every quantum measurement reducible to measurements of position and time?
I am currently studying Path Integrals and was unable to resolve the following problem. In the famous book Quantum Mechanics and Path Integrals, written by Feynman and Hibbs, it says (at the beginning ...
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### Why isn't data lost when sent over large distances?
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### Intuition behind the notion of reflection positivity
I came across Yuji's question. I'm finding it difficult to parse the meaning behind what's said on Wikipedia. Could someone give an explanation of the concept involved? I would also appreciate ...
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### Does phase lead or lag in a plasma?
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2015-10-04 05:24:26
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https://stats.stackexchange.com/questions/179565/multiple-comparison-in-multiple-imputation?noredirect=1
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# Multiple comparison in Multiple imputation
I am wondering if it is appropriate to use the term "multiple comparison problem" when applied to multiple imputation. I know that the multiple comparison problem arises when we have one set of data and ask many questions about it. Is this theoretically the same thing as having multiple data sets, and asking the same question on each dataset?
The reason I ask is because I have a MI dataset, and want to run a log rank test on each of the 50 datasets, but I don't believe that running the test on each dataset and then pooling is valid (because of the multiple comparison problem).
• What exactly do you impute? The group variable or something else? – Theodor Nov 2 '15 at 12:06
• Correct. In my original dataset, the survival time and censoring indicator are fully observed, but the treatment/group needs imputation. As well, in another instance, I have that same setup, but a variable is imputed that I subset on (ie coxph(Surv(time,cens)~treat,subset=(receptor==TRUE)) – RayVelcoro Nov 2 '15 at 14:20
• I am currently doing the Wald like test as you suggested in the second paragraph. My logic is that we want the pooled log rank test (from kaplan meier curves), but since this is not normally distributed, we can run a cox model (equivalent with no ties), and then to a Wald test, since the score test is the log rank test, and the wald test is asymptotically equivalent to it. I'm just afraid that. Besides, pooling on $\chi^2$ doesn't seem to work well. I'm just afraid of the theoretical soundness of this method. – RayVelcoro Nov 2 '15 at 16:38
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2020-02-22 00:06:56
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https://socratic.org/questions/how-do-you-solve-and-write-the-following-in-interval-notation-19-10-x-11
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# How do you solve and write the following in interval notation: -19<10-x<=-11?
Jun 14, 2016
$21 \le x < 29.$
Interval Form : $x \in \left[21 , 29\right) .$
Given that, $- 19 < 10 - x \le - 11.$
We add -10 in the inequality (ineql.) to get, $- 29 < - x \le - 21.$
Then, we multiply this ineql. by $- 1$, a negative number, causing reversal of the order, $29 > + x \ge 21 ,$,i.e., $21 \le x < 29.$
We can write this in Interval Form as $x \in \left[21 , 29\right) .$
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2019-10-21 07:12:42
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https://andreygogolev.wordpress.com/
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## Shenzhen conference photos
July 12, 2018
Some highlights of Shenzhen conference are under the fold.
## Shenzhen problems: zero entropy
July 11, 2018
These two questions were stated by me in Shenzhen after Federico Rodriguez Hertz’s talk on flexibility of Lyapunov exponents. I stumbled into these problems after discussions with Bryce Weaver, when we unsuccessfully tried to show that certain higher dimensional geodesic flows are stably non-uniformly hyperbolic. My last mathematical discussion in January 2018 with late Anatole Katok was revolving around these questions and he was leaning towards existence of counterexamples.
Question 1
Let ${S}$ be a surface of genus ${\ge 2}$ equipped with a smooth (at least ${C^{2+\varepsilon}}$) Riemannian (symmetric Finsler) metric. Is it true that the metric entropy of the geosedic flow with respect to the Liouville measure is positive?
Question 2
Let ${f\colon\mathbb T^2\rightarrow\mathbb T^2}$ be an area preserving smooth (at least ${C^2}$ or ${C^{1+\varepsilon}}$) diffeomorphism homotopic to 2-1-1-1 automorphism. Is it true that the metric entropy of ${f}$ with respect to the area is positive?
## Shenzhen problems
July 11, 2018
Below the fold I record open problems from my Shenzhen lectures. These may seem quite random, however they appeared naturally in the lectures.
## Transitivity of strong unstable foliation
May 12, 2018
This is to give an update on problem 3 from my 2009 post. Recently Aleksey Kolmogorov, Itai Maimon and I performed high precision computer experiments which confirmed that the strong unstable manifold through the fixed point $W^{uu}(p)$ is dense in $\mathbb T^3$. Based on our computer experiments we conjectured that the strong unstable foliation is transitive and that there is a unique invariant measure with absolutely continuous conditionals on strong unstable leaves ($u$-Gibbs measure), which is then, of course, the SRB measure. For example the image below shows the points of intersection of the strong unstable manifold of the fixed point and a $\mathbb T^2$ transversal for the Anosov diffeomorphism
$(x,y,z)\mapsto (2x+y+0.1\sin(2\pi x),x+2y+z,y+z)$
Our first conjecture was proved by Jana Rodriguez Hertz and Raul Ures in a paper posted on arXiv yesterday. In fact, they proved a more general statement.
Theorem. Let $L\colon\mathbb T^3\to\mathbb T^3$ be a hyperbolic automophism with real spectrum $0<\lambda^s<1<\lambda^{wu}<\lambda^{uu}$. Let $f$ be an Anosov diffeomorphism homotopic to A with a partially hyperbolic splitting of the unstable bundle into weak unstable and strong unstable subbundles. Then the strong unstable foliation $W^{uu}$ of $f$ is transitive.
Some ingredients in the proof come from earlier results of Rodriguez Hertz-Rodriguez Hertz-Ures, Didier and Ren-Gan-Zhang. Below the fold I record a self-contained proof following Rodriguez Hertz-Ures. Needless to say that all possible mistakes are due to me.
Note however that denseness of leaves $W^{uu}(p)$ through fixed or periodic points $p$ remains unknown as well as the minimality question.
## Anatole Katok
May 1, 2018
In this posting I will be collecting links to online materials.
1. Anatole’s own page at PennState contains a lot of his writings, including expository ones such as papers on history of dynamics and mathematics in general. http://personal.psu.edu/axk29/ In particular: preface to the 60th year old BD volume, which includes the 1960 Kronrod seminar picture; 1965 Humsan school; tribute to Anosov; Women in Soviet Math (joint w Svetlana); 2014 MSRI photos;
2. Moscow Math Journal on the occasion of Anatole’s 60th birthday https://www.ams.org/distribution/mmj/vol4-4-2004/katok-birthday.html
3. Mathnet-ru page gives a good idea on Anatole’s work prior to emigration http://www.mathnet.ru/php/person.phtml?personid=24724&option_lang=eng
4. Pictures from 2004 conference on Svetlana’s page: http://www.personal.psu.edu/sxk37/PICTURES/Tolya-60/Tolya-60.html
5. E.B. Dynkin interviews with Anatole and Svetlana https://ecommons.cornell.edu/handle/1813/17063, https://ecommons.cornell.edu/handle/1813/17062, https://ecommons.cornell.edu/handle/1813/17059, https://ecommons.cornell.edu/handle/1813/17058, https://ecommons.cornell.edu/handle/1813/17057,
6. BIRS group photo 2014: www.birs.ca/workshops/2014/14w5058/groupphoto.jpg
7. Oberwolfach photo collection: https://opc.mfo.de/person_detail?id=6987
8. Kiev Mathematics Colloquium. Flexibility of entropies and Lyapunov exponents. Anatole and Svetlana visited Kiev in (May?) 2015 after the orange revolution to show support for Ukraine and Ukrainian Mathematics. https://www.youtube.com/watch?v=rpD46tPJ2uw
9. Math genealogy seem to be pretty accurate with a few omissions (Satayev for example) https://www.genealogy.math.ndsu.nodak.edu/id.php?id=10482
10. Memorial Website: http://anatolekatok.com
May 1, 2018
## Anatole Katok, August 9, 1944 — April 30, 2018
It is really hard to believe Anatole (Tolya) passed away yesterday.
He was born in Washington D.C. in August of 1944. His parents were Soviet citizens working in the american capital in relation with Lend-Lease Act. Then he was brought to the Soviet Union as a baby in 1945. Mathematical career of Anatole began in Moscow in the 60s with work on periodic approximations in ergodic theory joint with A. Stepin. His advisor was Ya. G. Sinai and, later, Anatole was also very much influenced by D. V. Anosov. In 1978 Anatole and Svetlana emigrated to the United States (via Vienna and Rome if I remember correctly). Anatole went on to have a distinguished career in the US. He will be remembered for his mathematics, his personality, his “bible” of dynamical systems joint with B. Hasselblatt. I am sure that once the shock subsides a lot more will be said about his life and his mathematics.
This picture reflects very well how I remember Anatole. R.I.P.
## 50 years of Berkeley encounter
March 20, 2018
So, if all goes well, such as me securing a Chinese visa, I will be participating in the International Conference on Dynamical Systems in Shenzhen, China, in June. The occasion is somewhat unusual and romantic: it is 50 years anniversary of Berkeley encounter.
## Rigidity of hyperbolic automorphisms from volume Lyapunov spectra
March 15, 2018
A recent preprint of Radu Saghin and Jiagang Yang is devoted to rigidity of hyperbolic automorphisms and partially hyperbolic skew products. The authors take a perspective similar to that of A. Katok’s entropy rigidity for geodesic flows on surfaces. Recall that by entropy rigidity the Lyapunov exponent of the Liouville measure achieves its maximum value for hyperbolic surfaces, when metrics are varied in the space of metrics of negative curvature with a fixed area. Hence the Lyapunov exponent determines the hyperbolic metric up to isometry and up to Teichmuller coordinate.
The model of Saghin-Yang is a hyperbolic automorphism. The most basic, and already very interesting, version of their result is the following.
Theorem 1 Let ${L\colon\mathbb T^3\rightarrow\mathbb T^3}$ be a hyperbolic automorphism with distinct Lyapunov exponents
$\displaystyle \chi^s<0<\chi^{wu}<\chi^{uu}$
Assume that diffeomorphism ${f}$ is a volume preserving ${C^1}$-perturbation of ${L}$ and that the volume Lyapunov exponents stay the same:
$\displaystyle \chi^s_f=\chi^s,\,\, \chi^{wu}_f=\chi^{wu},\,\, \chi^{uu}_f=\chi^{uu}$
Then ${f}$ is ${C^\infty}$ conjugate to ${L}$.
## A-operation
February 14, 2018
I learned about the ${\mathcal A}$-operation from Neretin’s book. The Continuum Hypothesis (CH) for Borel sets says that any Borel subset of the real line ${\mathbb R}$ is either countable or has continuum cardinality. Indeed what a natural problem!
## Luzin and the Continuum Hypothesis
February 4, 2018
So I finished reading Yury Neretin’s “Nikolay Luzin, his students, adversaries, and defenders (notes on the history of Moscow mathematics, 1914-1936)” which is an impressive historical investigation around Luzin’s life and, of course, Luzin’s affair.
Neretin performed a monumental combing through available sources and his manuscript is full of quotations. Regarding the affair per se Neretin holds an unorthodox view that Moscow mathematicians were at the origin of the attack on Luzin. This is at odds with Yushkewich-Demidov explanation that the affair was launched by party apparatchik Kol’man with assistance of Editor in Chief of Pravda newspaper Mekhlis. In any case, I guess, this is no way of knowing for sure who wrote the anonymous Pravda article and it is not that important anyway. Read the rest of this entry »
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2018-07-15 23:03:25
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https://socratic.org/questions/how-do-you-solve-3-tan-2-x-3-tan-x-in-interval-0-x-360#605624
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# How do you solve 3 tan 2 x = √ 3 tan x in interval 0<=x<=360?
May 2, 2018
$x = \left\{{0}^{\circ} , {180}^{\circ} , {360}^{\circ}\right\}$
#### Explanation:
As $\tan 2 x = \frac{2 \tan x}{1 - {\tan}^{2} x}$, we can write $3 \tan 2 x = \sqrt{3} \tan x$ as
$3 \frac{2 \tan x}{1 - {\tan}^{2} x} = \sqrt{3} \tan x$
or $6 \tan x = \sqrt{3} \tan x - \sqrt{3} {\tan}^{3} x$
or $\sqrt{3} {\tan}^{3} x + \tan x \left(6 - \sqrt{3}\right) = 0$
or $\sqrt{3} \tan x \left({\tan}^{2} x + 2 \sqrt{3} - 1\right) = 0$
As ${\tan}^{2} x + 2 \sqrt{3} - 1 \ne 0$,
hence $\tan x = 0$ i.e. $x = n \pi$, where $n$ is an integer
and in ${0}^{\circ} \le x \le {360}^{\circ}$, $x = \left\{{0}^{\circ} , {180}^{\circ} , {360}^{\circ}\right\}$.
May 2, 2018
$\implies x = {0}^{\circ} , {180}^{\circ} , {360}^{\circ} .$
#### Explanation:
Here,
3 tan 2 x = √ 3 tan x
$\implies 3 \left(\frac{2 \tan x}{1 - {\tan}^{2} x}\right) = \sqrt{3} \tan x$
$\implies 6 \tan x = \sqrt{3} \tan x - \sqrt{3} {\tan}^{3} x$
$\implies \sqrt{3} {\tan}^{3} x + 6 \tan x - \sqrt{3} \tan x = 0$
$\implies \tan x \left(\sqrt{3} {\tan}^{2} x + 6 - \sqrt{3}\right) = 0$
$\implies \tan x = 0 \mathmr{and} \sqrt{3} {\tan}^{2} x + 6 - \sqrt{3} = 0$
$\left(i\right) \tan x = 0 \implies x = k \pi , k \in \mathbb{Z}$
$\left(i i\right) \sqrt{3} {\tan}^{2} x + 6 - \sqrt{3} = 0$
$\implies {\tan}^{2} x = - \frac{6 - \sqrt{3}}{\sqrt{3}} = - \left(2 \sqrt{3} - 1\right) < 0$
$i . e . {\tan}^{2} x < 0 \implies x \notin \mathbb{R}$
Hence,
$x = k \pi , k \in \mathbb{Z} , w h e r e , x \in \left[{0}^{\circ} , {360}^{\circ}\right]$
$\implies x = {0}^{\circ} , {180}^{\circ} , {360}^{\circ} .$
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2022-01-28 08:34:28
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https://people.maths.bris.ac.uk/~matyd/GroupNames/320/C2xDic40.html
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Copied to
clipboard
G = C2×Dic40order 320 = 26·5
Direct product of C2 and Dic40
Series: Derived Chief Lower central Upper central
Derived series C1 — C40 — C2×Dic40
Chief series C1 — C5 — C10 — C20 — C40 — Dic20 — C2×Dic20 — C2×Dic40
Lower central C5 — C10 — C20 — C40 — C2×Dic40
Upper central C1 — C22 — C2×C4 — C2×C8 — C2×C16
Generators and relations for C2×Dic40
G = < a,b,c | a2=b80=1, c2=b40, ab=ba, ac=ca, cbc-1=b-1 >
Subgroups: 382 in 82 conjugacy classes, 39 normal (21 characteristic)
C1, C2, C2, C4, C4, C22, C5, C8, C2×C4, C2×C4, Q8, C10, C10, C16, C2×C8, Q16, C2×Q8, Dic5, C20, C2×C10, C2×C16, Q32, C2×Q16, C40, Dic10, C2×Dic5, C2×C20, C2×Q32, C80, Dic20, Dic20, C2×C40, C2×Dic10, Dic40, C2×C80, C2×Dic20, C2×Dic40
Quotients: C1, C2, C22, D4, C23, D5, D8, C2×D4, D10, Q32, C2×D8, D20, C22×D5, C2×Q32, D40, C2×D20, Dic40, C2×D40, C2×Dic40
Smallest permutation representation of C2×Dic40
Regular action on 320 points
Generators in S320
(1 152)(2 153)(3 154)(4 155)(5 156)(6 157)(7 158)(8 159)(9 160)(10 81)(11 82)(12 83)(13 84)(14 85)(15 86)(16 87)(17 88)(18 89)(19 90)(20 91)(21 92)(22 93)(23 94)(24 95)(25 96)(26 97)(27 98)(28 99)(29 100)(30 101)(31 102)(32 103)(33 104)(34 105)(35 106)(36 107)(37 108)(38 109)(39 110)(40 111)(41 112)(42 113)(43 114)(44 115)(45 116)(46 117)(47 118)(48 119)(49 120)(50 121)(51 122)(52 123)(53 124)(54 125)(55 126)(56 127)(57 128)(58 129)(59 130)(60 131)(61 132)(62 133)(63 134)(64 135)(65 136)(66 137)(67 138)(68 139)(69 140)(70 141)(71 142)(72 143)(73 144)(74 145)(75 146)(76 147)(77 148)(78 149)(79 150)(80 151)(161 295)(162 296)(163 297)(164 298)(165 299)(166 300)(167 301)(168 302)(169 303)(170 304)(171 305)(172 306)(173 307)(174 308)(175 309)(176 310)(177 311)(178 312)(179 313)(180 314)(181 315)(182 316)(183 317)(184 318)(185 319)(186 320)(187 241)(188 242)(189 243)(190 244)(191 245)(192 246)(193 247)(194 248)(195 249)(196 250)(197 251)(198 252)(199 253)(200 254)(201 255)(202 256)(203 257)(204 258)(205 259)(206 260)(207 261)(208 262)(209 263)(210 264)(211 265)(212 266)(213 267)(214 268)(215 269)(216 270)(217 271)(218 272)(219 273)(220 274)(221 275)(222 276)(223 277)(224 278)(225 279)(226 280)(227 281)(228 282)(229 283)(230 284)(231 285)(232 286)(233 287)(234 288)(235 289)(236 290)(237 291)(238 292)(239 293)(240 294)
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80)(81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160)(161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240)(241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320)
(1 310 41 270)(2 309 42 269)(3 308 43 268)(4 307 44 267)(5 306 45 266)(6 305 46 265)(7 304 47 264)(8 303 48 263)(9 302 49 262)(10 301 50 261)(11 300 51 260)(12 299 52 259)(13 298 53 258)(14 297 54 257)(15 296 55 256)(16 295 56 255)(17 294 57 254)(18 293 58 253)(19 292 59 252)(20 291 60 251)(21 290 61 250)(22 289 62 249)(23 288 63 248)(24 287 64 247)(25 286 65 246)(26 285 66 245)(27 284 67 244)(28 283 68 243)(29 282 69 242)(30 281 70 241)(31 280 71 320)(32 279 72 319)(33 278 73 318)(34 277 74 317)(35 276 75 316)(36 275 76 315)(37 274 77 314)(38 273 78 313)(39 272 79 312)(40 271 80 311)(81 167 121 207)(82 166 122 206)(83 165 123 205)(84 164 124 204)(85 163 125 203)(86 162 126 202)(87 161 127 201)(88 240 128 200)(89 239 129 199)(90 238 130 198)(91 237 131 197)(92 236 132 196)(93 235 133 195)(94 234 134 194)(95 233 135 193)(96 232 136 192)(97 231 137 191)(98 230 138 190)(99 229 139 189)(100 228 140 188)(101 227 141 187)(102 226 142 186)(103 225 143 185)(104 224 144 184)(105 223 145 183)(106 222 146 182)(107 221 147 181)(108 220 148 180)(109 219 149 179)(110 218 150 178)(111 217 151 177)(112 216 152 176)(113 215 153 175)(114 214 154 174)(115 213 155 173)(116 212 156 172)(117 211 157 171)(118 210 158 170)(119 209 159 169)(120 208 160 168)
G:=sub<Sym(320)| (1,152)(2,153)(3,154)(4,155)(5,156)(6,157)(7,158)(8,159)(9,160)(10,81)(11,82)(12,83)(13,84)(14,85)(15,86)(16,87)(17,88)(18,89)(19,90)(20,91)(21,92)(22,93)(23,94)(24,95)(25,96)(26,97)(27,98)(28,99)(29,100)(30,101)(31,102)(32,103)(33,104)(34,105)(35,106)(36,107)(37,108)(38,109)(39,110)(40,111)(41,112)(42,113)(43,114)(44,115)(45,116)(46,117)(47,118)(48,119)(49,120)(50,121)(51,122)(52,123)(53,124)(54,125)(55,126)(56,127)(57,128)(58,129)(59,130)(60,131)(61,132)(62,133)(63,134)(64,135)(65,136)(66,137)(67,138)(68,139)(69,140)(70,141)(71,142)(72,143)(73,144)(74,145)(75,146)(76,147)(77,148)(78,149)(79,150)(80,151)(161,295)(162,296)(163,297)(164,298)(165,299)(166,300)(167,301)(168,302)(169,303)(170,304)(171,305)(172,306)(173,307)(174,308)(175,309)(176,310)(177,311)(178,312)(179,313)(180,314)(181,315)(182,316)(183,317)(184,318)(185,319)(186,320)(187,241)(188,242)(189,243)(190,244)(191,245)(192,246)(193,247)(194,248)(195,249)(196,250)(197,251)(198,252)(199,253)(200,254)(201,255)(202,256)(203,257)(204,258)(205,259)(206,260)(207,261)(208,262)(209,263)(210,264)(211,265)(212,266)(213,267)(214,268)(215,269)(216,270)(217,271)(218,272)(219,273)(220,274)(221,275)(222,276)(223,277)(224,278)(225,279)(226,280)(227,281)(228,282)(229,283)(230,284)(231,285)(232,286)(233,287)(234,288)(235,289)(236,290)(237,291)(238,292)(239,293)(240,294), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320), (1,310,41,270)(2,309,42,269)(3,308,43,268)(4,307,44,267)(5,306,45,266)(6,305,46,265)(7,304,47,264)(8,303,48,263)(9,302,49,262)(10,301,50,261)(11,300,51,260)(12,299,52,259)(13,298,53,258)(14,297,54,257)(15,296,55,256)(16,295,56,255)(17,294,57,254)(18,293,58,253)(19,292,59,252)(20,291,60,251)(21,290,61,250)(22,289,62,249)(23,288,63,248)(24,287,64,247)(25,286,65,246)(26,285,66,245)(27,284,67,244)(28,283,68,243)(29,282,69,242)(30,281,70,241)(31,280,71,320)(32,279,72,319)(33,278,73,318)(34,277,74,317)(35,276,75,316)(36,275,76,315)(37,274,77,314)(38,273,78,313)(39,272,79,312)(40,271,80,311)(81,167,121,207)(82,166,122,206)(83,165,123,205)(84,164,124,204)(85,163,125,203)(86,162,126,202)(87,161,127,201)(88,240,128,200)(89,239,129,199)(90,238,130,198)(91,237,131,197)(92,236,132,196)(93,235,133,195)(94,234,134,194)(95,233,135,193)(96,232,136,192)(97,231,137,191)(98,230,138,190)(99,229,139,189)(100,228,140,188)(101,227,141,187)(102,226,142,186)(103,225,143,185)(104,224,144,184)(105,223,145,183)(106,222,146,182)(107,221,147,181)(108,220,148,180)(109,219,149,179)(110,218,150,178)(111,217,151,177)(112,216,152,176)(113,215,153,175)(114,214,154,174)(115,213,155,173)(116,212,156,172)(117,211,157,171)(118,210,158,170)(119,209,159,169)(120,208,160,168)>;
G:=Group( (1,152)(2,153)(3,154)(4,155)(5,156)(6,157)(7,158)(8,159)(9,160)(10,81)(11,82)(12,83)(13,84)(14,85)(15,86)(16,87)(17,88)(18,89)(19,90)(20,91)(21,92)(22,93)(23,94)(24,95)(25,96)(26,97)(27,98)(28,99)(29,100)(30,101)(31,102)(32,103)(33,104)(34,105)(35,106)(36,107)(37,108)(38,109)(39,110)(40,111)(41,112)(42,113)(43,114)(44,115)(45,116)(46,117)(47,118)(48,119)(49,120)(50,121)(51,122)(52,123)(53,124)(54,125)(55,126)(56,127)(57,128)(58,129)(59,130)(60,131)(61,132)(62,133)(63,134)(64,135)(65,136)(66,137)(67,138)(68,139)(69,140)(70,141)(71,142)(72,143)(73,144)(74,145)(75,146)(76,147)(77,148)(78,149)(79,150)(80,151)(161,295)(162,296)(163,297)(164,298)(165,299)(166,300)(167,301)(168,302)(169,303)(170,304)(171,305)(172,306)(173,307)(174,308)(175,309)(176,310)(177,311)(178,312)(179,313)(180,314)(181,315)(182,316)(183,317)(184,318)(185,319)(186,320)(187,241)(188,242)(189,243)(190,244)(191,245)(192,246)(193,247)(194,248)(195,249)(196,250)(197,251)(198,252)(199,253)(200,254)(201,255)(202,256)(203,257)(204,258)(205,259)(206,260)(207,261)(208,262)(209,263)(210,264)(211,265)(212,266)(213,267)(214,268)(215,269)(216,270)(217,271)(218,272)(219,273)(220,274)(221,275)(222,276)(223,277)(224,278)(225,279)(226,280)(227,281)(228,282)(229,283)(230,284)(231,285)(232,286)(233,287)(234,288)(235,289)(236,290)(237,291)(238,292)(239,293)(240,294), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80)(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160)(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320), (1,310,41,270)(2,309,42,269)(3,308,43,268)(4,307,44,267)(5,306,45,266)(6,305,46,265)(7,304,47,264)(8,303,48,263)(9,302,49,262)(10,301,50,261)(11,300,51,260)(12,299,52,259)(13,298,53,258)(14,297,54,257)(15,296,55,256)(16,295,56,255)(17,294,57,254)(18,293,58,253)(19,292,59,252)(20,291,60,251)(21,290,61,250)(22,289,62,249)(23,288,63,248)(24,287,64,247)(25,286,65,246)(26,285,66,245)(27,284,67,244)(28,283,68,243)(29,282,69,242)(30,281,70,241)(31,280,71,320)(32,279,72,319)(33,278,73,318)(34,277,74,317)(35,276,75,316)(36,275,76,315)(37,274,77,314)(38,273,78,313)(39,272,79,312)(40,271,80,311)(81,167,121,207)(82,166,122,206)(83,165,123,205)(84,164,124,204)(85,163,125,203)(86,162,126,202)(87,161,127,201)(88,240,128,200)(89,239,129,199)(90,238,130,198)(91,237,131,197)(92,236,132,196)(93,235,133,195)(94,234,134,194)(95,233,135,193)(96,232,136,192)(97,231,137,191)(98,230,138,190)(99,229,139,189)(100,228,140,188)(101,227,141,187)(102,226,142,186)(103,225,143,185)(104,224,144,184)(105,223,145,183)(106,222,146,182)(107,221,147,181)(108,220,148,180)(109,219,149,179)(110,218,150,178)(111,217,151,177)(112,216,152,176)(113,215,153,175)(114,214,154,174)(115,213,155,173)(116,212,156,172)(117,211,157,171)(118,210,158,170)(119,209,159,169)(120,208,160,168) );
G=PermutationGroup([[(1,152),(2,153),(3,154),(4,155),(5,156),(6,157),(7,158),(8,159),(9,160),(10,81),(11,82),(12,83),(13,84),(14,85),(15,86),(16,87),(17,88),(18,89),(19,90),(20,91),(21,92),(22,93),(23,94),(24,95),(25,96),(26,97),(27,98),(28,99),(29,100),(30,101),(31,102),(32,103),(33,104),(34,105),(35,106),(36,107),(37,108),(38,109),(39,110),(40,111),(41,112),(42,113),(43,114),(44,115),(45,116),(46,117),(47,118),(48,119),(49,120),(50,121),(51,122),(52,123),(53,124),(54,125),(55,126),(56,127),(57,128),(58,129),(59,130),(60,131),(61,132),(62,133),(63,134),(64,135),(65,136),(66,137),(67,138),(68,139),(69,140),(70,141),(71,142),(72,143),(73,144),(74,145),(75,146),(76,147),(77,148),(78,149),(79,150),(80,151),(161,295),(162,296),(163,297),(164,298),(165,299),(166,300),(167,301),(168,302),(169,303),(170,304),(171,305),(172,306),(173,307),(174,308),(175,309),(176,310),(177,311),(178,312),(179,313),(180,314),(181,315),(182,316),(183,317),(184,318),(185,319),(186,320),(187,241),(188,242),(189,243),(190,244),(191,245),(192,246),(193,247),(194,248),(195,249),(196,250),(197,251),(198,252),(199,253),(200,254),(201,255),(202,256),(203,257),(204,258),(205,259),(206,260),(207,261),(208,262),(209,263),(210,264),(211,265),(212,266),(213,267),(214,268),(215,269),(216,270),(217,271),(218,272),(219,273),(220,274),(221,275),(222,276),(223,277),(224,278),(225,279),(226,280),(227,281),(228,282),(229,283),(230,284),(231,285),(232,286),(233,287),(234,288),(235,289),(236,290),(237,291),(238,292),(239,293),(240,294)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80),(81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160),(161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240),(241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320)], [(1,310,41,270),(2,309,42,269),(3,308,43,268),(4,307,44,267),(5,306,45,266),(6,305,46,265),(7,304,47,264),(8,303,48,263),(9,302,49,262),(10,301,50,261),(11,300,51,260),(12,299,52,259),(13,298,53,258),(14,297,54,257),(15,296,55,256),(16,295,56,255),(17,294,57,254),(18,293,58,253),(19,292,59,252),(20,291,60,251),(21,290,61,250),(22,289,62,249),(23,288,63,248),(24,287,64,247),(25,286,65,246),(26,285,66,245),(27,284,67,244),(28,283,68,243),(29,282,69,242),(30,281,70,241),(31,280,71,320),(32,279,72,319),(33,278,73,318),(34,277,74,317),(35,276,75,316),(36,275,76,315),(37,274,77,314),(38,273,78,313),(39,272,79,312),(40,271,80,311),(81,167,121,207),(82,166,122,206),(83,165,123,205),(84,164,124,204),(85,163,125,203),(86,162,126,202),(87,161,127,201),(88,240,128,200),(89,239,129,199),(90,238,130,198),(91,237,131,197),(92,236,132,196),(93,235,133,195),(94,234,134,194),(95,233,135,193),(96,232,136,192),(97,231,137,191),(98,230,138,190),(99,229,139,189),(100,228,140,188),(101,227,141,187),(102,226,142,186),(103,225,143,185),(104,224,144,184),(105,223,145,183),(106,222,146,182),(107,221,147,181),(108,220,148,180),(109,219,149,179),(110,218,150,178),(111,217,151,177),(112,216,152,176),(113,215,153,175),(114,214,154,174),(115,213,155,173),(116,212,156,172),(117,211,157,171),(118,210,158,170),(119,209,159,169),(120,208,160,168)]])
86 conjugacy classes
class 1 2A 2B 2C 4A 4B 4C 4D 4E 4F 5A 5B 8A 8B 8C 8D 10A ··· 10F 16A ··· 16H 20A ··· 20H 40A ··· 40P 80A ··· 80AF order 1 2 2 2 4 4 4 4 4 4 5 5 8 8 8 8 10 ··· 10 16 ··· 16 20 ··· 20 40 ··· 40 80 ··· 80 size 1 1 1 1 2 2 40 40 40 40 2 2 2 2 2 2 2 ··· 2 2 ··· 2 2 ··· 2 2 ··· 2 2 ··· 2
86 irreducible representations
dim 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 type + + + + + + + + + + + - + + + + - image C1 C2 C2 C2 D4 D4 D5 D8 D8 D10 D10 Q32 D20 D20 D40 D40 Dic40 kernel C2×Dic40 Dic40 C2×C80 C2×Dic20 C40 C2×C20 C2×C16 C20 C2×C10 C16 C2×C8 C10 C8 C2×C4 C4 C22 C2 # reps 1 4 1 2 1 1 2 2 2 4 2 8 4 4 8 8 32
Matrix representation of C2×Dic40 in GL4(𝔽241) generated by
240 0 0 0 0 240 0 0 0 0 1 0 0 0 0 1
,
27 85 0 0 156 27 0 0 0 0 98 138 0 0 152 187
,
41 138 0 0 138 200 0 0 0 0 47 70 0 0 175 194
G:=sub<GL(4,GF(241))| [240,0,0,0,0,240,0,0,0,0,1,0,0,0,0,1],[27,156,0,0,85,27,0,0,0,0,98,152,0,0,138,187],[41,138,0,0,138,200,0,0,0,0,47,175,0,0,70,194] >;
C2×Dic40 in GAP, Magma, Sage, TeX
C_2\times {\rm Dic}_{40}
% in TeX
G:=Group("C2xDic40");
// GroupNames label
G:=SmallGroup(320,532);
// by ID
G=gap.SmallGroup(320,532);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-5,224,254,142,675,192,1684,102,12550]);
// Polycyclic
G:=Group<a,b,c|a^2=b^80=1,c^2=b^40,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
×
𝔽
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2021-05-10 02:39:07
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|
http://mathhelpforum.com/differential-equations/141707-d-e-mixing-problem.html
|
# Math Help - D.e mixing problem
1. ## D.e mixing problem
300 gallon tank contains 100 gallons of brine with a concentration of 1 pound of salt per gallon.a brine containing one half point of salt per gallon runs into the tank at rate of four gallons per minute nad the well stirred mixture drains from the tank at the same rate .when is the concentration in the tank 0.7 pound per gallon .
2. Let c be the concentration. Then c changes according to:
$\frac{dc}{dt}=\frac{\text{salt entering}-\text{salt leaving}}{100\text{ gallons}}$
The amount of salt entering the tank is $\frac{1}{2}*4$ pounds per minute.
The amount of salt leaving the tank is c*4 pounds per minute.
So you solve the differential equation and apply the initial condition c(0)=1 pound per gallon to evaluate the constant of integration, then set c(t)=0.7 and solve for t.
Post again in this thread if you are still having trouble.
- Hollywood
|
2015-08-01 19:37:57
|
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https://hunch.net/?p=1358
|
Aggregation of estimators, sparsity in high dimension and computational feasibility
(I’m channeling for Jean-Yves Audibert here, with some minor tweaking for clarity.)
Since Nemirovski’s Saint Flour lecture notes, numerous researchers have studied the following problem in least squares regression: predict as well as
(MS) the best of d given functions (like in prediction with expert advice; model = finite set of d functions)
(C) the best convex combination of these functions (i.e., model = convex hull of the d functions)
(L) the best linear combination of these functions (i.e., model = linear span of the d functions)
It is now well known (see, e.g., Sacha Tsybakov’s COLT’03 paper) that these tasks can be achieved since there exist estimators having an excess risk of order (log d)/n for (MS), min( sqrt((log d)/n), d/n ) for (C) and d/n for (L), where n is the training set size. Here, “risk” is amount of extra loss per example which may be suffered due to the choice of random sample.
The practical use of these results seems rather limited to trivial statements like: do not use the OLS estimator when the dimension d of the input vector is larger than n (here the d functions are the projections on each of the d components). Nevertheless, it provides a rather easy way to prove that there exists a learning algorithm having an excess risk of order s (log d)/n, with respect to the best linear combination of s of the d functions (s-sparse linear model). Indeed, it suffices to consider the algorithm which
1. cuts the training set into two parts, say of equal size for simplicity,
2. uses the first part to train linear estimators corresponding to every possible subset of s features. Here you can use your favorite linear estimator (the empirical risk minimizer on a compact set or robust but more involved ones are possible rather than the OLS), as long as it solves (L) with minimal excess risk.
3. uses the second part to predict as well as the “d choose s” linear estimators built on the first part. Here you choose your favorite aggregate solving (MS). The one I prefer is described in p.5 of my NIPS’07 paper, but you might prefer the progressive mixture rule or the algorithm of Guillaume Lecué and Shahar Mendelson. Note that empirical risk minimization and cross-validation completely fail for this task with excess risk of order sqrt((log d)/n) instead of (log d)/n.
It is an easy exercise to combine the different excess risk bounds and obtain that the above procedure achieves an excess risk of s (log d)/n. The nice thing compared to works on Lasso, Dantzig selectors and their variants is that you do not need all these assumptions saying that your features should be “not too much” correlated. Naturally, the important limitation of the above procedure, which is often encountered when using classical model selection approach, is its computational intractability. So this leaves open the following fundamental problem:
is it possible to design a computationally efficient algorithm with the s (log d)/n guarantee without assuming low correlation between the explanatory variables?
7 Replies to “Aggregation of estimators, sparsity in high dimension and computational feasibility”
1. If we want to consider computationally intractable methods, why not just compute the solution of the ell_0 penalized problem? Isn’t that minimax optimal?
2. Anonymous says:
Penalization proportional to the number of nonzero coefficients is indeed the basic algorithm. Typical criterion to tune this penalty are the well-known
Mallows Cp, AIC and BIC. The relevant references I know for the theoretical guarantees of this type of methods are (and are contained in) the work of Bunea, Tsybakov and Wegkamp (Aggregation for Gaussian regression, 2007, Annals of Statistics) and the work of Birgé and Massart (Minimal penalties for Gaussian model selection, 2007, Probability theory and related fields). To my knowledge, the results concerning the ell_0 regularization are not that good compared to the ones of the procedure in the post since the Cst (s log d) / n excess risk bound holds only when the regression function, that is the conditional expectation of the output knowing the input, is inside the model (i.e., is a linear combination of at most s of the d basis functions).
Besides they concern regression with fixed design (with Gaussian noise) and it is unclear how they generalize to the random design setting considered in the post.
Jean-Yves
1. There is some work on ell_0 penalized estimator for random design too. I don’t know of older literature, but the most recent one is due to Raskutti, Wainwright and Yu http://arxiv.org/abs/0910.2042. The comment about model being true is right, I don’t know of any analysis for that case, but it would be a little surprising if you cannot prove an excess risk bound there. The assumption about model being true is more in order to get convergence in parameter instead of convergence in risk, rather than being a fundamental limitation of the estimator in my understanding.
Alekh
3. Anonymous says:
The assumption about model being true is strong and does influence the rate. For instance, consider the MS problem described in the post. If we assume that one of the d functions is the true regression function, then it is easy to show that the empirical risk minimizer on the set of d functions has an excess risk of order (log d)/n, whereas, without this assumption, it only has a sqrt((log d)/n) excess risk rate (in bad cases; see, e.g., Theorem 2 of my NIPS’07 paper). Here it is likely that the same thing occurs: sqrt((s log d)/n) excess risk rate (instead of (s log d)/n) for ell_0 regularization if we do not assume that the conditional expectation of the output knowing the input is a linear combination of at most s of the d basis functions.
Jean-Yves
4. Dean Foster says:
I would argue that the issue isn’t whether the model is true or not, but the continuity of the space. So the MS problem isn’t going to work well for general LS due to the digital nature of the space. But for the problems C and L, i would be surprized if you could get much of a gap between the “model is true” bounds and the worst case bounds.
I’m curious if there are any approximation bounds on model selection that aren’t either exponential in s or assume some sort of orthoganlity. I’ve always taken that problem as simply NP complete and assumed we had to go with much weaker statements. Have I missed any cool new results? I.e. no assumption on colinearlity. But still Poly(s). And some sort of risk efficiency?
later,
dean
5. Anonymous says:
A small precision: the MS problem is mainly due to non-convexity. The problem of suboptimality of empirical risk minimization (and its variants) typically occurs if the model is non-convex.
Jean-Yves
6. sham says:
I believe there is an NP-Hardness result for this problem. See:
Natara jan, B. K. (1995). Sparse approximate solutions to linear systems. SIAM J. Comput.
24 227-234.
I vaguely recall an earlier hardness result as well, but not sure where I saw it.
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2022-08-15 19:46:23
|
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|
https://pos.sissa.it/336/249/
|
Volume 336 - XIII Quark Confinement and the Hadron Spectrum (Confinement2018) - H. Statistical Methods for Physics Analysis in the XXI Century
Pseudosignificances as figures of merit: a systematic study and exploration of Bayesian solutions
P. Vischia
Full text: pdf
Pre-published on: September 12, 2019
Published on: September 26, 2019
Abstract
Optimization problems in HEP often involve maximizing a measure of how sensitive is a given analysis to an hypothesis with respect to another hypothesis; the latter is referred to as $\it null$ hypothesis and in a frequentist framework is tested against the former, which is referred to as $\it alternative$ hypothesis.
In most cases, it is desirable to fully compute the expected frequentist significance, accounting for all sources of systematic uncertainty and interpreting the result as the real sensitivity of the analysis to the effect sought.
Sometimes, however, either computational or conceptual reasons can favour the use of different or approximate figures of merit, often collectively called "pseudosignificances", which exhibit different properties depending on the relationship between the hypotheses being tested.
This work will review the most common definitions of sensitivity (pseudosignificances), and compare them with the fully frequentist significances computed in toy analyses spanning a spectrum of typical HEP use cases. A connection will be made with the concept of Bayes Factor, and evidence values from Bayesian significance tests will be studied and evaluated in the same toy cases, attempting to build an improved approximate condition-aspecific figure of merit. Finally, an attempt will be made at transporting to the typical HEP cases a Bayesian solutions to the on-off problem developed in an astrophysics context.
DOI: https://doi.org/10.22323/1.336.0249
How to cite
Metadata are provided both in "article" format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in "proceeding" format which is more detailed and complete.
Open Access
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2020-12-04 15:22:34
|
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https://bookdown.org/ronsarafian/IntrotoDS/basics.html
|
# Chapter 3 R Basics
We now start with the basics of R. If you have any experience at all with R, you can probably skip this section.
First, make sure you work with the RStudio IDE. Some useful pointers for this IDE include:
• Ctrl+Return(Enter) to run lines from editor.
• Alt+Shift+k for RStudio keyboard shortcuts.
• Ctrl+r to browse the command history.
• Alt+Shift+j to navigate between code sections
• tab for auto-completion
• Code Folding:
• Alt+l collapse chunk.
• Alt+Shift+l unfold chunk.
• Alt+o collapse all.
• Alt+Shift+o unfold all.
• Alt+“-” for the assignment operator <-.
### 3.0.1 Other IDEs
Currently, I recommend RStudio, but here are some other IDEs:
1. Jupyter Lab: a very promising IDE, originally designed for Python, that also supports R. At the time of writing, it seems that RStudio is more convenient for R, but it is definetly an IDE to follow closely. See Max Woolf’s review.
2. Eclipse: If you are a Java programmer, you are probably familiar with Eclipse, which does have an R plugin: StatEt.
3. Emacs: If you are an Emacs fan, you can find an R plugin: ESS.
4. Vim: Vim-R.
5. Visual Studio also supports R. If you need R for commercial purposes, it may be worthwhile trying Microsoft’s R, instead of the usual R. See here for installation instructions.
## 3.1 File types
The file types you need to know when using R are the following:
• .R: An ASCII text file containing R scripts only.
• .Rmd: An ASCII text file. If opened in RStudio can be run as an R-Notebook or compiled using knitr, bookdown, etc.
## 3.2 Simple calculator
R can be used as a simple calculator. Create a new R Notebook (.Rmd file) within RStudio using File-> New -> R Notebook, and run the following commands.
10+5
## [1] 15
70*81
## [1] 5670
2**4
## [1] 16
2^4
## [1] 16
log(10)
## [1] 2.302585
log(16, 2)
## [1] 4
log(1000, 10)
## [1] 3
## 3.3 Probability calculator
R can be used as a probability calculator. You probably wish you knew this when you did your Intro To Probability classes.
The Binomial density function:
dbinom(x=3, size=10, prob=0.5) # Compute P(X=3) for X~B(n=10, p=0.5)
## [1] 0.1171875
Notice that arguments do not need to be named explicitly
dbinom(3, 10, 0.5)
## [1] 0.1171875
The Binomial cumulative distribution function (CDF):
pbinom(q=3, size=10, prob=0.5) # Compute P(X<=3) for X~B(n=10, p=0.5)
## [1] 0.171875
The Binomial quantile function:
qbinom(p=0.1718, size=10, prob=0.5) # For X~B(n=10, p=0.5) returns k such that P(X<=k)=0.1718
## [1] 3
Generate random variables:
rbinom(n=10, size=10, prob=0.5)
## [1] 4 4 5 7 4 7 7 6 6 3
R has many built-in distributions. Their names may change, but the prefixes do not:
• d prefix for the density function.
• p prefix for the cummulative distribution function (CDF).
• q prefix for the quantile function (i.e., the inverse CDF).
• r prefix to generate random samples.
Demonstrating this idea, using the CDF of several popular distributions:
• pbinom() for the Binomial CDF.
• ppois() for the Poisson CDF.
• pnorm() for the Gaussian CDF.
• pexp() for the Exponential CDF.
For more information see ?distributions.
## 3.4 Getting Help
One of the most important parts of working with a language, is to know where to find help. R has several in-line facilities, besides the various help resources in the R ecosystem.
Get help for a particular function.
?dbinom
help(dbinom)
If you don’t know the name of the function you are looking for, search local help files for a particular string:
??binomial
help.search('dbinom')
Or load a menu where you can navigate local help in a web-based fashion:
help.start()
## 3.5 Variable Asignment
Assignment of some output into an object named “x”:
x = rbinom(n=10, size=10, prob=0.5) # Works. Bad style.
x <- rbinom(n=10, size=10, prob=0.5)
If you are familiar with other programming languages you may prefer the = assignment rather than the <- assignment. We recommend you make the effort to change your preferences. This is because thinking with <- helps to read your code, distinguishes between assignments and function arguments: think of function(argument=value) versus function(argument<-value). It also helps understand special assignment operators such as <<- and ->.
Remark. Style: We do not discuss style guidelines in this text, but merely remind the reader that good style is extremely important. When you write code, think of other readers, but also think of future self. See Hadley’s style guide for more.
To print the contents of an object just type its name
x
## [1] 7 4 6 3 4 5 2 5 7 4
which is an implicit call to
print(x)
## [1] 7 4 6 3 4 5 2 5 7 4
Alternatively, you can assign and print simultaneously using parenthesis.
(x <- rbinom(n=10, size=10, prob=0.5)) # Assign and print.
## [1] 5 5 5 4 6 6 6 3 6 5
Operate on the object
mean(x) # compute mean
## [1] 5.1
var(x) # compute variance
## [1] 0.9888889
hist(x) # plot histogram
R saves every object you create in RAM1. The collection of all such objects is the workspace which you can inspect with
ls()
## [1] "a" "A"
## [3] "allphat" "allphat_m"
## [5] "allq" "allqp"
## [7] "allqp_m" "auto"
## [9] "b" "B"
## [11] "big1" "borders"
## [13] "borders_data" "bst1"
## [15] "bst2" "bstSparse"
## [17] "c" "clean.example"
## [19] "compute_remoteness" "condition1"
## [21] "condition2" "coords"
## [23] "coords_trn" "coords_tst"
## [25] "createmap" "CV_LME_LGP"
## [27] "CV_split" "d"
## [29] "db" "db_test"
## [31] "db_train" "db_trn"
## [33] "db_tst" "db0us"
## [35] "df" "di"
## [37] "distributions1" "distributions2"
## [39] "distributions3" "dtest"
## [41] "dtest_nw" "dtrain"
## [43] "dtrain_nw" "e"
## [45] "estimate_dist" "EuStockMarkets"
## [47] "evalerror" "example1"
## [49] "example1_1" "example1_2"
## [51] "example1_3" "example2"
## [53] "features" "fib"
## [55] "fileURL" "frame1"
## [57] "glm.1" "grid_n"
## [59] "i" "in_train"
## [61] "intest" "intrn"
## [63] "j" "ker"
## [65] "long" "loss"
## [67] "m" "m_glm"
## [69] "m_lm" "m_lmm"
## [71] "m_xgb" "make_data"
## [73] "make_distributions" "missing.example"
## [75] "my.data" "my.sum"
## [77] "my.sum.2" "nontrn"
## [79] "num_round" "p"
## [81] "p_xgb" "p1"
## [83] "p1_xgb" "p2"
## [85] "p2_xgb" "p3_lmm"
## [87] "param1" "param2"
## [89] "phat" "Pima.te"
## [91] "pp" "preproc"
## [93] "q" "quantile.25"
## [95] "results_remotness_plot" "risk"
## [97] "rlogo" "run_cv"
## [99] "s" "sample_over_space"
## [101] "sample_P" "sample_Q0"
## [103] "scoping" "sigmoid"
## [105] "start" "stn"
## [107] "stn_trn" "stn_tst"
## [109] "t" "temp.file.name"
## [111] "test_data" "test_inla_LGP"
## [113] "test_labels" "the.list"
## [115] "time1" "time2"
## [117] "time3" "tirgul1"
## [119] "today" "train_data"
## [121] "train_inla_LGP" "train_labels"
## [123] "train_weights" "watchlist1"
## [125] "watchlist2" "weight.factor"
## [127] "weightedloss" "x"
## [129] "X" "X_tst"
## [131] "xindex" "y"
## [133] "y_hat_glm" "y_hat_glm_binar"
## [135] "y_hat_lm" "y_hat_lm_binar"
## [137] "y_tst" "yhat_glm"
## [139] "yhat_glm_binar" "yhat_glm_binar_0.3"
## [141] "yindex"
or with Ctrl+8 in RStudio.
If you lost your object, you can use ls with a text pattern to search for it
ls(pattern='x')
## [1] "clean.example" "example1" "example1_1"
## [4] "example1_2" "example1_3" "example2"
## [7] "m_xgb" "missing.example" "p_xgb"
## [10] "p1_xgb" "p2_xgb" "x"
## [13] "xindex" "yindex"
To remove objects from the workspace:
rm(x) # remove variable
ls() # verify
## [1] "a" "A"
## [3] "allphat" "allphat_m"
## [5] "allq" "allqp"
## [7] "allqp_m" "auto"
## [9] "b" "B"
## [11] "big1" "borders"
## [13] "borders_data" "bst1"
## [15] "bst2" "bstSparse"
## [17] "c" "clean.example"
## [19] "compute_remoteness" "condition1"
## [21] "condition2" "coords"
## [23] "coords_trn" "coords_tst"
## [25] "createmap" "CV_LME_LGP"
## [27] "CV_split" "d"
## [29] "db" "db_test"
## [31] "db_train" "db_trn"
## [33] "db_tst" "db0us"
## [35] "df" "di"
## [37] "distributions1" "distributions2"
## [39] "distributions3" "dtest"
## [41] "dtest_nw" "dtrain"
## [43] "dtrain_nw" "e"
## [45] "estimate_dist" "EuStockMarkets"
## [47] "evalerror" "example1"
## [49] "example1_1" "example1_2"
## [51] "example1_3" "example2"
## [53] "features" "fib"
## [55] "fileURL" "frame1"
## [57] "glm.1" "grid_n"
## [59] "i" "in_train"
## [61] "intest" "intrn"
## [63] "j" "ker"
## [65] "long" "loss"
## [67] "m" "m_glm"
## [69] "m_lm" "m_lmm"
## [71] "m_xgb" "make_data"
## [73] "make_distributions" "missing.example"
## [75] "my.data" "my.sum"
## [77] "my.sum.2" "nontrn"
## [79] "num_round" "p"
## [81] "p_xgb" "p1"
## [83] "p1_xgb" "p2"
## [85] "p2_xgb" "p3_lmm"
## [87] "param1" "param2"
## [89] "phat" "Pima.te"
## [91] "pp" "preproc"
## [93] "q" "quantile.25"
## [95] "results_remotness_plot" "risk"
## [97] "rlogo" "run_cv"
## [99] "s" "sample_over_space"
## [101] "sample_P" "sample_Q0"
## [103] "scoping" "sigmoid"
## [105] "start" "stn"
## [107] "stn_trn" "stn_tst"
## [109] "t" "temp.file.name"
## [111] "test_data" "test_inla_LGP"
## [113] "test_labels" "the.list"
## [115] "time1" "time2"
## [117] "time3" "tirgul1"
## [119] "today" "train_data"
## [121] "train_inla_LGP" "train_labels"
## [123] "train_weights" "watchlist1"
## [125] "watchlist2" "weight.factor"
## [127] "weightedloss" "X"
## [129] "X_tst" "xindex"
## [131] "y" "y_hat_glm"
## [133] "y_hat_glm_binar" "y_hat_lm"
## [135] "y_hat_lm_binar" "y_tst"
## [137] "yhat_glm" "yhat_glm_binar"
## [139] "yhat_glm_binar_0.3" "yindex"
You may think that if an object is removed then its memory is freed. This is almost true, and depends on a negotiation mechanism between R and the operating system. R’s memory management is discussed in Chapter ??.
## 3.6 Missing
Unlike typically programming, when working with real life data, you may have missing values: measurements that were simply not recorded/stored/etc. R has rather sophisticated mechanisms to deal with missing values. It distinguishes between the following types:
1. NA: Not Available entries.
2. NaN: Not a number.
R tries to defend the analyst, and return an error, or NA when the presence of missing values invalidates the calculation:
missing.example <- c(10,11,12,NA)
mean(missing.example)
## [1] NA
Most functions will typically have an inner mechanism to deal with these. In the mean function, there is an na.rm argument, telling R how to Remove NAs.
mean(missing.example, na.rm = TRUE)
## [1] 11
A more general mechanism is removing these manually:
clean.example <- na.omit(missing.example)
mean(clean.example)
## [1] 11
## 3.7 Piping
Because R originates in Unix and Linux environments, it inherits much of its flavor. Piping is an idea taken from the Linux shell which allows to use the output of one expression as the input to another. Piping thus makes code easier to read and write.
Prerequisites:
library(magrittr) # load the piping functions
x <- rbinom(n=1000, size=10, prob=0.5) # generate some toy data
Examples
x %>% var() # Instead of var(x)
x %>% hist() # Instead of hist(x)
x %>% mean() %>% round(2) %>% add(10)
The next example2 demonstrates the benefits of piping. The next two chunks of code do the same thing. Try parsing them in your mind:
# Functional (onion) style
car_data <-
transform(aggregate(. ~ cyl,
data = subset(mtcars, hp > 100),
FUN = function(x) round(mean(x, 2))),
kpl = mpg*0.4251)
# Piping (magrittr) style
car_data <-
mtcars %>%
subset(hp > 100) %>%
aggregate(. ~ cyl, data = ., FUN = . %>% mean %>% round(2)) %>%
transform(kpl = mpg %>% multiply_by(0.4251)) %>%
print
Tip: RStudio has a keyboard shortcut for the %>% operator. Try Ctrl+Shift+m.
## 3.8 Vector Creation and Manipulation
The most basic building block in R is the vector. We will now see how to create them, and access their elements (i.e. subsetting). Here are three ways to create the same arbitrary vector:
c(10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21) # manually
10:21 # the : operator
seq(from=10, to=21, by=1) # the seq() function with "by"
seq(from=10, to=21, len=12) # the seq() function with "len"
Let’s assign it to the object named “x”:
x <- c(10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21)
Operations usually work element-wise:
x+2
## [1] 12 13 14 15 16 17 18 19 20 21 22 23
x*2
## [1] 20 22 24 26 28 30 32 34 36 38 40 42
x^2
## [1] 100 121 144 169 196 225 256 289 324 361 400 441
sqrt(x)
## [1] 3.162278 3.316625 3.464102 3.605551 3.741657 3.872983 4.000000
## [8] 4.123106 4.242641 4.358899 4.472136 4.582576
log(x)
## [1] 2.302585 2.397895 2.484907 2.564949 2.639057 2.708050 2.772589
## [8] 2.833213 2.890372 2.944439 2.995732 3.044522
## 3.9 Search Paths and Packages
R can be easily extended with packages, which are merely a set of documented functions, which can be loaded or unloaded conveniently. Let’s look at the function read.csv. We can see its contents by calling it without arguments:
read.csv
## function (file, header = TRUE, sep = ",", quote = "\"", dec = ".",
## fill = TRUE, comment.char = "", ...)
## dec = dec, fill = fill, comment.char = comment.char, ...)
## <bytecode: 0x55fc9026d6a0>
## <environment: namespace:utils>
Never mind what the function does. Note the environment: namespace:utils line at the end. It tells us that this function is part of the utils package. We did not need to know this because it is loaded by default. Here are some packages that I have currently loaded:
head(search())
## [1] ".GlobalEnv" "package:gridExtra" "package:reshape2"
## [4] "package:RCurl" "package:bitops" "package:mlbench"
Other packages can be loaded via the library function, or downloaded from the internet using the install.packages function before loading with library. R’s package import mechanism is quite powerful, and is one of the reasons for R’s success.
## 3.10 Simple Plotting
R has many plotting facilities as we will further detail in the Plotting Chapter 6. We start with the simplest facilities, namely, the plot function from the graphics package, which is loaded by default.
x<- 1:100
y<- 3+sin(x)
plot(x = x, y = y) # x,y syntax
Given an x argument and a y argument, plot tries to present a scatter plot. We call this the x,y syntax. R has another unique syntax to state functional relations. We call y~x the “tilde” syntax, which originates in works of Wilkinson and Rogers (1973) and was adopted in the early days of S.
plot(y ~ x) # y~x syntax
The syntax y~x is read as “y is a function of x”. We will prefer the y~x syntax over the x,y syntax since it is easier to read, and will be very useful when we discuss more complicated models.
Here are some arguments that control the plot’s appearance. We use type to control the plot type, main to control the main title.
plot(y~x, type='l', main='Plotting a connected line')
We use xlab for the x-axis label, ylab for the y-axis.
plot(y~x, type='h', main='Sticks plot', xlab='Insert x axis label', ylab='Insert y axis label')
We use pch to control the point type.
plot(y~x, pch=5) # Point type with pcf
We use col to control the color, cex for the point size, and abline to add a straight line.
plot(y~x, pch=10, type='p', col='blue', cex=4)
abline(3, 0.002)
For more plotting options run these
example(plot)
example(points)
?plot
help(package='graphics')
When your plotting gets serious, go to Chapter 6.
## 3.11 Object Types
We already saw that the basic building block of R objects is the vector. Vectors can be of the following types:
• character Where each element is a string, i.e., a sequence of alphanumeric symbols.
• numeric Where each element is a real number in double precision floating point format.
• integer Where each element is an integer.
• logical Where each element is either TRUE, FALSE, or NA3
• complex Where each element is a complex number.
• list Where each element is an arbitrary R object.
• factor Factors are not actually vector objects, but they feel like such. They are used to encode any finite set of values. This will be very useful when fitting linear model because they include information on contrasts, i.e., on the encoding of the factors levels. You should always be alert and recall when you are dealing with a factor or with a character vector. They have different behaviors.
• Date for dates
• "POSIXct and POSIXt for times
Vectors can be combined into larger objects. A matrix can be thought of as the binding of several vectors of the same type. In reality, a matrix is merely a vector with a dimension attribute, that tells R to read it as a matrix and not a vector.
## 3.12 Vectors and Matrices Linear Algebra
Vectors can be involved in algebric operations. Here are some examples for vectors multiplications:
x <- rnorm(4) # generating 4 standard normal random variables
y <- exp(-x) # taking the exponent of x
x * y
## [1] -1.5412664 0.2173503 -2.1436542 0.1689432
x %*% y
## [,1]
## [1,] -3.298627
t(x) %*% y
## [,1]
## [1,] -3.298627
x %*% t(y)
## [,1] [,2] [,3] [,4]
## [1,] -1.5412664 -0.5513476 -1.7862644 -0.5988587
## [2,] 0.6075926 0.2173503 0.7041748 0.2360800
## [3,] -1.8496379 -0.6616595 -2.1436542 -0.7186764
## [4,] 0.4348046 0.1555399 0.5039206 0.1689432
Note that * implement an entrywise product, where %*% is a dot product. While not specifing whether the vectors are horizontal or vertical, R treats the operation as $$(1 \times n) * (n \times 1)$$. Note that t() is the vector/ matrix transpose.
The same hold for vector - matrices multiplication. Take a look at the following examples:
(x <- rep(1,5))
## [1] 1 1 1 1 1
(A <- matrix(data = rep(1:5,5), nrow = 5, ncol = 5, byrow = TRUE)) # generating a 5 by 5 matrix, where each row is the vector 1:5
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 2 3 4 5
## [2,] 1 2 3 4 5
## [3,] 1 2 3 4 5
## [4,] 1 2 3 4 5
## [5,] 1 2 3 4 5
x * A # equivalent to column-binding every x * A[,i] for i in 1:5
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1 2 3 4 5
## [2,] 1 2 3 4 5
## [3,] 1 2 3 4 5
## [4,] 1 2 3 4 5
## [5,] 1 2 3 4 5
x %*% A # (1X5) * (5X5) => (1X5)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 5 10 15 20 25
A %*% x # (5X5) * (5X1) => (1X5)
## [,1]
## [1,] 15
## [2,] 15
## [3,] 15
## [4,] 15
## [5,] 15
Note that R transform x to the correct (possible) dimension. if you want to fix the dimention of a vector, turn it to a column/row matrix (as.matrix(x)/as.matrix(t(x))). We now move to some matrix multiplications:
0.5 * A
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.5 1 1.5 2 2.5
## [2,] 0.5 1 1.5 2 2.5
## [3,] 0.5 1 1.5 2 2.5
## [4,] 0.5 1 1.5 2 2.5
## [5,] 0.5 1 1.5 2 2.5
A %*% t(A)
## [,1] [,2] [,3] [,4] [,5]
## [1,] 55 55 55 55 55
## [2,] 55 55 55 55 55
## [3,] 55 55 55 55 55
## [4,] 55 55 55 55 55
## [5,] 55 55 55 55 55
t(x) %*% A %*% x
## [,1]
## [1,] 75
We can perform algebric operations even with vectors and matrices that are of logical class:
(big1 <- 1:3>1.5) # logical vector indicate whether elements in 1:3 are greater than 1.5
## [1] FALSE TRUE TRUE
(B <- matrix(data = sample(c(TRUE, FALSE), 9, replace = T), nrow = 3, ncol = 3))
## [,1] [,2] [,3]
## [1,] TRUE FALSE FALSE
## [2,] FALSE TRUE TRUE
## [3,] TRUE FALSE FALSE
big1 * B # columns-wise
## [,1] [,2] [,3]
## [1,] 0 0 0
## [2,] 0 1 1
## [3,] 1 0 0
Note that R transform the output to 0-1 integer matrix.
## 3.13 Data Frames
If vectors of different types (but same length) are binded, we get a data.frame which is the most fundamental object in R for data analysis. Data frames are brilliant, but a lot has been learned since their invention. They have thus been extended in recent years with the tbl class, pronounced [Tibble] (https://cran.r-project.org/web/packages/tibble/vignettes/tibble.html), and the data.table class.
The latter is discussed in Chapter 4, and is strongly recommended.
Creating a simple data frame:
x<- 1:10
y<- 3 + sin(x)
frame1 <- data.frame(x=x, sin=y)
Let’s inspect our data frame:
head(frame1)
## x sin
## 1 1 3.841471
## 2 2 3.909297
## 3 3 3.141120
## 4 4 2.243198
## 5 5 2.041076
## 6 6 2.720585
Now using the RStudio Excel-like viewer:
frame1 %>% View()
We highly advise against editing the data this way since there will be no documentation of the changes you made. Always transform your data using scripts, so that everything is documented.
Verifying this is a data frame:
class(frame1) # the object is of type data.frame
## [1] "data.frame"
Check the dimension of the data
dim(frame1)
## [1] 10 2
Note that checking the dimension of a vector is different than checking the dimension of a data frame.
length(x)
## [1] 10
The length of a data.frame is merely the number of columns.
length(frame1)
## [1] 2
## 3.14 Exctraction
R provides many ways to subset and extract elements from vectors and other objects. The basics are fairly simple, but not paying attention to the “personality” of each extraction mechanism may cause you a lot of headache.
For starters, extraction is done with the [ operator. The operator can take vectors of many types.
Extracting element with by integer index:
frame1[1, 2] # exctract the element in the 1st row and 2nd column.
## [1] 3.841471
Extract column by index:
frame1[,1]
## [1] 1 2 3 4 5 6 7 8 9 10
Extract row by index:
frame1[7,]
## x sin
## 7 7 3.656987
Extract column by name:
frame1[, 'sin']
## [1] 3.841471 3.909297 3.141120 2.243198 2.041076 2.720585 3.656987
## [8] 3.989358 3.412118 2.455979
As a general rule, extraction with [ will conserve the class of the parent object. There are, however, exceptions. Notice the extraction mechanism and the class of the output in the following examples.
class(frame1[, 'sin']) # extracts a column vector
## [1] "numeric"
class(frame1['sin']) # extracts a data frame
## [1] "data.frame"
class(frame1[,1:2]) # extracts a data frame
## [1] "data.frame"
class(frame1[2]) # extracts a data frame
## [1] "data.frame"
class(frame1[2, ]) # extract a data frame
## [1] "data.frame"
class(frame1$sin) # extracts a column vector ## [1] "numeric" The subset() function does the same subset(frame1, select=sin) subset(frame1, select=2) subset(frame1, select= c(2,0)) We can also subset by conditioning on variables values. Here are two examples: subset(frame1, sin < mean(frame1$sin))
## x sin
## 4 4 2.243198
## 5 5 2.041076
## 6 6 2.720585
## 10 10 2.455979
frame1[frame1$sin < mean(frame1$sin),]
## x sin
## 4 4 2.243198
## 5 5 2.041076
## 6 6 2.720585
## 10 10 2.455979
In the second exaple, we created a logical vector and used it for subsetting. Let’s see this:
frame1$sin < mean(frame1$sin)
## [1] FALSE FALSE FALSE TRUE TRUE TRUE FALSE FALSE FALSE TRUE
We can use this approach to create conditions. Here is another examples:
condition1 <- frame1$sin < mean(frame1$sin)
condition2 <- frame1$x %in% c(2,3,4,9,10) # the %in% operator is a logical for whether the elements of the first vector are also elements in the second. frame1[condition1,] # only condition1==TRUE ## x sin ## 4 4 2.243198 ## 5 5 2.041076 ## 6 6 2.720585 ## 10 10 2.455979 frame1[!condition1,] # only condition1==FALSE ## x sin ## 1 1 3.841471 ## 2 2 3.909297 ## 3 3 3.141120 ## 7 7 3.656987 ## 8 8 3.989358 ## 9 9 3.412118 frame1[condition2,] # only condition2==TRUE ## x sin ## 2 2 3.909297 ## 3 3 3.141120 ## 4 4 2.243198 ## 9 9 3.412118 ## 10 10 2.455979 frame1[condition1 & condition2,] # only condition1==TRUE and condition2==TRUE ## x sin ## 4 4 2.243198 ## 10 10 2.455979 frame1[condition1 | condition2,] # only (condition1==TRUE or condition2==TRUE) ## x sin ## 2 2 3.909297 ## 3 3 3.141120 ## 4 4 2.243198 ## 5 5 2.041076 ## 6 6 2.720585 ## 9 9 3.412118 ## 10 10 2.455979 If you want to force the stripping of the class attribute when extracting, try the [[ mechanism instead of [. a <- frame1[1] # [ extraction b <- frame1[[1]] # [[ extraction class(a)==class(b) # objects have differing classes ## [1] FALSE a==b # objects are element-wise identical ## x ## [1,] TRUE ## [2,] TRUE ## [3,] TRUE ## [4,] TRUE ## [5,] TRUE ## [6,] TRUE ## [7,] TRUE ## [8,] TRUE ## [9,] TRUE ## [10,] TRUE The different types of output classes cause different behaviors. Compare the behavior of [ on seemingly identical objects. frame1[1][1] ## x ## 1 1 ## 2 2 ## 3 3 ## 4 4 ## 5 5 ## 6 6 ## 7 7 ## 8 8 ## 9 9 ## 10 10 frame1[[1]][1] ## [1] 1 Adding variables to a data.frame can be done by assigning new vectors. The power of the data.frame object is in that it accepts almost any type of vectors, i.e. integers, numericals, logicals, factors and characters. frame1$newvar1 <- frame1$x - frame1$sin
frame1$newvar2 <- frame1$newvar1 > 0
frame1$newvar3 <- ifelse(frame1$newvar2, "good", "bad")
frame1$newvar4 <- factor(frame1$newvar1>3 & frame1$newvar3=="good", labels = c("level1","level2")) head(frame1) ## x sin newvar1 newvar2 newvar3 newvar4 ## 1 1 3.841471 -2.841471 FALSE bad level1 ## 2 2 3.909297 -1.909297 FALSE bad level1 ## 3 3 3.141120 -0.141120 FALSE bad level1 ## 4 4 2.243198 1.756802 TRUE good level1 ## 5 5 2.041076 2.958924 TRUE good level1 ## 6 6 2.720585 3.279415 TRUE good level2 You can get a quick summary of the data.frame with summary function. A more compact display can be achived with the str function, provide you also the class of each column, the first values, and some more useful information. summary(frame1) ## x sin newvar1 newvar2 ## Min. : 1.00 Min. :2.041 Min. :-2.8415 Mode :logical ## 1st Qu.: 3.25 1st Qu.:2.522 1st Qu.: 0.3334 FALSE:3 ## Median : 5.50 Median :3.277 Median : 3.1192 TRUE :7 ## Mean : 5.50 Mean :3.141 Mean : 2.3589 ## 3rd Qu.: 7.75 3rd Qu.:3.795 3rd Qu.: 3.8437 ## Max. :10.00 Max. :3.989 Max. : 7.5440 ## newvar3 newvar4 ## Length:10 level1:5 ## Class :character level2:5 ## Mode :character ## ## ## str(frame1) ## 'data.frame': 10 obs. of 6 variables: ##$ x : int 1 2 3 4 5 6 7 8 9 10
## $sin : num 3.84 3.91 3.14 2.24 2.04 ... ##$ newvar1: num -2.841 -1.909 -0.141 1.757 2.959 ...
## $newvar2: logi FALSE FALSE FALSE TRUE TRUE TRUE ... ##$ newvar3: chr "bad" "bad" "bad" "good" ...
## $newvar4: Factor w/ 2 levels "level1","level2": 1 1 1 1 1 2 2 2 2 2 If you want to learn more about subsetting see Hadley’s guide. ## 3.15 Augmentations of the data.frame class As previously mentioned, the data.frame class has been extended in recent years. The best known extensions are the data.table and the tbl. For beginners, it is important to know R’s basics, so we keep focusing on data frames. For more advanced users, I recommend learning the (amazing) data.table syntax. ## 3.16 Data Import and Export For any practical purpose, you will not be generating your data manually. R comes with many importing and exporting mechanisms which we now present. If, however, you do a lot of data “munging”, make sure to see Hadley-verse Chapter ??. If you work with MASSIVE data sets, read the Memory Efficiency Chapter ??. Sometimes our data is saved in our local directory. Before moving to data importing, we need to know what how to get and set R’s active directory: getwd() #What is the working directory? setwd("~/folder1/folder2") #Setting the working directory in Linux setwd("./folder3") The dot sign "." indicate a relative path to the curent working directory. the "~" the home directory. In Windows this is a bit different, e.g. setwd("C:\\Users\\User\\folder1"). ### 3.16.1 Reading data files The read.table function is the main importing workhorse. It can import directly from the web. URL <- 'http://statweb.stanford.edu/~tibs/ElemStatLearn/datasets/bone.data' tirgul1 <- read.table(URL) Alternatively, load from a local directory: tirgul1 <- read.table('data/bone.data') Always look at the imported result! head(tirgul1) ## V1 V2 V3 V4 ## 1 idnum age gender spnbmd ## 2 1 11.7 male 0.01808067 ## 3 1 12.7 male 0.06010929 ## 4 1 13.75 male 0.005857545 ## 5 2 13.25 male 0.01026393 ## 6 2 14.3 male 0.2105263 Ohh dear. read.,table tried to guess the structure of the input, but failed to recognize the header row. Set it manually with header=TRUE: tirgul1 <- read.table('data/bone.data', header = TRUE) head(tirgul1) Other important parameters: • na.strings - set the character represent a missing value • nrows - how many rows to read • skip - number of lines to skip before reading A faster alternative for reading data frames is the fst::read.fst() from fst package, but make sure before that the data file is of the .fst format. ### 3.16.2 Export as CSV Let’s write a simple file so that we have something to import head(airquality) # examine the data to export ## Ozone Solar.R Wind Temp Month Day ## 1 41 190 7.4 67 5 1 ## 2 36 118 8.0 72 5 2 ## 3 12 149 12.6 74 5 3 ## 4 18 313 11.5 62 5 4 ## 5 NA NA 14.3 56 5 5 ## 6 28 NA 14.9 66 5 6 temp.file.name <- tempfile() # get some arbitrary file name write.csv(x = airquality, file = temp.file.name) # export Now let’s import the exported file. Being a .csv file, I can use read.csv instead of read.table. my.data<- read.csv(file=temp.file.name) # import head(my.data) # verify import ## X Ozone Solar.R Wind Temp Month Day ## 1 1 41 190 7.4 67 5 1 ## 2 2 36 118 8.0 72 5 2 ## 3 3 12 149 12.6 74 5 3 ## 4 4 18 313 11.5 62 5 4 ## 5 5 NA NA 14.3 56 5 5 ## 6 6 28 NA 14.9 66 5 6 Remark. Windows users may need to use “\” instead of “/”. ### 3.16.3 Export non-CSV files You can export your R objects in endlessly many ways: If instead of the comma delimiter in .csv you want other column delimiters, look into ?write.table. If you are exporting only for R users, you can consider exporting as binary objects with saveRDS, feather::write_feather, or fst::write.fst. See (http://www.fstpackage.org/) for a comparison. ### 3.16.4 Reading source files With RCurl packge we can read webpages source. The getURL function is used to retrieve the source of a webpage, which is especially useful for retrieving pages for data processing (also known as web scraping / web harvesting / web data extraction). Example: library(RCurl) rlogo <- getURL("https://www.r-project.org/logo/") What can we do with this data? Well, if we know how this text file is writen we can extract some relevant data. Web scraping is cool, but not in our scope. More on this and on extracting data from the web can be found here ### 3.16.5 Reading From Text Files Sometimes the data has the shape of data.frame but stored as a text file. We can also call the read.table function to import such text files. If you care about your sanity, see ?read.table before starting imports. Some notable properties of the function: • read.table will try to guess column separators (tab, comma, etc.) • read.table will try to guess if a header row is present. • read.table will convert character vectors to factors unless told not to using the stringsAsFactors=FALSE argument. • The output of read.table needs to be explicitly assigned to an object for it to be saved. ### 3.16.6 Download a file from the web If you have the file URL, you can download a file and save it in a desired destination: fileURL <- "https://data.cityofnewyork.us/api/views/kku6-nxdu/rows.csv?accessType=DOWNLOAD" download.file(fileURL, destfile = "./data/Demographic.csv", method = "curl") # check the file has indeed been downloaded with list.files("./data") ### 3.16.7 Writing Data to Text Files The function write.table is the exporting counterpart of read.table. ### 3.16.8 .XLS(X) files Strongly recommended to convert to .csv in Excel, and then import as csv. If you still insist see the xlsx package. ### 3.16.9 Massive files The above importing and exporting mechanisms were not designed for massive files. See the section on the data.table package (4), or read the sections Sparse Representation and Memory Efficiency (Out-of-Ram Algorithms) in Johnathan’s R BGU course for more on working with massive data files. ### 3.16.10 Databases R does not need to read from text files; it can read directly from a database. This is very useful since it allows the filtering, selecting and joining operations to rely on the database’s optimized algorithms. Then again, if you will only be analyzing your data with R, you are probably better of by working from a file, without the databases’ overhead. See the SQL Chapter for more on this matter. ### 3.16.11 Reading images data files See the excellent magick package ## 3.17 Functions One of the most basic building blocks of programming is the ability of writing your own functions. A function in R, like everything else, is an object accessible using its name. We first define a simple function that sums its two arguments my.sum <- function(x,y) { return(x+y) } my.sum(10,2) ## [1] 12 From this example you may notice that: • The function function tells R to construct a function object. • Unlike some programming languages, a period (.) is allowed as part of an object’s name. • The arguments of the function, i.e. (x,y), need to be named but we are not required to specify their class. This makes writing functions very easy, but it is also the source of many bugs, and slowness of R compared to type declaring languages (C, Fortran,Java,…). • A typical R function does not change objects4 but rather creates new ones. To save the output of my.sum we will need to assign it using the <- operator. Here is a (slightly) more advanced function: my.sum.2 <- function(x, y , absolute=FALSE) { if(absolute==TRUE) { result <- abs(x+y) } else{ result <- x+y } result } my.sum.2(-10,2,TRUE) ## [1] 8 Things to note: • if(condition){expression1} else{expression2} does just what the name suggests. • The function will output its last evaluated expression. You don’t need to use the return function explicitly. • Using absolute=FALSE sets the default value of absolute to FALSE. This is overridden if absolute is stated explicitly in the function call. An important behavior of R is the scoping rules. This refers to the way R seeks for variables used in functions. As a rule of thumb, R will first look for variables inside the function and if not found, will search for the variable values in outer environments5. Think of the next example. a <- 1 b <- 2 x <- 3 scoping <- function(a,b){ a+b+x } scoping(10,11) ## [1] 24 ## 3.18 Looping The real power of scripting is when repeated operations are done by iteration. R supports the usual for, while, and repated loops. Here is an embarrassingly simple example for (i in 1:5){ print(i) } ## [1] 1 ## [1] 2 ## [1] 3 ## [1] 4 ## [1] 5 A slightly more advanced example, is vector multiplication result <- 0 n <- 1e3 x <- 1:n y <- (1:n)/n for(i in 1:n){ result <- result+ x[i]*y[i] } Remark. Vector Operations: You should NEVER write your own vector and matrix products like in the previous example. Only use existing facilities such as %*%, sum(), etc. Remark. Parallel Operations: If you already know that you will be needing to parallelize your work, get used to working with foreach loops in the foreach package, rather then regular for loops. ## 3.19 Apply For applying the same function to a set of elements, there is no need to write an explicit loop. This is such en elementary operation that every programming language will provide some facility to apply, or map the function to all elements of a set. R provides several facilities to perform this. The most basic of which is lapply which applies a function over all elements of a list, and return a list of outputs: the.list <- list(1,'a',mean) # a list of 3 elements from different calsses lapply(X = the.list, FUN = class) # apply the function class to each elements ## [[1]] ## [1] "numeric" ## ## [[2]] ## [1] "character" ## ## [[3]] ## [1] "function" sapply(X = the.list, FUN = class) # lapply with cleaned output ## [1] "numeric" "character" "function" What is the function you are using requires some arguments? One useful trick is to create your own function that takes only one argument: quantile.25 <- function(x) quantile(x,0.25) sapply(USArrests, quantile.25) ## Murder.25% Assault.25% UrbanPop.25% Rape.25% ## 4.075 109.000 54.500 15.075 R provides many variations on lapply to facilitate programming. Here is a partial list: • sapply: The same as lapply but tries to arrange output in a vector or matrix, and not an unstructured list. • vapply: A safer version of sapply, where the output class is pre-specified. • apply: For applying over the rows or columns of matrices. • mapply: For applying functions with more than a single input. • tapply: For splitting vectors and applying functions on subsets. • rapply: A recursive version of lapply. • eapply: Like lapply, only operates on environments instead of lists. • Map+Reduce: For a Common Lisp look and feel of lapply. • parallel::parLapply: A parallel version of lapply from the package parallel. • parallel::parLBapply: A parallel version of lapply, with load balancing from the package parallel. ## 3.20 Recursion The R compiler is really not designed for recursion, and you will rarely need to do so. See the RCpp Chapter in R-BGU-course for linking C code, which is better suited for recursion. If you really insist to write recursions in R, make sure to use the Recall function, which, as the name suggests, recalls the function in which it is place. Here is a demonstration with the Fibonacci series. fib<-function(n) { if (n < 2) fn<-1 else fn <- Recall(n - 1) + Recall(n - 2) return(fn) } fib(5) ## [1] 8 ## 3.21 Dates and Times R provides several options for dealing with date and date/time data. We will start by the default options from R’s base library. Unless you tell it to R, R doesn’t know something is a date. The as.Date function convert values to dates. You can pass it a character, a numeric, or a POSIXct (we’ll soon explain what it is). Let’s see some examples: start <- "1948-05-14" class(start) ## [1] "character" start <- as.Date(start) class(start) ## [1] "Date" But what if our date is not in the yyyy-mm-dd format? We can tell R what is the charater date’s format. as.Date("14/5/1948", "%d/%m/%Y") ## [1] "1948-05-14" as.Date("14may1948", "%d%b%Y") ## [1] "1948-05-14" Look for ?strptime to see more options for date-time conversion functions to and from character. Another option is to set the date given the number of days from the origin. e.g.: as.Date(1e6, origin = "1948-05-14") ## [1] "4686-04-10" Once R knows its a date, some functions and operators adapt themselves: (today <- Sys.Date()) # the current date ## [1] "2020-12-02" today + 1 ## [1] "2020-12-03" today - start ## Time difference of 26500 days min(start,today) ## [1] "1948-05-14" month(today) ## [1] 12 We now move to Times, which have a more quantitative meaning. You can set a time object in R just like as in dates, but now you will have to specify more units (or R will set it for you to the default). The POSIXct is R’s object class for time, and it expects strings to be in the format YYYY-MM-DD HH:MM:SS. with POSIXct you can also specify the timezone, e.g., "Asia/Jerusalem". time1 <- Sys.time() class(time1) ## [1] "POSIXct" "POSIXt" time2 <- time1 + 72*60*60 # add 72 hours time2-time1 ## Time difference of 3 days class(time2-time1) ## [1] "difftime" If you convert POSIXct to POSIXlt object, time components can be extracted easily: time3 <- as.POSIXlt(time2) attributes(time2) ##$class
## [1] "POSIXct" "POSIXt"
time3$hour ## [1] 13 We can get more specific information about time difference: difftime(time2,time1, units = "hour") ## Time difference of 72 hours difftime(time2,time1, units = "week") ## Time difference of 0.4285714 weeks And we can also generate sequences with times: seq(from = time1, to = time2, by = "day") ## [1] "2020-12-02 13:04:39 IST" "2020-12-03 13:04:39 IST" ## [3] "2020-12-04 13:04:39 IST" "2020-12-05 13:04:39 IST" seq(time1, by = "month", length.out = 12) ## [1] "2020-12-02 13:04:39 IST" "2021-01-02 13:04:39 IST" ## [3] "2021-02-02 13:04:39 IST" "2021-03-02 13:04:39 IST" ## [5] "2021-04-02 13:04:39 IDT" "2021-05-02 13:04:39 IDT" ## [7] "2021-06-02 13:04:39 IDT" "2021-07-02 13:04:39 IDT" ## [9] "2021-08-02 13:04:39 IDT" "2021-09-02 13:04:39 IDT" ## [11] "2021-10-02 13:04:39 IDT" "2021-11-02 13:04:39 IST" Except from R base, the lubridate package offer an efficient and convenient functionalities for dates and time. Yoy can creat a date data by passing the order in which year, month, and day appear in your dates by the function name. For instance ymd() means (left to right): year, month, day. You can also add the time in a day with ymd_hms(). Once the order was specified, the exact format is not a matter: library(lubridate) ymd("2017/01/31") ## [1] "2017-01-31" mdy("January 31st, 2017") ## [1] "2017-01-31" dmy("31-Jan-2017") ## [1] "2017-01-31" ymd_hms("2000-01-01 00:00:01") ## [1] "2000-01-01 00:00:01 UTC" ymd_hms("20000101000001") ## [1] "2000-01-01 00:00:01 UTC" Another nice thing in lubridate, is that periods can be created with a number of friendly constructor functions that you can combine time objects. E.g.: seconds(1) ## [1] "1S" minutes(c(2,3)) ## [1] "2M 0S" "3M 0S" hours(4) ## [1] "4H 0M 0S" days(5) ## [1] "5d 0H 0M 0S" months(c(6,7,8)) ## [1] "6m 0d 0H 0M 0S" "7m 0d 0H 0M 0S" "8m 0d 0H 0M 0S" weeks(9) ## [1] "63d 0H 0M 0S" years(10) ## [1] "10y 0m 0d 0H 0M 0S" (t <- ymd_hms("20000101000001")) ## [1] "2000-01-01 00:00:01 UTC" t + seconds(1) ## [1] "2000-01-01 00:00:02 UTC" t + minutes(c(2,3)) + years(10) ## [1] "2010-01-01 00:02:01 UTC" "2010-01-01 00:03:01 UTC" And you can also extract and assign the time components: t ## [1] "2000-01-01 00:00:01 UTC" second(t) ## [1] 1 second(t) <- 26 t ## [1] "2000-01-01 00:00:26 UTC" There are many more things to know about working with dates and times and how to analyze temporal data. If you are intrested in time-series analysis, look up for tseries, forecast and zoo packages. ## 3.22 Working with strings strings are common in R, especially as: files names, paths (directories), names of elements in the data, text elements (e.g. title in a plot), and more. Here are some examples of manipulating strings. The paste function does what its name suggest, with sep argument for the character string that separate the terms. a <- "good" b <- "morning" is.character(a) ## [1] TRUE paste(a,b) ## [1] "good morning" (c <- paste(a,b, sep = ".")) ## [1] "good.morning" The substr function extract or replace substrings in a character vector. E.g.: substr(c, start=2, stop=4) ## [1] "ood" substr(c, start=6, stop=12) <- "evening" The grep function searches for matches to argument pattern within each element of a character vector. It differs in the format of detail in the results. Here are some examples: (d <- c(a,b,c)) ## [1] "good" "morning" "good.evening" grep("good",d) # returns the elements indices in d where "good" is part of the string element. ## [1] 1 3 grep("good",d, value=TRUE, ignore.case=TRUE) # whith value=TRUE we get the value of these elements. Here we also ask the matching to be case sensitive ## [1] "good" "good.evening" We can use gsub to replace characters in a string object: gsub("o", "q", d) ## [1] "gqqd" "mqrning" "gqqd.evening" The strsplit allows to split string vectors to list: (x <- c(a = "thiszis", b = "justzan", c = "example")) ## a b c ## "thiszis" "justzan" "example" strsplit(x, "z") # split x on the letter z ##$a
## [1] "this" "is"
##
## $b ## [1] "just" "an" ## ##$c
## [1] "example"
Lastly. here are some more simple and useful functions in R to work with strings
nchar(x) # count the nuber of characters in every element of a string vector.
## a b c
## 7 7 7
toupper(x) # translate characters in character vectors from to upper case
## a b c
## "THISZIS" "JUSTZAN" "EXAMPLE"
tolower(toupper(x)) # vice verca
## a b c
## "thiszis" "justzan" "example"
letters[1:10] # lower case letters vector
## [1] "a" "b" "c" "d" "e" "f" "g" "h" "i" "j"
LETTERS[1:10] # upper case letters vector
## [1] "A" "B" "C" "D" "E" "F" "G" "H" "I" "J"
cat("the sum of", 1, "and", 2, "is", 1+2) # concatenate and print strings and values
## the sum of 1 and 2 is 3
(long <- rownames(mtcars)[1:5]) #is these strings are too long
## [1] "Mazda RX4" "Mazda RX4 Wag" "Datsun 710"
## [4] "Hornet 4 Drive" "Hornet Sportabout"
abbreviate(long, minlength = 3, method = "both.sides") # try abbreviate function to short them while maintain the meaning
## Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive
## "MRX" "MRW" "D71" "H4D"
## "HrS"
If you need more than this, look for the stringr package that provides a set of internally consistent tools.
## 3.23 Bibliographic Notes
There are endlessly many introductory texts on R. For a list of free resources see CrossValidated. I personally recommend the official introduction Venables et al. (2004), available online, or anything else Bill Venables writes.
For Importing and Exporting see (https://cran.r-project.org/doc/manuals/r-release/R-data.html). For working with databases see (https://rforanalytics.wordpress.com/useful-links-for-r/odbc-databases-for-r/).
For advanced R programming see Wickham (2014), available online, or anything else Hadley Wickham writes.
For a curated list of recommended packages see here.
## 3.24 Practice Yourself
1. Load the package MASS. That was easy. Now load ggplot2, after looking into install.pacakges().
2. Save the numbers 1 to 1,000,000 (1e6) into an object named object.
3. Write a function that computes the mean of its input. Write a version that uses sum(), and another that uses a for loop and the summation +. Try checking which is faster using system.time. Is the difference considerable? Ask me about it in class.
4. Write a function that returns TRUE if a number is divisible by 13, FALSE if not, and a nice warning to the user if the input is not an integer number.
5. Apply the previous function to all the numbers in object. Try using a for loop, but also a mapping/apply function.
6. Make a matrix of random numbers using A <- matrix(rnorm(40), ncol=10, nrow=4). Compute the mean of each columns. Do it using your own loop and then do the same with lapply or apply.
7. Make a data frame (dataA) with three columns, and 100 rows. The first column with 100 numbers generated from the $$\mathcal{N}(10,1)$$ distribution, second column with samples from $$Poiss(\lambda=4)$$. The third column contains only 1.
Make another data frame (dataB) with three columns and 100 rows. Now with $$\mathcal{N}(10,0.5^2)$$, $$Poiss(\lambda=4)$$ and 2. Combine the two data frames into an object named dataAB with rbind. Make a scatter plot of dataAB where the x-axes is the first column, the y-axes is the second and define the shape of the points to be the third column.
8. In a sample generated of 1,000 observations from the $$\mathcal{N}(10,1)$$ distribution:
1. What is the proportion of samples smaller than $$12.4$$ ?
2. What is the $$0.23$$ percentile of the sample?
9. Nothing like cleaning a dataset, to paractice your R basics. Have a look at RACHAEL TATMAN collected several datasets which BADLY need some cleansing.
### References
Venables, William N, David M Smith, R Development Core Team, and others. 2004. “An Introduction to R.” Network Theory Limited.
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2021-06-23 06:43:28
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https://www.math.ku.dk/english/calendar/events/ghys_hblecture/
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# Harald Bohr Lecture: Etienne Ghys (ENS Lyon)
Title: The topology of a curve in the neighborhood of a singular point
Speaker: Etienne Ghys (Directeur de recherche CNRS, ENS Lyon)
Abstract: I would like to start with a clever (and elementary) observation of M. Kontsevich. When we draw the graphs of four real polynomials in one variable intersecting in some point, some local qualitative pictures turn out to be impossible. I will then generalize to any number of polynomials and then to singularities of real algebraic curves. Some interesting algebraic structures appear and open questions arise…
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2019-07-19 08:05:53
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http://users.humboldt.edu/doug/blog/2016/09/14/20160914.html
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## Scheduling R scripts in Windows
2016-09-14 22:17 PDT
I need to schedule several R scripts on a Windows 2012 server. I've had to figure out how to do this in the past, but did not take great notes on how to set it up. So here I am hopefully putting together some useable notes on how to schedule an R script in Windows. I found a useful YouTube video on how to do this. You can find it here: https://www.youtube.com/watch?v=UDKy5_SQy2o
The basic steps are to:
1. Add R to the scheduling user's local PATH environment variable.
• In Windows 7 you can type "environment" into the search path and you should see a program titled "Edit environment variables for your account."
• Create the new variable PATH for the user that will be running the scheduled task. I recommend using an account with administrative priveleges. Add the path to your preferred R installation's bin to the local PATH variable for the administrative user.
Example:
C:\Program Files\R\R-3.3.1\bin
2. Write an R script to perform a task that is to be performed on a schedule. When writing the R-script keep the following in mind:
• Make sure that any libraries used in the R-script are installed for the user under which the task will be scheduled.
• Set the working directory within the R-script to make referencing directories easier.
3. Create a batch script to run your R script. Example content:
echo off
R CMD BATCH D:\path\to\my\script.R
4. Use Windows Task Scheduler to run the batch script with the desired start trigger and frequency. From my experience, an administrator account should be used to author and run the scheduled task.
If you are having trouble with your R script running when triggered, checkout the .Rout file in a text editor to observe any errors from R.
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2017-12-17 00:34:56
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http://tex.stackexchange.com/questions/35884/easy-way-to-remove-formatting-e-g-linebreaks?answertab=active
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Easy way to remove formatting (e.g. linebreaks)
I have defined the following shortcut for some text
\newcommand{\sometext}{text\\text\\text}
Now I would like to use this in some other place but with the linebreaks removed. So is there an easy way to do it (e.g. something like "\remove_linebreaks{\sometext}")?
-
This will change \\ into a space:
\newcommand{\removelinebreaks}[1]{%
\\ has an optional star and an optional argument. Something like \def\\{\@ifstar {\@gobbleopt}{\@gobbleopt}}\providecommand*\@gobbleopt[1][]{} would handle these too. – Schweinebacke Nov 23 '11 at 13:56
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2015-04-26 21:26:02
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https://www.gamedev.net/topic/57355-what-should-i-do/
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# What should I do?
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.
7 replies to this topic
### #1afransen Members
Posted 12 August 2001 - 02:31 PM
I am interested in getting into a career in the PC game programming industry. I have a few questions for anyone who is willing to give me a hand. I need some advice and there is really no where else I can find it. Anyway, to start off I''ll tell you a bit about what I hope to do: I hope the learn as many skills as possible to help me get a good paying job. I am interested in programming and design, and I''m nothing even approaching an artist. I live in southern Ontario (in Canada, if you didn''t know ;-) and I hope to get a job somewhere in the area. Now here are the questions. I''ll number them to make them easier to respond to. 1. What post-secondary education should I pursue? I am currently considering attending the University of Waterloo (located in S. Ontario) for a B.A. in Computer Science. It is a very open-ended course, and deals with things like object-oriented programming and AI among many other things. Is this a wise decision? What type of education would be better? Will this help me in finding a good job or a well paying job? 2. In the gaming industry, what is the likelihood of me gaining a position that will give me creative input as well as requiring me to to perform technical tasks? 3. What are the chances of finding employment in the gaming industry in Southern Ontario (Toronto or Kitchener-Waterloo-Cambridge)? I do not expect many to know this, but its worth asking. If the chances are not good, where would I have to move to in order to find a job? California or BC? 4. What skills, if any, should I try to develop prior to attending post-secondary education? I currently have two years. 5. What is the average pay for a position in which I am interested? Thanks a lot for reading this far. I would appretiate it greatly if you could give me this information as it will help me greatly in making decisions in the my immediate future. AFransen
### #2afransen Members
Posted 14 August 2001 - 12:46 AM
Awww, come on. Someone has to know something....
### #3Calibur as boolean Members
Posted 16 August 2001 - 04:37 AM
actually im 14! and i got a job already offered to me for a major netowork company.. lol they game me tonz of hardware and there catch was i have to apply for a job when im 16.. guess the average pay? 60,000$A FREAKING YEAR! yeah. that means ill be making 1/2 of what my dad makes, and im like 1/4 of his age :D lol.. but see programmers make alot of money.. ### #4afransen Members Posted 17 August 2001 - 06:48 AM quote: Original post by Calibur as boolean actually im 14! and i got a job already offered to me for a major netowork company.. lol they game me tonz of hardware and there catch was i have to apply for a job when im 16.. guess the average pay? 60,000$ A FREAKING YEAR! yeah. that means ill be making 1/2 of what my dad makes, and im like 1/4 of his age :D lol.. but see programmers make alot of money..
uwaterloo has a very good computer science programme (its said that no one can graduate the course without being approached at some point by Microsoft) but I am wondering if it is appropriate for the career field I want to enter. I''m just wondering if I have to learn all the design aspects of making games after I get a job.
I''m really hoping I don''t have to move to Cali or something.
Btw, is that \$60k in US dollars?
### #5Anonymous Poster_Anonymous Poster_* Guests
Posted 17 August 2001 - 07:51 AM
Afransen, where about do you live in Ontairo? Anyways, I''m 16, and I''ve been offerred 2 50k+ jobs ... Unfourtantly, they assumed I had a degree, and was *slightly* older ;-) But I did program a game on contract for an inventor. The pay was ok (excluding my stake in the game) and it took about 6 months while attending school. Anyways this ties in to question 2 and 3, if you are writting small games, maybe for a portal page or value pak games, you might get all the input. Working for maxis will mean doing what the designer says from a creative stand point. Also doing what the lead programmer says from a technical stand point. As for working in Ontario on games, I don''t know of any software houses that create games...
As for question one, I tried to take university courses at Trent, but they won''t accept me until I''m at least in my OAC year, which is .... well, that''s another story. Every game programming postion I''ve ever seen wants you to have 1-5 years experience in the game industry and/or a publushed title. A CS or related degree is also usually a requirment. Besides, if you want to work in Ontario, you might need to take a job in *shudder* data bases or (even worse =) e-commerce. And those jobs are a dime a dozen if you have a degree. Waterloo has a reputation, but then again, so does MIT. Is your average above 90? Waterloo is out to keep it''s reputation =)
Pay in the game industry varies. Don''t believe the joke that game programmers are paid less then there counterparts. Take a look at Software developer magazine they publish salary statistics once a year. Game programmers (unless they are lying) make similar wages. Of course, you could always send an email to a couple deveolper houses, and ask them what the average wage is.
Finally skills... I take it you''ve already got some good programming background? I''d suggest working at making a couple complete games. Then work on some really cool demos that show off your talent. You might as well create a portfollio as you go ;-)
Anyways, I hope I''ve provided the little insight I have.
~Michael Sikora
### #6Remnex Members
Posted 17 August 2001 - 08:11 PM
Calibur, I am SO sure you got offered a job like that. But, since I have never heard of a netowork company, I bet they hire young
------------------------------
"I''m a decorated astronaut, I don''t make those kind of mistakes."
"Oh now wait a minute. Look I''ll show ya. I''ll enter the same calculations using what we like to call ''The Right Way''."
-Rem
Zirem Software
### #7afransen Members
Posted 24 August 2001 - 05:02 PM
quote:
Original post by Anonymous Poster
Afransen, where about do you live in Ontairo?
I live in the Niagara Region, south of Toronto.
...but they won''t accept me until I''m at least in my OAC year, which is .... well, that''s another story.
You''re sixteen? OAC is being phased out for my year, so I presume you were in Grade Eleven for 2000/2001 and you will be entering Grade Twelve in a week and a half?
Every game programming postion I''ve ever seen wants you to have 1-5 years experience in the game industry and/or a publushed title. A CS or related degree is also usually a requirment. Besides, if you want to work in Ontario, you might need to take a job in *shudder* data bases or (even worse =) e-commerce. And those jobs are a dime a dozen if you have a degree.
That''s what I was afraid of. I know of an individual who got a job with EA in British Columbia. He graduated from University of Waterloo''s Computer Science program. I am not sure how truthful the individual was, as he claimed to be involved in design as well as programming (he was working on a sports game... NHL ''99, I believe) and also claimed to be very generously paid (going by the numbers you listed... he claimed over 100k Cdn., which I found suspect) but since I did not speak with him directly I was not certain (hence my post here).
Waterloo has a reputation, but then again, so does MIT. Is your average above 90? Waterloo is out to keep it''s reputation =)
Yes. I would imagine they don''t get too many applicants that way, though. Since I will be graduating during the so-called "double-cohort" entry requirements will be even more demanding. I find a minimum average in the 90''s% to be a bit unusual. Are you certain of this?
Pay in the game industry varies. Don''t believe the joke that game programmers are paid less then there counterparts. Take a look at Software developer magazine they publish salary statistics once a year. Game programmers (unless they are lying) make similar wages. Of course, you could always send an email to a couple deveolper houses, and ask them what the average wage is.
I will do that, thanks.
Finally skills... I take it you''ve already got some good programming background? I''d suggest working at making a couple complete games. Then work on some really cool demos that show off your talent. You might as well create a portfollio as you go ;-)
Yes and no. I have been fooling around with C++ and Basic... is there anything else you would recommend learning?
Anyways, I hope I''ve provided the little insight I have.
I am just wondering if there is somewhere else that would be more appropriate than Waterloo given the field of work I want to join.
~Michael Sikora
### #8Drizzt DoUrden Members
Posted 24 August 2001 - 05:12 PM
I also asked a question quite like this and was told that going solo is bad. What you should do is realy alot of books on C++ and OpenGL/Direct X and go to school for it, then build acouple games for a portfolio. I read this is a interview of gamedevelopers book so im sure its right. Then you should go to a company who is hiring, and give them your portfolio, your background with programming(like school) and your resume.
Old topic!
Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.
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2017-04-30 16:50:41
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https://www.physicsforums.com/threads/measure-defined-on-borel-sets-that-it-is-finite-on-compact-sets.741586/
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# Measure defined on Borel sets that it is finite on compact sets
1. Mar 4, 2014
### mahler1
The problem statement
Let $\mu$ be a measure defined on the Borel sets of $\mathbb R^n$ such that $\mu$ is finite on the compact sets. Let $\mathcal H$ be the class of Borel sets $E$ such that:
a)$\mu(E)=inf\{\mu(G), E \subset G\}$, where $G$ is open.
b)$\mu(E)=sup\{\mu(K), K \subset E\}$, where $K$ is compact.
Prove the following:
i. The open and compact sets belong to $\mathcal H$.
ii. If $\mu$ is finite, $\mathcal H$ is a $\sigma-$algebra.
iii. $\mathcal H$ coincides with the $\sigma-$algebra of Borel.
The attempt at a solution
For i., maybe I could find an increasing sequence of compact sets $\{K_n\}_{n \in \mathbb N}$($K_n \subset K_{n+1}$) such that all are contained in $E$, the problem is that I don't know how to construct this sequence; I suppose that, in an analogous way, I can construct a decreasing sequence of open sets $\{G_n\}_{n \in \mathbb N}$ ($G_{n+1} \subset G_n$) such that $E$ is contained in all of them.
For ii., it's easy to verify that $\emptyset \in \mathcal H$, it remains to prove that if $E \in \mathcal H$, then $E^c \in \mathcal H$, and that if $E_n \in \mathcal H$ for a sequence of sets, then $\bigcup_{n \in \mathbb N} E_n \in \mathcal H$. I couldn't prove that the complement of $E$ must be in $\mathcal H$, I'll write what I did for countable unions:
Suppose $E_n \in \mathcal H$ for a sequence of sets, call $E=\bigcup_{n \in \mathbb N} E_n$. By hypothesis, we have that $\mu(E_n)$ is finite for each $n$. Given $\epsilon>0$, we can choose for each $n$, an open set $G_n$ : $\mu(G_n)\leq \mu(E_n)+\dfrac{\epsilon}{2^n}$, if I call $G=\bigcup_{n \in \mathbb N} G_n$, then $E \subset G$ and $\mu(G) \leq \mu(E)+ \epsilon$. This means that $\mu(E)$ satisfies a). Analogously, we can show that $\mu(E)$ satisfies b), from here it follows $E \in \mathcal H$.
For iii., assuming I could prove i., I can say that $B \subset \mathcal H$ since the open sets are contained in $\mathcal H$, it remains to show that $\mathcal H \subset B$.
I am pretty stuck in all three items, I would appreciate some help with this exercise and if someone could tell me if what I did for countable unions in ii. is correct.
2. Mar 4, 2014
### micromass
Staff Emeritus
You need to use that $E$ is actually compact (or open). So take $E$ compact. Then (b) shouldn't be too difficult. For $A$, perhaps you should think of
$$\{x\in \mathbb{R}^n~\vert~d(x,E)<1/n\}$$
Take an $E\in \mathcal{H}$. Let's prove $(a)$ for $E^c$. You must find an open set $G$ such that $E^c\subseteq G$ and such that $\mu(G) - \varepsilon<\mu(E^c)$. Take complements, then you need to find a certain closed subset of $E$. Use that $E\in \mathcal{H}$ to find this.
I don't see why $\mu(E_n)$ is finite.
Not sure if this is easy to see. We don't have necessarily that the $G_n$ and $E_n$ are pairswise disjoint. So you might not be able to use $\sigma$-additivity.
But $\mu$ is a Borel measure, so it's only defined on the Borel sets.
3. Mar 4, 2014
### Dick
I think you are trying to go too fast here. Let's just stick with i) for a while. You are dealing with $\mathbb R^n$. You probably know a lot about $\mathbb R^n$. You probably know Heine-Borel. Use that to attack i).
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2017-11-18 11:26:32
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https://forum.azimuthproject.org/discussion/477/delayed-feedback
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#### Howdy, Stranger!
It looks like you're new here. If you want to get involved, click one of these buttons!
Options
# Delayed feedback
I made a new article about delayed feedback, since I introduced the concept in the logistic equation article. It's related to stochastic delay differential equation but as always I think it's good to separate the qualitative features that don't come from stochasticity. In this case, the fact that if you add delay to your favourite ODE you probably break its (in)stability properties in some regimes. Which then means that the equation amplifies noise and therefore both numerical approximations and stochastically driven versions are likely to be problematic.
The article is still half-cooked.
• Options
1.
I have now expanded the article with a short analytical discussion of instability of a particular delayed-feedback system:
$$\dot x(t) = - x(t-\Delta)$$ and some observations about the implications for numerical stability and the noise-driven version.
To reassure myself about the claims I have been doing some numerical experiments with R which I should probably add to the wiki in the vein of Staffan Liljegren's Experiments in predator-prey in Sage.
Comment Source:I have now expanded the article with a short analytical discussion of instability of a particular delayed-feedback system: $$\dot x(t) = - x(t-\Delta)$$ and some observations about the implications for numerical stability and the noise-driven version. Comments solicited. To reassure myself about the claims I have been doing some numerical experiments with R which I should probably add to the wiki in the vein of Staffan Liljegren's [Experiments in predator-prey in Sage](http://www.azimuthproject.org/azimuth/show/Experiments+in+predator-prey+in+Sage).
• Options
2.
edited February 2011
GREAT!
I really want to write about the delayed action oscillator and El Niño in This Week's Finds. When I do it, I'll take advantage of all the stuff we have on the Azimuth Wiki, credit everyone who helped, and link to it.
By the way: we follow the Wikipedia conventions on capitalizing page titles. So, I changed the title of your page from delayed feedback to Delayed feedback. This process creates a redirect so that now both links work.
category: mathematical methods
to the bottom of your page. This makes it easier for the lab elves to add a link, and someday a description, to the page Methodology.
I'm so happy you've joined our team!
Comment Source:GREAT! <img src = "http://math.ucr.edu/home/baez/emoticons/thumbsup.gif" alt = ""/> I really want to write about the delayed action oscillator and El Niño in This Week's Finds. When I do it, I'll take advantage of all the stuff we have on the Azimuth Wiki, credit everyone who helped, and link to it. Yes, please add your R code to [[Delayed feedback]], just as Graham did in [[Quantitative ecology]]. By the way: we follow the Wikipedia conventions on capitalizing page titles. So, I changed the title of your page from [[delayed feedback]] to [[Delayed feedback]]. This process creates a redirect so that now both links work. I also added category: mathematical methods to the bottom of your page. This makes it easier for the lab elves to add a link, and someday a description, to the page [[Methodology]]. I'm so happy you've joined our team!
• Options
3.
Now done...
Comment Source:Now done...
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2022-12-09 03:19:18
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https://www.queryxchange.com/q/20_341369/1-variance-chi-2-test-odd-behavior/
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# 1-Variance $\chi^2$ Test - Odd behavior
by Jared Goguen Last Updated April 18, 2018 19:19 PM
Every resource I have found states that the sample variance of a normal random variable follows a $\chi^2$-distribution such that $(n-1)\dfrac{s^2}{\sigma^2} \sim \chi^2_{n-1}$.
I am confused about how to find the $P$-value for a two-tailed test when the $s \approx \sigma$. Suppose $s$ is very slightly less than $\sigma$. I would expect that the $P$-value of a two-tailed test could be found by multiplying the left-tail area by $2$. However, this produces a $P$-value that is greater than $1$.
Many technologies instead use the right-tail area (which is less than $0.5$) and multiply that by $2$, but this does not sit well with me because (a) the sample variance is less than the population variance, and (b) this makes the upper limit for a $P$-value strictly less than $1$.
Am I missing something here? Is there a good way to calculate the $P$-value for this type of test that does not run into these issues?
example distribution
Tags :
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2018-10-16 13:57:29
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http://www.dsplog.com/2007/12/31/minimum-frequency-spacing-for-having-orthogonal-sinusoidals/
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(8 votes, average: 4.63 out of 5)
# Minimum frequency spacing for having orthogonal sinusoidals
by on December 31, 2007
In this post, the objective is to figure out the minimum separation between two sinusoidals having frequencies $f_1$, $f_2$ of duration $T$each to be orthogonal. Let the phase difference between the sinusoidals is $\phi$ where $\phi$ can take any value from $0$ to $2\pi$ (Refer Example 4.3 [DIG-COMM-SKLAR]).
For the two sinuosidals to be orthogonal,
$\int_0^Tcos(2\pi f_1 t+\phi)cos(2 \pi f_2t)dt = 0$
Integrating and applying the limits, the above equation simplifies to (thanks to the detailed simplification in Example 4.3 [DIG-COMM-SKLAR]) ,
$cos(\phi)\left[\frac{sin(2\pi (f_1+f_2)T)}{2\pi(f_1+f_2)} + \frac{sin(2\pi (f_1-f_2)T)}{2\pi(f_1-f_2)} \right] \\ + sin(\phi)\left[\frac{cos(2\pi (f_1+f_2)T)-1}{2\pi(f_1+f_2)} + \frac{cos(2\pi (f_1-f_2)T)-1}{2\pi(f_1-f_2)} \right]=0$.
Note:
$sin(n\pi)=0$ and $cos(2n\pi)=1$ where $n$ is an integer.
Let as assume that $(f_1+f_2)T$ is an integer. Then two terms in the above equation vanishes as
$sin(\2\pi (f_1+f_2)T)=0$ and $cos(\2\pi (f_1+f_2)T)=1$.
The above equation simplifies to,
$cos(\phi)\frac{sin(2\pi (f_1-f_2)T)}{2\pi(f_1-f_2)} + sin(\phi)\frac{cos(2\pi (f_1-f_2)T)-1}{2\pi(f_1-f_2)} =0$.
For an arbitrary value of $\phi$from $0$ to $2\pi$
In a such a case, for the above equation to be zero, then the cosine term to be equal to 1 and the sine term need to be equal to 0 for making the above equation zero. To satisfy that requirement, need to have,
$2\pi (f_1-f_2)T=2n\pi$
$f_1-f_2=\frac{n}{T}$.
Ofcourse, the minimum value of $n$is 1, then
$f_1-f_2=\frac{1}{T}$.
For $\phi$= $0$
When $\phi$= $0$, then cosine term in the equation is already zero. To make the eqution 0, the sine term need to be equal to be zero. To satisfy that requirement, need to have,
$2\pi (f_1-f_2)T=n\pi$
$f_1-f_2=\frac{n}{2T}$.
Ofcourse, the minimum value of $n$is 1, then
$f_1-f_2=\frac{1}{2T}$.
% Simple Matlab/Octave code
% Minimum frequency seperation between two sinusoidals
T = 1;
fs = 100;
t = 0:1/fs:T;
t = t(1:end-1);
% with random phase
f1 = 1;
f2 = 2;
phi = 2*pi*rand; % uniformly distributed from 0 tp 2pi
s1 = cos(2*pi*f1*t+phi);
s2 = cos(2*pi*f2*t);
sum_with_phi_random = sum(s1.*s2)
% with zero phase difference
f3 = 3/4;
f4 = 5/4;
s3 = cos(2*pi*f3*t);
s4 = cos(2*pi*f4*t);
sum_with_phi_zero = sum(s3.*s4)
close all
figure
plot(t,s1,’b.-’)
hold on
plot(t,s2,’rx-’)
legend(‘s1′,’s2′)
title(‘Minimum frequency seperation for random phase’)
grid on
xlabel(‘time’)
ylabel(‘amplitude’)
figure
plot(t,s3,’b.-’)
hold on
plot(t,s4,’rx-’)
legend(‘s3′,’s4′)
title(‘Minimum frequency seperation for zero phase’)
grid on
xlabel(‘time’)
ylabel(‘amplitude’)
Figure: Two sinusoidals with frequency difference = 1/T
Figure: Two sinusoidals with frequency difference = 1/2T
Summary
1. When the phase difference between two sinuosidals is not known, then the minimum frequency separation between them is $\frac{1}{T}$ for the sinusoidals to be orthogonal.
2. When the phase difference between two sinuosidals is zero, then the minimum frequency separation between them is $\frac{1}{2T}$ for the sinusoidals to be orthogonal.
3. In the above Matlab code snippet, with $\frac{1}{2T}$seperation, the sum of the product of two sinusoidals is only nearly equal to zero (and not zero). Need to think more and revert.
References
Hope this helps,
Krishna
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fly4ever January 10, 2010 at 9:32 am
3. In the above Matlab code snippet, with seperation, the sum of the product of two sinusoidals is only nearly equal to zero (and not zero). Need to think more and revert.
I think it is because that the Matlab sum function cannot present the real meaning of integrate, (the area of the curve of the product of two sinusoidals).
Hence
sum_with_phi_random = sum(s1.*s2)
should be add the factor 1/fs, as below:
sum_with_phi_random = sum(s1.*s2)*1/fs
ram February 7, 2009 at 11:52 pm
one more question it was mentioned that for what ever value of phi form 0 to 2pi the cos term should be one and the sin term is zero..
But it is not necessary…
check out for phi = 135degress and the cos term and sin term as 1 then even the equation goes to zero…..
ram February 7, 2009 at 3:46 pm
everything is ok. But, what about the condition (f1+f2)T is integer that is assumed in the derivation???
what about if (f1+f2)T is not integer???
???
Krishna Sankar February 10, 2009 at 8:07 pm
@ram: I did not do the detailed analysis, but I think (f1+f2)T being an integer is required for saying that two sinusoidals with zero phase difference to be orthogonal is f1-f2 = 1/2T
ram February 7, 2009 at 3:45 pm
everything is ok. But, what about the condition (f1+f2)T is integer that is assumed in the derivation???
what about if (f1+f2)T is not integer???
Krishna Sankar May 6, 2008 at 8:23 am
amr alaa May 3, 2008 at 10:59 pm
thanks
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2020-04-07 23:37:54
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https://electronics.stackexchange.com/questions/66407/why-should-any-unit-be-used-instead-of-the-watt-w-as-a-power-unit
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# Why should any unit be used instead of the watt (W) as a power unit?
I am taking a course on AC circuits and so far I have seen that for the different types of power (read real, reactive and complex) different units are used.
For the real power, which is power in fact dissipated by the system, the SI compliant watt is used. I am very much in agreement with this.
However, for reactive and complex power the equivalent SI derived unit volt-ampere is used. In the special case of reactive power, a lowercase "r" is appended.
Now, I wonder: why should any other unit be used instead of watt, if the purpose of the unit is to specify the type of magnitude of a value? Moreover, why should a symbol be appended to the unit when its use is simply that of a reminder?
Also, is there a reason why using watts for reactive power would be considered wrong?
• Why don't we use Joules for torque also? Like work, it's force times distance, just not in the same direction. – Kaz Apr 21 '13 at 20:31
• It is different to compare energy and force, than to compare an energy transfer rate with another. One comparison deals with different types of quantities, the other does not. – Severo Raz Apr 22 '13 at 4:53
• If you apply voltage V to a Resistor and current I flows then power dissipated is V x I Watts. If the load is "complex" with R + L + C components then multiplying V x I at any given time will NOT give you power. If the voltage source is a hand cranked alternator then you will be very clearly be able to distinguish between a pure resistive and pure reactive load even when V and I are the same in each case. So too can a grid power station. – Russell McMahon Apr 22 '13 at 5:37
• Should the product of V·I be not a measure of power when dealing with reactive components, then why would reactive power be called power in the first place? The product yields the rate at which energy is being transferred to/from the reactive component, how is that not power? – Severo Raz Apr 22 '13 at 5:54
Simply because a watt is a measure of work done. The real part of V*A is watts. There are exact equivalents in mechanical systems. $W=\dfrac{J}{s}=\dfrac{N*m}{s}$ so ${N*m}$ here is Force that does work through a distance but it can also be a measure of Torque over a distance and that is static(non moving). One is the potential to do work, one is the work itself.
Using watts for reactive power would be wrong because reactive power is stored power and not capable of doing work.
Using VAr - r for reactive is just short hand for the purely imaginary part, instead of using i or j (for you physicists out there).
• I get the torque-energy unit duality, since each represents a different type of magnitude. However, I still don't get why two measures of power will need to be represented with different units. The watt is not a measure of work done, it is a measure of energy conversion or transfer rate. The reactive power is the energy transfer rate from and to a reactive load; this latter definition does not collide at all with the former. Energy dissipation is a form of energy transfer, but not vice versa. – Severo Raz Apr 22 '13 at 4:35
• What you are calling energy dissipation is real work done by the VI. From the voltage/current point of view, if it moves something, creates heat, makes sound that is all work. Imaginary VA is just stored. It is called reactive power but that is misusing the term power. If you have an ideal reactive load (purely imaginary) there is no average energy transfer. There is instantaneous energy flow but the Expected value is zero. These terms are used are indiscriminately in EE. You see in more recent years the attempt to tighten usage up, don't know if this is intentional or not. – placeholder Apr 22 '13 at 4:43
• I think we have a misunderstanding when it comes to the difference between the terms "work" and "power". While "work" (energy) can be stored, how could power? You cannot store a flow as itself, however you can store whatever flows in the flow. Sorry for the word game. I don't see how the reactive power is a misuse of the term "power", since it is the energy transfer rate from the active source to the reactive load, be it an inductor storing the energy in a magnetic field, or the capacitor in an electric field. – Severo Raz Apr 22 '13 at 4:51
• Well it's a pedants question to begin with, with watts being real and also the real part. It makes sense to call the imaginary part it something different. Even for calculation reasons. – placeholder Apr 22 '13 at 4:56
• My short answer is that if you consider a transformer (traditional copper iron for instance), the VA is what you get as useful output and the Watts is what comes out as heat. So a 120VA transformer with a 12V secondary will supply 10A, but may draw (say) 150W, which you could measure as heat. So that's why it's useful to make the distinction, because I'm far more interested in knowing I've got 10A at 12V coming out than in what load it presents to the upstream supply. In this context. – Ian Bland Nov 4 '16 at 0:09
These are three different powers therefore they have different units:
P [W] - real power
Q [var] - reactive power
S [VA] - complex power
Complex power S is a sum of real and reactive powers:
$$S = P + jQ$$
where j is a an imaginary unit. This can be shown on a complex plane like this:
A power transformer is rated in VA. It is not rated in watts because that would be wrong. The transformer can supply a certain rated voltage at a certain rated current and if the load on the transformer is purely reactive then no-watts (net) are transferred BUT the transformer is at its limit.
To say a 50VA transformer is rated at 50W is nonsence - the load may not "lose", "transfer" or "dissipate" any watts but it sure will be pushing the 50VA transformer to its maximum ratings.
• The fact is that the transformer will be undoubtedly "transferring" energy, at a rate. This is why such phenomenon can be called "power". In the case of an inductor, it is known that power delivered to it will be converted to a magnetic field. It is also valid to say that power can be drawed from an inductor in a time-varying magnetic field. Since the watt is the unit for energy conversion or transfer rate, I don't see where is the nonsense in rating a transformer with watts. – Severo Raz Apr 22 '13 at 4:43
Here's an example: I have a device that apparent power of 10 VA with $cos \phi=0.7$. It uses $P=S*cos \phi=0.7*10 \mbox{ } W=7 \mbox{ }W$. On the other hand it also uses $Q=S*sin \phi=0.714*10=7.14 \mbox{ }W$.
We could then add those two together since hey, it's both consuming 7 W and 7.14 W at the same time and get 14.14 W, which is obviously incorrect, since device will never use more than 10 W, even if its power factor somehow got corrected back to 1.
Basically var is used to signify that the reactive power is not in phase with active power and that you can't add them together. On paper, power is power but by using var (sometimes incorrectly referred to as VAr, so r isn't just appended, it's part of a different unit whose name is often misspelled), volt-ampere and watt, we (at least hope to) clearly signify the context in which such unit is used. So var not only signifies magnitude, it signifies phase as well.
This is actually nothing new and is common in other fields as well. For example we have radian and steradian as measurement units for angles which are actually 1. Same thing goes for bit as well. So while we could technically say that speed of a communication link is 1 MHz, it implies different context than 1 Mb/s.
• Why would you add together reactive power and the active power, units aside? This is what I meant with the "reminder" purpose of the var unit. – Severo Raz Apr 22 '13 at 4:44
• @Wolter Hellmund Well I wouldn't, but from my experience many people would if they wanted to calculate total load on the system (which is needed when choosing dimensions of conductors, transformers etc.), producing incorrect result. If we use a different unit, hopefully people will remember that they can't be just added together. – AndrejaKo Apr 22 '13 at 8:07
If a wall transformer is driving a reactive load, then during part of each AC cycle it will be transferring energy from the mains to the load, but during another part of each AC cycle it will be transferring energy from the load back to the mains. If during each 1/60sec cycle a load takes one joule and returns 0.25 joules, then the power taken by that load will be 60 watts and the power returned will be 15 watts, so the total power consumed will be 45 watts--the 60 to the load minus the 60 to the mains. On the other hand, the total power conveyed by the transformer would be 75VA--60 watts to the load plus the 15 watts to the mains.
It is just a convention. It explicitly differentiates the different types of power when speaking or writing (which have different meanings mathematically, even though they have the same fundamental units).
If the different types of power are given "different-looking/sounding" units (even though VA = W), than it is very clear to a person familiar with the field what you are talking about, even if you don't tell them.
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2020-10-23 22:32:44
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http://stla.github.io/stlapblog/posts/Bratteli.html
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1. Drawing a Bratteli graph with R
14/08/2015
Source
Hey, ergodicians! How do you draw your Bratteli graphs ? Are you using Xfig? Are you typing raw pstricks or TikZ code? Are you crazy? I have written the Bgraph R function, and it does the job without pain for you (feel free to take it here). You just have to write a R function returning the incidence matrices of the graph.
Bratelli graphs - The Pascal example
A Bratteli graph, such as the Pascal graph shown below, is a graded graph whose edges only connect vertices from one level to some vertices of the next level.
Such a graph is defined by a sequence of incidence matrices $M_n$. Denoting by $c_n$ the number of vertices at level $n$, the incidence matrix $M_n$ is a $c_n \times c_{n+1}$ matrix showing all connections between level $n$ and level $n+1$. A “$0$” means there’s no edge, a “$1$” means there’s one edge, a “$2$” means there’s a double edge, etc. The first three incidence matrices of the Pascal graph are
$M_0= \begin{pmatrix}{} 1 & 1 \\ \end{pmatrix} , \, M_1= \begin{pmatrix}{} 1 & 1 & 0 \\ 0 & 1 & 1 \\ \end{pmatrix} , \, M_2= \begin{pmatrix}{} 1 & 1 & 0 & 0 \\ 0 & 1 & 1 & 0 \\ 0 & 0 & 1 & 1 \\ \end{pmatrix} .$
and I get them with this function:
Pascal_Mn <- function(n){
M <- matrix(0, nrow=n+1, ncol=n+2)
for(i in 1:(n+1)){
M[i, ][c(i, i+1)] <- 1
}
return(M)
}
Given a function fun_Mn taking a nonnegative integer n as argument and returning an incidence matrix, such as the Pascal_Mn function, my Bgraph function, based on the diagram package, draws the corresponding Bratteli graph from the root level to a desired level N. Its arguments are:
formalArgs(Bgraph)
## [1] "fun_Mn" "N" "title" "path"
## [5] "col_path" "lwd_path" "labels_path" "labels_vertex"
## [9] "USE.COLNAMES" "first_vertex" "label_root" "only_end"
## [13] "cex_vertex" "labels_edges" "cex_edge" "ellipse_vertex"
## [17] "ellipse_edge" "LaTeX" "..."
The effects of most of the arguments will be illustrated below. The ellipsis ... is intended for additional arguments to the coordinates function of the diagram package. For example the hor argument allows to rotate the picture.
The figure above has been generated by this code, except that this time we change its orientation with the hor argument:
par(mar=c(.1,.1,.1,.1))
Bgraph(Pascal_Mn, N=3, path=c(1,0,1), first_vertex=1, hor=FALSE)
The path shown in blue on the figure, is given as the sequence of labels on the edges of this path. The first_vertex argument, intended to be 0 or 1, controls the label of the first vertex at each level. The user can decide to show the edge labels of the blue path only with the labels_path argument. By setting the only_end argument to TRUE, only the vertex labels at the last level are shown:
par(mar=c(.1,.1,.1,.1))
Bgraph(Pascal_Mn, N=3, path=c(1,0,1), first_vertex=0, labels_path=TRUE, only_end=TRUE)
By setting the USE.COLNAMES argument to TRUE, the vertex labels appearing at level $n$ are the column names of $M_n$. For example, on figure below we display the binomial numbers on the vertices Pascal graph, which give the number of paths from the root vertex. We also show the effect of the ellipse_vertex argument.
Pascal_Mn <- function(n){
M <- matrix(0, nrow=n+1, ncol=n+2)
for(i in 1:(n+1)){
M[i, ][c(i, i+1)] <- 1
}
colnames(M) <- choose(n+1, 0:(n+1))
return(M)
}
par(mar=c(.1,.1,.1,.1))
Bgraph(Pascal_Mn, N=4, path=c(1,0,1,1), labels_path=TRUE, USE.COLNAMES=TRUE, ellipse_vertex=TRUE)
Odometers
Bratteli graphs are well-known in ergodic theory since Vershik has shown that every invertible measure-preserving transformations can be represented as a transformation on the set of paths of such a graph.
The canonical Bratteli graph of an odometer is given by incidence matrixes full of “$1$”:
Odometer_Mn <- function(sizes){
sizes <- c(1,sizes)
function(n){
return(matrix(1, nrow=sizes[n+1], ncol=sizes[n+2]))
}
}
par(mar=c(.1,.1,.1,.1))
fun_Mn <- Odometer_Mn(c(3,4,5))
Bgraph(fun_Mn, N=3, labels_vertex=TRUE, path=c(2,1,2), labels_path=TRUE)
This graph is related to Cantor expansions. For the previous example, the paths starting from the root level and going to the third level provide a representation of the Cartesian product $\{0,1,2\}\times\{0,1,2,3\}\times\{0,1,2,3,4\}$.
Homogeneous trees
A homogeneous tree is a Bratteli graph. I use a trick to generate the incidence matrices, the same I already used before.
Tree_Mn <- function(sizes){
function(n){
if(n==0) return(matrix(1, ncol=sizes[1]))
unname(t(model.matrix(~0+gl(prod(sizes[1:n]),sizes[n+1])))[,])
}
}
As for the odometer, the paths of the tree provide a representation of a Cartesian producct, but in less compact form:
par(mar=c(.1,.1,.1,.1))
fun_Mn <- Tree_Mn(c(3,4,5))
Bgraph(fun_Mn, N=3, labels_vertex=FALSE, labels_edges=FALSE, path=c(2,1,2))
Conversion to TikZ
Mathematicians like $\LaTeX$ figures. The tikzDevice package allows to convert any R figure to a TikZ figure. For example we generate below the Pascal graph with the binomial numbers ${n \choose k}$ as vertex labels. We set the argument LaTeX to TRUE in the Bgraph function to generate edge labels in $\LaTeX$ math mode.
Pascal_Mn <- function(n){
M <- matrix(0, nrow=n+1, ncol=n+2)
for(i in 1:(n+1)){
M[i, ][c(i, i+1)] <- 1
}
colnames(M) <- sprintf("${%s \\choose %s}$", n+1, 0:(n+1))
return(M)
}
# convert to TikZ code:
library(tikzDevice)
texfile <- "bratteli-Pascal.tex"
tikz(texfile, standAlone=TRUE,
packages=c(getOption("tikzLatexPackages"), "\\usepackage{amsmath}\n\\usepackage{amssymb}\n"))
par(mar=c(.1,.1,.1,.1))
Bgraph(Pascal_Mn, N=3, path=c(1,0,1), labels_path=TRUE, USE.COLNAMES=TRUE, LaTeX=TRUE, label_root="$\\varnothing$", relsize=.6)
dev.off()
# convert to pdf:
tools::texi2dvi(texfile, pdf=TRUE, clean=TRUE)
# crop the figure (remove white margins):
knitr::plot_crop("bratteli-Pascal.pdf")
This is the result:
Multiples edges
My Bgraph function currently handles double edges too. Let us try the Pascal graph with some double edges taken at random.
Pascal2_Mn <- function(n){
M <- matrix(0, nrow=n+1, ncol=n+2)
for(i in 1:(n+1)){
M[i, ][c(i, i+1)] <- sample.int(2, 1)
}
return(M)
}
set.seed(666)
par(mar=c(.1,.1,.1,.1))
Bgraph(Pascal2_Mn, N=4, labels_vertex=FALSE, labels_path=TRUE, path=c(1,0,1,0))
Currently, the rendering of the colored path is not correct, because the two edges of a double edge appears in color. The label edges are not correct too. This will be fixed in a next version of the Bgraph function.
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2022-01-17 10:18:58
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https://chemistry.stackexchange.com/questions/37845/what-is-the-internal-energy-at-constant-pressure
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# What is the internal energy at constant pressure?
What is the internal energy when a reaction is run at constant volume and $9.19\ \mathrm{kJ}$ of heat is absorbed, when run at constant pressure $8.62\ \mathrm{kJ}$ is absorbed? (for an ideal gas)
I know that internal energy for constant volume is equal to the heat then $\Delta U=9.19\ \mathrm{kJ}$, but what is the internal energy for a reaction at constant pressure? I know that $\Delta H=\Delta U+p\Delta V$ and from this I know that $\Delta H=8.62\ \mathrm{kJ}$ but how does it relate to the internal energy?
• it is an ideal gas – Jake Sep 24 '15 at 19:25
$$\mathrm dU = \delta Q + \delta W$$For an ideal gas expanding against an external pressure $p$: $$\mathrm dU = \delta Q -p\,\mathrm dV$$
So at constant volume, $\mathrm dU = \delta Q$. Therefore $\mathrm dU = \pu{9.19kJ}$
If the reaction is identical, then $\mathrm dU = \pu{9.19kJ}$ for the ideal gas at constant pressure. From this we can then work out $\delta w$ at constant pressure as $\pu{9.19kJ} - \pu{8.62kJ} = \pu{0.57kJ}$.
Asking for the 'internal energy' and not the change in internal energy is meaningless here, because internal energy, $U$, is a state-function without a scale (unlike $S$) to define absolute values against.
So really you answered your own question in your question, $\Delta U=\pu{9.19 kJ}$
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2021-03-05 08:05:33
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https://brilliant.org/problems/remainders-or-what/
|
# Remainders or what?
What is the remainder obtained when $43^{101} +23^{101}$ is divided by 66?
×
Problem Loading...
Note Loading...
Set Loading...
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2020-07-11 03:54:13
|
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|
https://zenodo.org/record/2650324/export/schemaorg_jsonld
|
Presentation Open Access
# Presentation: metajelo, a metadata package for journals to support external linked objects
Vilhuber, Lars; Lagoze, Carl
### JSON-LD (schema.org) Export
{
"description": "<p>We propose a metadata package (called metajelo) that is intended to provide academic journals with a lightweight means of registering, at the time of publication, the existence and disposition of supplementary materials. Information about the supplementary materials is, in most cases, critical for the reproducibility and replicability of scholarly results. In many instances, these materials are curated by a third party, which may or may not follow developing standards for the identification and description of those materials. Researchers struggle when attempting to fully comply with data documentation and provenance documentation standards.</p>\n\n<p>However, many of the required elements are present in DDI, and when properly populated by data custodians using DDI, generation of the metajelo package is straightforward. In this presentation, we describe the rationale behind metajelo, and how archives that use DDI can easily provide researchers with a compact metadata package that enhances reproducibility while reducing researcher effort.</p>",
"creator": [
{
"affiliation": "Cornell University",
"@id": "https://orcid.org/0000-0001-5733-8932",
"@type": "Person",
"name": "Vilhuber, Lars"
},
{
"affiliation": "University of Michigan",
"@id": "https://orcid.org/0000-0002-5281-5215",
"@type": "Person",
"name": "Lagoze, Carl"
}
],
"url": "https://zenodo.org/record/2650324",
"datePublished": "2019-04-24",
"keywords": [
"datacite",
"re3data",
"reproducibility"
],
"@context": "https://schema.org/",
"identifier": "https://doi.org/10.5281/zenodo.2650324",
"@id": "https://doi.org/10.5281/zenodo.2650324",
"@type": "PresentationDigitalDocument",
"name": "Presentation: metajelo, a metadata package for journals to support external linked objects"
}
234
126
views
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2022-08-16 09:54:23
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http://15418.courses.cs.cmu.edu/spring2016/lecture/transactionalmem/slide_008
|
Previous | Next --- Slide 8 of 64
Back to Lecture Thumbnails
trappedin418
In databases, there is the idea of ACID - atomicity, consistency, isolation, and durability. The concepts of atomicity and isolation are very similar. Consistency (which means that transactions bring the state from a correct state to another correct state) is somewhat implied because we assume that the write operations aren't going to randomly fail in the middle of running. Durability (which means data writes are "permanent") isn't mentioned because we aren't concerned about preventing data loss due to crashes or power loss.
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2022-05-28 17:43:35
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https://www.gamedev.net/forums/topic/390340-c-gurus-mixindependent-name-question-maybe/
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# C++ Gurus: Mixin/Dependent Name Question (Maybe)
## Recommended Posts
I'm trying to implement a cheap little RTTI system for hierarchies of classes using only single inheritance. To do this, between each level of inheritance, I sandwich in a class that generates the RTTI info. This class (called TInheritor, in my code) needs to know the name of the direct subclass and needs to be able to access static members of the direct base class. In code:
// Normal inheritance looks like this:
namespace Normal
{
class CBase { };
class CDerived : public CBase { };
}
// With the RTTI system:
namespace RTTI
{
template< typename tSub, typename tSuper >
class TInheritor : public tSuper
{
public:
// Static RTTI stuff.
private:
TInheritor( ) { }
friend tSub;
};
class CBase { };
class CDerived : TInheritor< CDerived, CBase > { };
}
This works just fine, but I'd prefer to use a syntax like this:
namespace RTTI
{
class CBase : public /* some starter mechanism.*/ { };
class CDerived : public CBase::TInheritor< CDerived > { };
}
The problem is: I haven't been able to figure out how to make something like that work. Here's my attempted implementation:
// Includes
#include <iostream>
// Class definitions
template< typename tSub, typename tSuper >
class TIntermediate : public tSuper
{
public:
template< typename tNewSub > class TInheritor;
};
template< typename tSub, typename tSuper> template< typename tNewSub >
class TIntermediate<tSub, tSuper>::TInheritor : public TIntermediate<tNewSub, tSub>
{
private:
TInheritor( ) { }
friend tNewSub;
};
class CDummy { };
class CBase : public TIntermediate< CBase, CDummy >
{
public:
void Print( ) { std::cout << "Base" << std::endl; }
};
class CDerived : public CBase::TInheritor< CDerived >
{
public:
void Print( ) { std::cout << "Derived" << std::endl; }
};
class CDoubleDerived : public CDerived::TInheritor< CDoubleDerived >
{
};
// Main
int _tmain(int argc, _TCHAR* argv[])
{
CDoubleDerived dubDer;
dubDer.Print( ); // Prints "Base"!!!
return 0;
}
Both CDerived and CDoubleDerived inherit from CBase::TInheritor, meaning CDoubleDerived never inherits from CDerived at all. Changing the class definitions as follows makes everything work as expected, but ruins the nice syntax:
class CDummy { };
class CBase : public TIntermediate< CDummy, CDummy >::TInheritor< CBase > { };
class CDerived : public CBase::TIntermediate<CBase,CDummy>::TInheritor< CDerived > { };
class CDoubleDerived : public CDerived::TIntermediate<CDerived,CBase>::TInheritor< CDoubleDerived > { };
Now, for anyone who's still awake, my question: Is there a way to make my desired syntax work? If not, why not? (I feel like it has something to do with #35.18 in the C++ FAQ Lite, but I can't quite make the connection.) Thanks for you help, John Edwards
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Your first option sounds like the happy medium.
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Yeah, it certainly works, and I think it's just a matter of preference whether it or the second method is better (they are both about the same number of keystrokes). At this point I'm just kind of curious as to why the second method doesn't behave as you would expect it to in the absence of templates. I don't need to know the answer to finish implementing my system, but I'm always interested in developing a deeper understanding of the workings of C++.
John Edwards
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2017-10-22 00:50:02
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http://nag.com/numeric/FL/nagdoc_fl24/html/F08/f08hcf.html
|
F08 Chapter Contents
F08 Chapter Introduction
NAG Library Manual
# NAG Library Routine DocumentF08HCF (DSBEVD)
Note: before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.
Warning. The specification of the parameters LWORK and LIWORK changed at Mark 20 in the case where ${\mathbf{JOB}}=\text{'V'}$ and ${\mathbf{N}}>1$: the minimum dimension of the array WORK has been reduced whereas the minimum dimension of the array IWORK has been increased.
## 1 Purpose
F08HCF (DSBEVD) computes all the eigenvalues and, optionally, all the eigenvectors of a real symmetric band matrix. If the eigenvectors are requested, then it uses a divide-and-conquer algorithm to compute eigenvalues and eigenvectors. However, if only eigenvalues are required, then it uses the Pal–Walker–Kahan variant of the $QL$ or $QR$ algorithm.
## 2 Specification
SUBROUTINE F08HCF ( JOB, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO)
INTEGER N, KD, LDAB, LDZ, LWORK, IWORK(max(1,LIWORK)), LIWORK, INFO REAL (KIND=nag_wp) AB(LDAB,*), W(*), Z(LDZ,*), WORK(max(1,LWORK)) CHARACTER(1) JOB, UPLO
The routine may be called by its LAPACK name dsbevd.
## 3 Description
F08HCF (DSBEVD) computes all the eigenvalues and, optionally, all the eigenvectors of a real symmetric band matrix $A$. In other words, it can compute the spectral factorization of $A$ as
$A=ZΛZT,$
where $\Lambda$ is a diagonal matrix whose diagonal elements are the eigenvalues ${\lambda }_{i}$, and $Z$ is the orthogonal matrix whose columns are the eigenvectors ${z}_{i}$. Thus
$Azi=λizi, i=1,2,…,n.$
## 4 References
Anderson E, Bai Z, Bischof C, Blackford S, Demmel J, Dongarra J J, Du Croz J J, Greenbaum A, Hammarling S, McKenney A and Sorensen D (1999) LAPACK Users' Guide (3rd Edition) SIAM, Philadelphia http://www.netlib.org/lapack/lug
Golub G H and Van Loan C F (1996) Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
## 5 Parameters
1: JOB – CHARACTER(1)Input
On entry: indicates whether eigenvectors are computed.
${\mathbf{JOB}}=\text{'N'}$
Only eigenvalues are computed.
${\mathbf{JOB}}=\text{'V'}$
Eigenvalues and eigenvectors are computed.
Constraint: ${\mathbf{JOB}}=\text{'N'}$ or $\text{'V'}$.
2: UPLO – CHARACTER(1)Input
On entry: indicates whether the upper or lower triangular part of $A$ is stored.
${\mathbf{UPLO}}=\text{'U'}$
The upper triangular part of $A$ is stored.
${\mathbf{UPLO}}=\text{'L'}$
The lower triangular part of $A$ is stored.
Constraint: ${\mathbf{UPLO}}=\text{'U'}$ or $\text{'L'}$.
3: N – INTEGERInput
On entry: $n$, the order of the matrix $A$.
Constraint: ${\mathbf{N}}\ge 0$.
4: KD – INTEGERInput
On entry: if ${\mathbf{UPLO}}=\text{'U'}$, the number of superdiagonals, ${k}_{d}$, of the matrix $A$.
If ${\mathbf{UPLO}}=\text{'L'}$, the number of subdiagonals, ${k}_{d}$, of the matrix $A$.
Constraint: ${\mathbf{KD}}\ge 0$.
5: AB(LDAB,$*$) – REAL (KIND=nag_wp) arrayInput/Output
Note: the second dimension of the array AB must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{N}}\right)$.
On entry: the upper or lower triangle of the $n$ by $n$ symmetric band matrix $A$.
The matrix is stored in rows $1$ to ${k}_{d}+1$, more precisely,
• if ${\mathbf{UPLO}}=\text{'U'}$, the elements of the upper triangle of $A$ within the band must be stored with element ${A}_{ij}$ in ${\mathbf{AB}}\left({k}_{d}+1+i-j,j\right)\text{ for }\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,j-{k}_{d}\right)\le i\le j$;
• if ${\mathbf{UPLO}}=\text{'L'}$, the elements of the lower triangle of $A$ within the band must be stored with element ${A}_{ij}$ in ${\mathbf{AB}}\left(1+i-j,j\right)\text{ for }j\le i\le \mathrm{min}\phantom{\rule{0.125em}{0ex}}\left(n,j+{k}_{d}\right)\text{.}$
On exit: AB is overwritten by values generated during the reduction to tridiagonal form.
The first superdiagonal or subdiagonal and the diagonal of the tridiagonal matrix $T$ are returned in AB using the same storage format as described above.
6: LDAB – INTEGERInput
On entry: the first dimension of the array AB as declared in the (sub)program from which F08HCF (DSBEVD) is called.
Constraint: ${\mathbf{LDAB}}\ge {\mathbf{KD}}+1$.
7: W($*$) – REAL (KIND=nag_wp) arrayOutput
Note: the dimension of the array W must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{N}}\right)$.
On exit: the eigenvalues of the matrix $A$ in ascending order.
8: Z(LDZ,$*$) – REAL (KIND=nag_wp) arrayOutput
Note: the second dimension of the array Z must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{N}}\right)$ if ${\mathbf{JOB}}=\text{'V'}$ and at least $1$ if ${\mathbf{JOB}}=\text{'N'}$.
On exit: if ${\mathbf{JOB}}=\text{'V'}$, Z is overwritten by the orthogonal matrix $Z$ which contains the eigenvectors of $A$. The $i$th column of $Z$ contains the eigenvector which corresponds to the eigenvalue ${\mathbf{W}}\left(i\right)$.
If ${\mathbf{JOB}}=\text{'N'}$, Z is not referenced.
9: LDZ – INTEGERInput
On entry: the first dimension of the array Z as declared in the (sub)program from which F08HCF (DSBEVD) is called.
Constraints:
• if ${\mathbf{JOB}}=\text{'V'}$, ${\mathbf{LDZ}}\ge \mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{N}}\right)$;
• if ${\mathbf{JOB}}=\text{'N'}$, ${\mathbf{LDZ}}\ge 1$.
10: WORK($\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{LWORK}}\right)$) – REAL (KIND=nag_wp) arrayWorkspace
On exit: if ${\mathbf{INFO}}={\mathbf{0}}$, ${\mathbf{WORK}}\left(1\right)$ contains the required minimal size of LWORK.
11: LWORK – INTEGERInput
On entry: the dimension of the array WORK as declared in the (sub)program from which F08HCF (DSBEVD) is called.
If ${\mathbf{LWORK}}=-1$, a workspace query is assumed; the routine only calculates the minimum dimension of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued.
Constraints:
• if ${\mathbf{N}}\le 1$, ${\mathbf{LWORK}}\ge 1$ or ${\mathbf{LWORK}}=-1$;
• if ${\mathbf{JOB}}=\text{'N'}$ and ${\mathbf{N}}>1$, ${\mathbf{LWORK}}\ge 2×{\mathbf{N}}$ or ${\mathbf{LWORK}}=-1$;
• if ${\mathbf{JOB}}=\text{'V'}$ and ${\mathbf{N}}>1$, ${\mathbf{LWORK}}\ge 2×{{\mathbf{N}}}^{2}+5×{\mathbf{N}}+1$ or ${\mathbf{LWORK}}=-1$.
12: IWORK($\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{LIWORK}}\right)$) – INTEGER arrayWorkspace
On exit: if ${\mathbf{INFO}}={\mathbf{0}}$, ${\mathbf{IWORK}}\left(1\right)$ contains the required minimal size of LIWORK.
13: LIWORK – INTEGERInput
On entry: the dimension of the array IWORK as declared in the (sub)program from which F08HCF (DSBEVD) is called.
If ${\mathbf{LIWORK}}=-1$, a workspace query is assumed; the routine only calculates the minimum dimension of the IWORK array, returns this value as the first entry of the IWORK array, and no error message related to LIWORK is issued.
Constraints:
• if ${\mathbf{JOB}}=\text{'N'}$ or ${\mathbf{N}}\le 1$, ${\mathbf{LIWORK}}\ge 1$ or ${\mathbf{LIWORK}}=-1$;
• if ${\mathbf{JOB}}=\text{'V'}$ and ${\mathbf{N}}>1$, ${\mathbf{LIWORK}}\ge 5×{\mathbf{N}}+3$ or ${\mathbf{LIWORK}}=-1$.
14: INFO – INTEGEROutput
On exit: ${\mathbf{INFO}}=0$ unless the routine detects an error (see Section 6).
## 6 Error Indicators and Warnings
Errors or warnings detected by the routine:
${\mathbf{INFO}}<0$
If ${\mathbf{INFO}}=-i$, argument $i$ had an illegal value. An explanatory message is output, and execution of the program is terminated.
${\mathbf{INFO}}>0$
if ${\mathbf{INFO}}=i$ and ${\mathbf{JOB}}=\text{'N'}$, the algorithm failed to converge; $i$ elements of an intermediate tridiagonal form did not converge to zero; if ${\mathbf{INFO}}=i$ and ${\mathbf{JOB}}=\text{'V'}$, then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and column $i/\left({\mathbf{N}}+1\right)$ through .
## 7 Accuracy
The computed eigenvalues and eigenvectors are exact for a nearby matrix $\left(A+E\right)$, where
$E2 = Oε A2 ,$
and $\epsilon$ is the machine precision. See Section 4.7 of Anderson et al. (1999) for further details.
The complex analogue of this routine is F08HQF (ZHBEVD).
## 9 Example
This example computes all the eigenvalues and eigenvectors of the symmetric band matrix $A$, where
$A = 1 2 3 0 0 2 2 3 4 0 3 3 3 4 5 0 4 4 4 5 0 0 5 5 5 .$
### 9.1 Program Text
Program Text (f08hcfe.f90)
### 9.2 Program Data
Program Data (f08hcfe.d)
### 9.3 Program Results
Program Results (f08hcfe.r)
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2015-07-04 03:47:39
|
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|
http://scholar.cnki.net/result.aspx?q=X%E5%B0%84%E7%BA%BF%E8%A1%8D%E5%B0%84%E6%B3%95&rt=Journal&rl=&udb=
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高级检索
作者：E. M. Moroz 来源：[J].Journal of Structural Chemistry(IF 0.575), 2017, Vol.58 (8), pp.1510-1514Springer 摘要：The possibilities of using powder X-ray diffraction methods in the study of carbon materials are discussed. To determine the phase composition of the crystalline materials the X-ray phase analysis is employed; the real structure is established by the harmonic analysis of diffraction...
作者：Yuanyuan Liu , Shaomin Lei , Yang Li ... 来源：[J].Journal of Wuhan University of Technology-Mater. Sci. Ed.(IF 0.484), 2019, Vol.34 (3), pp.614-621Springer 摘要：Abstract(#br)The influence of replacement level of calcined coal-series kaolin (CCK) on hydration of ordinary Portland cement (OPC) was studied by X-ray diffraction(XRD)/Rietveld method. X-ray diffraction/Rietveld method was used to quantify the crystalline phase composition...
作者：Marinkovic Bojan , Avillez Roberto Ribeiro de , Saavedra Alvaro ... 来源：[J].Materials Research(IF 0.516), 2001, Vol.4 (2), pp.71DOAJ 摘要：The fundamental parameters approach is used to simulate the instrument contribution to the X-Ray diffraction profile. This procedure eliminates the need to experimentally prepare a reference sample of the studied crystalline material when using the Warren-Averbach method to i...
作者：Bojan Marinkovic , Roberto Ribeiro de Avillez , Alvaro Saavedra ... 来源：[J].Materials Research(IF 0.516), 2001, Vol.4 (2), pp.71-76DOAJ 摘要：The fundamental parameters approach is used to simulate the instrument contribution to the X-Ray diffraction profile. This procedure eliminates the need to experimentally prepare a reference sample of the studied crystalline material when using the Warren-Averbach method to i...
作者：Marinkovic Bojan , Avillez Roberto Ribeiro de , Saavedra Alvaro ... 来源：[J].Materials Research(IF 0.516), 2001, Vol.4 (2), pp.71-76DOAJ 摘要：The fundamental parameters approach is used to simulate the instrument contribution to the X-Ray diffraction profile. This procedure eliminates the need to experimentally prepare a reference sample of the studied crystalline material when using the Warren-Averbach method to i...
作者：Zeynep Demircioğlu , Fethi Ahmet Özdemir , Osman Dayan ... 来源：[J].Journal of Molecular Structure(IF 1.404), 2018, Vol.1161, pp.122-137Elsevier 摘要：... Two new Schiff base ligands containing aromatic sulfonamide fragment of (Z)-N-(2-((3-nitrobenzylidene)amino)phenyl)benzenesulfonamide 3 and (Z)-N-(2-((4-nitrobenzylidene)amino)phenyl)benzenesulfonamide 4 were synthesized and investigated by spectroscopic techniques including 1 H and 13 C NMR, FT-IR, single crystal X-ray...
作者：É. M. Moroz 来源：[J].Journal of Structural Chemistry(IF 0.575), 2012, Vol.53 (1), pp.63-85Springer 摘要：Abstract(#br)X-ray diffraction structural diagnostics of nanomaterials needs the development of special methods taking into account the features of X-ray scattering from small objects. Data on the development of the X-ray diffraction method of the radial electron density dis...
作者：P. Angerer , T. Klünsner , M. Morstein ... 来源：[J].International Journal of Refractory Metals and Hard Materials(IF 1.858), 2019Elsevier 摘要：... In the current work, the equi-penetration grazing incidence X-ray diffraction (EP-GIXD) method was adapted for the determination of the residual stress depth profile in the WC-Co hardmetal substrate below an AlCrN-based hard coating. The limits of this method in terms of coat...
作者：Manojit De , H S Tewari 来源：[J].Pramana(IF 0.562), 2017, Vol.89 (1)Springer 摘要：In the present paper, we are reporting the synthesis of pure nickel and magnesium ferrite [ $$\hbox {NiFe}_2\hbox {O}_4$$ , $$\hbox {MgFe}_2\hbox {O}_4$$ ] and magnesium-substituted nickel ferrite $$(\hbox {Ni}_{1-x}\hbox {Mg}_{x/y}\hbox {Fe}_{2-y}\hbox {O}_4; x=y=0.60)$$ on A/B ...
作者：B. Levieil , F. Bridier , C. Doudard ... 来源：[J].Experimental Mechanics(IF 1.548), 2016, Vol.56 (9), pp.1641-1652Springer 摘要：Abstract(#br)The combination of various residual stress measurement methods is a common practice to complete knowledge that a single measurement method cannot provide. In this study, incremental X-Ray diffraction is combined with the contour method to measure a bent notched speci...
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2019-07-20 04:53:36
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https://us.sofatutor.com/mathematics/practice/writing-products-as-sums-and-sums-as-products
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# Writing Products as Sums and Sums as Products – Practice ProblemsHaving fun while studying, practice your skills by solving these exercises!
For now, Practice Problems are only available on tablets and desktop computers. Please log in on one of these devices.
Do you need help? Watch the Video Lesson for this Practice Problem.
To express a product as a sum, apply the distributive property of multiplication over addition. And the other way around, to express a sum as a product, apply factoring. The ability to rewrite an expression in a different form allows flexibility and opens the mind to various possibilities in solving a mathematical problem. Learn how to express products as sums and sums as products by helping superhero En Fuego prepare a training regimen that would allow her to match the skills of her arch-rival superhero Ice Queen, the reigning champion, in a duel for this year’s upcoming Superhero supremacy showdown. Common Core Reference: CCSS.MATH.CONTENT.7.EE.A.1
Exercises in this Practice Problem
Explain how to express the product $4(32x+2)$ as a sum. Determine how the different factors alter the expression $16x+1$. Explain how to express the sum $120x+16$ as a product. Write each sum as a product. State how to express the product $4(16x+1)$ as a sum. Represent products as sums and vice versa.
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2017-12-17 10:00:42
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https://ts.gluon.ai/api/gluonts/gluonts.nursery.anomaly_detection.supervised_metrics.html
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# gluonts.nursery.anomaly_detection.supervised_metrics package¶
gluonts.nursery.anomaly_detection.supervised_metrics.aggregate_precision_recall(labels_pred_iterable: Iterable, precision_recall_fn: Callable = <function buffered_precision_recall>) → Tuple[float, float][source]
Computes aggregate range-based precision recall metrics for the given prediction labels.
Parameters
• labels_pred_iterable – An iterable that gives 2-tuples of boolean lists corresponding to true_labels and pred_labels respectively.
• precision_recall_fn – Function to call in order to get the precision, recall metrics.
Returns
Return type
A tuple containing average precision and recall in that order.
gluonts.nursery.anomaly_detection.supervised_metrics.aggregate_precision_recall_curve(label_score_iterable: Iterable, thresholds: Optional[numpy.array] = None, partial_filter: Optional[Callable] = None, singleton_curve: bool = False, precision_recall_fn: Callable = <function buffered_precision_recall>, n_jobs: int = -1)[source]
Computes aggregate range-based precision recall curves over a data set, iterating over individual time series. Optionally takes partially constructed filter that converts given scores/thresholds to anomaly labels. See gluonts.nursery.anomaly_detection.supervised_metrics.filters for example filters.
Parameters
• label_score_iterable (Iterable) – An iterable that gives 2-tuples of np.arrays (of identical length), corresponding to true_labels and pred_scores respectively.
• thresholds (np.array) – An np.array of score thresholds for which to compute precision recall values. If the filter_type argument is provided, these are the threshold values of the filter. If not, they will be applied as a single step hard threshold to predicted scores.
• partial_filter (Callable) – Partial constructor for a “filter” object. If provided, this function can be called with a “score_threshold” to return labels used for precision and recall computation. If not provided, labels will be assigned with a hard threshold. See gluonts.nursery.anomaly_detection.supervised_metrics.filters for example filters.
• singleton_curve (bool) – If true, range-based precision recall will not be computed
• precision_recall_fn – Function to call in order to get the precision, recall metrics.
• n_jobs (int) – How many concurrent threads for parallelization, default is -1 (use all cpu available)
Returns
• (Same as output of sklearn.metrics.precision_recall_curve)
• precision (array, shape = [n_thresholds + 1]) – Precision values such that element i is the precision of predictions with score >= thresholds[i] and the last element is 1.
• recall (array, shape = [n_thresholds + 1]) – Decreasing recall values such that element i is the recall of predictions with score >= thresholds[i] and the last element is 0.
• thresholds (array, shape = [n_thresholds <= len(np.unique(scores))]) – Increasing thresholds on the decision function used to compute precision and recall.
gluonts.nursery.anomaly_detection.supervised_metrics.buffered_precision_recall(real_ranges: List[range], pred_ranges: List[range], buffer_length: int = 5) → Tuple[float, float][source]
Implements a new range-based precision recall metric, that measures how well anomalies (real_ranges) are caught with labels (pred_ranges).
We extend anomaly ranges by a number of time steps (buffer_length) to accomodate those raised with a lag. For example, if an annotator has marked range(5, 9), and the model has labeled range(11, 13) as an anomaly, we would often like to mark this as a correctly raised anomaly. There are two reasons for this. (i) Human annotators often draw boxes around anomalies with a certain “margin,” i.e., with a lead and a lag around the true anomaly. (ii) The low-pass filter raises anomalies with a certain latency.
Therefore, this function looks for intersections between “extended” anomaly ranges, those with a buffer of buffer_length added after the annotated range, and the predicted ranges. Any intersection is counted as a success. More precisely,
• If an “extended” anomaly range intersects with any labeled range, it’s “caught.” If an anomaly intersects with no predicted range, it’s not caught. Recall is, n_caught_anomalies / n_all_anomalies.
• If a predicted range intersects with any “extended” anomaly range, it’s a good alarm. Precision is n_good_pred_ranges / n_pred_ranges.
Note that the numerators (numbers of true positives) are different for precision and recall. This is since an anomaly can be caught by multiple pred ranges, as well as a pred range marking two separate anomalies. This function allows for this behavior. Moreover, a prediction range is either “good” (it intersects with an extended anomaly range, and is a “true positive predicted range”) or or “bad” (false positive). This is different than segment_precision_recall, since there a predicted range is counted towards true positives and false positives at the same time if it spans the intersection of an anomaly segment and a non-anomaly segment.
Parameters
• real_ranges (List[range]) – Python range objects representing ground truth anomalies (e.g., as annotated by human labelers). Ranges must ve non-overlapping and in sorted order.
• pred_ranges (List[range]) – Python range objects representing labels produced by the model. Ranges must be non-overlapping and in sorted order.
• buffer_length (int) – The number of time periods which a predicted range is allowed lag after an anomaly, for which it will be marked as a “good” raise. For example, if the actual range is range(5,7) and the predicted range is range(8, 9), this prediction will be deemed accurate with a buffer length of 2 or above.
Returns
• precision (float) – Precision. Ratio of predicted ranges that overlap with an (extended) anomaly range.
• recall (float) – Recall. Ratio of (extended) anomaly ranges that were caught by (overlaps with) at least one prediction range.
gluonts.nursery.anomaly_detection.supervised_metrics.segment_precision_recall(real_ranges: List[range], pred_ranges: List[range]) → Tuple[float, float][source]
Segment based metric is less lenient than the range based metric.
This metric counts
• a ground truth anomaly range as true-positive as long as there is an overlapping predicted
anomaly range; it does not penalize the position of the overlap. If there is no overlapping predicted range for given ground truth range, then it counts as one false-negative irrespective of its size.
• a predicted anomaly range as false positive if it has a nonempty overlap with a “normal” range.
Parameters
• real_ranges – List of ranges corresponding to ground truth anomalies.
• pred_ranges – List of predicted anomaly ranges.
Returns
Return type
Tuple containing segment based precision and recall.
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2021-05-07 23:16:28
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|
https://www.precisionmicrodrives.com/content/dc-motor-speed-voltage-and-torque-relationships/
|
# DC Motor Speed: Voltage and Torque Relationships
Typical DC Motor / DC Gearmotor Performance Characteristics (The 108-104 DC Motor)
Something we have discussed in the past is how varying the voltage to a vibration motor can change the amplitude, particularly with reference to haptic feedback and playing different effects. However, something we haven’t explicitly shown is why this happens, or discussed it in the context of a normal DC motor. So in this short article, we will demonstrate how an increased voltage will increase the speed and an increased load will decrease the speed of a motor.
It is important to note that this is valid for all of our products that are based on brushed DC motors, so it applies to:
• DC motors, directly
• DC gearmotors, directly with a simple mechanical speed reduction
• Vibration motors, which have a fixed load
We start with the equivalent circuit of a brushed DC motor:
DC Motor Equivalent Circuit
Using a simple voltage loop we can see that the input voltage ($$V)$$ is equal to the voltage drop across the coil resistance ($$R)$$ and the inductor ($$L)$$, with the back EMF ($$E)$$ produced by the motor in motion, i.e.:
$$V = IR + L \frac{dI}{dt} + E$$
However, to demonstrate the effect voltage and torque have on speed, we are only concerned with steady-state behaviour at the moment. In steady-state we benefit from two simplifications:
• First, the current is constant which means the inductor $$L$$ can be removed
• Secondly, as there is no change in speed, the torque produced by the motor and the torque produced by the load must be equal
The second simplification helps as we consider how torque is produced in the motor, given by the following equation:
$$T = K_{T} \phi I$$
Where $$K_{T}$$ represents a constant inherited from its internal design, $$\phi$$ is the total flux and $$T$$ can represent our load torque. We rearrange this for $$I$$ and enter it into our original equation:
$$V = \frac{T}{K_{T} \phi} R + E$$
Now we turn our attention to the emf $$E$$, which is dependent upon the total flux $$\phi$$ motor specific factors (such as its radius and length) that make a second constant $$K_{E}$$ and the speed of the motor $$n$$:
$$E = K_{E} \phi n$$
Substituting this value of $$E$$ into our equation yields the following:
$$V = \frac{T}{K_{T} \phi} R + K_{E} \phi n$$
The equation above actually represents a linear motor, in adapting this to an angular rotating motor we consider the flux to be constant at its full value. In doing so it is combined with each constant to produce the torque constant and electrical constant of the motor, denoted $$k_{t}$$ and $$k_{e}$$ respectively. As discussed before, these constants actually share the same units, so we can replace both constants in our equation to the value $$k$$. Also, we now replace linear speed $$n$$ with angular velocity $$\omega$$, so our equation becomes:
$$V = \frac{T}{k} R + k \omega$$
Rearranged for angular velocity:
$$\omega = \frac{V}{k} – \frac {T}{k^{2}} R$$
In summary, we can highlight the two main variables which affect the speed of the motor in our final equation:
1. Input Voltage: For a fixed load, the speed of the motor is affected by applied voltage. Increase in voltage = increase in speed
2. Load Torque: For a fixed voltage, the speed of the motor is inversely affected by the load. Increase in load torque = decrease in speed
If you have any questions about this relationship, or how the theory applies to a ‘real-world’ motor, please contact our sales engineers to help with your application.
|
2019-10-21 23:16:00
|
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|
http://openstudy.com/updates/50e9f46ae4b0d4a537cc14b8
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## anonymous 3 years ago Verify that cot x sec4x = cot x + 2 tan x + tan3x
1. anonymous
so i know cotx is cos/sin
2. anonymous
idk if we can change the tan though to sin/cos?
3. anonymous
this one is hard but try this
4. anonymous
first divide everything by cot x
5. anonymous
$\sec^{4} x = 1 + 2\frac{ \tan x }{ \cot x } + \frac{ \tan^{3} x }{ \cot x }$
6. anonymous
and we know that $\frac{ \tan x }{ \cot x } = \frac{ \frac{ \sin x }{ \cos x } }{ \frac{ \cos x }{ \sin x } } = \frac{\sin^{2} x }{ \cos^{2} x } = \tan^{2} x$
7. anonymous
would it apply to the second one but it would be (sin^3x/cos^3x)/cosx/sinx ?
8. anonymous
that would simplify it to: $\sec^{4} x = 1 + 2 \tan^{2} x + \tan^{4} x$
9. anonymous
yeah the second one is: $\frac{ \tan^{3} x }{ \cot x } = \frac{ \tan x }{ \cot x } * \tan^{2} x = \tan^{2} x * \tan^{2} x = \tan^{4} x$
10. anonymous
where did you get the second tan^2x
11. anonymous
I divided tan^3 x into tan^x * tan^2 x
12. anonymous
|dw:1357511455432:dw|
13. anonymous
oh ok
14. anonymous
So this is why we have the following equation so far: $\sec^{4} x = 1 + 2 \tan^{2} x + \tan^{4} x$
15. anonymous
next step is to subtract both sides by tan^4 x
16. anonymous
$\sec^{4} x - \tan^{4} x = 1 + 2 \tan^{2} x$
17. anonymous
and divide both side by2?
18. anonymous
no there is a trick here now. notice the left side is the difference of two squares
19. anonymous
$\sec^{4} x - \tan^{4} x = (\sec^{2} x)^{2} - (\tan^{2} x)^{2}$
20. anonymous
remember that a^2 - b^2 = (a - b)(a + b) so we can now write the left side as: $\sec^{4} x - \tan^{4} x = (\sec^{2} x - \tan^{2} x)(\sec^{2} x + \tan^{2} x)$
21. anonymous
right you foil it?
22. anonymous
we kind of did the reverse of FOIL, we factored it
23. anonymous
So now we have: $(\sec^{2} x - \tan^{2} x)(\sec^{2} x + \tan^{2} x) = 1 + 2 \tan^{2} x$
24. anonymous
but do you remember the identity sec^2 x = tan^2 x + 1
25. anonymous
yes but there is the 2?
26. anonymous
we'll get to that :) so if sec^2 x = tan^2 x + 1 the if we subtract tan^2 from both sides we get sec^2 x - tan^2 x = 1
27. anonymous
Then we see how
28. anonymous
$(\sec^{2} x - \tan^{2} x)(\sec^{2} x + \tan^{2} x) = 1 + 2 \tan^{2} x$ becomes $(1)(\sec^{2} x + \tan^{2} x) = 1 + 2 \tan^2{x}$
29. anonymous
isnt it sec^4
30. anonymous
No we factored $\sec^{4} x - \tan^{4} x$ into $(\sec^{2} x - \tan^{2} x)(\sec^{2} x + \tan^{2} x)$ because it is a difference of sqaures
31. anonymous
ok so when you subtract tan^2x?
32. anonymous
There is a trig identity: $\sec^{2} x = 1 + \tan^{2} x$ i am saying, if we rewrite it as: $\sec^{2} x - \tan^{2} x = 1$ then the left factor on our left hand side reduces to just 1: $(\sec^{2} x - \tan^{2} x)(\sec^{2} x + \tan^{2} x) = (1)(\sec^{2} x + \tan^{2} x)$
33. anonymous
so we are now left with $\sec^2{x} + \tan^{2} x = 1 + 2 \tan^{2} x$
34. anonymous
ok you had lost me. now i get it sorry
35. anonymous
its a complicated problem compared to the last one o_o
36. anonymous
yes it is. i still have to do 5 more assignments. lol
37. anonymous
so now we have $\sec^2{x} + \tan^{2} x = 1 + 2 \tan^{2} x$ can you see the next step ?
38. anonymous
substitute the sec^2x with 1+ tan^2x?
39. anonymous
we could, or we could save a step and just subtract tan^2 x from both sides
40. anonymous
if we subtract tan^2 x from both sides we get $\sec^{2} x = 1 + \tan^{2} x$
41. anonymous
which is an identity
42. anonymous
ok
43. anonymous
but how does this equal to cotxsec^4x?
44. anonymous
the whole idea is to reduce the original equation into a trig identity
45. anonymous
if you follow the steps then that's precisely what we did
46. anonymous
to verify that it equals on both sides?
47. anonymous
if you manipulate an equation using algebra then whatever you end up with is equal to what you started with.
48. anonymous
oh ok thanks so much!
49. anonymous
np
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2016-08-31 23:29:23
|
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https://hal-cea.archives-ouvertes.fr/cea-01745392
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# Reentrant Superconductivity Driven by Quantum Tricritical Fluctuations in URhGe: Evidence from $^{59}$Co NMR in URh$_{0.9}$Co$_{0.1}$Ge
2 IMAPEC - Instrumentation, Material and Correlated Electrons Physics
PHELIQS - PHotonique, ELectronique et Ingénierie QuantiqueS : DRF/IRIG/PHELIQS
Abstract : Our measurements of the $^{59}$Co NMR spin-spin relaxation in URh$_{0.9}$Co$_{0.1}$Ge reveal a divergence of electronic spin fluctuations in the vicinity of the field-induced quantum critical point at $H_R$ $\approx$ 13 T, around which reentrant superconductivity (RSC) occurs in the ferromagnetic heavy fermion compound URhGe. We map out the strength of spin fluctuations in the ($H_b$; $H_c$) plane of magnetic field components and show that critical fluctuations develop in the same limited region near the field $H_R$ as that where RSC is observed. This strongly suggests these quantum fluctuations as the pairing glue responsible for the RSC. The fluctuations observed are characteristic of a tricritical point, followed by a phase bifurcation toward quantum critical end points.
Keywords :
Document type :
Journal articles
Domain :
https://hal-cea.archives-ouvertes.fr/cea-01745392
Contributor : Jérôme Planès <>
Submitted on : Wednesday, March 28, 2018 - 10:56:52 AM
Last modification on : Tuesday, May 11, 2021 - 11:36:11 AM
### Citation
Y. Tokunaga, Dai Aoki, H. Mayaffre, S. Kraemer, M. H. Julien, et al.. Reentrant Superconductivity Driven by Quantum Tricritical Fluctuations in URhGe: Evidence from $^{59}$Co NMR in URh$_{0.9}$Co$_{0.1}$Ge. Physical Review Letters, American Physical Society, 2015, 114, pp.216401. ⟨10.1103/PhysRevLett.114.216401⟩. ⟨cea-01745392⟩
Record views
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2021-07-23 19:34:36
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https://www.poeppelmann.com/us/teku/products/eco-bp-jp
|
TEKU® PRODUKTPROGRAMM
# ECO | BP | JP
#### Trouble-free denesting from the stack
With evenly-formed contours and reliable stacking TEKU® trays are easier to separate quickly.
## Technical data
JP 2553/72 T 20 7/8 9 7/8 1 5/8 1 3/8 1 1/8 1 1/8 1 1/2 1,39 fl oz 41 ml 72 50
JP 3040/54 P 14 5/8 11 2 1/4 1 5/8 1 1/8 1 1 1/2 2 fl oz 59 ml 54 48
JP 3040/80 P 14 5/8 11 1 3/4 1 1/8 7/8 3/4 1 5/8 0,95 fl oz 28 ml 80 72
JP 3040/104 14 5/8 11 1 5/8 1 3/4 0,61 fl oz 18 ml 104
JP 3050/28 19 2/3 11 2 2 1/4 1 3/4 3,38 fl oz 100 ml 28 19
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JP 3050/50 T 19 2/3 11 2 1 1/3 1 1/3 1 5/8 1,39 fl oz 41 ml 50 33
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JP 3050/72 P 19 2/3 11 2 1/8 1 5/8 1 1/8 1 1 7/8 1,69 fl oz 50 ml 72 48
JP 3050/104 T 19 2/3 11 1 1/2 1 1/8 1 1 1 1/8 0,71 fl oz 21 ml 104 69
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JP 3050/230 H 19 2/3 11 1 3/8 3/4 5/8 0,24 fl oz 7 ml 230
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2022-09-30 23:30:18
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https://forum.allaboutcircuits.com/threads/help-with-boolean-algebra.3177/
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# Help with Boolean algebra
#### bigga
Joined Aug 27, 2006
1
Prove i. AD + BD + BC + ABD = BC + D
ii. (x'y' + z)' + z + xy + wz = x + y + z
I'm new to Boolean algebra and I've tried all the rules for Boolean algebra without success. Help anyone?
#### Papabravo
Joined Feb 24, 2006
16,776
Consider the following identities:
Rich (BB code):
A' = A'B + A'B' and
B = BA' + BA
Now
A'D + BD + B'C + AB'D =
(A' + B + AB')D + B'C =
(A'B + A'B' + A'B + AB + AB')D + B'C =
(1)D + B'C
Show us what you got for the other one - eh?
I shouldn't have to do all the heavy lifting.
#### shivani
Joined Mar 31, 2010
2
a'd + bd + b'c + ab'd
= a'd + d(b+ab') + b'c
= a'd + d(a + b) + b'c
= a'd + ad + db + b'c
= d(a' + a) + db + b'c
= d + db + b'c
= d(1 + b) + b'c
= d + b'c
#### mps
Joined Feb 4, 2010
8
Prove i. AD + BD + BC + ABD = BC + D
ii. (x'y' + z)' + z + xy + wz = x + y + z
I'm new to Boolean algebra and I've tried all the rules for Boolean algebra without success. Help anyone?
The 1st question is solved by 2 gentlemen
Now the 2nd question is wrong as the lhs is 1
the actual question must be
(x'y' + z')' + z + xy + wz = x + y + z
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2021-09-19 04:47:11
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https://web2.0calc.com/questions/help_36611
|
+0
# help!
0
40
1
Point P is on side $$\overline{AC}$$ of triangle ABC such that $$\angle APB =\angle ABP$$, and$$\angle ABC - \angle ACB = 39^\circ$$ . Find $$\angle PBC$$ in degrees.
Apr 27, 2020
|
2020-06-03 01:25:43
|
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|
https://codingstructure.net/post/2020-04-09-mathematical-expressions-part-3/
|
# Mathematical Expressions as Trees 3: Proper Expression Modelling
If you haven’t done so yet, read parts one and two first or watch the video that inspired these posts.
You can find a notebook with the state after this blog post here.
Last time there was a problem in the expression simplification left, which is apparent when looking at these two expressions:
str(Mul(Con(2), Mul(Con(3), Var('x'))).simplify()) # returns '2*3*x'
str(Mul(Mul(Con(2), Con(3)), Var('x')).simplify()) # returns '6*x'
They model the same expression, so both should return the second (simpler) string. The actual solution to this will come later in the post, but first I noticed another problem:
## Proper Operation Modelling
The way we model subtraction and division at the moment is not really correct. They are currently binary operations on the same binding level as addition and multiplication respectively. In reality a - b is more of shorthand for a + (-b) (similarly for division and the inverse) and that’s the way I want to model it now.
Let’s start with the simpler of the two cases and replace Sub():
### Representation for Debugging purposes
For some debugging that I had to do, I first implemented the __repr__ function in all base classes. This allows me to call repr(expr) on any expression and get a string that would work as a constructor for the expression. The implementation is relatively straight forward:
class SinExpr(Expr):
# ...
def __repr__(self):
return str("{t}({a})".format(
t=self.__class__.__name__,
a=str(self))
)
class BinExpr(Expr):
# ...
def __repr__(self):
return str("{t}({a}, {b})".format(
t=self.__class__.__name__,
a=repr(self.a),b=repr(self.b))
)
And of cause adding a small test:
assert repr(expr) == 'Add(Mul(Con(3), Pow(Var(x), Con(2))), Sub(Var(y), Div(Con(6), Con(3))))'
### Replacement of Sub()
Ok, now to the replacement of Sub(). First we add a new base class for operations with just one argument, the unary operations:
class UnaExpr(Expr):
def __init__(self, a):
self.a = a
def __repr__(self):
return str("{t}({a})".format(
t=self.__class__.__name__,
a=repr(self.a))
)
@property
def _bindingLevel(self):
return 4
These get the binding level 4, consequently I shifted the binding level of the singular expressions to 5. Hard coding these values is not really a good idea though, and in C++ I would use an enum instead. I’ll have to think about how to do this in a better way later. But first I implemented the negation class Neg():
class Neg(UnaExpr):
def __str__(self):
return '-{sub}'.format(sub=self.a)
def eval(self, env):
return -self.a.eval(env)
def partial(self, var):
return Neg(self.a.partial(var))
@property
def constValue(self):
self.cv_a = self.a.constValue
if self.cv_a:
return -self.cv_a
return None
def simplify(self):
self.a = self.a.simplify()
if self.a.constValue == 0:
return Con(0)
return self
This probably does not need to be discussed in detail.
The class Sub gets deleted now and is replaced by a function of the same name, that mimics the behaviour of the previous constructor of Sub:
def Sub(expr_a, expr_b):
You might notice, that some of the previous simplification logic got lost on the way. This actually already caught by a more general rule in Add:
class Add(BinExpr):
# ...
def _selfSimplify(self):
# if one child is zero, return the other one
if self.cv_a == 0:
return self.b
if self.cv_b == 0:
return self.a
return self
There’s one other change to Add that we need:
class Add(BinExpr):
# ...
@property
def _strOperator(self):
if isinstance(self.b, Neg):
return "" # Neg will produce the minus sign
return "+"
Ok, great. If we now run all our test again, we see should only need to change the __repr__ test to:
assert repr(expr) == 'Add(Mul(Con(3), Pow(Var(x), Con(2))), Add(Var(y), Neg(Div(Con(6), Con(3)))))'
Everything else should be passing fine.
### Replacement of Div()
We now do the same thing for division, deleting the class Div and introducing:
class Inv(UnaExpr):
def __str__(self):
return '1/{sub}'.format(sub=self.a)
def eval(self, env):
return 1/self.a.eval(env)
def partial(self, var):
return Neg(Mul(
self.a.partial(var),
Inv(Pow(self.a, Con(2)))
))
@property
def constValue(self):
self.cv_a = self.a.constValue
if self.cv_a:
return 1/self.cv_a
return None
def simplify(self):
self.a = self.a.simplify()
if isinstance(self.a, Inv):
return self.a.a
if self.a.constValue == 0:
raise ValueError("Division by zero")
return self
def Div(expr_a, expr_b):
return Mul(expr_a, Inv(expr_b))
The arguments are very analogous to the Sub case, so I’m not repeating them again.
Running the tests, I needed to change the simple str() and repr() tests to:
assert str(expr) == '3*x^2+y-6*1/3'
And I deleted the other “simple” str() tests, since I really just care about the simplified string representation. All the tests there stayed valid.
str(Mul(Con(2), Mul(Con(3), Var('x'))).simplify()) # returns '2*3*x'
|
2021-04-16 13:34:37
|
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|
http://geoscien.neigae.ac.cn/CN/10.13249/j.cnki.sgs.1982.04.337
|
• 论文 •
### 广西大化水库库区喀斯特地形和渗漏分析
1. 1. 中国科学院自然资源综合考察委员会;
2. 中国科学院地理研究所
• 出版日期:1982-07-20 发布日期:1982-07-20
### KARST LANDFORMS AND LEAKAGE ANALYSES OF DAHUA RESERVOIR AREA IN GUANGXI
Zhu Jingjioo1, Lin Junshu2, Zhang Yaoguang2
1. 1. Commission for Intergrated Survey of Natural Resources, Academia Sinica;
2. Institute of Geography, Academia Sinica
• Online:1982-07-20 Published:1982-07-20
Abstract: Dahua Reservoir is cated on the Hongshui River which forms the boundary between Dauan and Mashan Counties.When it has been completed,the reservoir will be the largest hydroelectric station in Guangxi. High temperature,abundant precipitation,massive and pure carbonate rocks, much folding and faulting are the major factors in the karst development of this area.Since the Quaternary Period,the land surface has been uplifted continuously and is now typical of the geomorphological landscape of karst“Fengcong”(peak cluster)and depression. Dolines are widely distributed within the karst depression.Underground water is usually below the level of the cave mouths,although it often emerges from the Caves during the flood season.This phenomenon suggests the possibility that there is an underground river.On the basis of the evidence provided by the distribution of water sinks and the dynamic behaviour of the water level,the water sinks were used to inject fluorescent dyes and coloured lycopodium spores at different times and at possible leakage points.Tracing experiments were conducted six times basically to establish the distribution of flow and the character of the underground river in this area.The results of the observations could be related to the dynamic state of the water level. We concluded that there is no leakage from the reservoir along underground passages as a result of the series of surveys and observations concerning the geological and geomorphological conditions,cave prospecting,long-term observations of underground water slnks,pumping tests,drilling exploration,as well as tracing experiments.This research provided a scientific basis for the construction of the reservoir.
|
2022-05-28 07:54:18
|
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|
https://www.varsitytutors.com/isee_middle_level_quantitative-help/numbers-and-operations/whole-and-part
|
# ISEE Middle Level Quantitative : Whole and Part
## Example Questions
### Example Question #1 : How To Find The Part From The Whole
Harvey bought a suit at a 25% employee discount at the store where he works. The suit originally cost $350.00. How much did he end up paying? Possible Answers: Correct answer: Explanation: Finding 25% of a number is the same as multiplying it by 0.25; to get the discount, multiply 0.25 by the original purchase price of$350.00
To get the price Harvey paid, subtract the discount from the original price:
### Example Question #211 : Numbers And Operations
Which of the following is true if ?
Explanation:
Two expressions are equivalent in modulo 9 arithmetic if and only if, when each is divided by 9, the same remainder is yielded.
,
so
, so
is the correct choice.
### Example Question #3 : How To Find The Part From The Whole
is a positive integer. Which is the greater quantity?
(a) The remainder if is divided by 5
(b) The remainder if is divided by 4
(b) is the greater quantity
(a) and (b) are equal
It is impossible to determine which is greater from the information given
(a) is the greater quantity
It is impossible to determine which is greater from the information given
Explanation:
The information is insufficient.
For example, if :
This gives the division in (b) the greater remainder.
But if :
This gives the division in (a) the greater remainder.
### Example Question #4 : How To Find The Part From The Whole
is a positive even integer. Which is the greater quantity?
(a) The remainder if is divided by 6
(b) The remainder if is divided by 3.
(b) is the greater quantity
(a) is the greater quantity
(a) and (b) are equal
It is impossible to determine which is greater from the information given
(a) and (b) are equal
Explanation:
Since is an even integer, by definition, there is an integer such that
.
; therefore,
; the remainder is 0.
Also,
; the remainder is 0.
The two remainders are both equal to 0.
### Example Question #5 : How To Find The Part From The Whole
is a positive odd integer. Which is the greater quantity?
(a) The remainder if is divided by 8
(b) The remainder if is divided by 4
(b) is the greater quantity
(a) and (b) are equal
It is impossible to determine which is greater from the information given
(a) is the greater quantity
(a) is the greater quantity
Explanation:
, with a remainder of 0.
If were to yield a remainder of 0, then must be a whole number; this can only happen if is even. Since is odd, it follows that is not a whole number, and must yield a nonzero remainder. (a) must be the greater quantity.
### Example Question #1 : How To Find The Whole From The Part
150% of what number is 9,000?
Explanation:
Taking 150% of a number is the same as multiplying that number by 1.5. We can find our number, therefore, by dividing 9,000 by 1.5:
### Example Question #2 : How To Find The Whole From The Part
is a multiple of 2, but not a multiple of 6. If is divided by 6, What could be the remainder?
|
2021-11-28 00:45:25
|
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|
https://leetcode.ca/2016-05-10-162-Find-Peak-Element/
|
# Question
Formatted question description: https://leetcode.ca/all/162.html
162. Find Peak Element
A peak element is an element that is greater than its neighbors.
Given an input array nums, where nums[i] ≠ nums[i+1], find a peak element and return its index.
The array may contain multiple peaks, in that case return the index to any one of the peaks is fine.
You may imagine that nums[-1] = nums[n] = -∞.
Example 1:
Input: nums = [1,2,3,1]
Output: 2
Explanation: 3 is a peak element and your function should return the index number 2.
Example 2:
Input: nums = [1,2,1,3,5,6,4]
Output: 1 or 5
Explanation: Your function can return either index number 1 where the peak element is 2,
or index number 5 where the peak element is 6.
Note:
Your solution should be in logarithmic complexity.
@tag-array
# Algorithm
If you traverse the entire array to find the maximum value here, Time Limit Exceeded will definitely appear, but the title says that this peak can be a local maximum, so we only need to find the first local peak.
The so-called peak value is a number that is larger than the surrounding two numbers, so you only need to compare it with the surrounding two numbers.
• Since you want to compare with the left and right numbers, you have to consider the problem of out-of-bounds. The title gives nums[-1] = nums[n] = -∞, then add these two integer minimums directly to the array, and then Traverse from the second number to the penultimate number, so that there is no possibility of crossing the boundary.
• Since the question says that the peak must exist, there is a very important corner case that we should pay attention to, that is, when there is only one number in the original array, and it is the minimum value of an integer, if we have to add numbers at the beginning and end, A horizontal line will be formed, and there will be no peak value, so we directly judge the situation that there is only one number in the array at the beginning
Then, based on idea above, you can omit the step of padding the first and last values, and you can traverse from the second number to the next,
• If the second number is smaller than the first number, it means that the first number is a local peak at this time;
• Otherwise, it will continue to traverse back, and now it is an increasing trend. If a certain number is less than the previous number at this time, it means that the previous number is a local peak, just return to the position.
• If the loop ends, it means that the original array is an increasing array, just return to the last position
Java
|
2022-07-05 09:39:28
|
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|
https://physics.meta.stackexchange.com/questions/4288/how-to-get-the-only-answer-marked-as-correct
|
# How to get the only answer marked as correct
I have answered a question here. It is the only answer to a reasonably up-voted question (+7), but it has not been selected as the correct one. Short of tracking down the original poster, is there any way to 1) get it marked correct or 2) increase the chances of it getting marked correct in the future?
Nope. Especially since the OP deleted his/her account.
Sorry about that; but the only person who can mark an answer as accepted is the OP.
"Accept" - that little checkmark - does not mean "this answer is correct."
It just means the author of the question accepted it. Hence the name.
Folks accept all kinds of things. Things they find helpful, or reassuring, or funny, or insightful, or don't like but are convinced are unavoidable...
Sometimes, folks accept the truth. But there's no guarantee that something is true just because someone accepts it. In particular, if there's no actual problem being solved, the asker's opinion on answers means very little.
Fortunately, the asker isn't the only arbiter. Anyone with a bit of useful participation on the site can vote on answers. If your answer is getting up-voted, that probably means a lot more than the checkmark.
• Yeah, that is certainly fair enough, but the reputation gain makes people ($ie$ me) feel like they are contributing. It seems a reasonable thing to ask if there are other ways to get an answer marked as accepted. – levitopher May 14 '13 at 23:01
• If you're answering a lot of questions, particularly stuff that's fairly specific to the asker, that little boost from the accept - both in rep and just in what it represents (you helped someone) - is fantastic. Long-term though, most of your reputation will come from others' votes (unless you're busting the rep-cap every day by collecting dozens of accepts). – Shog9 May 14 '13 at 23:38
• Hi @levitopher, I think the amount of rep is not everything, quality and level of what you contribute counts more, and that is not always too strongly correlated with rep. High level research level theoretical physics as you are obviously doing, has at present a smaller audience than popular questions and answers here. There are some people who do very high level contributions who do not have the amount of rep they deserve because of this (and because it takes them longer to come up with new questions and answers of very high quality), but their contributions to the site are appreciated :-). – Dilaton May 15 '13 at 10:07
• I like that this answer has more votes and isn't accepted. Fine irony. – krs013 May 17 '13 at 23:47
• If only there was some way we could get the OP to accept this answer instead of the other one... – Michael May 28 '13 at 0:10
|
2020-02-27 21:48:03
|
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|
https://www.vedantu.com/question-answer/if-cos-x-tan-y-cot-y-tan-z-and-cot-z-tan-x-then-class-11-maths-cbse-5f2fa07bd2506876eca55f67
|
Question
# If cos x = tan y, cot y = tan z and cot z = tan x, then sin x is equal to:(a) $\dfrac{\sqrt{5}+1}{4}$(b) $\dfrac{\sqrt{5}-1}{4}$(c) $\dfrac{\sqrt{5}+1}{2}$(d) $\dfrac{\sqrt{5}-1}{2}$
Hint: In this question, take any one of the given equations and try to substitute other equations by manipulating the first equation using various identities and ratios of trigonometry.
It is given that,
$\cos x=\tan y....\left( i \right)$
$\cot y=\tan z....\left( ii \right)$
$\cot z=\tan x....\left( iii \right)$
Let us first solve cos x = tan y and try to simplify it.
We know by trigonometric ratios that, $\tan y=\dfrac{1}{\cot y}$
Substituting this value of tan y in the above equation we get,
$\cos x=\dfrac{1}{\cot y}$
Now we are given that tan z = cos y in equation (ii). Substituting this value of tan z in the above expression we get,
$\cos x=\dfrac{1}{\tan z}....\left( from\left( ii \right) \right)$
By using the trigonometric ratio $\tan z=\dfrac{1}{\cot z},$we get,
$\cos x=\cot z$
Also, given equation (iii) is cot z = tan x…..(from (iii))
Substituting the value of cot z from equation (iii) in the above expression, we get,
$\cos x=\tan x$
By using the trigonometric ratio, $\tan x=\dfrac{\sin x}{\cos x},$ we get,
$\cos x=\dfrac{\sin x}{\cos x}$
Cross multiplying the above equation we get,
$\Rightarrow {{\cos }^{2}}x=\sin x$
We have, ${{\sin }^{2}}x+{{\cos }^{2}}x=1,$we can write,
$\Rightarrow {{\cos }^{2}}x=1-{{\sin }^{2}}x$
Substituting this in the above equation, we get,
$1-{{\sin }^{2}}x=\sin x$
$\Rightarrow {{\sin }^{2}}x+\sin x-1=0$
This is a quadratic equation. Therefore, by using the quadratic formula, we get,
$\sin x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$
Here, a = 1, b = 1 and c = – 1.
$\sin x=\dfrac{-1\pm \sqrt{{{1}^{2}}-4\left( 1 \right)\left( -1 \right)}}{2\left( 1 \right)}$
$\Rightarrow \sin x=\dfrac{-1\pm \sqrt{1+4}}{2}$
$\Rightarrow \sin x=\dfrac{-1\pm \sqrt{5}}{2}$
$\sin x=\dfrac{-1+\sqrt{5}}{2}\text{ or }\sin x=\dfrac{-1-\sqrt{5}}{2}$
Hence, $\dfrac{-1-\sqrt{5}}{2}<-1$ and the value of sin x should lie between 0 and 1.
Therefore, ignoring $\dfrac{-1-\sqrt{5}}{2},$ we are left with $\dfrac{-1+\sqrt{5}}{2}.$
$\sin x=\dfrac{-1+\sqrt{5}}{2}$
On rearranging, we get,
$\sin x=\dfrac{\sqrt{5}-1}{2}$
Hence, option (d) is the right answer.
Note: For these types of questions to be solved very easily, you should remember all the trigonometric formulas, those are – reciprocal identities, Pythagorean identities, sum and difference identities, double angle identities, and half-angle identities. Here, by looking at the options, you can guess that the quadratic formula has been used. Therefore, to get the final answer, you must try to simplify the given equation into a quadratic equation by using any of the above mentioned formulas.
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2020-10-29 19:38:42
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https://forum.math.toronto.edu/index.php?PHPSESSID=i6kgsan0vsfpkpiho8afbjkju3&action=printpage;topic=4.0
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Toronto Math Forum
General Category => General Discussion => Technical Questions => Topic started by: Victor Ivrii on September 18, 2012, 11:59:02 PM
Title: Testing Math
Post by: Victor Ivrii on September 18, 2012, 11:59:02 PM
Testing how MathJax was hooked up
\begin{align*}
u(x,t)= &\underbracket{\frac{1}{2}\bigl[ g(x+ct)+g(x-ct)\bigr]+\frac{1}{2c}\int_{x-ct}^{x+ct} h(y)\,dy}_{=u_2}+\3pt] &\underbracket{\frac{1}{2c} \iint_{\Delta (x,t)} f(x',t' )\,dx\,d t' }_{=u_1}. \label{eq-4} \end{align*} Title: Re: Testing Math Post by: James McVittie on September 20, 2012, 10:04:04 PM This is just a test to see whether I can copy and paste from LyX: u(x, t) = \varphi(x-ct)+\phi(x+ct)-\intop_{x-ct}^{x+ct}g(y)dy Title: Re: Testing Math Post by: Victor Ivrii on September 21, 2012, 02:55:35 AM This is just a test to see whether I can copy and paste from LyX: u(x, t) = \varphi(x-ct)+\phi(x+ct)-\intop_{x-ct}^{x+ct}g(y)dy Yes, you can but need to switch on math (inline or display respectively) Code: [Select] u(x, t) = \varphi(x-ct)+\phi(x+ct)-\intop_{x-ct}^{x+ct}g(y)dyu(x, t) = \varphi(x-ct)+\phi(x+ct)-\intop_{x-ct}^{x+ct}g(y)dy Code: [Select] u(x, t) = \varphi(x-ct)+\phi(x+ct)-\intop_{x-ct}^{x+ct}g(y)dyu(x, t) = \varphi(x-ct)+\phi(x+ct)-\intop_{x-ct}^{x+ct}g(y)dy Actually I never saw \intop (just \int) and double dollars are deprecated (see my code), but your example works Title: test for math Post by: Jinlong Fu on September 23, 2012, 02:38:04 AM x>b^2, is it the same as latex? local\ mean\ level\ \qquad S_t = \alpha(\dfrac{X_t}{D_{t-s_1}W_{t-s_2}})+ (1-\alpha)(S_{t-1} + T_{t-1}) trend\ \qquad T_t = \gamma (S_t - S_{t-1}) + (1-\gamma)T_{t-1} seasonality\ 1 \ \qquad D_t = \delta (\dfrac{X_t}{S_t W_{t-s_2}}) + (1-\delta)D_{t-S_1} seasonality\ 2 \ \qquad W_t = \omega (\dfrac{X_t}{S_t D_{t-S_1}}) + (1-\omega)W_{t-s_2} \hat{X_t} = (S_t + kT_t)D_{t-s_1+k}W_{t-s_2+k} Title: Re: test for math Post by: Victor Ivrii on September 23, 2012, 05:55:35 AM x>b^2, is it the same as latex? Yes -- except MathJax neither is nor intended to be a complete LaTeX. See http://www.math.toronto.edu/courses/apm346h1/20129/about_mathjax.html (http://www.math.toronto.edu/courses/apm346h1/20129/about_mathjax.html) Note: If you have text snippet inside of math you should use \text{Your text} rather than format it as math as you did. You can also use \textrm{Your text}, \textit{Your text}. Also DoubleDollars are deprecated in LaTeX, you use \[ or \begin{equation*} \end{equation*} (without * for a numbered version)
PS I disabled and as they in the forum environment have funny side effects.
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2021-11-28 15:41:31
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https://www.physicsforums.com/threads/finding-the-r-value-for-the-series-to-converge.957110/
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# Finding the r value for the series to converge
## Homework Statement
Let ##r\in \mathbb{R}##. Determine whether ##\displaystyle \sum_{n=1}^{\infty}\sin \left(\frac{n\pi}{3}\right)\frac{1}{n^r}## converges
## The Attempt at a Solution
If ##r>1##, then ##|\sin \left(\frac{n\pi}{3}\right)\frac{1}{n^r}| \le |\frac{1}{n^r}|##. The latter converges, so by the direct comparison test, the original series converges.
Now I want to show that when ##-\infty < r \le 1## the series diverges, but I am having trouble figuring out how. Should I show that the limit of the terms is not zero?
Mark44
Mentor
## Homework Statement
Let ##r\in \mathbb{R}##. Determine whether ##\displaystyle \sum_{n=1}^{\infty}\sin \left(\frac{n\pi}{3}\right)\frac{1}{n^r}## converges
## The Attempt at a Solution
If ##r>1##, then ##|\sin \left(\frac{n\pi}{3}\right)\frac{1}{n^r}| \le |\frac{1}{n^r}|##. The latter converges, so by the direct comparison test, the original series converges.
Now I want to show that when ##-\infty < r \le 1## the series diverges, but I am having trouble figuring out how. Should I show that the limit of the terms is not zero?
If ##r \in (-\infty, 0]##, it's easy to show that the series diverges, using the Nth term test for divergence (i.e,, if ##\lim_{n \to \infty}a_n \ne 0##, then ##\sum a_n## diverges). For ##r \in (0, 1]##, a comparison of limit comparison test might be used.
If ##r \in (-\infty, 0]##, it's easy to show that the series diverges, using the Nth term test for divergence (i.e,, if ##\lim_{n \to \infty}a_n \ne 0##, then ##\sum a_n## diverges). For ##r \in (0, 1]##, a comparison of limit comparison test might be used.
I'm actually having a hard time showing the case when ##r\in(-\infty, 0]##. For argument's sake let ##p=-r##, then we have ##\lim \sin(\frac{n\pi}{3})n^p##. But I am not sure how to explicitly show that this product diverges. I am not even sure how to show that ##\sin(\frac{n\pi}{3})## diverges...
Mark44
Mentor
I'm actually having a hard time showing the case when ##r\in(-\infty, 0]##. For argument's sake let ##p=-r##, then we have ##\lim \sin(\frac{n\pi}{3})n^p##. But I am not sure how to explicitly show that this product diverges.
Let's look at things with some numbers, say r = -1.
##\frac 1 {n^r} = \frac 1 {n^{-1}} = n##. What is ##\lim_{n \to \infty} \frac 1 {n^r}##?
What if r = -1/2? What if r = -2? Etc.
Mr Davis 97 said:
I am not even sure how to show that ##\sin(\frac{n\pi}{3})## diverges...
The sine expression takes on only three different values: ##0, \frac{\sqrt 3} 2, -\frac{\sqrt 3} 2##. For n = 0, ..., 5, the sequence is ##0, \frac{\sqrt 3} 2, \frac{\sqrt 3} 2, 0, -\frac{\sqrt 3} 2, -\frac{\sqrt 3} 2##, and then repeats these terms endlessly . Can this sequence converge?
For the series, for ##r \in (\infty, 0]##, take a look again at what I said about the Nth term test for divergence.
Let's look at things with some numbers, say r = -1.
##\frac 1 {n^r} = \frac 1 {n^{-1}} = n##. What is ##\lim_{n \to \infty} \frac 1 {n^r}##?
What if r = -1/2? What if r = -2? Etc.
The sine expression takes on only three different values: ##0, \frac{\sqrt 3} 2, -\frac{\sqrt 3} 2##. For n = 0, ..., 5, the sequence is ##0, \frac{\sqrt 3} 2, \frac{\sqrt 3} 2, 0, -\frac{\sqrt 3} 2, -\frac{\sqrt 3} 2##, and then repeats these terms endlessly . Can this sequence converge?
For the series, for ##r \in (\infty, 0]##, take a look again at what I said about the Nth term test for divergence.
What I can see is that if ##r\in (-\infty, 0)##, then ##\lim_{n\to\infty}\frac{1}{n^r} = \infty##. I also see that ##\sin(\frac{n\pi}{3})## diverges because subsequneces can converge to different numbers. But I don't know how to combine these facts to show that the product diverges.
Mark44
Mentor
What I can see is that if ##r\in (-\infty, 0)##, then ##\lim_{n\to\infty}\frac{1}{n^r} = \infty##. I also see that ##\sin(\frac{n\pi}{3})## diverges because subsequneces can converge to different numbers. But I don't know how to combine these facts to show that the product diverges.
Can you show that for ##r\in (-\infty, 0)##, ##\lim_{n \to \infty} \sin(\frac{n\pi} 3)\frac 1 {n^r} \ne 0##? That's all you need to show per the Nth Term Test I cited.
Can you show that for ##r\in (-\infty, 0)##, ##\lim_{n \to \infty} \sin(\frac{n\pi} 3)\frac 1 {n^r} \ne 0##? That's all you need to show per the Nth Term Test I cited.
It's intuitively obvious. The sin oscillates while the other term blows up. So clearly it doesn't converge. But I'm not sure how to show this rigorously...
LCKurtz
Homework Helper
Gold Member
It's intuitively obvious. The sin oscillates while the other term blows up. So clearly it doesn't converge. But I'm not sure how to show this rigorously...
Take a subsequence of ##\frac{k\pi} 3## so the sine doesn't oscillate and isn't zero.
Ray Vickson
Homework Helper
Dearly Missed
What I can see is that if ##r\in (-\infty, 0)##, then ##\lim_{n\to\infty}\frac{1}{n^r} = \infty##. I also see that ##\sin(\frac{n\pi}{3})## diverges because subsequneces can converge to different numbers. But I don't know how to combine these facts to show that the product diverges.
There is a fundamental theorem which states that the infinite series ##\sum_n t_n## converges only if ##|t_n| \to 0## as ##n \to \infty.## So, terms going to zero is a necessary (but by no means sufficient) condition for convergence of the series. I would be shocked if your book or notes does not state and prove this very fundamental fact---it is the first order of business when discussing infinite series!
You can (and should) look at the values of ##\sin(\pi n/3)## for a few values of ##n = 1,2,3, \ldots##, to understand whether or not the presence of the sine factor really complicates things very much.
Take a subsequence of ##\frac{k\pi} 3## so the sine doesn't oscillate and isn't zero.
So I want to show that for ##r\in (-\infty, 0)##, the series diverges. If we look at the subsequence ##a_{6k-5} = \frac{\sqrt{3}}{2}\frac{1}{(6k-5)^r}##, we see that ##\lim_{k\to\infty}a_{6k-5}=+\infty##. Since a subsequence diverges to infinity, ##\lim_{n\to\infty}a_n \not = 0##, so the series diverges. Is this correct?
LCKurtz
Homework Helper
Gold Member
So I want to show that for ##r\in (-\infty, 0)##, the series diverges. If we look at the subsequence ##a_{6k-5} = \frac{\sqrt{3}}{2}\frac{1}{(6k-5)^r}##, we see that ##\lim_{k\to\infty}a_{6k-5}=+\infty##. Since a subsequence diverges to infinity, ##\lim_{n\to\infty}a_n \not = 0##, so the series diverges. Is this correct?
That looks OK. But I wouldn't phrase it as ##\lim_{n\to\infty}a_n \ne 0## because that seems to suggest it has a limit but the limit isn't ##0##. It's better to just say ##\lim_{n\to\infty}a_n## does not exist to avoid the ambiguity.
Mr Davis 97
That looks OK. But I wouldn't phrase it as ##\lim_{n\to\infty}a_n \ne 0## because that seems to suggest it has a limit but the limit isn't ##0##. It's better to just say ##\lim_{n\to\infty}a_n## does not exist to avoid the ambiguity.
I'm not really seeing how to do the ##0<r\le 1## case. Mark44 said one might use the comparison test, but I am not seeing what to compare it to...
Mark44
Mentor
I'm not really seeing how to do the ##0<r\le 1## case. Mark44 said one might use the comparison test, but I am not seeing what to compare it to...
I don't either. I thought that it might work by comparing it to a divergent p-series, but after some thought, I don't think that would work.
Here's a different direction to try. The ##\sin(\frac{n\pi}3)## factor repeats a cycle of length 6: ##0, \frac{\sqrt 3} 2, \frac{\sqrt 3} 2, 0, -\frac{\sqrt 3} 2, -\frac{\sqrt 3} 2##, so your series looks like ##\left(\frac{\sqrt 3} 2 (\frac 1 {1^r} + \frac 1 {2^r}) - \frac{\sqrt 3} 2(\frac 1 {4^r} + \frac 1 {5^r})\right) + \left(\frac{\sqrt 3} 2(\frac 1 {7^r} + \frac 1 {8^r}) - \frac{\sqrt 3} 2(\frac 1 {10^r} + \frac 1 {11^r})\right) + \dots##
##=\frac{\sqrt 3} 2 \left( (\frac 1 {1^r} + \frac 1 {2^r} - \frac 1 {4^r} - \frac 1 {5^r} ) + (\frac 1 {7^r} + \frac 1 {8^r} - \frac 1 {10^r} - \frac 1 {11^r}) + \dots \right)##. If you can figure out what the general term looks like, I don't think it would be hard to show that the series diverges for ##r \in [0, 1]##
Ray Vickson
Homework Helper
Dearly Missed
I don't either. I thought that it might work by comparing it to a divergent p-series, but after some thought, I don't think that would work.
Here's a different direction to try. The ##\sin(\frac{n\pi}3)## factor repeats a cycle of length 6: ##0, \frac{\sqrt 3} 2, \frac{\sqrt 3} 2, 0, -\frac{\sqrt 3} 2, -\frac{\sqrt 3} 2##, so your series looks like ##\left(\frac{\sqrt 3} 2 (\frac 1 {1^r} + \frac 1 {2^r}) - \frac{\sqrt 3} 2(\frac 1 {4^r} + \frac 1 {5^r})\right) + \left(\frac{\sqrt 3} 2(\frac 1 {7^r} + \frac 1 {8^r}) - \frac{\sqrt 3} 2(\frac 1 {10^r} + \frac 1 {11^r})\right) + \dots##
##=\frac{\sqrt 3} 2 \left( (\frac 1 {1^r} + \frac 1 {2^r} - \frac 1 {4^r} - \frac 1 {5^r} ) + (\frac 1 {7^r} + \frac 1 {8^r} - \frac 1 {10^r} - \frac 1 {11^r}) + \dots \right)##. If you can figure out what the general term looks like, I don't think it would be hard to show that the series diverges for ##r \in [0, 1]##
The series actually converges when ##r = 1,## but showing that is a bit tricky.
In fact, the series can be written as
$$S = \frac{\sqrt{3}}{2} \sum_{k=0}^{\infty} \left( \frac{1}{(6k+1)^r}+\frac{1}{(6k+2)^r}-\frac{1}{(6k+4)^r} - \frac{1}{(6k+5)^r} \right)$$
Would Dirichlet's test work in this case? https://en.wikipedia.org/wiki/Dirichlet's_test
If we let ##a_n=\frac{1}{n^r}## and ##b_n=\sin\frac{n\pi}{3}##. Then we see that ##\frac{1}{(n+1)^r}\le\frac{1}{n^r}## and ##\lim_{n\to\infty}\frac{1}{n^r} = 0##. We also have that ##\sum_{k=1}^{n}\sin (\frac{n\pi}{3}) \le \sqrt{3}## for all ##n\in\mathbb{N}##.
Last edited:
Mark44
Mentor
Would Dirichlet's test work in this case? https://en.wikipedia.org/wiki/Dirichlet's_test
If we let ##a_n=\frac{1}{n^r}## and ##b_n=\sin\frac{n\pi}{3}##. Then we see that ##\frac{1}{(n+1)^r}\le\frac{1}{n^r}## and ##\lim_{n\to\infty}\frac{1}{n^r} = 0##. We also have that ##\sum_{k=1}^{n}\sin (\frac{n\pi}{3}) \le \sqrt{3}## for all ##n\in\mathbb{N}##.
Dirichlet's Theorem requires that ##|\sum_{n = 1}^N b_n | \le M## for every positive integer N. With ##b_n = \sin(\frac{n\pi} 3)## that inequality isn't satisfied. Also, the theorem says that ##\sum_{n = 1}^\infty a_nb_n## converges, and you're trying to show that it diverges, at least for values of ##r \in (-\infty, 1)##.
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2021-04-12 17:14:26
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https://www.physicsforums.com/threads/euler-substitution-good-sources.515810/
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# Euler substitution (Good sources)
1. Jul 21, 2011
Both online and books would be suffice. Also videos, if there are any.
All help would be greatly appreciated =)
2. Jul 21, 2011
### MathematicalPhysicist
Shouldn't it be in any integral and differential calculus books?
3. Jul 21, 2011
Well it is not in my book =(
And ofcourse different books explain things in different ways. Some good and some horrendous. So I was wondering if anyone knew about a book having a clear, good explenation of it.
4. Jul 21, 2011
### nickalh
Are you meaning integrals and derivatives with e^x, e^u, ln x & ln u ?
A solid grasp of the substitution guidelines is a great starting point.
Are you looking principles like, when integrating,
Choose the most complex u, which has the derivative of u multiplied elsewhere in the integrand.
?
I don't or rarely see those principles written in textbooks. Usually, the professor or a tutor is the best source for guidelines. Most colleges have free tutoring clinics available with varying instructional quality. Several in my area will tutor students from other colleges.
5. Jul 22, 2011
I was talking about three substitutions, I thought they were called euler substitutions. But I had a hard time finding them left.
$$\sqrt{ax^2+bx+c}=t-\sqrt{a}x$$
$$\sqrt{ax^2+bx+c}=xt + \sqrt{c}$$
$$\sqrt{ax^2+bx+c}=x(t-c)$$'
Sorry about my english, nt sure what these are called.
6. Jul 22, 2011
### nickalh
Again give us a context.
Are these for evaluating integrals? For differential equations? Something else like cubic and higher degree equations?
7. Jul 22, 2011
Yeah, they are for evaluating integrals. Called euler substitutions, or atleast I think they are calle thath.
I sort of want to know when these are useful, when to preffer one over the other one. When to use this over for example trigonometric substitution. Also wondering if there are any integrals that "must" be solved by this method
8. Jul 22, 2011
### disregardthat
I think what you may be looking for is Abel substitution. It is basically t = sqrt(ax^2+bx+c). After that a simple linear transformation will give your examples.
9. Jul 22, 2011
### nickalh
I doubt you'll find an entire book on it. One might find a section using it or an entire chapter using it.
I google Able substitution which led me to Abel transforms. Not much success there.
Can you give me some example integrals you're trying to evaluate?
I can probably figure out application methods with more details.
Neither
http://www.wolframalpha.com/input/?i=integral+1%2F+root+%28ax^2%2Bbx%2Bc%29+dx
nor
http://www.wolframalpha.com/input/?i=integral+root+%28ax^2%2Bbx%2Bc%29+dx
are known to WolframAlpha, the most extensive, free computer integrator that exists. So I need at least a few examples to help you.
10. Jul 22, 2011
### nickalh
Correction to previous post:
http://www.wolframalpha.com/input/?i=integral+%28ax^2%2Bbx%2Bc%29+^.5dx
and
http://www.wolframalpha.com/input/?i=integral+1%2F+%28ax^2%2Bbx%2Bc%29+^.5dx
both evaluate. The show steps feature on the first link shows the substitution and uses one of yours. Notice how WolframAlpha, abbreviated W|A, first completes the square, then does the substitution?
So we've got a way to see how it works in practice. Perhaps ask WolframAlpha enough integrals and you figure out the how and why?
As to when to use these vs. when to use trig. substitution, trig. substitution on $\sqrt{trinomial}$ is probably even uglier than the method W|A shows. So wouldn't it make sense to use these for $\sqrt{trinomial}$, but trig. substitution for forms similar to $\sqrt{1\pm x^2}$?
I've reached the limit of how I can help. God bless you & bye.
11. Jul 22, 2011
### nickalh
One more thought occurred to me. The choice of which of the three t expressions to substitute will be influenced by what makes the square root real? Unless, you've learned or are learning calculus of complex numbers.
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2018-05-23 13:35:59
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https://www.physicsforums.com/threads/timelike-metrics.667893/
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# Timelike metrics
In a given metric say Scwarzchild is $\frac{\partial}{\partial t}$ time-like when the coefficient in front of the dxdx term is <0 and space-like when the coefficients in front of spatial terms >0 ?
and what is a timelike vector is it simply a vector in the coefficient that satisfies the above criteria?
Related Special and General Relativity News on Phys.org
#### PAllen
In a given metric say Scwarzchild is $\frac{\partial}{\partial t}$ time-like when the coefficient in front of the dxdx term is <0 and space-like when the coefficients in front of spatial terms >0 ?
and what is a timelike vector is it simply a vector in the coefficient that satisfies the above criteria?
Are you talking about the killing vector? That's the abbreviated notation normally used for it. You see that it is a killing vector in this case because it makes all the metric components vanish. You see that it is timelike or spacelike by the sign of gtt.
#### WannabeNewton
I believe he is talking about the basis vector that is dual to $dt$ i.e. $dt(\partial t) = 1$. This is very coordinate chart specific but yes as PAllen already stated it is based on the sign of gtt. In general on a space - time M, at $p\in M$ some $v\in T_{p}(M)$ is time - like if $g_{p}(v,v) < 0$ using the -+++ convention.
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2019-11-17 20:55:52
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https://eprints.lib.hokudai.ac.jp/dspace/handle/2115/69689
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Hokkaido University | Library | HUSCAP Advanced Search 言語 日本語 English
# Total absolute horospherical curvature of submanifolds in hyperbolic space
Files in This Item:
pre880.pdf 266.92 kB PDF View/Open
Title: Total absolute horospherical curvature of submanifolds in hyperbolic space Authors: Buosi, Marcelo Browse this author Izumiya, Shyuichi Browse this author Soares Ruas, Maria Aparecida Browse this author Keywords: hyperbolic space horospherical geometry the Chern-Lashof type inequality Issue Date: 2007 Publisher: Department of Mathematics, Hokkaido University Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 880 Start Page: 1 End Page: 16 Abstract: We study the horospherical geometry of submanifolds in hyperbolic space. The main result is a formula for the total absolute horospherical curvature of $M,$ which implies, for the horospherical geometry, the analogues of classical inequalities of the Euclidean Geometry. We prove the horospherical Chern-Lashof inequality for surfaces in $3$-space and the horospherical Fenchel and Fary-Milnor's theorems. Type: bulletin (article) URI: http://hdl.handle.net/2115/69689 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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2023-01-31 10:22:29
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http://www.tug.org/pipermail/texhax/2011-April/017168.html
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# [texhax] Placing unknown images arbitrarily by lower left corner
Peter Davis pfd at pfdstudio.com
Mon Apr 4 17:42:11 CEST 2011
On Sun, Apr 3, 2011 at 5:14 PM, Peter Davis <pfd at pfdstudio.com> wrote:
> I've been going around and around on this, and still have not come up with
> a general solution. I'm at my wit's end. (Apparently not a very long
> distance to travel.)
>
> The XML gives a rectangular region on the page (<fo:block-container>), a
> path to an image of unknown dimensions, and possible a transform matrix to
> apply to that image.
>
> Even ignoring rotation and shear at this point, the problem is:
>
> 1) \begin{textblock}[w](x,y) sets the width and the upper left corner of
> the <fo:block-container>
>
> 2) I have to get to the lower left corner to place the image with
> \includegraphics. I can do that with \raisebox or with Heiko's settobox
> package, using \setboxlower, or probably 3 or 4 other technique.
>
> 3) I then also have to translate the lower left corner by an amount
> specified by a transformation matrix in the XML. This is where I'm getting
> hung up, I think. I can't find any way to both position the lower left
> corner, and then translate the image by some amount relative to that.
>
>
Ok, I think I have a workable solution, at least for the cases I've tested
so far. If the image specifies a transformation matrix, then I wind up
generating something like:
\begin{picture}(0,0)(0,h) % h is the height of the image area
\put(tx,ty){\usebox{myimg}}
\end{picture}
On the other hand, if no transformation matrix is specified, I can just use:
\raisebox{-\height}{\usebox{myimg}}
There will be more complex cases where I have to scale the image to fit a
specified rectangle, or rotate or shear an image, but I think I can handle
those. (Well, actually, *is* there a way to apply a shear transform to an
image or a block of text?)
Thanks!
-pd
--
----
The Tech Curmudgeon
http://www.techcurmudgeon.com
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2018-01-22 14:17:09
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https://www.cut-the-knot.org/m/Algebra/InequalityWithCyclicSumsOnBothSides3.shtml
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# An Inequality with Cyclic Sums on Both Sides III
### Solution
By the AM-GM inequality,
$x^6z^3+x^6z^3+y^6x^3 \ge 3\sqrt[3]{x^{15}z^6y^6}=3x^5y^2z^2.$
Similarly,
\displaystyle \begin{align} &y^6x^3+y^6x^3+z^6y^3\ge 3x^2y^5z^2\\ &z^6y^3+z^6y^3+x^6z^3\geq 3x^2y^2z^5 \end{align}
$3(x^6z^3+y^6x^3+z^6y^3)\geq 3x^2y^2z^2(x^3+y^3+z^3),$
i.e.,
$x^6z^3+y^6z^3+z^6y^3\geq x^2y^2z^2(x^3+y^3+z^3)$
Suffice it to prove that
$\displaystyle \frac{x^2y^2z^2(x^3+y^3+z^3)}{x^2y^2z^2}\geq \frac{x^3+y^3+z^3+3xyz}{2},$
or, equivalently,
$\displaystyle 2(x^3+y^3+z^3)\geq x^3+y^3+z^3+3xyz,$
i.e.,
$\displaystyle x^3+y^3+z^3\geq 3xyz,$
which is true by the AM-GM inequality: $x^3+y^3+z^3\geq 3\sqrt[3]{x^3y^3z^3}=3xyz.$
### Acknowledgment
Dan Sitaru has kindly emailed me a LaTeX file with his solution to the above problem, originally from the School Science and Mathematics Association. The problem is by IULIANA TRAŞCĂ, SCORNICESTI, ROMANIA.
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2019-07-18 13:42:36
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https://zbmath.org/?q=ci%3A1158.57011
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# zbMATH — the first resource for mathematics
Bridge number and Conway products. (English) Zbl 1200.57003
By a classical result of H. Schubert, if $$\beta(K)$$ is the bridge number of a knot $$K$$, then $$\beta - 1$$ is additive with respect to the knot sum (or product). M. Scharlemann and M. Tomova [Mich. Math. J. 56, No. 1, 113–144 (2008; Zbl 1158.57011)] constructed a generalized Conway product of two knots such that $$\beta - 1$$ is subadditive. This construction is non-unique and connects two knots along two disjoint arcs of either knot in a certain way. In the present work, the above result is complemented by a lower bound on the bridge number of the above product, namely the inequality $$\beta(K) \geq \beta(K_1) - 1$$, where $$K$$ is a generalized Conway product and $$K_1$$ is the so-called distinguished factor. As a prerequisite, for a class of geometrically defined cases, it is proved that a knot and an accompanying Conway sphere can be moved to a standard situation with respect to the canonical height function of the 3-sphere.
##### MSC:
57M25 Knots and links in the $$3$$-sphere (MSC2010) 57M27 Invariants of knots and $$3$$-manifolds (MSC2010) 57M50 General geometric structures on low-dimensional manifolds
Full Text:
##### References:
[1] J H Conway, An enumeration of knots and links, and some of their algebraic properties, Pergamon (1970) 329 · Zbl 0202.54703 [2] W B R Lickorish, Prime knots and tangles, Trans. Amer. Math. Soc. 267 (1981) 321 · Zbl 0472.57004 · doi:10.2307/1998587 [3] M Scharlemann, Thin position in the theory of classical knots (editors W Menasco, M Thistlethwaite), Elsevier (2005) 429 · Zbl 1097.57013 [4] M Scharlemann, M Tomova, Conway products and links with multiple bridge surfaces, Michigan Math. J. 56 (2008) 113 · Zbl 1158.57011 · doi:10.1307/mmj/1213972401 [5] H Schubert, Über eine numerische Knoteninvariante, Math. Z. 61 (1954) 245 · Zbl 0058.17403 · doi:10.1007/BF01181346 · eudml:169462 [6] J Schultens, Additivity of bridge numbers of knots, Math. Proc. Cambridge Philos. Soc. 135 (2003) 539 · Zbl 1054.57011 · doi:10.1017/S0305004103006832
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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2021-06-24 09:21:14
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https://www.nag.com/numeric/py/nagdoc_latest/naginterfaces.library.stat.prob_beta_vector.html
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naginterfaces.library.stat.prob_beta_vector¶
naginterfaces.library.stat.prob_beta_vector(tail, beta, a, b)[source]
prob_beta_vector computes a number of lower or upper tail probabilities for the beta distribution.
For full information please refer to the NAG Library document for g01se
https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/g01/g01sef.html
Parameters
tailstr, length 1, array-like, shape
Indicates whether a lower or upper tail probabilities are required. For , for :
The lower tail probability is returned, i.e., .
The upper tail probability is returned, i.e., .
betafloat, array-like, shape
, the value of the beta variate.
afloat, array-like, shape
, the first parameter of the required beta distribution.
bfloat, array-like, shape
, the second parameter of the required beta distribution.
Returns
pfloat, ndarray, shape
, the probabilities for the beta distribution.
ivalidint, ndarray, shape
indicates any errors with the input arguments, with
No error.
On entry, invalid value supplied in when calculating .
On entry, , or, .
On entry, , or, .
Raises
NagValueError
(errno )
On entry, .
Constraint: .
(errno )
On entry, .
Constraint: .
(errno )
On entry, .
Constraint: .
(errno )
On entry, .
Constraint: .
Warns
NagAlgorithmicWarning
(errno )
On entry, at least one value of , , or was invalid.
Notes
The lower tail probability, is defined by
The function , also known as the incomplete beta function is calculated using specfun.beta_incomplete.
The input arrays to this function are designed to allow maximum flexibility in the supply of vector arguments by re-using elements of any arrays that are shorter than the total number of evaluations required. See the G01 Introduction for further information.
References
NIST Digital Library of Mathematical Functions
Hastings, N A J and Peacock, J B, 1975, Statistical Distributions, Butterworth
Majumder, K L and Bhattacharjee, G P, 1973, Algorithm AS 63. The incomplete beta integral, Appl. Statist. (22), 409–411
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2022-05-18 03:43:04
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https://sites.math.rutgers.edu/~bumby/nyntsem/ny201210.html
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# Multiplicative representations of integers and Ramsey's theorem
Let ${\mathcal B} = (B_1,\ldots, B_h)$ be an $h$-tuple of sets of positive integers. Let $g_{\mathcal B}(n)$ count the number of representations of $n$ in the form $n = b_1\cdots b_h$, where $b_i \in B_i$ for all $i \in \{1,\ldots, h\}$. It is proved that $\liminf_{n\rightarrow \infty} g_{\mathcal B}(n) \geq 2$ implies $\limsup_{n\rightarrow \infty} g_{\mathcal B}(n) = \infty$.
Mel Nathanson
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2022-07-06 20:10:53
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https://people.maths.bris.ac.uk/~matyd/GroupNames/448i1/C2xQ8.10D14.html
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Copied to
clipboard
## G = C2×Q8.10D14order 448 = 26·7
### Direct product of C2 and Q8.10D14
Series: Derived Chief Lower central Upper central
Derived series C1 — C14 — C2×Q8.10D14
Chief series C1 — C7 — C14 — D14 — C22×D7 — C2×C4×D7 — C2×Q8×D7 — C2×Q8.10D14
Lower central C7 — C14 — C2×Q8.10D14
Upper central C1 — C22 — C22×Q8
Generators and relations for C2×Q8.10D14
G = < a,b,c,d,e | a2=b4=1, c2=d14=e2=b2, ab=ba, ac=ca, ad=da, ae=ea, cbc-1=ebe-1=b-1, bd=db, dcd-1=ece-1=b2c, ede-1=d13 >
Subgroups: 2868 in 794 conjugacy classes, 447 normal (11 characteristic)
C1, C2, C2, C2, C4, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, Q8, Q8, C23, C23, D7, C14, C14, C14, C22×C4, C22×C4, C2×D4, C2×Q8, C2×Q8, C4○D4, Dic7, C28, D14, D14, C2×C14, C2×C14, C2×C14, C22×Q8, C22×Q8, C2×C4○D4, 2- 1+4, Dic14, C4×D7, D28, C2×Dic7, C7⋊D4, C2×C28, C7×Q8, C22×D7, C22×C14, C2×2- 1+4, C2×Dic14, C2×C4×D7, C2×D28, C4○D28, Q8×D7, Q82D7, C2×C7⋊D4, C22×C28, Q8×C14, C2×C4○D28, C2×Q8×D7, C2×Q82D7, Q8.10D14, Q8×C2×C14, C2×Q8.10D14
Quotients: C1, C2, C22, C23, D7, C24, D14, 2- 1+4, C25, C22×D7, C2×2- 1+4, C23×D7, Q8.10D14, D7×C24, C2×Q8.10D14
Smallest permutation representation of C2×Q8.10D14
On 224 points
Generators in S224
(1 169)(2 170)(3 171)(4 172)(5 173)(6 174)(7 175)(8 176)(9 177)(10 178)(11 179)(12 180)(13 181)(14 182)(15 183)(16 184)(17 185)(18 186)(19 187)(20 188)(21 189)(22 190)(23 191)(24 192)(25 193)(26 194)(27 195)(28 196)(29 126)(30 127)(31 128)(32 129)(33 130)(34 131)(35 132)(36 133)(37 134)(38 135)(39 136)(40 137)(41 138)(42 139)(43 140)(44 113)(45 114)(46 115)(47 116)(48 117)(49 118)(50 119)(51 120)(52 121)(53 122)(54 123)(55 124)(56 125)(57 156)(58 157)(59 158)(60 159)(61 160)(62 161)(63 162)(64 163)(65 164)(66 165)(67 166)(68 167)(69 168)(70 141)(71 142)(72 143)(73 144)(74 145)(75 146)(76 147)(77 148)(78 149)(79 150)(80 151)(81 152)(82 153)(83 154)(84 155)(85 218)(86 219)(87 220)(88 221)(89 222)(90 223)(91 224)(92 197)(93 198)(94 199)(95 200)(96 201)(97 202)(98 203)(99 204)(100 205)(101 206)(102 207)(103 208)(104 209)(105 210)(106 211)(107 212)(108 213)(109 214)(110 215)(111 216)(112 217)
(1 209 15 223)(2 210 16 224)(3 211 17 197)(4 212 18 198)(5 213 19 199)(6 214 20 200)(7 215 21 201)(8 216 22 202)(9 217 23 203)(10 218 24 204)(11 219 25 205)(12 220 26 206)(13 221 27 207)(14 222 28 208)(29 77 43 63)(30 78 44 64)(31 79 45 65)(32 80 46 66)(33 81 47 67)(34 82 48 68)(35 83 49 69)(36 84 50 70)(37 57 51 71)(38 58 52 72)(39 59 53 73)(40 60 54 74)(41 61 55 75)(42 62 56 76)(85 192 99 178)(86 193 100 179)(87 194 101 180)(88 195 102 181)(89 196 103 182)(90 169 104 183)(91 170 105 184)(92 171 106 185)(93 172 107 186)(94 173 108 187)(95 174 109 188)(96 175 110 189)(97 176 111 190)(98 177 112 191)(113 163 127 149)(114 164 128 150)(115 165 129 151)(116 166 130 152)(117 167 131 153)(118 168 132 154)(119 141 133 155)(120 142 134 156)(121 143 135 157)(122 144 136 158)(123 145 137 159)(124 146 138 160)(125 147 139 161)(126 148 140 162)
(1 139 15 125)(2 126 16 140)(3 113 17 127)(4 128 18 114)(5 115 19 129)(6 130 20 116)(7 117 21 131)(8 132 22 118)(9 119 23 133)(10 134 24 120)(11 121 25 135)(12 136 26 122)(13 123 27 137)(14 138 28 124)(29 184 43 170)(30 171 44 185)(31 186 45 172)(32 173 46 187)(33 188 47 174)(34 175 48 189)(35 190 49 176)(36 177 50 191)(37 192 51 178)(38 179 52 193)(39 194 53 180)(40 181 54 195)(41 196 55 182)(42 183 56 169)(57 85 71 99)(58 100 72 86)(59 87 73 101)(60 102 74 88)(61 89 75 103)(62 104 76 90)(63 91 77 105)(64 106 78 92)(65 93 79 107)(66 108 80 94)(67 95 81 109)(68 110 82 96)(69 97 83 111)(70 112 84 98)(141 217 155 203)(142 204 156 218)(143 219 157 205)(144 206 158 220)(145 221 159 207)(146 208 160 222)(147 223 161 209)(148 210 162 224)(149 197 163 211)(150 212 164 198)(151 199 165 213)(152 214 166 200)(153 201 167 215)(154 216 168 202)
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28)(29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56)(57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84)(85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112)(113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140)(141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196)(197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224)
(1 146 15 160)(2 159 16 145)(3 144 17 158)(4 157 18 143)(5 142 19 156)(6 155 20 141)(7 168 21 154)(8 153 22 167)(9 166 23 152)(10 151 24 165)(11 164 25 150)(12 149 26 163)(13 162 27 148)(14 147 28 161)(29 88 43 102)(30 101 44 87)(31 86 45 100)(32 99 46 85)(33 112 47 98)(34 97 48 111)(35 110 49 96)(36 95 50 109)(37 108 51 94)(38 93 52 107)(39 106 53 92)(40 91 54 105)(41 104 55 90)(42 89 56 103)(57 173 71 187)(58 186 72 172)(59 171 73 185)(60 184 74 170)(61 169 75 183)(62 182 76 196)(63 195 77 181)(64 180 78 194)(65 193 79 179)(66 178 80 192)(67 191 81 177)(68 176 82 190)(69 189 83 175)(70 174 84 188)(113 220 127 206)(114 205 128 219)(115 218 129 204)(116 203 130 217)(117 216 131 202)(118 201 132 215)(119 214 133 200)(120 199 134 213)(121 212 135 198)(122 197 136 211)(123 210 137 224)(124 223 138 209)(125 208 139 222)(126 221 140 207)
G:=sub<Sym(224)| (1,169)(2,170)(3,171)(4,172)(5,173)(6,174)(7,175)(8,176)(9,177)(10,178)(11,179)(12,180)(13,181)(14,182)(15,183)(16,184)(17,185)(18,186)(19,187)(20,188)(21,189)(22,190)(23,191)(24,192)(25,193)(26,194)(27,195)(28,196)(29,126)(30,127)(31,128)(32,129)(33,130)(34,131)(35,132)(36,133)(37,134)(38,135)(39,136)(40,137)(41,138)(42,139)(43,140)(44,113)(45,114)(46,115)(47,116)(48,117)(49,118)(50,119)(51,120)(52,121)(53,122)(54,123)(55,124)(56,125)(57,156)(58,157)(59,158)(60,159)(61,160)(62,161)(63,162)(64,163)(65,164)(66,165)(67,166)(68,167)(69,168)(70,141)(71,142)(72,143)(73,144)(74,145)(75,146)(76,147)(77,148)(78,149)(79,150)(80,151)(81,152)(82,153)(83,154)(84,155)(85,218)(86,219)(87,220)(88,221)(89,222)(90,223)(91,224)(92,197)(93,198)(94,199)(95,200)(96,201)(97,202)(98,203)(99,204)(100,205)(101,206)(102,207)(103,208)(104,209)(105,210)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)(112,217), (1,209,15,223)(2,210,16,224)(3,211,17,197)(4,212,18,198)(5,213,19,199)(6,214,20,200)(7,215,21,201)(8,216,22,202)(9,217,23,203)(10,218,24,204)(11,219,25,205)(12,220,26,206)(13,221,27,207)(14,222,28,208)(29,77,43,63)(30,78,44,64)(31,79,45,65)(32,80,46,66)(33,81,47,67)(34,82,48,68)(35,83,49,69)(36,84,50,70)(37,57,51,71)(38,58,52,72)(39,59,53,73)(40,60,54,74)(41,61,55,75)(42,62,56,76)(85,192,99,178)(86,193,100,179)(87,194,101,180)(88,195,102,181)(89,196,103,182)(90,169,104,183)(91,170,105,184)(92,171,106,185)(93,172,107,186)(94,173,108,187)(95,174,109,188)(96,175,110,189)(97,176,111,190)(98,177,112,191)(113,163,127,149)(114,164,128,150)(115,165,129,151)(116,166,130,152)(117,167,131,153)(118,168,132,154)(119,141,133,155)(120,142,134,156)(121,143,135,157)(122,144,136,158)(123,145,137,159)(124,146,138,160)(125,147,139,161)(126,148,140,162), (1,139,15,125)(2,126,16,140)(3,113,17,127)(4,128,18,114)(5,115,19,129)(6,130,20,116)(7,117,21,131)(8,132,22,118)(9,119,23,133)(10,134,24,120)(11,121,25,135)(12,136,26,122)(13,123,27,137)(14,138,28,124)(29,184,43,170)(30,171,44,185)(31,186,45,172)(32,173,46,187)(33,188,47,174)(34,175,48,189)(35,190,49,176)(36,177,50,191)(37,192,51,178)(38,179,52,193)(39,194,53,180)(40,181,54,195)(41,196,55,182)(42,183,56,169)(57,85,71,99)(58,100,72,86)(59,87,73,101)(60,102,74,88)(61,89,75,103)(62,104,76,90)(63,91,77,105)(64,106,78,92)(65,93,79,107)(66,108,80,94)(67,95,81,109)(68,110,82,96)(69,97,83,111)(70,112,84,98)(141,217,155,203)(142,204,156,218)(143,219,157,205)(144,206,158,220)(145,221,159,207)(146,208,160,222)(147,223,161,209)(148,210,162,224)(149,197,163,211)(150,212,164,198)(151,199,165,213)(152,214,166,200)(153,201,167,215)(154,216,168,202), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196)(197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224), (1,146,15,160)(2,159,16,145)(3,144,17,158)(4,157,18,143)(5,142,19,156)(6,155,20,141)(7,168,21,154)(8,153,22,167)(9,166,23,152)(10,151,24,165)(11,164,25,150)(12,149,26,163)(13,162,27,148)(14,147,28,161)(29,88,43,102)(30,101,44,87)(31,86,45,100)(32,99,46,85)(33,112,47,98)(34,97,48,111)(35,110,49,96)(36,95,50,109)(37,108,51,94)(38,93,52,107)(39,106,53,92)(40,91,54,105)(41,104,55,90)(42,89,56,103)(57,173,71,187)(58,186,72,172)(59,171,73,185)(60,184,74,170)(61,169,75,183)(62,182,76,196)(63,195,77,181)(64,180,78,194)(65,193,79,179)(66,178,80,192)(67,191,81,177)(68,176,82,190)(69,189,83,175)(70,174,84,188)(113,220,127,206)(114,205,128,219)(115,218,129,204)(116,203,130,217)(117,216,131,202)(118,201,132,215)(119,214,133,200)(120,199,134,213)(121,212,135,198)(122,197,136,211)(123,210,137,224)(124,223,138,209)(125,208,139,222)(126,221,140,207)>;
G:=Group( (1,169)(2,170)(3,171)(4,172)(5,173)(6,174)(7,175)(8,176)(9,177)(10,178)(11,179)(12,180)(13,181)(14,182)(15,183)(16,184)(17,185)(18,186)(19,187)(20,188)(21,189)(22,190)(23,191)(24,192)(25,193)(26,194)(27,195)(28,196)(29,126)(30,127)(31,128)(32,129)(33,130)(34,131)(35,132)(36,133)(37,134)(38,135)(39,136)(40,137)(41,138)(42,139)(43,140)(44,113)(45,114)(46,115)(47,116)(48,117)(49,118)(50,119)(51,120)(52,121)(53,122)(54,123)(55,124)(56,125)(57,156)(58,157)(59,158)(60,159)(61,160)(62,161)(63,162)(64,163)(65,164)(66,165)(67,166)(68,167)(69,168)(70,141)(71,142)(72,143)(73,144)(74,145)(75,146)(76,147)(77,148)(78,149)(79,150)(80,151)(81,152)(82,153)(83,154)(84,155)(85,218)(86,219)(87,220)(88,221)(89,222)(90,223)(91,224)(92,197)(93,198)(94,199)(95,200)(96,201)(97,202)(98,203)(99,204)(100,205)(101,206)(102,207)(103,208)(104,209)(105,210)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)(112,217), (1,209,15,223)(2,210,16,224)(3,211,17,197)(4,212,18,198)(5,213,19,199)(6,214,20,200)(7,215,21,201)(8,216,22,202)(9,217,23,203)(10,218,24,204)(11,219,25,205)(12,220,26,206)(13,221,27,207)(14,222,28,208)(29,77,43,63)(30,78,44,64)(31,79,45,65)(32,80,46,66)(33,81,47,67)(34,82,48,68)(35,83,49,69)(36,84,50,70)(37,57,51,71)(38,58,52,72)(39,59,53,73)(40,60,54,74)(41,61,55,75)(42,62,56,76)(85,192,99,178)(86,193,100,179)(87,194,101,180)(88,195,102,181)(89,196,103,182)(90,169,104,183)(91,170,105,184)(92,171,106,185)(93,172,107,186)(94,173,108,187)(95,174,109,188)(96,175,110,189)(97,176,111,190)(98,177,112,191)(113,163,127,149)(114,164,128,150)(115,165,129,151)(116,166,130,152)(117,167,131,153)(118,168,132,154)(119,141,133,155)(120,142,134,156)(121,143,135,157)(122,144,136,158)(123,145,137,159)(124,146,138,160)(125,147,139,161)(126,148,140,162), (1,139,15,125)(2,126,16,140)(3,113,17,127)(4,128,18,114)(5,115,19,129)(6,130,20,116)(7,117,21,131)(8,132,22,118)(9,119,23,133)(10,134,24,120)(11,121,25,135)(12,136,26,122)(13,123,27,137)(14,138,28,124)(29,184,43,170)(30,171,44,185)(31,186,45,172)(32,173,46,187)(33,188,47,174)(34,175,48,189)(35,190,49,176)(36,177,50,191)(37,192,51,178)(38,179,52,193)(39,194,53,180)(40,181,54,195)(41,196,55,182)(42,183,56,169)(57,85,71,99)(58,100,72,86)(59,87,73,101)(60,102,74,88)(61,89,75,103)(62,104,76,90)(63,91,77,105)(64,106,78,92)(65,93,79,107)(66,108,80,94)(67,95,81,109)(68,110,82,96)(69,97,83,111)(70,112,84,98)(141,217,155,203)(142,204,156,218)(143,219,157,205)(144,206,158,220)(145,221,159,207)(146,208,160,222)(147,223,161,209)(148,210,162,224)(149,197,163,211)(150,212,164,198)(151,199,165,213)(152,214,166,200)(153,201,167,215)(154,216,168,202), (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196)(197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224), (1,146,15,160)(2,159,16,145)(3,144,17,158)(4,157,18,143)(5,142,19,156)(6,155,20,141)(7,168,21,154)(8,153,22,167)(9,166,23,152)(10,151,24,165)(11,164,25,150)(12,149,26,163)(13,162,27,148)(14,147,28,161)(29,88,43,102)(30,101,44,87)(31,86,45,100)(32,99,46,85)(33,112,47,98)(34,97,48,111)(35,110,49,96)(36,95,50,109)(37,108,51,94)(38,93,52,107)(39,106,53,92)(40,91,54,105)(41,104,55,90)(42,89,56,103)(57,173,71,187)(58,186,72,172)(59,171,73,185)(60,184,74,170)(61,169,75,183)(62,182,76,196)(63,195,77,181)(64,180,78,194)(65,193,79,179)(66,178,80,192)(67,191,81,177)(68,176,82,190)(69,189,83,175)(70,174,84,188)(113,220,127,206)(114,205,128,219)(115,218,129,204)(116,203,130,217)(117,216,131,202)(118,201,132,215)(119,214,133,200)(120,199,134,213)(121,212,135,198)(122,197,136,211)(123,210,137,224)(124,223,138,209)(125,208,139,222)(126,221,140,207) );
G=PermutationGroup([[(1,169),(2,170),(3,171),(4,172),(5,173),(6,174),(7,175),(8,176),(9,177),(10,178),(11,179),(12,180),(13,181),(14,182),(15,183),(16,184),(17,185),(18,186),(19,187),(20,188),(21,189),(22,190),(23,191),(24,192),(25,193),(26,194),(27,195),(28,196),(29,126),(30,127),(31,128),(32,129),(33,130),(34,131),(35,132),(36,133),(37,134),(38,135),(39,136),(40,137),(41,138),(42,139),(43,140),(44,113),(45,114),(46,115),(47,116),(48,117),(49,118),(50,119),(51,120),(52,121),(53,122),(54,123),(55,124),(56,125),(57,156),(58,157),(59,158),(60,159),(61,160),(62,161),(63,162),(64,163),(65,164),(66,165),(67,166),(68,167),(69,168),(70,141),(71,142),(72,143),(73,144),(74,145),(75,146),(76,147),(77,148),(78,149),(79,150),(80,151),(81,152),(82,153),(83,154),(84,155),(85,218),(86,219),(87,220),(88,221),(89,222),(90,223),(91,224),(92,197),(93,198),(94,199),(95,200),(96,201),(97,202),(98,203),(99,204),(100,205),(101,206),(102,207),(103,208),(104,209),(105,210),(106,211),(107,212),(108,213),(109,214),(110,215),(111,216),(112,217)], [(1,209,15,223),(2,210,16,224),(3,211,17,197),(4,212,18,198),(5,213,19,199),(6,214,20,200),(7,215,21,201),(8,216,22,202),(9,217,23,203),(10,218,24,204),(11,219,25,205),(12,220,26,206),(13,221,27,207),(14,222,28,208),(29,77,43,63),(30,78,44,64),(31,79,45,65),(32,80,46,66),(33,81,47,67),(34,82,48,68),(35,83,49,69),(36,84,50,70),(37,57,51,71),(38,58,52,72),(39,59,53,73),(40,60,54,74),(41,61,55,75),(42,62,56,76),(85,192,99,178),(86,193,100,179),(87,194,101,180),(88,195,102,181),(89,196,103,182),(90,169,104,183),(91,170,105,184),(92,171,106,185),(93,172,107,186),(94,173,108,187),(95,174,109,188),(96,175,110,189),(97,176,111,190),(98,177,112,191),(113,163,127,149),(114,164,128,150),(115,165,129,151),(116,166,130,152),(117,167,131,153),(118,168,132,154),(119,141,133,155),(120,142,134,156),(121,143,135,157),(122,144,136,158),(123,145,137,159),(124,146,138,160),(125,147,139,161),(126,148,140,162)], [(1,139,15,125),(2,126,16,140),(3,113,17,127),(4,128,18,114),(5,115,19,129),(6,130,20,116),(7,117,21,131),(8,132,22,118),(9,119,23,133),(10,134,24,120),(11,121,25,135),(12,136,26,122),(13,123,27,137),(14,138,28,124),(29,184,43,170),(30,171,44,185),(31,186,45,172),(32,173,46,187),(33,188,47,174),(34,175,48,189),(35,190,49,176),(36,177,50,191),(37,192,51,178),(38,179,52,193),(39,194,53,180),(40,181,54,195),(41,196,55,182),(42,183,56,169),(57,85,71,99),(58,100,72,86),(59,87,73,101),(60,102,74,88),(61,89,75,103),(62,104,76,90),(63,91,77,105),(64,106,78,92),(65,93,79,107),(66,108,80,94),(67,95,81,109),(68,110,82,96),(69,97,83,111),(70,112,84,98),(141,217,155,203),(142,204,156,218),(143,219,157,205),(144,206,158,220),(145,221,159,207),(146,208,160,222),(147,223,161,209),(148,210,162,224),(149,197,163,211),(150,212,164,198),(151,199,165,213),(152,214,166,200),(153,201,167,215),(154,216,168,202)], [(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28),(29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56),(57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84),(85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112),(113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140),(141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196),(197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224)], [(1,146,15,160),(2,159,16,145),(3,144,17,158),(4,157,18,143),(5,142,19,156),(6,155,20,141),(7,168,21,154),(8,153,22,167),(9,166,23,152),(10,151,24,165),(11,164,25,150),(12,149,26,163),(13,162,27,148),(14,147,28,161),(29,88,43,102),(30,101,44,87),(31,86,45,100),(32,99,46,85),(33,112,47,98),(34,97,48,111),(35,110,49,96),(36,95,50,109),(37,108,51,94),(38,93,52,107),(39,106,53,92),(40,91,54,105),(41,104,55,90),(42,89,56,103),(57,173,71,187),(58,186,72,172),(59,171,73,185),(60,184,74,170),(61,169,75,183),(62,182,76,196),(63,195,77,181),(64,180,78,194),(65,193,79,179),(66,178,80,192),(67,191,81,177),(68,176,82,190),(69,189,83,175),(70,174,84,188),(113,220,127,206),(114,205,128,219),(115,218,129,204),(116,203,130,217),(117,216,131,202),(118,201,132,215),(119,214,133,200),(120,199,134,213),(121,212,135,198),(122,197,136,211),(123,210,137,224),(124,223,138,209),(125,208,139,222),(126,221,140,207)]])
94 conjugacy classes
class 1 2A 2B 2C 2D 2E 2F ··· 2M 4A ··· 4L 4M ··· 4T 7A 7B 7C 14A ··· 14U 28A ··· 28AJ order 1 2 2 2 2 2 2 ··· 2 4 ··· 4 4 ··· 4 7 7 7 14 ··· 14 28 ··· 28 size 1 1 1 1 2 2 14 ··· 14 2 ··· 2 14 ··· 14 2 2 2 2 ··· 2 4 ··· 4
94 irreducible representations
dim 1 1 1 1 1 1 2 2 2 4 4 type + + + + + + + + + - image C1 C2 C2 C2 C2 C2 D7 D14 D14 2- 1+4 Q8.10D14 kernel C2×Q8.10D14 C2×C4○D28 C2×Q8×D7 C2×Q8⋊2D7 Q8.10D14 Q8×C2×C14 C22×Q8 C22×C4 C2×Q8 C14 C2 # reps 1 6 4 4 16 1 3 9 36 2 12
Matrix representation of C2×Q8.10D14 in GL6(𝔽29)
28 0 0 0 0 0 0 28 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1
,
1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 24 13 0 0 0 0 16 5 0 0 5 16 0 0 0 0 13 24 0 0
,
1 0 0 0 0 0 0 1 0 0 0 0 0 0 27 11 0 0 0 0 18 2 0 0 0 0 0 0 2 18 0 0 0 0 11 27
,
19 10 0 0 0 0 19 7 0 0 0 0 0 0 0 0 26 8 0 0 0 0 21 21 0 0 3 21 0 0 0 0 8 8 0 0
,
28 22 0 0 0 0 0 1 0 0 0 0 0 0 7 20 0 0 0 0 12 22 0 0 0 0 0 0 7 20 0 0 0 0 12 22
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,5,13,0,0,0,0,16,24,0,0,24,16,0,0,0,0,13,5,0,0],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,27,18,0,0,0,0,11,2,0,0,0,0,0,0,2,11,0,0,0,0,18,27],[19,19,0,0,0,0,10,7,0,0,0,0,0,0,0,0,3,8,0,0,0,0,21,8,0,0,26,21,0,0,0,0,8,21,0,0],[28,0,0,0,0,0,22,1,0,0,0,0,0,0,7,12,0,0,0,0,20,22,0,0,0,0,0,0,7,12,0,0,0,0,20,22] >;
C2×Q8.10D14 in GAP, Magma, Sage, TeX
C_2\times Q_8._{10}D_{14}
% in TeX
G:=Group("C2xQ8.10D14");
// GroupNames label
G:=SmallGroup(448,1374);
// by ID
G=gap.SmallGroup(448,1374);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,184,297,136,1684,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^2=b^4=1,c^2=d^14=e^2=b^2,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,c*b*c^-1=e*b*e^-1=b^-1,b*d=d*b,d*c*d^-1=e*c*e^-1=b^2*c,e*d*e^-1=d^13>;
// generators/relations
×
𝔽
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2021-10-16 23:25:17
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https://zamlz.org/notes/lp_norm.html
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# Lp Norm
The $$L^p$$ norm function is a type of Norm Functions. It is defined as follows:
For a given vector $$x \in \mathbb{R}^n$$ and $$0 < p < \infty$$,
$||x||_p \ = \left( \sum^n_{i=1} |x_i |^p \right)^{\frac{1}{p}}$
## 1.L1-Norm
$||x||_1 = \sum^n_{i=1} |x_i|$
## 2.L2-Norm
The $$L^2$$-Norm is also known as the Euclidean Norm.
$||x||_2 = \sqrt{\sum^n_{i=1} |x_i|^2}$
## 3.L-Infinite-Norm
In this case, we must make use of the limit,
$||x||_{\infty} = \lim_{p \to \infty} \left(\sum^n_{i=1} |x_i|^p \right)^{\frac{1}{p}}$
This expression actually evaluates to the following! It is essentially equal to the max element of the vector $$x$$.
$||x||_{\infty} = \max_{1 \leq j \leq n} \left\{x_1, x_2, \ldots, x_n\right\}$
There is a detailed proof showing how to expand the limit, but no way I'm typing all that here.
Created: 2022-02-03
Emacs 26.1 (Org mode 9.5)
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2022-05-24 09:16:12
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|
http://clay6.com/qa/24672/sum-of-n-terms-of-series-s-1-2-2-2-2-3-2-2-4-2-5-2-when-n-is-even-is-
|
# Sum of n terms of series $\;S=1^2+2(2)^2+3^2+2(4)^2+5^2+\;....\;$ when n is even is :
$(a)\;\frac{1}{4}n(n+2)^2\qquad(b)\;\frac{1}{4}n^2(n+2)\qquad(c)\;\frac{1}{2}n^2(n+1)\qquad(d)\;\frac{1}{2}n(n+1)^2$
Answer : (d) $\;\frac{1}{2}n(n+1)^2$
Explanation : $Let \;n=2m$
$S=\;[1^2+2^2+3^2\;...\;+(2m)^2]+\;[2^2+4^2+6^2+\;...\;(2m)^2]$
$=\frac{1}{6}\;(2m)(2m+1)(4m+1)+\frac{4}{6}\;(m)(m+1)(2m+1)$
$=\frac{1}{3}m(2m+1)\;[4m+1+2m+2]$
$=\frac{1}{2}n(n+1)^2\;.$
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2018-06-19 19:54:01
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https://www.rdocumentation.org/packages/RSNNS/versions/0.4-12/topics/rsnnsObjectFactory
|
# rsnnsObjectFactory
0th
Percentile
##### Object factory for generating rsnns objects
The object factory generates an rsnns object and initializes its member variables with the values given as parameters. Furthermore, it generates an object of SnnsR-class. Later, this information is to be used to train the network.
##### Usage
rsnnsObjectFactory(subclass, nInputs, maxit, initFunc, initFuncParams,
learnFunc, learnFuncParams, updateFunc, updateFuncParams,
shufflePatterns = TRUE, computeIterativeError = TRUE,
pruneFunc = NULL, pruneFuncParams = NULL)
##### Arguments
subclass
the subclass of rsnns to generate (vector of strings)
nInputs
the number of inputs the network will have
maxit
maximum of iterations to learn
initFunc
the initialization function to use
initFuncParams
the parameters for the initialization function
learnFunc
the learning function to use
learnFuncParams
the parameters for the learning function
updateFunc
the update function to use
updateFuncParams
the parameters for the update function
shufflePatterns
should the patterns be shuffled?
computeIterativeError
should the error be computed in every iteration?
pruneFunc
the pruning function to use
pruneFuncParams
the parameters for the pruning function. Unlike the other functions, these have to be given in a named list. See the pruning demos for further explanation.
##### Details
The typical procedure implemented in rsnns subclasses is the following:
• generate the rsnns object with this object factory
• generate the network according to the architecture needed
• train the network (with train)
In every rsnns object, the iterative error is the summed squared error (SSE) of all patterns. If the SSE is computed on the test set, then it is weighted to take care of the different amount of patterns in the sets.
##### Value
a partly initialized rsnns object
mlp, dlvq, rbf, rbfDDA, elman, jordan, som, art1, art2, artmap, assoz
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2020-02-28 23:02:03
|
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|
http://math.stackexchange.com/questions/673460/differential-operator-is-self-adjoint
|
This is an exercise (13.8) in Rudin's Functional Analysis.
Let an operator $T$ in $L^{2}(\mathbb R)$ be defined as follows:
$\mathcal{D}(T)=\{f \textrm{ absolutely continuous}\in L^{2}(\mathbb{R}): f'\in L^{2}(\mathbb{R})\}; TF=if'$.
The exercise is to show that T is self adjoint. Here is what I have done so far:
Let $f,g \in \mathcal{D}(T)$.
Then $\int_{\mathbb{R}}Tf \bar{g}d\mu=\int_{\mathbb{R}}if'\bar{g}d\mu=-i\int_{\mathbb{R}}f\bar{g'}d\mu$ (using integration by parts and the fact that $f(t)\rightarrow 0$ as $t\rightarrow \pm\infty$).
So we have $<Tf,g>=<f,Tg> \forall f,g \in \mathcal{D}(T)$.
Hence $T$ is symmetric, i.e. $T\subset T^{*}$.
It remains to show that $T^{*}\subset T$.
I don't know if the rest of what follows is correct:
Let $f\in \mathcal{D}(T), g\in \mathcal{D}(T^{*})$ and let $\phi=T^{*}g$.
Let $\Phi(x)=\int_{-\infty}^{x}\phi(t)dt$ (Does this make sense? Is $\phi$ absolutely continuous?)
Then $\Phi'(x)=\phi(x)$
$\int_{-\infty}^{\infty}if'\bar{g}=<Tf,g>=<f,\phi>=\int_{-\infty}^{\infty}f\bar{\phi}d\mu=-\int_{-\infty}^{\infty}f'\bar{\Phi}d\mu$
Hence $\int_{-\infty}^{\infty}f'\overline{(\Phi-ig)}d\mu=0$.
Since this is true $\forall f \in \mathcal{D}(T)$, it follows that $ig-\Phi\in R(T)^{\perp}$.
Is it true that $R(T)=L^{2}$? In that case, $g$ is a scalar multiple of $\Phi$ and so $g\in \mathcal{D}(T)$.
-
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2014-10-23 22:22:43
|
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|
http://mathhelpforum.com/higher-math/217084-help-me-solve-print.html
|
# Help me solve this
find Z with $z^3 = \frac{1 + i}{\sqrt{2}}$
Change to polar form, then use $\sqrt[3]{r(cos(\theta)+ i sin(\theta))}= r^{1/3}(cos(\theta/3)+ i sin(\theta/3))$
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2017-12-15 18:37:26
|
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https://fpga-faq.com/archives/18550.html
|
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# Messages from 18550
Article: 18550
Subject: Re: Comparison between Altera and Xilinx
From: u8713501@cc.nctu.edu.tw (Child K.L. Sun)
Date: Sat, 30 Oct 1999 08:40:02 GMT
Links: << >> << T >> << A >>
On Thu, 28 Oct 1999 17:23:00 -0400, Ray Andraka <randraka@ids.net> wrote:
>Oops... I was about to yell back to say I didn't say altera was better in all
>other apps, but reading my post that is what my fingers typed. I would by no
>means say that Altera is best for everything else---it just plain isn't. Those of
>you who know me know that what I meant to type was "For other applications, the
>Altera is sometimes better". Altera tends to do better at collecting "random"
>logic, especially for the user who isn't willing to do placement. (Again, this is
>not meant to be a blanket statement by any means). Xilinx is better in the vast
>majority of datapath designs, and is a hands down winner in arithmetic designs or
>designs requiring delay queues. When it comes down to it, the best device depends
>on the application, and might even include non-technical considerations such as
>tools ownership, designer experience etc.
For the "random" logic performance issue, doesn't it merely related to
the synthesis tool??
Child :~{}
Article: 18551
Subject: Re: Comparison between Altera and Xilinx
From: Ray Andraka <randraka@ids.net>
Date: Sat, 30 Oct 1999 08:56:16 -0400
Links: << >> << T >> << A >>
NO.
Assuming reasonable synthesis, the routing delays and ability to handle wide fanins
have a large impact on performance. Altera's routing delays are relatively independent
of placement, so having not-so-local routing does not degrade performance
significantly. Connections within a LAB in Altera are quite fast, and the altera
compiler does a fairly good job at keeping stuff within a LAB when the stuff is
reasonably small (provided carry chains don't prevent that). In xilinx, routing delay
is much more dependent on placement, and the auto-place tools really don't do a very
good job. Local routing in the xilinx is very fast, and very structured. As you move
away from the structured placement there is a significant degradation of maximum clock
rate. Random logic takes longer to hand place than a structured data path.
Child K.L. Sun wrote:
> For the "random" logic performance issue, doesn't it merely related to
> the synthesis tool??
>
> Child :~{}
--
-Ray Andraka, P.E.
President, the Andraka Consulting Group, Inc.
401/884-7930 Fax 401/884-7950
email randraka@ids.net
http://users.ids.net/~randraka
Article: 18552
Subject: Re: need reference to first paper on FPGA
From: Tom Kean <tom@algotronix.com>
Date: Sat, 30 Oct 1999 14:01:30 +0100
Links: << >> << T >> << A >>
This is a multi-part message in MIME format.
--------------BB51596145F9BE5180CC1A9E
Content-Type: text/plain; charset=us-ascii
Content-Transfer-Encoding: 7bit
Hi,
Arrigo Benedetti wrote:
> does anyone have the reference to the paper where the FPGA
> was first introduced?
>
The question is bit more complex than it sounds:
- as far as I know the term FPGA was created by Actel's marketing people
but there were many programmable architectures around before the term
was coined.
- assuming you take the essential requirements of 'FPGA' as being general
purpose routing (not PAL like arrays) and electrical field reprogrammability
(i.e. not patch panels, laser cutting of links etc) then I'd recommend reading the following
references and making your own mind up:
S.E. Wahlstrom 'Programmable Logic Arrays' Electronics Vol 40, No 25, Dec. 11 1967.
R.C. Minnick 'Survey of Microcellular Research', J. ACM, Vol 14, No. 2, April 1967.
Note, before I get flamed I am not claiming that either of these are definitively
the first paper about FPGA's. The first document on the modern FPGA is probably
the famous Freeman patent US 4,870,302 (re-issued as Re. 34,363).
Tom Kean.
Tom
> Thanks in advance,
>
> -Arrigo
> --
> Dr. Arrigo Benedetti e-mail: arrigo@vision.caltech.edu
> Caltech, MS 136-93 phone: (626) 395-3695
> Pasadena, CA 91125 fax: (626) 795-8649
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n:Kean;Tom
tel;fax:UK +44 131 556 9247
tel;work:UK +44 131 556 9242
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org:Algotronix Ltd.
adr:;;P.O. Box 23116;Edinburgh;;EH8 8YB;Scotland
version:2.1
email;internet:tom@algotronix.com
title:Director
note:Web Site: www.algotronix.com
x-mozilla-cpt:;4768
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--------------BB51596145F9BE5180CC1A9E--
Article: 18553
Subject: Re: Comparison between Altera and Xilinx
From: martin@the-thompsons.freeserve.co.uk
Date: Sat, 30 Oct 1999 15:57:02 GMT
Links: << >> << T >> << A >>
If I can put a different point of view.
I'm new to the game, but I just implemented a signal processing type
design, which I wrote as 'behavioural-ish' (ie not aimed directly at
being synthesisable) VHDL. It isn't huge, but it has a collection of
multipliers/adders/comparators. I thought I'd just see how far off a
usefully synthesizable design it was so I ran it through FPGA Express.
It runs at 4MHz in a Virtex, and 14MHz in Flex10K (and 7MHz in a
Flex6016 - just to see). 4MHz is just fast enough, but the Altera
device gives me plenty of spare time to play with. The big plus for
me is that I can get the performance I want without having to mess
around hand-tuning the algorithm to the architecture, and at the
moment, all I'm (or my boss is :-) looking for it proof of concept.
It appears from what I've gathered so far - and as I say I am new to
this - that Xilinx will perform better, given the up front investment.
However, the Altera devices may well perform *well enough* straight
out of the box with very 'ordinary' VHDL.
So there's another view: The choice may depend on how much
time/inclination you have to tweak your implementation.
Which brings me to a question... This design fits in a 10K20, which
is nominally a 20K gates device, so clearly its not a huge design. Am
I going to find the Altera architecture limits me, and will also
require hand-tuning, as the design size goes up?
Martin
On Thu, 28 Oct 1999 10:45:39 -0400, Ray Andraka <randraka@ids.net>
wrote:
>Big architectural differences. Which is best depends on your
>application. For signal processing, Xilinx is a hands down winner. For
>other apps, the Altera is better. Look for my previous posts on this
>subject in deja-news for more details.
>
>Child K.L. Sun wrote:
>
>> Have you tried both of the chips/software from these two
>> companies?
>> What's the difference between them?
>>
>> Child
>
>
>
>--
>-Ray Andraka, P.E.
>President, the Andraka Consulting Group, Inc.
>401/884-7930 Fax 401/884-7950
>email randraka@ids.net
>http://users.ids.net/~randraka
>
>
Martin Thompson
martin@the-thompsons.freeserve.co.uk
http://www.the-thompsons.freeserve.co.uk/
Article: 18554
Subject: Re: Comparison between Altera and Xilinx
From: Ray Andraka <randraka@ids.net>
Date: Sat, 30 Oct 1999 16:27:50 -0400
Links: << >> << T >> << A >>
At only 4 MHz, you are leaving alot of the FPGA's potential performance on
the table. If your sample rate only needs 4 MHz, you ought to consider bit
serial design so that you can get into a smaller and cheaper part, for
example the Xilinx spartan series. Bit serial hardware is typically about
1/nth the hardware for an n bit wide process, although it also requires an n
times bit clock. you can use a hybrid digit-serial approach if the clock is
too high.
Altera does tend to do better with uninspired synthesis. That is mostly a
consequence of the global routing structure which makes placement
considerably less critical than xilinx. However, that is a double edged
sword: that same global routing limits how fast you can make a design go if
you are willing to put in the extra effort. For signal processing
applications, Altera is handicapped by the carry arithmetic structure which
limits you to a two input arithmetic function in one level of logic (compared
to 3 inputs in Xilinx 4K and 4 inputs in Virtex). That means an add/subtract
or accumulator with clear is forced to two levels of logic in ALtera. Also,
and probably more significant, Xilinx lets you use the LUTs in the array as
RAM or as shift registers, so that a 16 clock by 1 bit delay fits into the
space of one LUT. ALtera has nothing similar, so you wind up using an LE for
each clock delay for each bit. It gets rather expensive when you are dealing
with word wide, multiple clock delay queues of the type you find frequently
in filters etc.
So, if your application uses delay queues or arithmetic with more than two
inputs, you are going to use up alot of your logic in ALtera, where you
wouldn't in xilinx. Thus, you need a device with more "marketing gates" to
fulfill the same function. Also, the inability to use the LUTs as RAM is a
handicap if you are doing adaptive filtering, as it keeps you out of some
significant algorithmic optizations.
For low data rate stuff, I would prefer to use a smaller device and go with a
bit serial or digit serial design to keep unit costs down. The exception is
where the higher clock rates might cause you problems. The extra design
effort required for that type of architectural optimization is pretty small.
martin@the-thompsons.freeserve.co.uk wrote:
> If I can put a different point of view.
>
> I'm new to the game, but I just implemented a signal processing type
> design, which I wrote as 'behavioural-ish' (ie not aimed directly at
> being synthesisable) VHDL. It isn't huge, but it has a collection of
> multipliers/adders/comparators. I thought I'd just see how far off a
> usefully synthesizable design it was so I ran it through FPGA Express.
>
> It runs at 4MHz in a Virtex, and 14MHz in Flex10K (and 7MHz in a
> Flex6016 - just to see). 4MHz is just fast enough, but the Altera
> device gives me plenty of spare time to play with. The big plus for
> me is that I can get the performance I want without having to mess
> around hand-tuning the algorithm to the architecture, and at the
> moment, all I'm (or my boss is :-) looking for it proof of concept.
>
> It appears from what I've gathered so far - and as I say I am new to
> this - that Xilinx will perform better, given the up front investment.
> However, the Altera devices may well perform *well enough* straight
> out of the box with very 'ordinary' VHDL.
>
> So there's another view: The choice may depend on how much
> time/inclination you have to tweak your implementation.
>
> Which brings me to a question... This design fits in a 10K20, which
> is nominally a 20K gates device, so clearly its not a huge design. Am
> I going to find the Altera architecture limits me, and will also
> require hand-tuning, as the design size goes up?
>
--
-Ray Andraka, P.E.
President, the Andraka Consulting Group, Inc.
401/884-7930 Fax 401/884-7950
email randraka@ids.net
http://users.ids.net/~randraka
Article: 18555
Subject: which Xilinx package for Virtex ?
From: muzo <muzok@nospam.pacbell.net>
Date: 30 Oct 1999 16:44:54 PDT
Links: << >> << T >> << A >>
hi,
I looked at Xilinx web page and the choices there confused me a little
bit. I am trying to decide on an FPGA family for a very aggresive DSP
design with Verilog. I already have synthesis and Altera P&R tools.
What is the least expensive package I can use from Xilinx to P&R the
output of the synthesis for Virtex(-E) and see the performance ? I
don't need to program any parts yet and I don't need any design entry
in the Xilinx tool. I need at least the 400K part.
thanks
muzo
Verilog, ASIC/FPGA and NT Driver Development Consulting (remove nospam from email)
Article: 18556
Subject: Re: Comparison between Altera and Xilinx
From: murray@pa.dec.com (Hal Murray)
Date: 31 Oct 1999 01:53:43 GMT
Links: << >> << T >> << A >>
Suppose I had a design that was written without any
particular hardware in mind. Maybe it was written
by a software guy who didn't know about fan-in or routing.
How much can I gain in speed or density by rewriting
it to be more friendly to a paritcular architecture?
Are there a tricks that an experienced designer would
use from the beginning if he knew the target architecture?
Is there a list of that sort of tricks someplace? Maybe
a web page for each architecture? Or are they all so "obvious"
that nobody bothers to write them down?
How hard would it be to teach the compiler about those tricks?
Would hints from the programmer/designer help the compiler?
Or should it be able to figure all that out since it knows
all about the target architecture?
--
These are my opinions, not necessarily my employers.
Article: 18557
Subject: VPR for FPGAs
From: G.S. Vigneault <z180@hotmail.DOT.com>
Date: Sun, 31 Oct 1999 01:38:21 -0400
Links: << >> << T >> << A >>
If you missed the article in the October 18, 1999, issue of the
Electronic Engineering Times (page 73) -- you can read about the
Versatile Placement and Routing (VPR) package for FPGAs, and
download the software (free for noncommercial use) at the University
of Toronto at http://www.eecg.toronto.edu/~vaughn/vpr/vpr.html
Greg_
October 31, 1999.
{}{}{} Posted via Uncensored-News.Com, http://www.uncensored-news.com {}{}{}
{}{}{}{} Only $8.95 A Month, - The Worlds Uncensored News Source {}{}{}{} {}{}{}{}{} Five News Servers with a BINARIES ONLY Server {}{}{}{}{} Article: 18558 Subject: Re: Comparison between Altera and Xilinx From: martin@the-thompsons.freeserve.co.uk Date: Sun, 31 Oct 1999 14:00:33 GMT Links: << >> << T >> << A >> On Sat, 30 Oct 1999 16:27:50 -0400, Ray Andraka <randraka@ids.net> wrote: >At only 4 MHz, you are leaving alot of the FPGA's potential performance on >the table. If your sample rate only needs 4 MHz, you ought to consider bit >serial design so that you can get into a smaller and cheaper part, for >example the Xilinx spartan series. Bit serial hardware is typically about >1/nth the hardware for an n bit wide process, although it also requires an n >times bit clock. you can use a hybrid digit-serial approach if the clock is >too high. > My point was that smaller/cheaper is not the issue for me at the moment, once smaller/cheaper becomes important, we'll be in ASIC territory anyway. >Altera does tend to do better with uninspired synthesis. That is mostly a >consequence of the global routing structure which makes placement >considerably less critical than xilinx. However, that is a double edged >sword: that same global routing limits how fast you can make a design go if >you are willing to put in the extra effort. Presumably also a double edged sword in that if you can't/don't want to put in the extra effort it makes life harder in 'Xilinx-land' <snip lots of useful comparison of architectures> > >So, if your application uses delay queues or arithmetic with more than two >inputs, you are going to use up alot of your logic in ALtera, where you >wouldn't in xilinx. Thus, you need a device with more "marketing gates" to >fulfill the same function. Also, the inability to use the LUTs as RAM is a >handicap if you are doing adaptive filtering, as it keeps you out of some >significant algorithmic optizations. > I haven't looked hard enough at the architectures to work it out, but are they not both LUT based? What extras do the Xilinx arch. have that enables all these other features? And why aren't Altera interested in copying them :) >For low data rate stuff, I would prefer to use a smaller device and go with a >bit serial or digit serial design to keep unit costs down. The exception is >where the higher clock rates might cause you problems. The extra design >effort required for that type of architectural optimization is pretty small. > Again, units costs aren't really the issue, although if I can get an order of magnitude difference in price ... :) I have to say that I am torn, in that we already use Altera devices (7K's) for a number of applications, but everything I read here implies that we need to look at Xilinx for these new applications. Most of our applications so far have been glue-logic type things rather than arithmetic based work. My other problem is that I'm not au fait enough with either the Altera 10K's or the Xilinx devices to really know how far I could push my example design if I put the effort in (without actually doing it, which will involve a significant investment in terms of time and needing to buy Xilinx tools we may not need). Anyway, thanks for the input, Martin >martin@the-thompsons.freeserve.co.uk wrote: > >> If I can put a different point of view. >> >> I'm new to the game, but I just implemented a signal processing type >> design, which I wrote as 'behavioural-ish' (ie not aimed directly at >> being synthesisable) VHDL. It isn't huge, but it has a collection of >> multipliers/adders/comparators. I thought I'd just see how far off a >> usefully synthesizable design it was so I ran it through FPGA Express. >> >> It runs at 4MHz in a Virtex, and 14MHz in Flex10K (and 7MHz in a >> Flex6016 - just to see). 4MHz is just fast enough, but the Altera >> device gives me plenty of spare time to play with. The big plus for >> me is that I can get the performance I want without having to mess >> around hand-tuning the algorithm to the architecture, and at the >> moment, all I'm (or my boss is :-) looking for it proof of concept. >> >> It appears from what I've gathered so far - and as I say I am new to >> this - that Xilinx will perform better, given the up front investment. >> However, the Altera devices may well perform *well enough* straight >> out of the box with very 'ordinary' VHDL. >> >> So there's another view: The choice may depend on how much >> time/inclination you have to tweak your implementation. >> >> Which brings me to a question... This design fits in a 10K20, which >> is nominally a 20K gates device, so clearly its not a huge design. Am >> I going to find the Altera architecture limits me, and will also >> require hand-tuning, as the design size goes up? >> > > > >-- >-Ray Andraka, P.E. >President, the Andraka Consulting Group, Inc. >401/884-7930 Fax 401/884-7950 >email randraka@ids.net >http://users.ids.net/~randraka > > Martin Thompson martin@the-thompsons.freeserve.co.uk http://www.the-thompsons.freeserve.co.uk/ Article: 18559 Subject: Re: Comparison between Altera and Xilinx From: eml@riverside-machines.com.NOSPAM Date: Sun, 31 Oct 1999 17:19:36 GMT Links: << >> << T >> << A >> On Sun, 31 Oct 1999 14:00:33 GMT, martin@the-thompsons.freeserve.co.uk wrote: >My other problem is that I'm not au fait enough with either the Altera >10K's or the Xilinx devices to really know how far I could push my >example design if I put the effort in (without actually doing it, >which will involve a significant investment in terms of time and >needing to buy Xilinx tools we may not need). does this mean that you haven't got any xilinx tools? if so, how are you doing your performance comparisons - are you relying on figures reported by FPGA express? if you are: 1) forget it. you can't compare two designs unless they're both routed, and the vendor's timing analyser has given you a max frequency. it's not unusual to get at least a factor of two speed difference between the synth's estimate and the real device. 2) FPGA express seems to have been slow to catch up with virtex. i believe that you should be on v3.3 to get useful results. 3) i went through the 10k v. virtex exercise with a customer who was already using 10Ks, with no xilinx experience, about 9 months ago, for a DSP application. virtex was the no-brainer then, even though the virtex tools were poor at that stage. the altera FAE didn't even bother trying to change their minds. 20K vs. virtex might be a different matter, if it ever happens. evan Article: 18560 Subject: Re: Xilinx TPSYNC constraint From: Phil Hays <spampostmaster@sprynet.com> Date: Sun, 31 Oct 1999 11:02:03 -0800 Links: << >> << T >> << A >> Andy Peters wrote: > I'm using an XC4KE part, I have a 32-bit bidirectional bus that comes out to > the pins and I'd like to constrain the tristate enable so that it's faster. > ... I have a signal called dataoe, which is a flip-flop output, and > that signal is used as the tri-state enable for the outputs, which are > called ramdata[31:0]. I have usually not had very good luck getting the Xilinx tools to improve timing in a case like this by adding timing constraints. What I would suggest is that you floorplan the dataoe flip-flop to the middle of the tristate bus. If that's not fast enough, you might duplicate the dataoe flip-flop and floorplan the copies. Another way would be to add a gclk buffer, floorplan it the buffer that gives the best drive to the data bus pins and floorplan the dataoe flip-flop to be in that corner of the die. -- Phil Hays "Irritatingly, science claims to set limits on what we can do, even in principle." Carl Sagan Article: 18561 Subject: Re: Comparison between Altera and Xilinx From: Ray Andraka <randraka@ids.net> Date: Sun, 31 Oct 1999 15:30:12 -0500 Links: << >> << T >> << A >> martin@the-thompsons.freeserve.co.uk wrote: > On Sat, 30 Oct 1999 16:27:50 -0400, Ray Andraka <randraka@ids.net> > wrote: > > >At only 4 MHz, you are leaving alot of the FPGA's potential performance on > >the table. If your sample rate only needs 4 MHz, you ought to consider bit > >serial design so that you can get into a smaller and cheaper part, for > >example the Xilinx spartan series. Bit serial hardware is typically about > >1/nth the hardware for an n bit wide process, although it also requires an n > >times bit clock. you can use a hybrid digit-serial approach if the clock is > >too high. > > > > My point was that smaller/cheaper is not the issue for me at the > moment, once smaller/cheaper becomes important, we'll be in ASIC > territory anyway. At the prices of the spartan devices, I think you may be pleasantly surprised as to the cost compared with an ASIC. At under$10 in quantity, it requires a fairly
large production run with an ASIC to break even. Nice thing with an FPGA solution
is that is a lot easier and cheaper to make changes later if you need/want to.
>
>
> >Altera does tend to do better with uninspired synthesis. That is mostly a
> >consequence of the global routing structure which makes placement
> >considerably less critical than xilinx. However, that is a double edged
> >sword: that same global routing limits how fast you can make a design go if
> >you are willing to put in the extra effort.
>
> Presumably also a double edged sword in that if you can't/don't want
> to put in the extra effort it makes life harder in 'Xilinx-land'
As always. It depends.
> <snip lots of useful comparison of architectures>
> >
> >So, if your application uses delay queues or arithmetic with more than two
> >inputs, you are going to use up alot of your logic in ALtera, where you
> >wouldn't in xilinx. Thus, you need a device with more "marketing gates" to
> >fulfill the same function. Also, the inability to use the LUTs as RAM is a
> >handicap if you are doing adaptive filtering, as it keeps you out of some
> >significant algorithmic optizations.
> >
>
> I haven't looked hard enough at the architectures to work it out, but
> are they not both LUT based? What extras do the Xilinx arch. have
> that enables all these other features? And why aren't Altera
> interested in copying them :)
They are both LUT based, but the xilinx devices allow you to use the LUT as a 16x1
RAM (ie you can change the LUT contents from within the FPGA). That feature,
which xilinx holds a patent on, allows you to use the LUT as a 16 bit shift
register or as re-writable lookups. There is nothing equivalent in Altera. Most
DSP applications have filtering or something similar going on, which in turn
implies the fairly extensive use of delay queues. The xilinx LUT ram capability
gives you a compact way of doing the delays, where Altera uses up an LE for each
clock delay on each bit.
For arithmetic circuits, the altera breaks the 4 input LUT into a pair of 3 input
LUTs, one for the carry function and one for the 'sum' function. That means if
your arithmetic function is more than 2 inputs (an adder-subtractor or an
accumulator with clear for example), the altera design is forced to a second level
of logic (slower and twice the area). The xilinx carry chain uses additional
dedicated logic, which in the case of the 4K/spartan architecture is in front of
the 4 input LUT. That leaves you with a 4 input function at each bit whether or
not the carry is used. Thus you can realize a 3 input arithmetic function (like
ALtera, one input is used for the carry in) in one level of logic. Xilinx Virtex
puts the dedicated carry logic after the LUT, so the carry in does not feed the
LUT. In that case you can have arithmetic functions with four inputs.
Additionally, if you need to use a clock enable, the Altera architecture (10K, not
Apex), steals one of the LUT inputs for the clock enable, which reduces the
effective size of a LUT to 3 input or in the case of an arithmetic function a one
input arithmetic function (let's see - that would be a 2's complement or add a
fixed number and not much else). The Xilinx clock enable does not steal a LUT
input, so there is no logic penalty for using it.
An efficient method for filtering is distributed arithmetic, which essentially
puts all the possible 1xn sums for a 4 tap filter into a look-up table. That way
you get a serial 4 tap filter in n LUTs (n is the width of your coefficient plus 2
bits). You can combine them both for longer filters and for processing more than
one bit of the input per clock. See the latest paper on my website (FPGAs make
radar signal processor on a chip a reality) for more detail about how that is
done. This same method could be used in adaptive filters if you could reprogram
the LUTs to change the coefficients on demand. The xilinx architecture gives you
a method to do this since you can use the LUTs as RAM.
> >For low data rate stuff, I would prefer to use a smaller device and go with a
> >bit serial or digit serial design to keep unit costs down. The exception is
> >where the higher clock rates might cause you problems. The extra design
> >effort required for that type of architectural optimization is pretty small.
> >
>
> Again, units costs aren't really the issue, although if I can get an
> order of magnitude difference in price ... :)
>
I think you're close to an order of magnitude in required area. The pricing at
the lower end is a little compressed, but I think you'll still see a half a
magnitude price reduction. Again, we're not talking an absolutely tailored design
here, just a change from a bit-parallel to a bit serial solution.
> I have to say that I am torn, in that we already use Altera devices
> (7K's) for a number of applications, but everything I read here
> implies that we need to look at Xilinx for these new applications.
> Most of our applications so far have been glue-logic type things
> rather than arithmetic based work.
Ownership and familiarity of a particular vendor's tool set is a compelling reason
to stay with that vendor. Unless you find yourself hitting the wall because of
architectural differences, I'd probably stick with the Altera if I were in your
shoes (without knowing much about your design). On the other hand, you should at
least be aware of what can be done in other architectures so that you have an idea
of how much the altera solution is costing you in your system context. Also, it
might be worth comparing the cost of ownership of the Xilinx Spartan chips with an
Asic for your application.
>
>
> My other problem is that I'm not au fait enough with either the Altera
> 10K's or the Xilinx devices to really know how far I could push my
> example design if I put the effort in (without actually doing it,
> which will involve a significant investment in terms of time and
> needing to buy Xilinx tools we may not need).
>
> Anyway, thanks for the input,
> Martin
>
> >martin@the-thompsons.freeserve.co.uk wrote:
> >
> >> If I can put a different point of view.
> >>
> >> I'm new to the game, but I just implemented a signal processing type
> >> design, which I wrote as 'behavioural-ish' (ie not aimed directly at
> >> being synthesisable) VHDL. It isn't huge, but it has a collection of
> >> multipliers/adders/comparators. I thought I'd just see how far off a
> >> usefully synthesizable design it was so I ran it through FPGA Express.
> >>
> >> It runs at 4MHz in a Virtex, and 14MHz in Flex10K (and 7MHz in a
> >> Flex6016 - just to see). 4MHz is just fast enough, but the Altera
> >> device gives me plenty of spare time to play with. The big plus for
> >> me is that I can get the performance I want without having to mess
> >> around hand-tuning the algorithm to the architecture, and at the
> >> moment, all I'm (or my boss is :-) looking for it proof of concept.
> >>
> >> It appears from what I've gathered so far - and as I say I am new to
> >> this - that Xilinx will perform better, given the up front investment.
> >> However, the Altera devices may well perform *well enough* straight
> >> out of the box with very 'ordinary' VHDL.
> >>
> >> So there's another view: The choice may depend on how much
> >> time/inclination you have to tweak your implementation.
> >>
> >> Which brings me to a question... This design fits in a 10K20, which
> >> is nominally a 20K gates device, so clearly its not a huge design. Am
> >> I going to find the Altera architecture limits me, and will also
> >> require hand-tuning, as the design size goes up?
> >>
> >
> >
> >
> >--
> >-Ray Andraka, P.E.
> >President, the Andraka Consulting Group, Inc.
> >401/884-7930 Fax 401/884-7950
> >email randraka@ids.net
> >http://users.ids.net/~randraka
> >
> >
>
> Martin Thompson
> martin@the-thompsons.freeserve.co.uk
> http://www.the-thompsons.freeserve.co.uk/
--
-Ray Andraka, P.E.
President, the Andraka Consulting Group, Inc.
401/884-7930 Fax 401/884-7950
email randraka@ids.net
http://users.ids.net/~randraka
Article: 18562
Subject: Re: Xilinx TPSYNC constraint
From: Rickman <spamgoeshere4@yahoo.com>
Date: Sun, 31 Oct 1999 16:39:00 -0500
Links: << >> << T >> << A >>
To be honest, I find the whole constraint thing to be very, very
confusing. I think that the way they are set up and more so the way they
are documented makes them very, very hard to understand. I find this
doubly painful when it seems that the concept of constraints is so
simple.
But now that my beef is out of the way I will say that I have dealt with
this sort of thing using the OFFSET command. In my last Xilinx design
(which is starting to grow whiskers) I had a clock, LCLK and a bidir bus
LAD. I spec'ed using the statements below to assure that the outputs
were stable 5 nS before the rising edge of LCLK and could tolerate
changes on LAD up to 20 nS after LCLK. I did it this way because it
seemed easier to relate these numbers to the devices I was connecting to
(setup = 5 nS and output delay = 20 nS).
NET LAD<* OFFSET = IN 20 AFTER LCLK;
NET LAD<* OFFSET = OUT 5 BEFORE LCLK;
To the best of my knowledge this also took into account the path through
the enable on the tristate buffers. I did not need to place any special
constraints on that signal.
The data book does not show OFFSET being used with IN and AFTER or OUT
and BEFORE. Rather they show them used in the opposite combination. But
this did what I wanted and seemed to work.
Andy Peters wrote:
>
> I'm using an XC4KE part, I have a 32-bit bidirectional bus that comes out to
> the pins and I'd like to constrain the tristate enable so that it's faster.
>
> There's a constraint called TPSYNC, which "allows defintion of synchronous
> points that are <i>not</i> FFS, RAMS, PADS or LATCHES" and they are
> "commonly used with three-state buffers."
>
> The example given in the Xilinx "timing and constraints" presentation is a
> bit weak. I have a signal called dataoe, which is a flip-flop output, and
> that signal is used as the tri-state enable for the outputs, which are
> called ramdata[31:0]. Any hints as to how to write this constraint? Assume
> that I want to constrain it to be 10 ns.
>
> thanx,
>
> a
>
> --
> -----------------------------------------
> Andy Peters
> Sr Electrical Engineer
> National Optical Astronomy Observatories
> 950 N Cherry Ave
> Tucson, AZ 85719
> apeters (at) noao \dot\ edu
>
> "Creation Science" is oxymoronic.
--
Rick Collins
rick.collins@XYarius.com
remove the XY to email me.
Arius - A Signal Processing Solutions Company
Specializing in DSP and FPGA design
Arius
4 King Ave
Frederick, MD 21701-3110
301-682-7772 Voice
301-682-7666 FAX
Internet URL http://www.arius.com
Article: 18563
Subject: Re: Comparison between Altera and Xilinx
From: murray@pa.dec.com (Hal Murray)
Date: 1 Nov 1999 01:01:54 GMT
Links: << >> << T >> << A >>
[snip bit-serial suggestions]
> My point was that smaller/cheaper is not the issue for me at the
> moment, once smaller/cheaper becomes important, we'll be in ASIC
> territory anyway.
Won't the same techniques help you get a smaller/cheaper ASIC?
--
These are my opinions, not necessarily my employers.
Article: 18564
Subject: Re: Announcing Free VHDL Simulator for Windows
From: "Haneef D. Mohammed" <haneef@mindspring.com>
Date: Sun, 31 Oct 1999 20:51:53 -0800
Links: << >> << T >> << A >>
An update is now available for download
at www.symphonyeda.com that fixes this problem.
The fix is contained in Build#11
Thanx
Haneef
Allan Herriman <allan.herriman.hates.spam@fujitsu.com.au> wrote in message
news:3816b2cb.1582367@newshost.fujitsu.com.au...
> On Sat, 23 Oct 1999 10:19:41 -0700, "Haneef D. Mohammed"
> <haneef@mindspring.com> wrote:
>
>
> I tried it on an old project (which I had previously compiled with a
> few different tools), and it gave an internal error on the very first
> file I tried to compile.
>
> >vhdlp ..\src\ex_1164\ex_1164.vhd
> Symphony EDA (R) VHDL Compiler/Simulator Module VhdlP, Version 1.4,
> Build#10.
> Copyright(C) Symphony EDA 1997-1999. All rights reserved.
> Reading C:\Program Files\Symphony EDA\VHDL Simili\bin\symphony.ini ...
> Library 'ieee' ==> $SYMPHONY/Lib/Ieee/Ieee.sym > Library 'work' ==> work.sym > Reading$SYMPHONY\Lib\Ieee\Ieee.sym\std_logic_1164\std_logic_1164.var
> Parsing Package:exemplar_1164 @ line ..\src\ex_1164\ex_1164.vhd:31
> Writing work.sym\exemplar_1164\exemplar_1164.var
> Parsing Package Body:exemplar_1164 @ line
> .\src\ex_1164\ex_1164.vhd:297
> Internal Error: D:\home\proj\SimVHDL\VhdlExpr\CSTypeConversion.cpp:
> (line 79): E
> xpecting Aggregate here
>
> And the source around line 297 was:
>
> 290: signal q : out std_ulogic_vector);
> 291:
> 292:end exemplar_1164;
> 293:
> 294:library ieee ;
> 295:use ieee.std_logic_1164.all ;
> 296:
> 297:package body exemplar_1164 is
> 298:
> 299: ---
>
>
> Any idea what is wrong?
>
> Regards,
> Allan.
Article: 18565
Subject: Inkjets 4 you!
From: aoui0r93809@asadszlkjaslkjz.net
Date: Mon, 01 Nov 1999 06:38:34 GMT
Links: << >> << T >> << A >>
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51640A - $16.50 - Black Deskjet 1200 / CopyJet The Inkjet Company 1-310-517-9999 1-503-905-6652 Fax Visa, Mastercard, Amex, Discover Fast Free Delivery - usually in two days or less! Article: 18566 Subject: Altera Reset Strategy? From: Gary Cook <gc@sonyoxford.co.uk> Date: Mon, 01 Nov 1999 09:38:31 +0000 Links: << >> << T >> << A >> Hi, Using a Flex10K and have some code which has a bunch of FF's that reset, and a few that preset. Now I understand that the Flex will power up it's FF's in a low state, and it's up to a reset input to perform a functional reset once the device has configured. I also have a processor connected to the device and want to hold it in reset until the FPGA has configured. I have looked at using either INIT_DONE or CONF_DONE, but one de-actives before the end of config, and the other is inactive for a period at the start of config. I could also set a pin on the FPGA permanently high in the verilog, and us a pull-down externally so that during configuration it goes low, and when the user i/o is enabled, it gets driven high ... this could be my processor reset. I then connect a separate reset line from the processor to the fpga as the functional reset .... ... sounds abit clunky though ... is there a more elegant way of doing this? Thanks, Gary Cook, Sony Oxford, UK. Article: 18567 Subject: 16 bit counter in Abel From: "Luigi Funes" <fuzzy8888@hotmail.com> Date: Mon, 1 Nov 1999 12:20:56 +0100 Links: << >> << T >> << A >> I have a problem with Lattice ispExpert 7.1. I wrote this very simple 16 bit counter in ABEL-HDL MODULE counter16 count0..count15 pin istype 'reg'; countck pin; EQUATIONS [count0..count15].clk = countck; [count0..count15] := [count0..count15] + 1; END Someone can explain me why it requires 18 macrocells instead 16? I have to set some option in the compiler? Besides, if I write [count0..count15] := [count0..count15] + extpin; where extpin is a input pin assuming 0 or 1 values, this requires only 17 macrocells!!! Thanks in advance. Luigi Article: 18568 Subject: *Latest Inkjetz for Sale* From: 304830983@098340938.org Date: Mon, 01 Nov 1999 11:29:21 GMT Links: << >> << T >> << A >> The Inkjet Company has the following inkjet specials: All Prices Include Free Shipping and Free Sales Tax EPSON Epson -$8.00 - Black or 10 for $65.00 - All Models* Epson -$12.00 - Color or 10 for $100.00 - All Models* *Epson -$16.00 - Black or 10 for $135.00 - 900/3000 *Epson -$19.00 - Color or 10 for $165.00 - 750/900/1200/3000 CANON Canon BCI-21B -$5.00 - Black BJC-2500/4000/4400/5000
Canon BCI-21C - $8.00 - Color BJC-2500/4000/4400/5000 Canon BC-20 -$18.00 - Black BJC-2500/4000/4300/4400/
Canon BC-02 - $16.50 - Black BJC-210/230/BJ-200 Canon BC-05 -$28.00 - Tri-Color BJC-210/240
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Article: 18569
Subject: Virtex hardware debugging - help needed
From: Rick Filipkiewicz <rick@algor.co.uk>
Date: Mon, 01 Nov 1999 13:02:48 +0000
Links: << >> << T >> << A >>
Can anybody tell me how to do capture and readback though a Virtex's
JTAG port ? As far as I can see this is possible but is not supported by
either the Xilinx JTAG programmer or the H/W debugger. I don't have
access to the SelectMAP port so I probably need some s/w to drive the
JTAG port via e.g a parallel cable. I'm also very confused as to how to
define and get at the user definable internal scan chains.
One possible route seems to be through the JAVA based B-scan API.
Anybody tried this ?
Article: 18570
Subject: Re: Xilinx TPSYNC constraint
From: "Andrey Ushenin" <uab@novsu.ac.ru>
Date: Mon, 1 Nov 1999 17:21:53 +0300
Links: << >> << T >> << A >>
Hi Andy,
try to write in the your ucf file something like this:
NET ramdata(* TPSYNC=TRI_STATE_OUTPUTS;
TIMESPEC TS_OE_signal=FROM:FFS(dataoe):TO:TRI_STATE_OUTPUTS=10ns;
It will constrain path time from OE signal driver to your tri-state bus
outputs. If you want constrain path time from dataoe flip-flop to output
enable pin of OBUFE then you shoul attach TPSYNC attribute on these pins
directly.
Hope it will be small help for you.
Andrey Ushenin,
--------------------------
DSP laboratory,
Novgorod State University,
Russia
Andy Peters <apeters.nospam@nospam.noao.edu.nospam> wrote in message
news:7vdc8m$1uij$1@noao.edu...
> I'm using an XC4KE part, I have a 32-bit bidirectional bus that comes out
to
> the pins and I'd like to constrain the tristate enable so that it's
faster.
>
> There's a constraint called TPSYNC, which "allows defintion of synchronous
> points that are <i>not</i> FFS, RAMS, PADS or LATCHES" and they are
> "commonly used with three-state buffers."
>
> The example given in the Xilinx "timing and constraints" presentation is a
> bit weak. I have a signal called dataoe, which is a flip-flop output,
and
> that signal is used as the tri-state enable for the outputs, which are
> called ramdata[31:0]. Any hints as to how to write this constraint?
Assume
> that I want to constrain it to be 10 ns.
>
> thanx,
>
> a
>
> --
> -----------------------------------------
> Andy Peters
> Sr Electrical Engineer
> National Optical Astronomy Observatories
> 950 N Cherry Ave
> Tucson, AZ 85719
> apeters (at) noao \dot\ edu
>
> "Creation Science" is oxymoronic.
>
>
Article: 18571
Subject: Re: Announcing Free VHDL Simulator for Windows
From: allan.herriman.hates.spam@fujitsu.com.au (Allan Herriman)
Date: Mon, 01 Nov 1999 15:46:01 GMT
Links: << >> << T >> << A >>
On Sun, 31 Oct 1999 20:51:53 -0800, "Haneef D. Mohammed"
<haneef@mindspring.com> wrote:
>An update is now available for download
>at www.symphonyeda.com that fixes this problem.
>The fix is contained in Build#11
Thanks, it fixed that bug, but now there's another...
BTW, int2evec returns a 32 element slv if the second argument isn't
given.
(This is based on old code. I wouldn't use this function now.)
library ieee;
use ieee.std_logic_1164.all;
library work;
use work.exemplar_1164.all; -- you already have this
entity foobar is
end foobar;
architecture snafu of foobar is
signal foo : std_logic_vector(7 downto 0);
signal bar : integer;
begin
foo <= int2evec(bar, 8); -- this line is ok
foo <= int2evec(bar)(7 downto 0); -- this line gives an error
end snafu;
C:\>vhdlp tmp.vhd
Symphony EDA (R) VHDL Compiler/Simulator Module VhdlP, Version 1.4,
Build#11.
Copyright(C) Symphony EDA 1997-1999. All rights reserved.
Reading C:\tools\Symphony EDA\VHDL Simili\bin\symphony.ini ...
Library 'ieee' ==> $SYMPHONY/Lib/Ieee/Ieee.sym Library 'work' ==> work.sym Reading$SYMPHONY\Lib\Ieee\Ieee.sym\std_logic_1164\std_logic_1164.var
Reading work.sym\exemplar_1164\exemplar_1164.var
Parsing Entity:foobar @ line tmp.vhd:8
Writing work.sym\foobar\foobar.var
Parsing Architecture:foobar(snafu) @ line tmp.vhd:11
Error: CSVHDL0149: tmp.vhd: (line 20): Bad assignment. Expression on
RHS is not
of type ''std_logic_vector(7 DOWNTO 0)''
Errors: 1, Warnings: 0, Elapsed Time: 00h:00m:00s:736ms
C:\>
FYI,
Allan.
Article: 18572
Subject: Re: Xilinx TPSYNC constraint
From: "Andy Peters" <apeters.nospam@nospam.noao.edu.nospam>
Date: Mon, 1 Nov 1999 10:07:28 -0700
Links: << >> << T >> << A >>
Phil Hays wrote in message <381C922B.3603C633@sprynet.com>...
>Andy Peters wrote:
>
>> I'm using an XC4KE part, I have a 32-bit bidirectional bus that comes out
to
>> the pins and I'd like to constrain the tristate enable so that it's
faster.
>> ... I have a signal called dataoe, which is a flip-flop output, and
>> that signal is used as the tri-state enable for the outputs, which are
>> called ramdata[31:0].
>
>I have usually not had very good luck getting the Xilinx tools to improve
timing
>in a case like this by adding timing constraints. What I would suggest is
that
>you floorplan the dataoe flip-flop to the middle of the tristate bus. If
that's
>not fast enough, you might duplicate the dataoe flip-flop and floorplan the
>copies. Another way would be to add a gclk buffer, floorplan it the buffer
that
>gives the best drive to the data bus pins and floorplan the dataoe
flip-flop to
>be in that corner of the die.
Unfortunately, the pins are fixed, but I'll try floorplanning the dataoe
flop as you say.
I added a BUFGS to dataoe, and for some reason, it got slower! i think I
screwed something up, though, since it was 6:30 pm on a Friday...
-- a
-----------------------------------------
Andy Peters
Sr Electrical Engineer
National Optical Astronomy Observatories
950 N Cherry Ave
Tucson, AZ 85719
apeters (at) noao \dot\ edu
"Creation Science" is oxymoronic.
Article: 18573
Subject: Roots of development of FPGA's
From: project <projectdspNOprSPAM@yahoo.com.invalid>
Date: Mon, 01 Nov 1999 09:12:23 -0800
Links: << >> << T >> << A >>
Where can I find information about the roots of development
of FPGA's and evolution untill nowadays? Diferences between
others systems? ....
* Sent from AltaVista http://www.altavista.com Where you can also find related Web Pages, Images, Audios, Videos, News, and Shopping. Smart is Beautiful
Article: 18574
Subject: Re: Xilinx TPSYNC constraint
From: "Andy Peters" <apeters.nospam@nospam.noao.edu.nospam>
Date: Mon, 1 Nov 1999 10:26:40 -0700
Links: << >> << T >> << A >>
Rickman wrote in message <381CB6F4.1F6908AF@yahoo.com>...
>To be honest, I find the whole constraint thing to be very, very
>confusing. I think that the way they are set up and more so the way they
>are documented makes them very, very hard to understand. I find this
>doubly painful when it seems that the concept of constraints is so
>simple.
and the constraints editor GUI, which is supposed to make life easier, still
has problems: it dies with an access fault every time you exit, it screws up
the text file so you any kind of neat ordering you'd created gets blown
away, and it doesn't have a way to add all the possible constraints. I've
stopped using it.
>But now that my beef is out of the way I will say that I have dealt with
>this sort of thing using the OFFSET command. In my last Xilinx design
>(which is starting to grow whiskers) I had a clock, LCLK and a bidir bus
>LAD. I spec'ed using the statements below to assure that the outputs
>were stable 5 nS before the rising edge of LCLK and could tolerate
>changes on LAD up to 20 nS after LCLK. I did it this way because it
>seemed easier to relate these numbers to the devices I was connecting to
>(setup = 5 nS and output delay = 20 nS).
>
>NET LAD<* OFFSET = IN 20 AFTER LCLK;
>NET LAD<* OFFSET = OUT 5 BEFORE LCLK;
>
>To the best of my knowledge this also took into account the path through
>the enable on the tristate buffers. I did not need to place any special
>constraints on that signal.
>
>The data book does not show OFFSET being used with IN and AFTER or OUT
>and BEFORE. Rather they show them used in the opposite combination. But
>this did what I wanted and seemed to work.
OFFSET IN assumes that the FPGA is getting data from an upstream device.
OFFSET IN BEFORE specifies that the data will be valid at the FPGA input
pins x ns before the clock arrives AT THE FPGA.
OFFSET IN AFTER specifies that the data will be valid at the FPGA input pins
x ns AFTER the clock arrives at the UPSTREAM DEVICE.
OFFSET IN AFTER is probably more useful. If your FPGA is driven by an octal
flipflop with a clock-to-out time of 5 ns, all you need to do is specify
NET din OFFSET = IN 5 ns AFTER clock;
and the tools should (hopefully) take care of the rest.
OFFSET OUT is similar, 'cept that the FPGA is the data source, rather than
the sync.
OFFSET OUT AFTER specifies that the data will be valid at the FPGA OUTPUT x
ns AFTER the clock arrives at the FPGA INPUT.
OFFSET OUT BEFORE specifies that the data will be valid AT THE FPGA OUTPUT x
ns BEFORE the clock arrives at the DATA SINK (upstream device).
OFFSET OUT BEFORE would be used to specify a setup time for the data sink
(you need to include any board delay).
OFFSET OUT AFTER would be used to constrain the FPGA outputs to get the data
out in a certain time, but you have to make sure that you're still meeting
the data sink's setup requirements.
hope this helps...
-- a
-----------------------------------------
Andy Peters
Sr Electrical Engineer
National Optical Astronomy Observatories
950 N Cherry Ave
Tucson, AZ 85719
apeters (at) noao \dot\ edu
"Creation Science" is oxymoronic.
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Authors:A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Custom Search
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2021-09-25 08:59:02
|
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|
https://codegolf.stackexchange.com/questions/196792/count-the-length-of-head-movement
|
Count the length of head movement
Once upon a time I wanted to order custom tokens for a board game. They say they can do it, and then they present me their price list. I was confused because they charge per inch of head movement, and I have no idea how much will my tokens cost.
INPUT: a 2d grid:
• |,-,\,/ are straight cuts. Each has a length of 1.
• ┌,┐,└,┘ are 90 degree corner cuts. Each has length of 1.$$\^1\$$
• #,@ are 45 and 135 degree corner cuts respectively. Each has a length of 1.20.
• +,X are perpendicularly intersecting cuts. Each has a length of 1.
• >,v,<,^ are the cut ends. Each has a length of:
• 1.50, if the arrow points at the diagonal cut,
• 1, if the arrow points at the beginning of next cut,
• 0.50 otherwise.
• ABC...UVWYZabc...xyz are the cut start points given in that order. They have a length of:
• 1.50, if if the cut begins next to the diagonal cut,
• 1 otherwise.
OUTPUT: Distance that a head will move with up to 2 significant digits.
Assume that:
• The company doesn't count distance from resting position to starting point of the first cut,
• Each cut is made only once (intersections cut twice on the same character),
• All grids are valid,
• The head moves from the end of a cut to the beginning of another cut in a straight line.
Obviously no standard loopholes, and the shortest code in each language wins!
TEST CASES:
Output: 0
A> B>
Output: 4
A------v
^------B
Output: 16
A┌┐^
└┘└┘
Output: 7.5
#B┐
|\v
A<#
Output: 11.4 (Note: First the head cuts bottom-left triangle, then moves its head to the beginning of top-right triangle cut. 45 degree corners take continuations first instead of new cuts.)
A-@<--┐
^ \ |
└--B@-┘
Output: 21.15
A-┐ ┌--┐ ┌-┐ ┌--┐ C-┐ ┌--┐ ┌-┐ ┌--┐
^ | | | | | | | ^ | | | | | | |
└-+-+--┘ └-+-+--┘ └-+-+--┘ └-+-+--┘
| | B | | | D |
└-┘ ^-┘ └-┘ ^-┘
Output: 138.41
#-#
A X
X \
@ @-#
v
Output: 13.5
A> F> K> P> U> a>
B> G> L> Q> V> b>
C> H> M> R> W> c>
D> I> N> S> Y> d>
E> J> O> T> Z> e┐
<---------------┘
Output: 104.29
$$\^1\$$ If needed, replace this with a set of your choice.
• Can we use swap the 4 90 degree cut symbols for ASCII symbols (e.g. use 1,2,3,4) instead? – Veskah Dec 9 '19 at 13:13
• You should explain what you mean by "next to a diagonal cut". I thought it'd mean adjacent to # or @ (since 45° and 135° lines are diagonals), but this doesn't fit with the test cases. – Grimmy Dec 9 '19 at 15:43
• The output is defined as the distance that the head moves, but there's almost no explanation of how the head moves. Each character is associated with a "value"; are those actually distances? "The head moves from the end of the first cut to the beginning of the second cut in a straight line"; is that specific to the first cut, or true for all pairs of consecutive cuts? – Grimmy Dec 9 '19 at 17:00
|
2020-10-23 10:42:18
|
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|
https://lists.gnu.org/archive/html/lilypond-devel/2010-12/msg00651.html
|
lilypond-devel
[Top][All Lists]
From: Reinhold Kainhofer Subject: Re: PDF hyperlinks Date: Mon, 27 Dec 2010 17:11:09 +0100 User-agent: KMail/1.13.5 (Linux/2.6.35-23-generic; KDE/4.5.4; i686; ; )
```Am Montag, 27. Dezember 2010, um 15:34:05 schrieb Reinhold Kainhofer:
> 2) Of course, the non-trivial part of all this is how to get the
> information about label and link to the ps backend... I don't have a clear
> idea how to propagate that information from the markup interpretation to
> the backend. It might be able to do this in Scheme, but maybe also some
> C++ is required. From a quick look at the code, all labels are collected
> in the label-page- table variable of the paper object, but I don't know if
> this is available in the backend...
I forgot to add that the link itself would then be implemented completely
similar to \with-url. So, the only non-trivial thing is really how to get the
information about where to place the label (as a DEST pdfmark) into the ps
backend.
Cheers,
Reinhold
--
------------------------------------------------------------------
|
2019-05-21 11:40:16
|
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|
https://de.maplesoft.com/support/help/errors/view.aspx?path=GroupTheory%2FGroupOrder
|
GroupOrder - Maple Help
GroupTheory
GroupOrder
compute the order of a group
Calling Sequence GroupOrder( G )
Parameters
G - a permutation group
Description
• The order of a group is the cardinality of its underlying set.
• The GroupOrder( G ) command computes the order of the group G, if possible. (Note that the order of a finitely presented group cannot be determined, in general.)
• In most cases, it is much more efficient to use the GroupOrder command to determine the order of a group than to list its elements with the Elements command and then count them. In the case of a symbolic group, this is the only way to compute the group order.
Examples
> $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
> $G≔\mathrm{SymmetricGroup}\left(5\right)$
${G}{≔}{{\mathbf{S}}}_{{5}}$ (1)
> $\mathrm{GroupOrder}\left(G\right)$
${120}$ (2)
> $G≔\mathrm{BabyMonster}\left(\right)$
${G}{≔}{𝔹}$ (3)
> $\mathrm{GroupOrder}\left(G\right)$
${4154781481226426191177580544000000}$ (4)
> $\mathrm{GroupOrder}\left(\mathrm{DihedralGroup}\left(3k+1\right)\right)$
${6}{}{k}{+}{2}$ (5)
> $\mathrm{GroupOrder}\left(\mathrm{ElementaryGroup}\left(p,n\right)\right)$
${{p}}^{{n}}$ (6)
> $G≔⟨⟨a,b⟩|⟨{a}^{2},{b}^{3},{\left(a·b\right)}^{5}=1⟩⟩$
${G}{≔}⟨{}{a}{,}{b}{}{\mid }{}{{a}}^{{2}}{,}{{b}}^{{3}}{,}{a}{}{b}{}{a}{}{b}{}{a}{}{b}{}{a}{}{b}{}{a}{}{b}{}⟩$ (7)
> $\mathrm{GroupOrder}\left(G\right)$
${60}$ (8)
Compatibility
• The GroupTheory[GroupOrder] command was introduced in Maple 17.
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2022-01-24 20:52:42
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http://zbmath.org/?q=an:1025.90038
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# zbMATH — the first resource for mathematics
##### Examples
Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.
##### Operators
a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
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A limited-memory multipoint symmetric secant method for bound constrained optimization. (English) Zbl 1025.90038
The paper concerns a new iterative algorithm for the minimization of $f\left(x\right)$ subject to the box-constraint $x\in {\Omega }$. Here ${\Omega }=\left\{x\in {ℝ}^{n}\mid l\le x\le u\right\}$, whereas $f:{ℝ}^{n}\to ℝ$ is a continuously differentiable function. Given an iteration ${x}^{k}\in {\Omega }$, the new iteration ${x}^{k+1}\in {\Omega }$ is computed through the minimization of $\left(1/2\right)〈p,{B}^{k}p〉+〈\nabla f\left({x}^{k}\right),p〉$ subject to $p\in \overline{{F}_{I}}$. Here ${F}_{I}$ is the ${\Omega }$-face which contains ${x}^{k}$, whereas ${B}^{k}$ is a symmetric approximation of the Hessian of $f$. The matrices ${B}^{k}$ are generated by a multipoint symmetric secant method. The involved limited-memory formulae differ from the conventional ones because they are based on different quasi-Newton methods. Implementation details, numerical results, and final conclusions are presented.
##### MSC:
90C55 Methods of successive quadratic programming type
##### Keywords:
box constrained optimization
TRON; LANCELOT
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2014-04-23 11:25:28
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https://jp.maplesoft.com/support/help/maple/view.aspx?path=networks(deprecated)/octahedron&L=J
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networks(deprecated)/octahedron - Maple Help
networks
octahedron
creates a octahedron graph
Calling Sequence G:=octahedron()
Parameters
G - is returned as the octahedron
Description
• Important:The networks package has been deprecated. Use the superseding command GraphTheory[SpecialGraphs][OctahedronGraph]instead.
• The simple graph known as an octahedron is generated.
• This routine is normally loaded via the command with(networks) but may also be referenced using the full name networks[octahedron]().
Examples
Important:The networks package has been deprecated. Use the superseding command GraphTheory[SpecialGraphs][OctahedronGraph]instead.
> $\mathrm{with}\left(\mathrm{networks}\right):$
> $G≔\mathrm{octahedron}\left(\right):$
> $\mathrm{edges}\left(G\right)$
$\left\{{\mathrm{e1}}{,}{\mathrm{e10}}{,}{\mathrm{e11}}{,}{\mathrm{e12}}{,}{\mathrm{e2}}{,}{\mathrm{e3}}{,}{\mathrm{e4}}{,}{\mathrm{e5}}{,}{\mathrm{e6}}{,}{\mathrm{e7}}{,}{\mathrm{e8}}{,}{\mathrm{e9}}\right\}$ (1)
> $\mathrm{vertices}\left(G\right)$
$\left\{{0}{,}{1}{,}{2}{,}{3}{,}{4}{,}{5}\right\}$ (2)
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2022-01-28 02:35:14
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https://www.physicsforums.com/threads/find-where-one-graph-is-bigger-than-the-other.644959/
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# Find where one graph is bigger than the other
1. Oct 18, 2012
### Pi Face
1. The problem statement, all variables and given/known data
My question is part of a bigger one that I'm using in a graphical proof. I have two functions, tanh(ap) and 2a/(1+a^2). The a is the input and p is a constant. I'm trying to find the value for p which is the bridging point between the two functions having 1 intersection and 2 intersections. To do this, I said that we want to find the value for p which makes tanh(ap) greater than 2a(1+a^2) for every point on the interval (0,1) (because the second function's max is at 1, so the two intersections will be on the sides of a=1)
So I have tanhap>2a/(1+a^2)>0, but I'm not sure how to go about solving it. I can't set them equal to each other at a=1 because tanha never reaches 1 so I get an undefined answer. Is there something I can do with limits?
2. Oct 18, 2012
### Simon Bridge
Do I understand that your problem is to find $$p: \tanh(px) > \frac{2x}{1+x^2}: x\in (0,1)$$... what's wrong with putting LHS=RHS and finding the intersection in terms of p as a starting point?
You can gain an understanding of what p does by plotting tanh(px), and 2x(1+x^2), on the same axis, in the interval, for several values of p using a math-script program like matlab, mathematica, or gnu/octave.
But I think I see your problem ... if you had a hard interval like (0,1] then your requirements cannot be met since at x=1, RHS>LHS ... and this is unambiguous. However, you only need LHS>RHS for x values arbitrarily close to 1.
Interestingly, the RHS has a turning point at x=1 ... the slope of the RHS is a maximum at the origin, so any value of p that makes the slope of the LHS the same at the origin will make the LHS > RHS for much of the interval. But I suspect that you can only make the other two intersection points arbitrarily close together as p -> infinity. I suppose a limit formulation would be to find p that satisfies the conditions for an interval (0,z] in the limit z -> 1. Trouble is, p(x) is assymtotic at x=1.
Last edited: Oct 18, 2012
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2017-12-12 20:09:14
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https://cungthi.vn/cau-hoi/choose-the-word-or-phrase-a-b-c-or-d-that-best-fits-the-blan-206006.html
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# Choose the word or phrase (A, B, C or D) that best fits the blank space in the following passage: LOOK ON THE BRIGHT SIDE Do you ever wish you were more optimistic, some one who always (21)_____ to be successful? Having some one around who always fears the worst isn’t really a lot of (22)_____we all know someone who sees a single cloud on a sunny day and says: “It looks like rain.”. But if you catch yourself thinking such things, it’s important to do something (23)_____ it. You can change your view of life, (24)_____ to psychologists, it only takes a little effort, and you’ll find life more rewarding as a (25)______. Optimism, they say, is partly about self-respect and confidence, but it’s also a more positive way of looking at life and all it has to offer. Optimists are more (26)_______to start new projects and generally more prepared to take risks. Upbringing is obviously very important in forming your (27)_______ to the world. Some people are brought up to (28)______too much on others and grow up forever blaming other people when anything goes wrong. Most optimists, on the (29) _____hand, have been brought up not to regard failure as the end of the world - they just (30)_____with their lives. Question 24:
A.
A. judging
B.
B. concerning
C.
C. according
D.
D. following
Đáp án:C
Lời giải:
Đáp án C
Judge: phán xét
Concern: quan tâm
Accord: theo như
Follow: theo sau
You can change your view of life, (24)_____ to psychologists,=> Bạn có thể thay đổi cái nhìn về cuộc sống theo các nhà tâm lý học.
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2019-12-07 13:41:41
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http://specialfunctionswiki.org/index.php/Euler_phi
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# Euler phi
Jump to: navigation, search
The Euler phi function (not to be confused with the Euler totient) is defined for $q \in \mathbb{C}$ with $|q|<1$ by $$\phi(q) = \displaystyle\prod_{k=1}^{\infty} 1-q^k.$$
# References
Number theory functions
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2018-04-22 04:21:22
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http://deltaepsilons.wordpress.com/tag/noetherian-rings/
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## Dedekind domainsAugust 31, 2009
Posted by Akhil Mathew in algebra, algebraic number theory, commutative algebra, number theory.
Tags: , , , , ,
Today’s (quick) topic focuses on Dedekind domains. These come up when you take the ring of integers in any finite extension of ${\mathbb{Q}}$ (i.e. number fields). In these, you don’t necessarily have unique factorization. But you do have something close, which makes these crucial.
Definition 1 A Dedekind domain is a Noetherian integral domain ${A}$ that is integrally closed, and of Krull dimension one—that is, each nonzero prime ideal is maximal. (more…)
## DVRs IIAugust 30, 2009
Posted by Akhil Mathew in algebra, algebraic number theory, commutative algebra, number theory.
Tags: , , , ,
Earlier I went over the definition and first properties of a discrete valuation ring. Today, it’s time to say how we can tell a ring is a DVR–it turns out to be not too bad, which is nice because the properties we need in this criterion are often easier to work with than the existence of some discrete valuation.
Today’s result is:
Theorem 1 If the domain ${R}$ is Noetherian, integrally closed, and has a unique nonzero prime ideal ${\mathfrak{m}}$, then ${R}$ is a DVR. Conversely, any DVR has those properties. (more…)
## The finite presentation trick and completionsAugust 27, 2009
Posted by Akhil Mathew in algebra, category theory, commutative algebra.
Tags: , , , ,
The previous post got somewhat detailed and long, so today’s will be somewhat lighter. I’ll use completions to illustrate a well-known categorical trick using finite presentations.
The finite presentation trick
Our goal here is:
Theorem 1 Let ${A}$ be a Noetherian ring, and ${I}$ an ideal. If we take all completions with respect to the ${I}$-adic topology,
$\displaystyle \hat{M} = \hat{A} \otimes_A M$
for any f.g. ${A}$-module ${M}$. (more…)
## Completions of rings and modulesAugust 25, 2009
Posted by Akhil Mathew in algebra, commutative algebra.
Tags: , , , ,
So, we saw in the previous post that completion can be defined generally for abelian groups. Now, to specialize to rings and modules.
Rings
The case in which we are primarily interested comes from a ring ${A}$ with a descending filtration (satisfying ${A_0 =A}$), which implies the ${A_i}$ are ideals; as we saw, the completion will also be a ring. Most often, there will be an ideal ${I}$ such that ${A_i = I^i}$, i.e. the filtration is ${I}$-adic. We have a completion functor from filtered rings to rings, sending ${A \rightarrow \hat{A}}$. Given a filtered ${A}$-module ${M}$, there is a completion ${\hat{M}}$, which is also a ${\hat{A}}$-module; this gives a functor from filtered ${A}$-modules to ${\hat{A}}$-modules. (more…)
## Gradings, filtrations, and grAugust 18, 2009
Posted by Akhil Mathew in algebra, commutative algebra.
Tags: , , , , ,
Bourbaki has a whole chapter in Commutative Algebra devoted to “graduations, filtrations, and topologies,” which indicates the importance of these concepts. That’s the theme for the next few posts I’ll do here, although I will (of course) be more concise.
In general, all rings will be commutative.
The idea of a graded ring is necessary to define projective space.
Definition 1 A graded ring is ring ${A}$ together with a decomposition
$\displaystyle A = \bigoplus_{n=-\infty}^\infty A_n \ \mathrm{as \ abelian \ groups},$
such that ${A_i \cdot A_j \subset A_{i+j}}$. The set ${A_i}$ is said to consist of homogeneous elements of degree ${i}$. (more…)
## A prime ideal criterion for being NoetherianAugust 13, 2009
Posted by Akhil Mathew in algebra, commutative algebra.
Tags: , ,
1 comment so far
This post, the third in the mini-series so far, gives one more criterion for when a ring is Noetherian. I also discuss how prime ideals tend to crop up in commutative algebra.
Why prime ideals are important
As discussed in the end of my previous post and in the comments, ideals satisfying some property and maximal with respect to it are often prime. To prove these results, we often use the following convenient notation:
Definition 1
If ${I,J}$ are ideals of a commutative ring ${A}$, then we define
## Integrality, invariant theory for finite groups, and more tools for Noetherian testingAugust 11, 2009
Posted by Akhil Mathew in algebra, commutative algebra.
Tags: , , ,
There are quite a few more tools to tell whether a ring is Noetherian. In this post, I’ll discuss another basic tool: integrality. I’ll discuss the application to invariant theory for finite groups.
Subrings
In general, it is not true that a subring of a Noetherian ring is Noetherian. For instance, let ${A := k[X_1, X_2, \dots]}$ be the polynomial ring in infinitely many variables over a field ${k}$. Then ${A}$ is not Noetherian because of the ascending chain
$\displaystyle (X_0) \subset (X_0, X_1) \subset (X_0, X_1, X_2) \subset \dots.$
However, the quotient field of ${A}$ is Noetherian. This applies to any non-Noetherian integral domain.
There are special cases where we can conclude a subring of a Noetherian ring is Noetherian.
## How to tell if a ring is NoetherianAugust 9, 2009
Posted by Akhil Mathew in algebra, commutative algebra.
Tags: , , , ,
I briefly outlined the definition and first properties of Noetherian rings and modules a while back. There are several useful and well-known criteria to tell whether a ring is Noetherian, as I will discuss in this post. Actually, I’ll only get to the first few basic ones here, though these alone give us a lot of tools for, say, algebraic geometry, when we want to show our schemes are relatively well-behaved. But there are plenty more to go.
Hilbert’s basis theorem
It is the following:
Theorem 1 (Hilbert) Let ${A}$ be a Noetherian ring. Then the polynomial ring ${A[X]}$ is also Noetherian.
## Generic freeness IJuly 29, 2009
Posted by Akhil Mathew in algebra, commutative algebra.
Tags: , , , , ,
As I have already mentioned, a ring is Noetherian if each ideal of ${A}$ is finitely generated. Similarly, a module is Noetherian if every submodule is finitely generated. I will summarize the basic facts below briefly.
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2013-12-13 05:17:56
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https://intelligencemission.com/free-electricity-using-alternator-free-electricity-with-motor.html
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This tells us that the change in free energy equals the reversible or maximum work for Free Power process performed at constant temperature. Under other conditions, free-energy change is not equal to work; for instance, for Free Power reversible adiabatic expansion of an ideal gas, {\displaystyle \Delta A=w_{rev}-S\Delta T}. Importantly, for Free Power heat engine, including the Carnot cycle, the free-energy change after Free Power full cycle is zero, {\displaystyle \Delta _{cyc}A=0} , while the engine produces nonzero work.
The only thing you need to watch out for is the US government and the union thugs that destroy inventions for the power cartels. Both will try to destroy your ingenuity! Both are criminal elements! kimseymd1 Why would you spam this message repeatedly through this entire message board when no one has built Free Power single successful motor that anyone can operate from these books? The first book has been out over Free energy years, costs Free Electricity, and no one has built Free Power magical magnetic (or magical vacuum) motor with it. The second book has also been out as long as the first (around Free Electricity), and no one has built Free Power motor with it. How much Free Power do you get? Are you involved in the selling and publishing of these books in any way? Why are you doing this? Are you writing this from inside Free Power mental institution? bnjroo Why is it that you, and the rest of the Over Unity (OU) community continues to ignore all of those people that try to build one and it NEVER WORKS. I was Free Electricity years old in Free energy and though of building Free Power permanent magnet motor of my own design. It looked just like what I see on the phoney internet videos. It didn’t work. I tried all kinds of clever arrangements and angles but alas – no luck.
Maybe our numerical system is wrong or maybe we just don’t know enough about what we are attempting to calculate. Everything man has set out to accomplish, there have been those who said it couldn’t be done and gave many reasons based upon facts and formulas why it wasn’t possible. Needless to say, none of the ‘nay sayers’ accomplished any of them. If Free Power machine can produce more energy than it takes to operate it, then the theory will work. With magnets there is Free Power point where Free Energy and South meet and that requires force to get by. Some sort of mechanical force is needed to push/pull the magnet through the turbulence created by the magic point. Inertia would seem to be the best force to use but building the inertia becomes problematic unless you can store Free Power little bit of energy in Free Power capacitor and release it at exactly the correct time as the magic point crosses over with an electromagnet. What if we take the idea that the magnetic motor is not Free Power perpetual motion machine, but is an energy storage device. Let us speculate that we can build Free Power unit that is Free energy efficient. Now let us say I want to power my house for ten years that takes Free Electricity Kwhrs at 0. Free Energy /Kwhr. So it takes Free energy Kwhrs to make this machine. If we do this in Free Power place that produces electricity at 0. 03 per Kwhr, we save money.
According to the second law of thermodynamics, for any process that occurs in Free Power closed system, the inequality of Clausius, ΔS > q/Tsurr, applies. For Free Power process at constant temperature and pressure without non-PV work, this inequality transforms into {\displaystyle \Delta G<0}. Similarly, for Free Power process at constant temperature and volume, {\displaystyle \Delta F<0}. Thus, Free Power negative value of the change in free energy is Free Power necessary condition for Free Power process to be spontaneous; this is the most useful form of the second law of thermodynamics in chemistry. In chemical equilibrium at constant T and p without electrical work, dG = 0. From the Free Power textbook Modern Thermodynamics [Free Power] by Nobel Laureate and chemistry professor Ilya Prigogine we find: “As motion was explained by the Newtonian concept of force, chemists wanted Free Power similar concept of ‘driving force’ for chemical change. Why do chemical reactions occur, and why do they stop at certain points? Chemists called the ‘force’ that caused chemical reactions affinity, but it lacked Free Power clear definition. ”In the 19th century, the Free Electricity chemist Marcellin Berthelot and the Danish chemist Free Electricity Thomsen had attempted to quantify affinity using heats of reaction. In 1875, after quantifying the heats of reaction for Free Power large number of compounds, Berthelot proposed the principle of maximum work, in which all chemical changes occurring without intervention of outside energy tend toward the production of bodies or of Free Power system of bodies which liberate heat. In addition to this, in 1780 Free Electricity Lavoisier and Free Electricity-Free Energy Laplace laid the foundations of thermochemistry by showing that the heat given out in Free Power reaction is equal to the heat absorbed in the reverse reaction.
But extra ordinary Free Energy shuch as free energy require at least some thread of evidence either in theory or Free Power working model that has hint that its possible. Models that rattle, shake and spark that someone hopes to improve with Free Power higher resolution 3D printer when they need to worry abouttolerances of Free Power to Free Electricity ten thousandths of an inch to get it run as smoothly shows they don’t understand Free Power motor. The entire discussion shows Free Power real lack of under standing. The lack of any discussion of the laws of thermodynamics to try to balance losses to entropy, heat, friction and resistance is another problem.
NOTHING IS IMPOSSIBLE! Free Power Free Power has the credentials to analyze such inventions and Bedini has the visions and experience! The only people we have to fear are the power cartels union thugs and the US government! rychu Free Energy two books! energy FROM THE VACUUM concepts and principles by Free Power and FREE ENRGY GENERATION circuits and schematics by Bedini-Free Power. Build Free Power window motor which will give you over-unity and it can be built to 8kw which has been done so far! NOTHING IS IMPOSSIBLE! Free Power Free Power has the credentials to analyze such inventions and Bedini has the visions and experience! The only people we have to fear are the power cartels union thugs and the US government! Free Energy two books! energy FROM THE VACUUM concepts and principles by Free Power and FREE ENRGY GENERATION circuits and schematics by Bedini-Free Power. Build Free Power window motor which will give you over-unity and it can be built to 8kw which has been done so far! NOTHING IS IMPOSSIBLE! Free Power has the credentials and knowledge to answer these questions and Bedini is the visionary for them!
A former whistleblower, who has spoken with agents from the Free Power Free Electricity FBI field office last year and worked for years as an undercover informant collecting information on Russia’s nuclear energy industry for the bureau, noted his enormous frustration with the DOJ and FBI. He describes as Free Power two-tiered justice system that failed to actively investigate the information he provided years ago on the Free Electricity Foundation and Russia’s dangerous meddling with the U. S. nuclear industry and energy industry during the Obama administration.
Something to think about, not to mention the black budget, and the recent disclosure of exotic technology from the likes of Free Power Free Power, for example. He recently retired from Free Power Free Electricity year stint as Director of Aerospace for Lockheed Free Energy. Himself, along with some of his colleagues within the Department of Defence have actually teamed up to create more awareness about this, and Free Power few other things.
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2020-08-08 21:21:51
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https://www.szhang.net/notes/2015/10/01/Trap-System/
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# Practical Theory for Trapped Ion Experiments
###### 01 October 2015
• Trap System: 4-rod Paul trap with atom ovens
• Vaccum System: keep <$10^{-11}$ torr UHV to reduce the background collision rate to <1/hour
• Confine System: RF helical resonator and DC voltage board
• Detection System: PMT and CCD to detect the fluorescence of ions
• Laser System
• FP cavity and Iodine cell to stabilize diode laser frequency
• EOM to generate sidebands
• AOM to shift center frequency and act as an optical switch
• Control System
• coherent quantum control with microwave horn and pulse laser Raman beams
• programmable TTL sequencer and waveform generators
## Trap System
For atomic ions, $\Omega/2\pi>100$ kHz and $|V_0|<1000$ V, near the axis of the trap
where Laplace condition $\Delta\Phi=0$ implies
in Paul trap case
and
• time averaging of the AC field can be represented as a pseudopotential
• for single ion experiment, the small AC field along the z axis can be emitted
• there could be additional terms caused by
• imperfect geometry configuration
• phase difference between AC electrodes
• use CPO3D to simulate and verify all these electric fields
For single ion of mass m and charge Q, from
we get Mathieu equations
where
and
when $|a_ i|,|q_ i|\ll 1$, set $\beta_ i=\sqrt{a_ i+q_ i^2/2}$, the first-order solution
the main secular motion of the ion is harmonic oscillation, fast oscillation with frequency $\Omega$ is called ‘‘micromotion’’.
'’excess’’ micromotion caused by additional terms can be detected with TDC or Raman beams and then compensated with bias DC rods
The metal powder is heated and gasified from atom oven. A beam of Yb atoms is shooted into trap center, then ionized by a pair of strong 399nm and 370nm laser beams. Once the ion is Doppler cooled to limit
where $\gamma=2\pi\cdot 19.7$ MHz is the linewidth of the cooling transition for $^{171}\mathrm{Yb}^+$ case, its internal electric levels plus external trap oscillator can be written as
and the diople coupling hamiltonian
if we apply an external wave field from either microwave horn or laser beam. Take interaction picture with respect to wave frequency
where detuning $\delta=\nu-\omega_ 0-(m-n)\omega_1$, and apply rotating-wave approximation
The coupling term
where Laguerre polynomial
Specially, for carrier transition $|\downarrow,n\rangle\rightarrow |\uparrow,n\rangle$
For blue sideband $|\downarrow,n-1\rangle\rightarrow |\uparrow,n\rangle$, and red sideband $|\downarrow,n\rangle\rightarrow |\uparrow,n-1\rangle$
## Open Problems
two ions are not stable in high trap z direction rf from dc rods 崔凯枫 from Wuhan: protection sequence doesn’t work
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2019-03-21 05:46:02
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http://www.njohnston.ca/2014/08/obvious-does-not-imply-true-the-minimal-superpermutation-conjecture-is-false/
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Blog > “Obvious” Does Not Imply “True”: The Minimal Superpermutation Conjecture is False
## “Obvious” Does Not Imply “True”: The Minimal Superpermutation Conjecture is False
August 22nd, 2014
One of my favourite examples of an “obvious” mathematical statement that is actually false is the “fact” that if $R,S,T \subseteq \mathbb{R}^n$ are vector spaces then
$\dim(R + S + T) = \dim(R) + \dim(S) + \dim(T) \\ {}_{{}_{{}_{.}}}\quad\quad\quad\quad\quad\quad\quad\quad - \dim(R\cap S) -\dim(R\cap T) -\dim(S\cap T) \\ {}_{{}_{{}_{.}}}\quad\quad\quad\quad\quad\quad\quad\quad+\dim(R\cap S\cap T).$
The reason that the above statement seems so obvious is that the similar fact $\dim(R + S) = \dim(R) + \dim(S) - \dim(R\cap S)$ does hold, so it’s very tempting to think “inclusion-exclusion, yadda yadda, it’s simple enough to prove that it’s not worth writing down or working through the details”. However, it’s not true: a counterexample is provided by 3 distinct lines through the origin in $\mathbb{R}^2$.
There is another problem that I’ve been thinking about for quite some time that is also “obvious”: the minimal superpermutation conjecture. This conjecture was so obvious, in fact, that it appeared as a question in a national programming contest in 1998. Well, last night Robin Houston posted a note on the arXiv showing that, despite being obvious, the conjecture is false [1].
### Superpermutations
What is the shortest string that contains each permutation of “123” as a contiguous substring? It is straightforward to check that “123121321” contains each of “123”, “132”, “213”, “231”, “312”, and “321” as substrings (i.e., it is a superpermutation of 3 symbols), and it’s not difficult to argue (or use a computer search to show) that it is the shortest string with this property.
Well, we can repeat this question for any number of symbols. I won’t repeat all of the details (because I already wrote about the problem here), but there is a natural recursive construction that takes an (n-1)-symbol superpermutation of length L and spits out an n-symbol superpermutation of length L+n!. This immediately gives us an n-symbol superpermutation of length 1! + 2! + 3! + … + n! for all n. Importantly, it seemed like this construction was the best we could do: computer search verifies that these superpermutations are the smallest possible, and are even unique, for n ≤ 4.
Furthermore, it is not difficult to come up with some lower bounds on the length of superpermutations that seem to suggest that we have found the right answer. A trivial argument shows that an n-symbol superpermutation must have length at least (n-1) + n!, since we need n characters for the first permutation, and 1 additional character for each of the remaining n!-1 permutations. This argument can be refined to show that a superpermutation must actually have length at least (n-2) + (n-1)! + n!, since there is no way to pack the permutations tightly enough so that each one only uses 1 additional character (spend a few minutes trying to construct superpermutations by hand and you’ll see this for yourself). In fact, we can even refine this argument further (see a not-so-pretty proof sketch here) to show that n-symbol superpermutations must have length at least (n-3) + (n-2)! + (n-1)! + n!.
A-ha! A pattern has emerged – surely we can just keep refining this argument over and over again to eventually get a lower bound of 1! + 2! + 3! + … + n!, which shows that the superpermutations we already have are indeed minimal, right? Some variant of this line of thought seemed to be where almost everyone’s mind went when introduced to this problem, and it seemed fairly convincing: this argument is more or less contained within the answers when this question was posted on MathExchange and on StackOverflow (although the authors are usually careful to state that their method only appears to be optimal), and this problem was presented as a programming question in the 1998 Turkish Informatics Olympiad (see the resulting thread here). Furthermore, even on pages where this was acknowledged to be a difficult open problem, it was sometimes claimed that it had been proved for n ≤ 11 (example).
For the above reasons, it was a long time before I was even convinced that this problem was indeed unsolved – it seemed like people had solved this problem but just found it not worth the effort of writing up a full proof, or that people had found a simple way to tackle the problem for moderately large values of n like 10 or 11 that I couldn’t even dream of handling.
### The Conjecture is False
It turns out that the minimal superpermutation conjecture is false for all n ≥ 6. That is, there exists a superpermutation of length strictly less than 1! + 2! + 3! + … + n! in all of these cases [1]. In particular, Robin Houston found the following 6-symbol superpermutation of length 872, which is smaller than the conjectured minimum length of 1! + 2! + … + 6! = 873:
12345612345162345126345123645132645136245136425136452136451234651234156234152634
15236415234615234165234125634125364125346125341625341265341235641235461235416235
41263541236541326543126453162435162431562431652431625431624531642531462531426531
42563142536142531645231465231456231452631452361452316453216453126435126431526431
25643215642315462315426315423615423165423156421356421536241536214536215436215346
21354621345621346521346251346215364215634216534216354216345216342516342156432516
43256143256413256431265432165432615342613542613452613425613426513426153246513246
53124635124631524631254632154632514632541632546132546312456321456324156324516324
56132456312465321465324165324615326415326145326154326514362514365214356214352614
35216435214635214365124361524361254361245361243561243651423561423516423514623514
263514236514326541362541365241356241352641352461352416352413654213654123
So not only are congratulations due to Robin for settling the conjecture, but a big “thank you” are due to him as well for (hopefully) convincing everyone that this problem is not as easy as it appears upon first glance.
References
1. R. Houston. Tackling the Minimal Superpermutation Problem. E-print: arXiv:1408.5108 [math.CO], 2014.
Tags:
1. August 22nd, 2014 at 12:54 | #1
Thanks for this very nice write-up!
2. August 24th, 2014 at 10:32 | #2
Very interesting! I even wrote a simple program to convince myself — this is indeed a superpermutation for n=6 of length 872. Congratulations Robin!
Curiously, my program found 147 positions within the sequence that do not correspond to permutations (e.g., 123451 starting on 7th position). This means that there are 872 (all positions) – 720 (correct permutations) – 147 (not permutations) – 5 (beginning of the sequence) = 0 repetitions of valid permutations. That is, permutations are never repeated. It is not obvious for me if this must hold in all shortest superpermutations. Robin, do you know if this is always the case?
3. August 24th, 2014 at 17:18 | #3
@Andrey Mokhov That’s an excellent question. I’ve wondered the same thing. I’m pretty sure that permutations are never repeated in any of the minimal superpermutations we know about, but it isn’t obvious to me that must necessarily hold.
4. August 24th, 2014 at 21:36 | #4
@Robin Houston – Yep, I’ll just confirm that there are no repetitions in any of the known minimal (or even formerly smallest but now known not to be minimal) superpermutations. But I also am not aware of a proof that this fact must hold.
5. August 25th, 2014 at 05:39 | #5
@Robin Houston
@Nathaniel
Thank you! Perhaps, a search could be set up to find a 6-superpermutation of length 872, which contains 123456 twice. Due to symmetry, if we find such a superpermutation, it will generate a family of 720 solutions with all possible duplicates. On the other hand, if the search fails then there are no 6-superpermutations of length 872 with duplicates.
By the way, I just checked: Robin’s superpermutation doesn’t contain repetitions of non-permutations either. That is, all contiguous substrings of length 6 are distinct.
6. November 18th, 2014 at 19:26 | #6
Thank you for this post. It’s very interesting and yet comprehensible. Same goes for the article, by the way. He used a nice transformation to interpret the problem as a directed travelling salesman problem, for which powerful solvers exist. Unfortunately no new key insights though..
7. October 6th, 2015 at 04:37 | #7
Hi,
As per the arxiv paper should it be considered that the superpermutation problem is now resolved (in terms of algorithm to find one) ?
Thanks,
S
8. October 8th, 2015 at 06:23 | #8
@Shishir – Nope, it’s only resolved in that we know the original conjecture is false. We still don’t have an algorithm for finding minimal superpermutations, and we still don’t even know how long minimal superpermutations are.
9. October 8th, 2015 at 07:18 | #9
@Nathaniel
@Nathaniel – Thanks for your response. Do you reckon it makes for a good problem in quantum algorithm domain and whether anyone has already come up with one to solve this ?
Cheers,
S
10. October 13th, 2015 at 13:04 | #10
@Shishir – I doubt anyone has already come up with a good algorithm for this problem, since it’s not a particularly famous problem, so I probably would have heard of any substantial progress on it.
I don’t really know if there would be a quantum algorithm that would outperform classical algorithms — I don’t even know if there’s a classical algorithm better than greedy search!
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2016-12-04 01:53:15
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https://www.freebsd.org/doc/zh_TW/books/handbook/book.html
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FreeBSD 使用手冊
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2.22. 無效的選擇
2.23. 分析磁碟
2.24. 磁碟加密密碼
2.25. 最後修改
2.26. 最後確認
2.27. 取得發佈版本檔案
2.28. 檢驗發佈版本檔案
2.29. 解開發佈版本檔案
2.30. 設定 root 密碼
2.31. 選擇網路介面
2.32. 掃描無線網路存取點
2.33. 選擇無線網路
2.34. WPA2 設定
2.35. 選擇 IPv4 網路
2.36. 選擇 IPv4 DHCP 設定
2.37. IPv4 靜態位置設定
2.38. 選擇 IPv6 網路
2.39. 選擇 IPv6 SLAAC 設定
2.40. IPv6 靜態位置設定
2.41. DNS 設定
2.42. 選擇本地或 UTC 時鐘
2.43. 選擇區域
2.44. 選擇城市
2.45. 選擇時區
2.46. 確認時區
2.47. 選擇要開啟的其他服務
2.48. 開啟 Crash Dumps
2.49. 新增使用者帳號
2.50. 輸入使用者資訊
2.51. 離開使用者與群組管理
2.52. 最後設定
2.53. 手動設定
2.54. 完成安裝
30.1. 使用 NFS Root Mount 進行 PXE 開機程序
2.1. 磁碟分割格式
3.1. 管理使用者帳號的工具
3.2. UNIX® 權限
3.3. 磁碟裝置名稱
3.4. 常用環境變數
5.1. XDM 設定檔
7.1. 常見錯誤訊息
9.1. 輸出 PDL 格式
12.1. 載入程式內建指令
12.2. 開機時核心互動參數
13.1. 登入類別限制資源類型
16.1. 預設稽查事件類別
16.2. 稽查事件類別字首
22.1. 常用語言及城市代碼
22.2. 已定義供特定字元集使用的終端機類型
22.3. Ports 套件集中可用的 Console
22.4. 可用的輸入法
23.1. FreeBSD Versions and Repository Paths
25.1. RS-232C 信號名稱
25.2. DB-25 對 DB-25 Null-Modem 線
25.3. DB-9 對 DB-9 Null-Modem 線
25.4. DB-9 對 DB-25 Null-Modem 線
28.1. NIS 術語
28.2. 其他使用者
28.3. 其他系統
28.4. DNS 術語
29.1. 有用的 pfctl 選項
30.1. 常見路由表標記
30.2. 站台功能代號
30.3. 已保留的 IPv6 位址
2.1. 建立傳統分割的檔案系統分割區
3.1. 以超級使用者的身份安裝程式
3.2. 在 FreeBSD 新增使用者
3.3. rmuser 互動式帳號移除
3.4. 以超級使用者的身份使用 chpass
3.5. 以一般使用者的身份使用 chpass
3.6. 更改您的密碼
3.7. 以超級使用者的身份更改其他使用者的密碼
3.8. 使用 pw(8) 新增群組
3.9. 使用 pw(8) 加入使用者帳號到新的群組
3.10. 使用 pw(8) 加入新成員到群組
3.11. 使用 id(1) 來查看所屬群組
3.12. 磁碟、Slice 及分割區命名範例
3.13. 磁碟的概念模型
5.1. 在單檔中選擇 Intel® 影像驅動程式
5.3. 在單檔中選擇 VESA 影像驅動程式
5.4. 在單檔中選擇 scfb 影像驅動程式
5.5. 在單檔中設定螢幕解析度
5.6. 手動設定顯示器頻率
5.7. 設定鍵盤配置
5.8. 設定多個鍵盤配置
5.9. 開啟鍵盤離開 X 功能
5.10. 設定滑鼠按鍵編號
11.1. 日誌伺服器設定範例
11.2. 建立交換檔於 FreeBSD 10.X 及以後版本
11.3. 建立交換檔於 FreeBSD 9.X 及先前版本
12.1. boot0 螢幕截圖
12.2. boot2 螢幕截圖
12.3. /etc/ttys 設定不安全的 Console
13.1. 建立供 SMTP 使用的安全通道
13.2. 安全存取 POP3 伺服器
13.3. 跳過防火牆
14.1. 在不信任的 Jail 做 mergemaster(8)
14.2. 在信任的 Jail 做 mergemaster(8)
14.3. 在 Jail 中執行 BIND
17.1. ssh 使用 dump
17.2. ssh 使用 dump 透過 RSH 設定
17.3. 使用 tar 備份目前目錄
17.4. 使用 tar 還原目前目錄
17.5. 使用 lscpio 來製作目前目錄的遞迴備份
17.6. 使用 pax 備份目前目錄
18.1. 在開機磁碟標記分割區標籤
25.1. 設定終端機項目
28.1. 重新庫入 inetd 設定檔
28.2. 使用 amd 掛載 Export
28.3. 使用 autofs(5) 掛載 Export
28.4. /etc/ntp.conf 範例
30.1. Cisco® 交換器上設定 LACP Aggregation
30.2. 容錯移轉模式
30.3. 乙太網路與無線介面間的容錯移轉模式
序
自第二版後的主要修訂 (2004)
• 章 11, 設定與調校 已針對新內容作更新，如：ACPI 電源管理、cron 以及其他更多的核心調校選項說明內容。
• 章 13, 安全性 增加了虛擬私人網路(VPN)、檔案系統的存取控制(ACL)，以及安全報告。
• 章 15, 強制存取控制 (MAC) 是此版本新增的章節。該章介紹：什麼是 MAC 機制？以及如何運用它來使您的 FreeBSD 系統更安全。
• 章 17, 儲存設備 新增了像是：USB 隨身碟、檔案系統快照(snapshot)、檔案系統配額(quota) 、檔案及網路的備援檔案系統、以及如何對硬碟分割區作加密等詳解。
• 章 26, PPP 增加了疑難排解的章節。
• 章 27, 電子郵件 新增有關如何使用其它的傳輸代理程式、SMTP 認證、UUCP、fetchmailprocmail 的運用以及其它進階主題。
• 章 28, 網路伺服器 是該版中全新的一章。這一章介紹了如何架設 Apache HTTP 伺服器ftpd 以及用於支援 Microsoft® Windows® 客戶端的 Samba。其中有些段落來自原先的 章 30, 進階網路設定
• 章 30, 進階網路設定 新增有關在 FreeBSD 中使用藍牙®裝置、設定無線網路以及使用非同步傳輸模式 (Asynchronous Transfer Mode, ATM) 網路的介紹。
• 增加詞彙表，用以說明全書中出現的術語。
• 重新美編書中所列的圖表。
本書架構
Describes the jails framework, and the improvements of jails over the traditional chroot support of FreeBSD.
Explains what Mandatory Access Control (MAC) is and how this mechanism can be used to secure a FreeBSD system.
Describes what FreeBSD Event Auditing is, how it can be installed, configured, and how audit trails can be inspected or monitored.
Describes how to manage storage media and filesystems with FreeBSD. This includes physical disks, RAID arrays, optical and tape media, memory-backed disks, and network filesystems.
Describes what the GEOM framework in FreeBSD is and how to configure various supported RAID levels.
Examines support of non-native file systems in FreeBSD, like the Z File System from Sun™.
Describes what virtualization systems offer, and how they can be used with FreeBSD.
Describes how to use FreeBSD in languages other than English. Covers both system and application level localization.
Explains the differences between FreeBSD-STABLE, FreeBSD-CURRENT, and FreeBSD releases. Describes which users would benefit from tracking a development system and outlines that process. Covers the methods users may take to update their system to the latest security release.
Describes how to configure and use the DTrace tool from Sun™ in FreeBSD. Dynamic tracing can help locate performance issues, by performing real time system analysis.
Explains how to connect terminals and modems to your FreeBSD system for both dial in and dial out connections.
Describes how to use PPP to connect to remote systems with FreeBSD.
Explains the different components of an email server and dives into simple configuration topics for the most popular mail server software: sendmail.
Provides detailed instructions and example configuration files to set up your FreeBSD machine as a network filesystem server, domain name server, network information system server, or time synchronization server.
Explains the philosophy behind software-based firewalls and provides detailed information about the configuration of the different firewalls available for FreeBSD.
Describes many networking topics, including sharing an Internet connection with other computers on your LAN, advanced routing topics, wireless networking, Bluetooth®, ATM, IPv6, and much more.
Lists different sources for obtaining FreeBSD media on CDROM or DVD as well as different sites on the Internet that allow you to download and install FreeBSD.
This book touches on many different subjects that may leave you hungry for a more detailed explanation. The bibliography lists many excellent books that are referenced in the text.
Describes the many forums available for FreeBSD users to post questions and engage in technical conversations about FreeBSD.
Lists the PGP fingerprints of several FreeBSD Developers.
本書的編排體裁
文字編排體裁
等寬字
等寬字用於： 錯誤訊息、指令、環境變數、Port 名稱、主機名稱、帳號、群組、裝置名稱、變數、程式碼等。
Ctrl+Alt+Del
Ctrl+X, Ctrl+S
範例
E:\> tools\fdimage floppies\kern.flp A:
# dd if=kern.flp of=/dev/fd0
% top
部 I. 入門
• 介紹 FreeBSD 給您。
• 在安裝過程給您指引。
• 教您 UNIX® 的基礎及原理。
• 展示給您看如何安裝豐富的 FreeBSD 的應用軟體。
• 向您介紹 X，UNIX® 的視窗系統以及詳細的桌面環境設定，讓您更有生產力。
章 1. 簡介
Restructured, reorganized, and parts rewritten by .
1.1. 概述
• FreeBSD 與其他作業系統之間的關係。
• FreeBSD 計劃的歷史。
• FreeBSD 計劃的目標。
• FreeBSD 開源開發模式的基礎概念。
• 當然囉，還有 FreeBSD 這名字的由來。
1.2. 歡迎使用 FreeBSD!
FreeBSD 是一個從 4.4BSD-Lite 衍生出而能在以 Intel (x86 與 Itanium®), AMD64, Sun UltraSPARC® 為基礎的電腦上執行的作業系統。同時，移植到其他平台的工作也在進行中。 對於本計劃歷史的介紹，請看 FreeBSD 歷史， 對於 FreeBSD 的最新版本介紹，請看 最新的發行版本。 若打算對於 FreeBSD 計劃有所貢獻的話 (程式碼、硬體、經費)， 請看 如何對 FreeBSD 有貢獻
1.2.1. FreeBSD 能做什麼？
FreeBSD 提供給你許多先進功能。這些功能包括：
• 動態優先權調整的 先佔式多工 能夠確保，即使在系統負擔很重的情況下，程式執行平順並且應用程式與使用者公平地共享資源。
• 多人共用 代表著許多人可以同時使用一個 FreeBSD 系統來處理各自的事務。 系統的硬體周邊 (如印表機及磁帶機) 也可以讓所有的使用者適當地分享。 也可以針對各別使用者或一群使用者的系統資源，予以設限，以保護系統不致被過度使用。
• 強大的 TCP/IP 網路 功能可支援許多業界標準，如：SCTP、DHCP、NFS、NIS、PPP、SLIP、IPSec、IPv6 的支援，也就是說 FreeBSD 可以容易地跟其他作業系統透過網路共同運作，或是當作企業的伺服器用途 ，例如提供遠端檔案共享(NFS)及電子郵件等服務， 或是讓您的企業連上網際網路並提供 WWW、FTP、路由及防火牆 (安全性) 等必備服務。
• 記憶體保護 能確保程式 (或使用者) 不會互相干擾，即使任何程式有不正常的運作，都不會影響其他程式的執行。
• 業界標準的 X Window 系統 (X11R7) 可以在常見的便宜 VGA 顯示卡/螢幕， 提供了圖形化的使用者介面 (GUI)，並且包括了完整的原始程式碼。
• Binary 相容性 可執行許多其他作業系統 (如： Linux、SCO、SVR4、BSDI 和 NetBSD) 的可執行檔。
• 數以萬計的 立即可以執行 的應用程式，這些都可透過 FreeBSD 的 ports套件 管理機制來取得。 不再需要費心到網路上到處搜尋所需要的軟體。
• 在網路上有數以千計 易於移植 的應用程式。FreeBSD 的原始程式碼與許多常見的商業版 UNIX® 系統都相容， 所以大部分的程式都只需要很少的修改(或根本不用修改) ，就可以編譯執行。
• 需要時才置換的 虛擬記憶體merged VM/buffer cache 的設計， 這點在系統中有用去大量記憶體的程式執行時，仍然有不錯的效率表現。
• 支援 CPU 的對稱多工處理(SMP)：可以支援多 CPU 的電腦系統。
• 完全相容的 CC++ 以及 Fortran 的環境和其他開發工具。 以及其他許多可供進階研發的程式語言也收集在 ports 和套件。
• 整個系統都有 原始程式碼， 這讓你對作業環境擁有最完全的掌握度。 既然能擁有完全開放的系統，何苦被特定封閉軟體所約束，任廠商擺佈呢？
• 廣泛且豐富的 線上文件
• 當然囉，還不止如此！
FreeBSD 系統乃是基於美國加州大學柏克萊分校的電腦系統研究組 (Computer Systems Research Group 也就是 CSRG) 所發行的 4.4BSD-Lite，以及基於 BSD 系統開發的優良傳統。 除了由 CSRG 所提供的高品質的成果， 為了提供可處理真正具負荷的工作， FreeBSD 計劃也投入了數千小時以上的細部調整， 以能獲得最好的執行效率以及系統的穩定度。 正當許多商業上的巨人正努力地希望能提供效能及穩定時，FreeBSD 已經具備這樣的特質，並具有其他地方沒有的尖端功能。
FreeBSD 的運用範圍無限，其實完全限制在你的想像力上。 從軟體的開發到工廠自動化，或是人造衛星上面的天線的方位角度的遠端控制； 這些功能若可以用商用的 UNIX® 產品來達成， 那麼極有可能使用 FreeBSD 也能辦到！ FreeBSD 也受益於來自於全球各研究中心及大學所開發的數千個高品質的軟體 ，這些通常只需要花費很少的費用或根本就是免費的。 當然也有商業軟體，而且出現的數目是與日俱增。
• 網際網路服務： FreeBSD 內建強勁的網路功能使它成為網路服務(如下例)的理想平台：
• 全球資訊網伺服器 (標準的或更安全的 [SSL])
• IPv4 及 IPv6 路由
• 防火牆以及 NAT (IP masquerading) 通訊閘。
• 檔案傳輸協定伺服器
• 電子郵件伺服器
• 還有更多...
• 教育：若您是資工相關領域的學生，再也沒有比使用 FreeBSD 能學到更多作業系統、計算機結構、及網路的方法了。 另外如果你想利用電腦來處理一些其他的工作，還有一些如 CAD、 數學運算以及圖形處理軟體等可以免費地取得使用。
• 研究：有了完整的原始程式碼，FreeBSD 是研究作業系統及電腦科學的極佳環境。 具有免費且自由取得特性的 FreeBSD 也使得一個分置兩地的合作計劃，不必擔心版權及系統開放性的問題， 而能自在的交流。
• 網路： 你如果需要 路由器、名稱伺服器 (DNS) 或安全的防火牆， FreeBSD 可以輕易的將你沒有用到的 386 或 486 PC 變身成為絕佳的伺服器，甚至具有過濾封包的功能。
• 嵌入式： FreeBSD 是一套可用來建立嵌入式系統的傑出平台。 支援 ARM®, MIPS® 以及 PowerPC® 平台，再加上健全的網路環境、尖端的功能以及自由的 BSD 授權條款，FreeBSD 成為用來建置嵌入式路由器、防火牆及其他裝置的絕佳基礎。
• 桌面: FreeBSD 同時也是低成本桌面解決方案中不錯的選擇，使用了免費的 X11 伺服器。FreeBSD 提供許多開源桌面環境可選擇，包含了標準 GNOMEKDE 圖型化使用者介面。FreeBSD 甚至可以透過中央伺服器做 無磁碟 開機，讓個人工作站變的更便宜、更易於管理。
• 軟體開發： 基本安裝的 FreeBSD 就包含了完整的程式開發工具，如 C/C++ 編譯器及除錯器。 透過 port 與套件管理系統也可支援需多其他語言。
1.2.2. 誰在用 FreeBSD？
FreeBSD 先進的功能、成熟的安全性、可預測的發佈週期以及自由的授權條款，讓 FreeBSD 已經被用來做為建立許多商業、開源應用、裝置以及產品的平台，有許多世界上最大的資訊公司使用 FreeBSD：
• Apache - The Apache Software Foundation runs most of its public facing infrastructure, including possibly one of the largest SVN repositories in the world with over 1.4 million commits, on FreeBSD.
• Apple - OS X borrows heavily from FreeBSD for the network stack, virtual file system, and many userland components. Apple iOS also contains elements borrowed from FreeBSD.
• Cisco - IronPort network security and anti-spam appliances run a modified FreeBSD kernel.
• Citrix - The NetScaler line of security appliances provide layer 4-7 load balancing, content caching, application firewall, secure VPN, and mobile cloud network access, along with the power of a FreeBSD shell.
• Dell KACE - The KACE system management appliances run FreeBSD because of its reliability, scalability, and the community that supports its continued development.
• Experts Exchange - All public facing web servers are powered by FreeBSD and they make extensive use of jails to isolate development and testing environments without the overhead of virtualization.
• Isilon - Isilon's enterprise storage appliances are based on FreeBSD. The extremely liberal FreeBSD license allowed Isilon to integrate their intellectual property throughout the kernel and focus on building their product instead of an operating system.
• iXsystems - The TrueNAS line of unified storage appliances is based on FreeBSD. In addition to their commercial products, iXsystems also manages development of the open source projects PC-BSD and FreeNAS.
• Juniper - The JunOS operating system that powers all Juniper networking gear (including routers, switches, security, and networking appliances) is based on FreeBSD. Juniper is one of many vendors that showcases the symbiotic relationship between the project and vendors of commercial products. Improvements generated at Juniper are upstreamed into FreeBSD to reduce the complexity of integrating new features from FreeBSD back into JunOS in the future.
• McAfee - SecurOS, the basis of McAfee enterprise firewall products including Sidewinder is based on FreeBSD.
• NetApp - The Data ONTAP GX line of storage appliances are based on FreeBSD. In addition, NetApp has contributed back many features, including the new BSD licensed hypervisor, bhyve.
• Netflix - The OpenConnect appliance that Netflix uses to stream movies to its customers is based on FreeBSD. Netflix has made extensive contributions to the codebase and works to maintain a zero delta from mainline FreeBSD. Netflix OpenConnect appliances are responsible for delivering more than 32% of all Internet traffic in North America.
• Sandvine - Sandvine uses FreeBSD as the basis of their high performance realtime network processing platforms that make up their intelligent network policy control products.
• Sony - The PlayStation 4 gaming console runs a modified version of FreeBSD.
• Sophos - The Sophos Email Appliance product is based on a hardened FreeBSD and scans inbound mail for spam and viruses, while also monitoring outbound mail for malware as well as the accidental loss of sensitive information.
• Spectra Logic - The nTier line of archive grade storage appliances run FreeBSD and OpenZFS.
• The Weather Channel - The IntelliStar appliance that is installed at each local cable providers headend and is responsible for injecting local weather forecasts into the cable TV network's programming runs FreeBSD.
• Verisign - Verisign is responsible for operating the .com and .net root domain registries as well as the accompanying DNS infrastructure. They rely on a number of different network operating systems including FreeBSD to ensure there is no common point of failure in their infrastructure.
• Voxer - Voxer powers their mobile voice messaging platform with ZFS on FreeBSD. Voxer switched from a Solaris derivative to FreeBSD because of its superior documentation, larger and more active community, and more developer friendly environment. In addition to critical features like ZFS and DTrace, FreeBSD also offers TRIM support for ZFS.
• WhatsApp - When WhatsApp needed a platform that would be able to handle more than 1 million concurrent TCP connections per server, they chose FreeBSD. They then proceeded to scale past 2.5 million connections per server.
• Wheel Systems - The FUDO security appliance allows enterprises to monitor, control, record, and audit contractors and administrators who work on their systems. Based on all of the best security features of FreeBSD including ZFS, GELI, Capsicum, HAST, and auditdistd.
FreeBSD 也催生了數個相關的開源計劃：
• BSD Router - A FreeBSD based replacement for large enterprise routers designed to run on standard PC hardware.
• FreeNAS - A customized FreeBSD designed to be used as a network file server appliance. Provides a python based web interface to simplify the management of both the UFS and ZFS file systems. Includes support for NFS, SMB/CIFS, AFP, FTP, and iSCSI. Includes an extensible plugin system based on FreeBSD jails.
• GhostBSD - A desktop oriented distribution of FreeBSD bundled with the Gnome desktop environment.
• mfsBSD - A toolkit for building a FreeBSD system image that runs entirely from memory.
• NAS4Free - A file server distribution based on FreeBSD with a PHP powered web interface.
• OPNSense - OPNsense is an open source, easy-to-use and easy-to-build FreeBSD based firewall and routing platform. OPNsense includes most of the features available in expensive commercial firewalls, and more in many cases. It brings the rich feature set of commercial offerings with the benefits of open and verifiable sources.
• PC-BSD - A customized version of FreeBSD geared towards desktop users with graphical utilities to exposing the power of FreeBSD to all users. Designed to ease the transition of Windows and OS X users.
• pfSense - A firewall distribution based on FreeBSD with a huge array of features and extensive IPv6 support.
• ZRouter - An open source alternative firmware for embedded devices based on FreeBSD. Designed to replace the proprietary firmware on off-the-shelf routers.
FreeBSD 也同時被用來驅動一些網際網路上的大型網站，包括：
1.3. 關於 FreeBSD 計劃
1.3.1. FreeBSD 歷史簡介
FreeBSD 計畫的想法是在 1993 年初所形成的， 那是源自於維護一組『非官方 386BSD 的修正工具』計劃的三個協調維護人 Nate Williams，Rod Grimes 和 Jordan Hubbard。
386BSD 是 Bill Jolitz 的作業系統，在當時就已有約一年的分裂討論。 當該修正工具 (patchkit) 日漸龐雜得令人不舒服，我們無異議地同意要作一些事了， 並決定提供一份臨時性的 淨化版(cleanup) 來幫助 Bill。 然而，由於 Bill Jolitz 忽然決定取消其對該計劃的認可，且沒有明確指出未來的打算， 所以該計劃便突然面臨斷炊危機。
FreeBSD 便開始了這宛如『重新發明輪子』的艱鉅工作 -- 從全新的且不完整的 4.4BSD-Lite 重新整合。 這個 Lite 版本是不完整的，因為 Berkeley 的 CSRG 已經刪除了大量在建立一個可以開機執行的系統所需要的程式碼 (基於若干法律上的要求)，且該版本在 Intel 平台的移植是非常不完整的。 直到 1994 年 11 月本計劃才完成了這個轉移， 同時在該年 12 月底以 CD-ROM 以及網路的形式發行了 FreeBSD 2.0。 雖然該份版本在當時有點匆促粗糙，但仍是富有意義的成功。 隨之於 1995 年 6 月又發行了更容易安裝，更好的 FreeBSD 2.0.5。
1.3.2. FreeBSD 計劃目標
Contributed by .
FreeBSD 計劃的目標在於提供可作任意用途的軟體而不附帶任何限制條文。 我們之中許多人對程式碼 (以及計畫本身) 都有非常大的投入， 因此，當然不介意偶爾有一些資金上的補償，但我們並沒打算堅決地要求得到這類資助。 我們認為我們的首要使命是為任何人提供程式碼， 不管他們打算用這些程式碼做什麼， 因為這樣程式碼將能夠被更廣泛地使用，從而發揮其價值。 我認為這是自由軟體最基本的，同時也是我們所倡導的一個目標。
1.3.3. FreeBSD 開發模式
Contributed by .
FreeBSD 的開發是一個非常開放且具彈性的過程，就像從 貢獻者名單 所看到的，是由全世界成千上萬的貢獻者發展起來的。 FreeBSD 的開發基礎架構允許數以百計的開發者透過網際網路協同工作。 我們也經常關注著那些對我們的計畫感興趣的新開發者和新的創意， 那些有興趣更進一步參與計劃的人只需要在 FreeBSD 技術討論郵遞論壇 連繫我們。 FreeBSD 公告郵遞論壇 對那些希望了解我們進度的人也是相當有用的。
SVN 檔案庫
FreeBSD 核心團隊
注意:
FreeBSD 貢獻者名單 相當長且不斷成長中， 只要有貢獻就會被列入其中， 要不要立即考慮貢獻 FreeBSD 一些回饋呢？
1.3.4. 第三方程式
In addition to the base distributions, FreeBSD offers a ported software collection with thousands of commonly sought-after programs. At the time of this writing, there were over 24,000 ports! The list of ports ranges from http servers, to games, languages, editors, and almost everything in between. The entire Ports Collection requires approximately 500 MB. To compile a port, you simply change to the directory of the program you wish to install, type make install, and let the system do the rest. The full original distribution for each port you build is retrieved dynamically so you need only enough disk space to build the ports you want. Almost every port is also provided as a pre-compiled package, which can be installed with a simple command (pkg install) by those who do not wish to compile their own ports from source. More information on packages and ports can be found in 章 4, 安裝應用程式: 套件與 Ports.
1.3.5. 其他文件
All recent FreeBSD versions provide an option in the installer (either sysinstall(8) or bsdinstall(8)) to install additional documentation under /usr/local/share/doc/freebsd during the initial system setup. Documentation may also be installed at any later time using packages as described in 節 23.3.2, “自 Ports 更新說明文件”. You may view the locally installed manuals with any HTML capable browser using the following URLs:
章 2. 安裝 FreeBSD
Restructured, reorganized, and parts rewritten by .
Updated for bsdinstall by and .
Updated for root-on-ZFS by .
2.1. 概述
注意:
• 最低的硬體需求和 FreeBSD 支援的架構。
• 如何建立 FreeBSD 的安裝媒體。
• 如何開始執行 bsdinstall
• bsdinstall 會詢問的問題，問題代表的意思，以及如何回答。
• 安裝失敗時如何做故障排除。
• 如何在正式安裝前使用 live 版本的 FreeBSD。
• 閱讀即將安裝的 FreeBSD 版本所附帶的硬體支援清單，並核對系統的硬體是否有支援。
2.2. 最低硬體需求
FreeBSD 最小安裝需要至少 64 MB 的 RAM 和 1.5 GB 的可用硬碟空間 但是這真的是 最小，幾乎沒有剩下多餘的空間。 RAM 的需求視實際使用而訂，經特殊處理過後的 FreeBSD 系統可只使用 128MB RAM，圖形化環境最少需要 4 GB 的 RAM
amd64
i386
CPU 有支援實體位址延伸(PAE) 功能，FreeBSD 可以運用這項功能的所帶來優點。有開啟 PAE 支援的核心會偵測超過 4 GB 的記憶體，並讓這些記憶體能夠被系統使用。 這項功能會限制驅動程式以及 FreeBSD 可能使用的其他功能，詳情請見 pae(4)
ia64
pc98
NEC PC-9801/9821 系列幾乎所有 i386 相容處理器包括 80486、Pentium®、 Pentium® Pro 和 Pentium® II 都有支援。 所有 AMD, Cyrix, IBM, 及 IDT 的i386 相容處理器都有支援。 相容 NEC PC-9801 的 EPSON PC-386/486/586 系列都有支援。 NEC FC-9801/9821 及 NEC SV-98 系列也有支援。
powerpc
32 位元的核心只能使用前 2 GB 的 RAM
sparc64
FreeBSD/sparc64 支援的系統列在 FreeBSD/sparc64 計劃 (http://www.freebsd.org/platforms/sparc.html)。
2.3. 安裝前準備工作
1. 備份重要資料
安裝任何作業系統前， 總是 要先備份所有重要資料。 不要儲存備份在即將安裝的系統上。改為將資料儲存在可移除磁碟，像是 USB 隨身碟，網路上的另一個系統或是線上備份服務上。 開始安裝前，要測試備份，確定它含有所有需要的檔案。 一旦安裝程式格式化系統的磁碟，所有儲存在上面的資料都會遺失。
2. 決定 FreeBSD 安裝在哪裡
如果 FreeBSD 是唯一要安裝的作業系統，這個步驟可以略過。 但是假如 FreeBSD 將和其他作業系統分享磁碟空間的話，要決定 FreeBSD 要安裝在哪個磁碟或是哪個分割區。
在 i386 和 amd64 平台，磁碟可以使用兩種分割區配置之一來分割成多個分割區。 傳統的主開機紀錄 (Master Boot Record, MBR) 有一個分割區表定義最多到 主分割區。 因為歷史性的理由， FreeBSD 稱這些主分割區為 slices。 其中一個主分割區可以分成一個 延伸分割區 ，他包含多個 邏輯分割區。 GUID 分割區表 (GUID Partition Table, GPT) 是較新和較簡單的分割磁碟的方法，一般 GPT 實作允許每個磁碟最多達 128 個分割區，減少使用邏輯分割區的需要。
警告:
一些比較舊的作業系統，像是 Windows® XP 不相容 GPT 分割區配置。 如果 FreeBSD 將和這樣的作業系統共享一個磁碟，那就需要用 MBR 分割。
FreeBSD 開機啟動程式需要主分割區或是 GPT 分割區。如果所有的主分割區或 GPT 分割區都已使用，必須釋放其中一個分割區讓 FreeBSD 使用。如果要建立一個分割區而不刪除原有的資料，可以使用磁碟分割工具來縮小現有的分割區，並使用多出的空間來建立新分割區。
各種自由的和商業化的磁碟分割工具列於 http://en.wikipedia.org/wiki/List_of_disk_partitioning_softwareGParted Live (http://gparted.sourceforge.net/livecd.php) 是包含分割編輯工具 GParted 的自由的 live CD。 GParted 也包含在許多 Linux live CD 套件裡。
警告:
當正確地使用，磁碟分割工具可以安全地建立空間讓新的分割區使用。 因為有可能會誤選已經存在的分割區，所以在修改磁碟分割區前， 一定要備份重要資料，並確認備份的完整性。
包含不同作業系統的磁碟分割區可以讓一台電腦安裝多重作業系統。 另一種作法是使用虛擬化 (章 21, 虛擬化) ，可以讓多重作業系統同時間執行而不需要改變任何磁碟分割區。
3. 收集網路資訊
有些 FreeBSD 安裝方法為了下載安裝檔案需要網路連線。 在系統安裝之後，安裝程式將會讓您設定系統的網路介面。
如果網路有 DHCP 伺服器，可以自動設定網路。 如果沒有 DHCP ， 需要從區域網路管理者或是網際網路服務商取得以下系統的網路資訊：
需要的網路資訊
1. IP 位址
2. 子網路遮罩
3. 預設閘道器 IP 位址
4. 網路的網域名稱
5. 網路 DNS 伺服器 IP 位址
4. 檢查 FreeBSD 勘誤表
儘管 FreeBSD Project 努力確保每個 FreeBSD 發行版能夠儘可能地穩定，錯誤偶爾還是會悄悄出現。 有極小的機會錯誤會影響安裝過程。 當這些問題被發現並修正後，會被紀錄在 FreeBSD 網站的 FreeBSD 勘誤表 (http://www.freebsd.org/releases/10.3R/errata.html)。 安裝前要檢查勘誤表，確保沒有會影響到安裝的問題。
所有發行版的資訊和勘誤表可以在 FreeBSD 網站的發行資訊找到 (http://www.freebsd.org/releases/index.html)。
2.3.1. 準備安裝的媒體
The FreeBSD installer is not an application that can be run from within another operating system. Instead, download a FreeBSD installation file, burn it to the media associated with its file type and size (CD, DVD, or USB), and boot the system to install from the inserted media.
FreeBSD installation files are available at www.freebsd.org/where.html#download. Each installation file's name includes the release version of FreeBSD, the architecture, and the type of file. For example, to install FreeBSD 10.2 on an amd64 system from a DVD, download FreeBSD-10.2-RELEASE-amd64-dvd1.iso, burn this file to a DVD, and boot the system with the DVD inserted.
Installation files are available in several formats. The formats vary depending on computer architecture and media type.
Additional installation files are included for computers that boot with UEFI (Unified Extensible Firmware Interface). The names of these files include the string uefi.
File types:
• -bootonly.iso: This is the smallest installation file as it only contains the installer. A working Internet connection is required during installation as the installer will download the files it needs to complete the FreeBSD installation. This file should be burned to a CD using a CD burning application.
• -disc1.iso: This file contains all of the files needed to install FreeBSD, its source, and the Ports Collection. It should be burned to a CD using a CD burning application.
• -dvd1.iso: This file contains all of the files needed to install FreeBSD, its source, and the Ports Collection. It also contains a set of popular binary packages for installing a window manager and some applications so that a complete system can be installed from media without requiring a connection to the Internet. This file should be burned to a DVD using a DVD burning application.
• -memstick.img: This file contains all of the files needed to install FreeBSD, its source, and the Ports Collection. It should be burned to a USB stick using the instructions below.
After downloading the image file, download CHECKSUM.SHA256 from the same directory. Calculate a checksum for the image file. FreeBSD provides sha256(1) for this, used as sha256 imagefilename. Other operating systems have similar programs.
Compare the calculated checksum with the one shown in CHECKSUM.SHA256. The checksums must match exactly. If the checksums do not match, the image file is corrupt and must be downloaded again.
2.3.1.1. 寫入映象檔到 USB
The *.img file is an image of the complete contents of a memory stick. It cannot be copied to the target device as a file. Several applications are available for writing the *.img to a USB stick. This section describes two of these utilities.
警告:
This example uses /dev/da0 as the target device where the image will be written. Be very careful that the correct device is used as this command will destroy the existing data on the specified target device.
• The dd(1) command-line utility is available on BSD, Linux®, and Mac OS® systems. To burn the image using dd, insert the USB stick and determine its device name. Then, specify the name of the downloaded installation file and the device name for the USB stick. This example burns the amd64 installation image to the first USB device on an existing FreeBSD system.
# dd if=FreeBSD-10.2-RELEASE-amd64-memstick.img of=/dev/da0 bs=1M conv=sync
If this command fails, verify that the USB stick is not mounted and that the device name is for the disk, not a partition. Some operating systems might require this command to be run with sudo(8). Systems like Linux® might buffer writes. To force all writes to complete, use sync(8).
警告:
Be sure to give the correct drive letter as the existing data on the specified drive will be overwritten and destroyed.
1. 取得 Image Writer Windows® 版
Image Writer Windows® 版 是一個免費的應用程式，可以正確地將映像檔寫入隨身碟。 從 https://launchpad.net/win32-image-writer/ 下載，並解壓縮到一個資料夾。
2. 用 Image Writer 寫入映象檔
雙擊 Win32DiskImager 圖示啟動程式。 確認 Device 顯示的磁碟機代號是隨身碟的磁碟機代號。 按下資料夾圖示選擇要寫入隨身碟的映像檔。 按下 按鈕確定映像檔名。 確認所有東西都正確，隨身碟的資料夾並沒有在其他視窗開啟。 所有東西準備好後，按下 將映像檔寫入隨身碟。
2.4. 開始安裝
重要:
Your changes will now be written to disk. If you
have chosen to overwrite existing data, it will
be PERMANENTLY ERASED. Are you sure you want to
commit your changes?
This section describes how to boot the system from the installation media which was prepared using the instructions in 節 2.3.1, “準備安裝的媒體”. When using a bootable USB stick, plug in the USB stick before turning on the computer. When booting from CD or DVD, turn on the computer and insert the media at the first opportunity. How to configure the system to boot from the inserted media depends upon the architecture.
2.4.1. 在 i386™ 及 amd64 開機
These architectures provide a BIOS menu for selecting the boot device. Depending upon the installation media being used, select the CD/DVD or USB device as the first boot device. Most systems also provide a key for selecting the boot device during startup without having to enter the BIOS. Typically, the key is either F10, F11, F12, or Escape.
If the computer loads the existing operating system instead of the FreeBSD installer, then either:
1. The installation media was not inserted early enough in the boot process. Leave the media inserted and try restarting the computer.
2. The BIOS changes were incorrect or not saved. Double-check that the right boot device is selected as the first boot device.
3. This system is too old to support booting from the chosen media. In this case, the Plop Boot Manager (http://www.plop.at/en/bootmanagers.html) can be used to boot the system from the selected media.
2.4.2. 在 PowerPC® 開機
On most machines, holding C on the keyboard during boot will boot from the CD. Otherwise, hold Command+Option+O+F, or Windows+Alt+O+F on non-Apple® keyboards. At the 0 > prompt, enter
boot cd:,\ppc\loader cd:0
2.4.3. 在 SPARC64® 開機
Most SPARC64® systems are set up to boot automatically from disk. To install FreeBSD from a CD requires a break into the PROM.
To do this, reboot the system and wait until the boot message appears. The message depends on the model, but should look something like this:
Sun Blade 100 (UltraSPARC-IIe), Keyboard Present
OpenBoot 4.2, 128 MB memory installed, Serial #51090132.
Ethernet address 0:3:ba:b:92:d4, Host ID: 830b92d4.
If the system proceeds to boot from disk at this point, press L1+A or Stop+A on the keyboard, or send a BREAK over the serial console. When using tip or cu, ~# will issue a BREAK. The PROM prompt will be ok on systems with one CPU and ok {0} on SMP systems, where the digit indicates the number of the active CPU.
At this point, place the CD into the drive and type boot cdrom from the PROM prompt.
2.4.4. FreeBSD 開機選單
Once the system boots from the installation media, a menu similar to the following will be displayed:
By default, the menu will wait ten seconds for user input before booting into the FreeBSD installer or, if FreeBSD is already installed, before booting into FreeBSD. To pause the boot timer in order to review the selections, press Space. To select an option, press its highlighted number, character, or key. The following options are available.
• Boot Multi User: This will continue the FreeBSD boot process. If the boot timer has been paused, press 1, upper- or lower-case B, or Enter.
• Boot Single User: This mode can be used to fix an existing FreeBSD installation as described in 節 12.2.4.1, “單使用者模式”. Press 2 or the upper- or lower-case S to enter this mode.
• Escape to loader prompt: This will boot the system into a repair prompt that contains a limited number of low-level commands. This prompt is described in 節 12.2.3, “階段三”. Press 3 or Esc to boot into this prompt.
• Reboot: Reboots the system.
• Configure Boot Options: Opens the menu shown in, and described under, 圖形 2.2, “FreeBSD 開機選項選單”.
The boot options menu is divided into two sections. The first section can be used to either return to the main boot menu or to reset any toggled options back to their defaults.
The next section is used to toggle the available options to On or Off by pressing the option's highlighted number or character. The system will always boot using the settings for these options until they are modified. Several options can be toggled using this menu:
• ACPI Support: If the system hangs during boot, try toggling this option to Off.
• Safe Mode: If the system still hangs during boot even with ACPI Support set to Off, try setting this option to On.
• Single User: Toggle this option to On to fix an existing FreeBSD installation as described in 節 12.2.4.1, “單使用者模式”. Once the problem is fixed, set it back to Off.
• Verbose: Toggle this option to On to see more detailed messages during the boot process. This can be useful when troubleshooting a piece of hardware.
After making the needed selections, press 1 or Backspace to return to the main boot menu, then press Enter to continue booting into FreeBSD. A series of boot messages will appear as FreeBSD carries out its hardware device probes and loads the installation program. Once the boot is complete, the welcome menu shown in 圖形 2.3, “歡迎選單” will be displayed.
Press Enter to select the default of to enter the installer. The rest of this chapter describes how to use this installer. Otherwise, use the right or left arrows or the colorized letter to select the desired menu item. The can be used to access a FreeBSD shell in order to use command line utilities to prepare the disks before installation. The option can be used to try out FreeBSD before installing it. The live version is described in 節 2.10, “使用 Live CD.
提示:
To review the boot messages, including the hardware device probe, press the upper- or lower-case S and then Enter to access a shell. At the shell prompt, type more /var/run/dmesg.boot and use the space bar to scroll through the messages. When finished, type exit to return to the welcome menu.
2.5. 使用 bsdinstall
This section shows the order of the bsdinstall menus and the type of information that will be asked before the system is installed. Use the arrow keys to highlight a menu option, then Space to select or deselect that menu item. When finished, press Enter to save the selection and move onto the next screen.
2.5.1. 選擇鍵盤對應表選單
Depending on the system console being used, bsdinstall may initially display the menu shown in 圖形 2.4, “鍵盤對應表選擇”.
To configure the keyboard layout, press Enter with selected, which will display the menu shown in 圖形 2.5, “選擇鍵盤選單”. To instead use the default layout, use the arrow key to select and press Enter to skip this menu screen.
When configuring the keyboard layout, use the up and down arrows to select the keymap that most closely represents the mapping of the keyboard attached to the system. Press Enter to save the selection.
注意:
Pressing Esc will exit this menu and use the default keymap. If the choice of keymap is not clear, United States of America ISO-8859-1 is also a safe option.
In FreeBSD 10.0-RELEASE and later, this menu has been enhanced. The full selection of keymaps is shown, with the default preselected. In addition, when selecting a different keymap, a dialog is displayed that allows the user to try the keymap and ensure it is correct before proceeding.
2.5.2. 設定主機名稱
The next bsdinstall menu is used to set the hostname for the newly installed system.
Type in a hostname that is unique for the network. It should be a fully-qualified hostname, such as machine3.example.com.
2.5.3. 選擇要安裝的元件
Next, bsdinstall will prompt to select optional components to install.
Deciding which components to install will depend largely on the intended use of the system and the amount of disk space available. The FreeBSD kernel and userland, collectively known as the base system, are always installed. Depending on the architecture, some of these components may not appear:
• doc - Additional documentation, mostly of historical interest, to install into /usr/share/doc. The documentation provided by the FreeBSD Documentation Project may be installed later using the instructions in 節 23.3, “更新文件集”.
• games - Several traditional BSD games, including fortune, rot13, and others.
• lib32 - Compatibility libraries for running 32-bit applications on a 64-bit version of FreeBSD.
• ports - The FreeBSD Ports Collection is a collection of files which automates the downloading, compiling and installation of third-party software packages. 章 4, 安裝應用程式: 套件與 Ports discusses how to use the Ports Collection.
警告:
The installation program does not check for adequate disk space. Select this option only if sufficient hard disk space is available. The FreeBSD Ports Collection takes up about 500 MB of disk space.
• src - The complete FreeBSD source code for both the kernel and the userland. Although not required for the majority of applications, it may be required to build device drivers, kernel modules, or some applications from the Ports Collection. It is also used for developing FreeBSD itself. The full source tree requires 1 GB of disk space and recompiling the entire FreeBSD system requires an additional 5 GB of space.
2.5.4. 從網路安裝
The menu shown in 圖形 2.9, “從網路安裝” only appears when installing from a -bootonly.iso CD as this installation media does not hold copies of the installation files. Since the installation files must be retrieved over a network connection, this menu indicates that the network interface must be first configured.
To configure the network connection, press Enter and follow the instructions in 節 2.8.2, “設定網路介面”. Once the interface is configured, select a mirror site that is located in the same region of the world as the computer on which FreeBSD is being installed. Files can be retrieved more quickly when the mirror is close to the target computer, reducing installation time.
Installation will then continue as if the installation files were located on the local installation media.
2.6. 配置磁碟空間
The next menu is used to determine the method for allocating disk space. The options available in the menu depend upon the version of FreeBSD being installed.
Guided partitioning automatically sets up the disk partitions, Manual partitioning allows advanced users to create customized partitions from menu options, and Shell opens a shell prompt where advanced users can create customized partitions using command-line utilities like gpart(8), fdisk(8), and bsdlabel(8). ZFS partitioning, only available in FreeBSD 10 and later, creates an optionally encrypted root-on-ZFS system with support for boot environments.
This section describes what to consider when laying out the disk partitions. It then demonstrates how to use the different partitioning methods.
2.6.1. 規劃分割區配置
When laying out file systems, remember that hard drives transfer data faster from the outer tracks to the inner. Thus, smaller and heavier-accessed file systems should be closer to the outside of the drive, while larger partitions like /usr should be placed toward the inner parts of the disk. It is a good idea to create partitions in an order similar to: /, swap, /var, and /usr.
The size of the /var partition reflects the intended machine's usage. This partition is used to hold mailboxes, log files, and printer spools. Mailboxes and log files can grow to unexpected sizes depending on the number of users and how long log files are kept. On average, most users rarely need more than about a gigabyte of free disk space in /var.
注意:
Sometimes, a lot of disk space is required in /var/tmp. When new software is installed, the packaging tools extract a temporary copy of the packages under /var/tmp. Large software packages, like Firefox, Apache OpenOffice or LibreOffice may be tricky to install if there is not enough disk space under /var/tmp.
The /usr partition holds many of the files which support the system, including the FreeBSD Ports Collection and system source code. At least 2 gigabytes is recommended for this partition.
When selecting partition sizes, keep the space requirements in mind. Running out of space in one partition while barely using another can be a hassle.
As a rule of thumb, the swap partition should be about double the size of physical memory (RAM). Systems with minimal RAM may perform better with more swap. Configuring too little swap can lead to inefficiencies in the VM page scanning code and might create issues later if more memory is added.
On larger systems with multiple SCSI disks or multiple IDE disks operating on different controllers, it is recommended that swap be configured on each drive, up to four drives. The swap partitions should be approximately the same size. The kernel can handle arbitrary sizes but internal data structures scale to 4 times the largest swap partition. Keeping the swap partitions near the same size will allow the kernel to optimally stripe swap space across disks. Large swap sizes are fine, even if swap is not used much. It might be easier to recover from a runaway program before being forced to reboot.
By properly partitioning a system, fragmentation introduced in the smaller write heavy partitions will not bleed over into the mostly read partitions. Keeping the write loaded partitions closer to the disk's edge will increase I/O performance in the partitions where it occurs the most. While I/O performance in the larger partitions may be needed, shifting them more toward the edge of the disk will not lead to a significant performance improvement over moving /var to the edge.
2.6.2. 引導式磁碟分割
When this method is selected, a menu will display the available disk(s). If multiple disks are connected, choose the one where FreeBSD is to be installed.
Once the disk is selected, the next menu prompts to install to either the entire disk or to create a partition using free space. If is chosen, a general partition layout filling the whole disk is automatically created. Selecting creates a partition layout from the unused space on the disk.
After the partition layout has been created, review it to ensure it meets the needs of the installation. Selecting will reset the partitions to their original values and pressing will recreate the automatic FreeBSD partitions. Partitions can also be manually created, modified, or deleted. When the partitioning is correct, select to continue with the installation.
2.6.3. 手動磁碟分割
Selecting this method opens the partition editor:
Highlight the installation drive (ada0 in this example) and select to display a menu of available partition schemes:
GPT is usually the most appropriate choice for amd64 computers. Older computers that are not compatible with GPT should use MBR. The other partition schemes are generally used for uncommon or older computers.
APMApple Partition Map, used by PowerPC®.
BSDBSD label without an MBR, sometimes called dangerously dedicated mode as non-BSD disk utilities may not recognize it.
GPTGUID Partition Table (http://en.wikipedia.org/wiki/GUID_Partition_Table).
MBRMaster Boot Record (http://en.wikipedia.org/wiki/Master_boot_record).
PC98MBR variant used by NEC PC-98 computers (http://en.wikipedia.org/wiki/Pc9801).
After the partitioning scheme has been selected and created, select again to create the partitions.
A standard FreeBSD GPT installation uses at least three partitions:
• freebsd-boot - Holds the FreeBSD boot code.
• freebsd-ufs - A FreeBSD UFS file system.
• freebsd-swap - FreeBSD swap space.
Another partition type worth noting is freebsd-zfs, used for partitions that will contain a FreeBSD ZFS file system (章 19, Z 檔案系統 (ZFS)). Refer to gpart(8) for descriptions of the available GPT partition types.
Multiple file system partitions can be created and some people prefer a traditional layout with separate partitions for /, /var, /tmp, and /usr. See 範例 2.1, “建立傳統分割的檔案系統分割區” for an example.
The Size may be entered with common abbreviations: K for kilobytes, M for megabytes, or G for gigabytes.
提示:
Proper sector alignment provides the best performance, and making partition sizes even multiples of 4K bytes helps to ensure alignment on drives with either 512-byte or 4K-byte sectors. Generally, using partition sizes that are even multiples of 1M or 1G is the easiest way to make sure every partition starts at an even multiple of 4K. There is one exception: the freebsd-boot partition should be no larger than 512K due to current boot code limitations.
A Mountpoint is needed if the partition will contain a file system. If only a single UFS partition will be created, the mountpoint should be /.
The Label is a name by which the partition will be known. Drive names or numbers can change if the drive is connected to a different controller or port, but the partition label does not change. Referring to labels instead of drive names and partition numbers in files like /etc/fstab makes the system more tolerant to hardware changes. GPT labels appear in /dev/gpt/ when a disk is attached. Other partitioning schemes have different label capabilities and their labels appear in different directories in /dev/.
提示:
Use a unique label on every partition to avoid conflicts from identical labels. A few letters from the computer's name, use, or location can be added to the label. For instance, use labroot or rootfslab for the UFS root partition on the computer named lab.
For a traditional partition layout where the /, /var, /tmp, and /usr directories are separate file systems on their own partitions, create a GPT partitioning scheme, then create the partitions as shown. Partition sizes shown are typical for a 20G target disk. If more space is available on the target disk, larger swap or /var partitions may be useful. Labels shown here are prefixed with ex for example, but readers should use other unique label values as described above.
By default, FreeBSD's gptboot expects the first UFS partition to be the / partition.
Partition TypeSizeMountpointLabel
freebsd-boot512K
freebsd-ufs2G/exrootfs
freebsd-swap4G exswap
freebsd-ufs2G/varexvarfs
freebsd-ufs1G/tmpextmpfs
freebsd-ufsaccept the default (remainder of the disk)/usrexusrfs
After the custom partitions have been created, select to continue with the installation.
2.6.4. Root-on-ZFS 自動磁碟分割
Support for automatic creation of root-on-ZFS installations was added in FreeBSD 10.0-RELEASE. This partitioning mode only works with whole disks and will erase the contents of the entire disk. The installer will automatically create partitions aligned to 4k boundaries and force ZFS to use 4k sectors. This is safe even with 512 byte sector disks, and has the added benefit of ensuring that pools created on 512 byte disks will be able to have 4k sector disks added in the future, either as additional storage space or as replacements for failed disks. The installer can also optionally employ GELI disk encryption as described in 節 17.12.2, “使用 geli 做磁碟加密”. If encryption is enabled, a 2 GB unencrypted boot pool containing the /boot directory is created. It holds the kernel and other files necessary to boot the system. A swap partition of a user selectable size is also created, and all remaining space is used for the ZFS pool.
The main ZFS configuration menu offers a number of options to control the creation of the pool.
Select T to configure the Pool Type and the disk(s) that will constitute the pool. The automatic ZFS installer currently only supports the creation of a single top level vdev, except in stripe mode. To create more complex pools, use the instructions in 節 2.6.5, “Shell 模式磁碟分割” to create the pool. The installer supports the creation of various pool types, including stripe (not recommended, no redundancy), mirror (best performance, least usable space), and RAID-Z 1, 2, and 3 (with the capability to withstand the concurrent failure of 1, 2, and 3 disks, respectively). while selecting the pool type, a tooltip is displayed across the bottom of the screen with advice about the number of required disks, and in the case of RAID-Z, the optimal number of disks for each configuration.
Once a Pool Type has been selected, a list of available disks is displayed, and the user is prompted to select one or more disks to make up the pool. The configuration is then validated, to ensure enough disks are selected. If not, select to return to the list of disks, or to change the pool type.
If one or more disks are missing from the list, or if disks were attached after the installer was started, select to repopulate the list of available disks. To ensure that the correct disks are selected, so as not to accidently destroy the wrong disks, the menu can be used to inspect each disk, including its partition table and various other information such as the device model number and serial number, if available.
The main ZFS configuration menu also allows the user to enter a pool name, disable forcing 4k sectors, enable or disable encryption, switch between GPT (recommended) and MBR partition table types, and select the amount of swap space. Once all options have been set to the desired values, select the option at the top of the menu.
If GELI disk encryption was enabled, the installer will prompt twice for the passphrase to be used to encrypt the disks.
The installer then offers a last chance to cancel before the contents of the selected drives are destroyed to create the ZFS pool.
The installation then proceeds normally.
2.6.5. Shell 模式磁碟分割
When creating advanced installations, the bsdinstall paritioning menus may not provide the level of flexibility required. Advanced users can select the option from the partitioning menu in order to manually partition the drives, create the file system(s), populate /tmp/bsdinstall_etc/fstab, and mount the file systems under /mnt. Once this is done, type exit to return to bsdinstall and continue the installation.
2.7. 確認安裝
Once the disks are configured, the next menu provides the last chance to make changes before the selected hard drive(s) are formatted. If changes need to be made, select to return to the main partitioning menu. will exit the installer without making any changes to the hard drive.
To instead start the actual installation, select and press Enter.
Installation time will vary depending on the distributions chosen, installation media, and speed of the computer. A series of messages will indicate the progress.
First, the installer formats the selected disk(s) and initializes the partitions. Next, in the case of a bootonly media, it downloads the selected components:
Next, the integrity of the distribution files is verified to ensure they have not been corrupted during download or misread from the installation media:
Finally, the verified distribution files are extracted to the disk:
Once all requested distribution files have been extracted, bsdinstall displays the first post-installation configuration screen. The available post-configuration options are described in the next section.
2.8. 安裝後注意事項
Once FreeBSD is installed, bsdinstall will prompt to configure several options before booting into the newly installed system. This section describes these configuration options.
提示:
Once the system has booted, bsdconfig provides a menu-driven method for configuring the system using these and additional options.
2.8.1. 設定 root 密碼
First, the root password must be set. While entering the password, the characters being typed are not displayed on the screen. After the password has been entered, it must be entered again. This helps prevent typing errors.
2.8.2. 設定網路介面
Next, a list of the network interfaces found on the computer is shown. Select the interface to configure.
注意:
The network configuration menus will be skipped if the network was previously configured as part of a bootonly installation.
If an Ethernet interface is selected, the installer will skip ahead to the menu shown in 圖形 2.35, “選擇 IPv4 網路”. If a wireless network interface is chosen, the system will instead scan for wireless access points:
Wireless networks are identified by a Service Set Identifier (SSID), a short, unique name given to each network. SSIDs found during the scan are listed, followed by a description of the encryption types available for that network. If the desired SSID does not appear in the list, select to scan again. If the desired network still does not appear, check for problems with antenna connections or try moving the computer closer to the access point. Rescan after each change is made.
Next, enter the encryption information for connecting to the selected wireless network. WPA2 encryption is strongly recommended as older encryption types, like WEP, offer little security. If the network uses WPA2, input the password, also known as the Pre-Shared Key (PSK). For security reasons, the characters typed into the input box are displayed as asterisks.
Next, choose whether or not an IPv4 address should be configured on the Ethernet or wireless interface:
There are two methods of IPv4 configuration. DHCP will automatically configure the network interface correctly and should be used if the network provides a DHCP server. Otherwise, the addressing information needs to be input manually as a static configuration.
注意:
Do not enter random network information as it will not work. If a DHCP server is not available, obtain the information listed in 需要的網路資訊 from the network administrator or Internet service provider.
If a DHCP server is available, select in the next menu to automatically configure the network interface. The installer will appear to pause for a minute or so as it finds the DHCP server and obtains the addressing information for the system.
If a DHCP server is not available, select and input the following addressing information in this menu:
• IP Address - The IPv4 address assigned to this computer. The address must be unique and not already in use by another piece of equipment on the local network.
• Subnet Mask - The subnet mask for the network.
• Default Router - The IP address of the network's default gateway.
The next screen will ask if the interface should be configured for IPv6. If IPv6 is available and desired, choose to select it.
IPv6 also has two methods of configuration. StateLess Address AutoConfiguration (SLAAC) will automatically request the correct configuration information from a local router. Refer to http://tools.ietf.org/html/rfc4862 for more information. Static configuration requires manual entry of network information.
If an IPv6 router is available, select in the next menu to automatically configure the network interface. The installer will appear to pause for a minute or so as it finds the router and obtains the addressing information for the system.
If an IPv6 router is not available, select and input the following addressing information in this menu:
• IPv6 Address - The IPv6 address assigned to this computer. The address must be unique and not already in use by another piece of equipment on the local network.
• Default Router - The IPv6 address of the network's default gateway.
The last network configuration menu is used to configure the Domain Name System (DNS) resolver, which converts hostnames to and from network addresses. If DHCP or SLAAC was used to autoconfigure the network interface, the Resolver Configuration values may already be filled in. Otherwise, enter the local network's domain name in the Search field. DNS #1 and DNS #2 are the IPv4 and/or IPv6 addresses of the DNS servers. At least one DNS server is required.
2.8.3. 設定時區
The next menu asks if the system clock uses UTC or local time. When in doubt, select to choose the more commonly-used local time.
The next series of menus are used to determine the correct local time by selecting the geographic region, country, and time zone. Setting the time zone allows the system to automatically correct for regional time changes, such as daylight savings time, and perform other time zone related functions properly.
The example shown here is for a machine located in the Eastern time zone of the United States. The selections will vary according to the geographical location.
The appropriate region is selected using the arrow keys and then pressing Enter.
Select the appropriate country using the arrow keys and press Enter.
The appropriate time zone is selected using the arrow keys and pressing Enter.
Confirm the abbreviation for the time zone is correct. If it is, press Enter to continue with the post-installation configuration.
2.8.4. 開啟服務
The next menu is used to configure which system services will be started whenever the system boots. All of these services are optional. Only start the services that are needed for the system to function.
Here is a summary of the services which can be enabled in this menu:
• sshd - The Secure Shell (SSH) daemon is used to remotely access a system over an encrypted connection. Only enable this service if the system should be available for remote logins.
• moused - Enable this service if the mouse will be used from the command-line system console.
• ntpd - The Network Time Protocol (NTP) daemon for automatic clock synchronization. Enable this service if there is a Windows®, Kerberos, or LDAP server on the network.
• powerd - System power control utility for power control and energy saving.
2.8.5. 開啟 Crash Dumps
The next menu is used to configure whether or not crash dumps should be enabled. Enabling crash dumps can be useful in debugging issues with the system, so users are encouraged to enable crash dumps.
2.8.6. 新增使用者
The next menu prompts to create at least one user account. It is recommended to login to the system using a user account rather than as root. When logged in as root, there are essentially no limits or protection on what can be done. Logging in as a normal user is safer and more secure.
Follow the prompts and input the requested information for the user account. The example shown in 圖形 2.50, “輸入使用者資訊” creates the asample user account.
Here is a summary of the information to input:
• Username - The name the user will enter to log in. A common convention is to use the first letter of the first name combined with the last name, as long as each username is unique for the system. The username is case sensitive and should not contain any spaces.
• Full name - The user's full name. This can contain spaces and is used as a description for the user account.
• Uid - User ID. Typically, this is left blank so the system will assign a value.
• Login group - The user's group. Typically this is left blank to accept the default.
• Invite user into other groups? - Additional groups to which the user will be added as a member. If the user needs administrative access, type wheel here.
• Login class - Typically left blank for the default.
• Shell - Type in one of the listed values to set the interactive shell for the user. Refer to 節 3.9, “Shell” for more information about shells.
• Home directory - The user's home directory. The default is usually correct.
• Home directory permissions - Permissions on the user's home directory. The default is usually correct.
• Use password-based authentication? - Typically yes so that the user is prompted to input their password at login.
• Use an empty password? - Typically no as it is insecure to have a blank password.
• Use a random password? - Typically no so that the user can set their own password in the next prompt.
• Enter password - The password for this user. Characters typed will not show on the screen.
• Enter password again - The password must be typed again for verification.
• Lock out the account after creation? - Typically no so that the user can login.
After entering everything, a summary is shown for review. If a mistake was made, enter no and try again. If everything is correct, enter yes to create the new user.
If there are more users to add, answer the Add another user? question with yes. Enter no to finish adding users and continue the installation.
2.8.7. 最後設定
After everything has been installed and configured, a final chance is provided to modify settings.
Use this menu to make any changes or do any additional configuration before completing the installation.
After any final configuration is complete, select .
bsdinstall will prompt if there are any additional configuration that needs to be done before rebooting into the new system. Select to exit to a shell within the new system or to proceed to the last step of the installation.
If further configuration or special setup is needed, select to boot the install media into Live CD mode.
If the installation is complete, select to reboot the computer and start the new FreeBSD system. Do not forget to remove the FreeBSD install media or the computer may boot from it again.
As FreeBSD boots, informational messages are displayed. After the system finishes booting, a login prompt is displayed. At the login: prompt, enter the username added during the installation. Avoid logging in as root. Refer to 節 3.3.1.3, “超級使用者帳號” for instructions on how to become the superuser when administrative access is needed.
The messages that appeared during boot can be reviewed by pressing Scroll-Lock to turn on the scroll-back buffer. The PgUp, PgDn, and arrow keys can be used to scroll back through the messages. When finished, press Scroll-Lock again to unlock the display and return to the console. To review these messages once the system has been up for some time, type less /var/run/dmesg.boot from a command prompt. Press q to return to the command line after viewing.
If sshd was enabled in 圖形 2.47, “選擇要開啟的其他服務”, the first boot may be a bit slower as the system will generate the RSA and DSA keys. Subsequent boots will be faster. The fingerprints of the keys will be displayed, as seen in this example:
Generating public/private rsa1 key pair.
Your identification has been saved in /etc/ssh/ssh_host_key.
Your public key has been saved in /etc/ssh/ssh_host_key.pub.
The key fingerprint is:
10:a0:f5:af:93:ae:a3:1a:b2:bb:3c:35:d9:5a:b3:f3 root@machine3.example.com
The key's randomart image is:
+--[RSA1 1024]----+
| o.. |
| o . . |
| . o |
| o |
| o S |
| + + o |
|o . + * |
|o+ ..+ . |
|==o..o+E |
+-----------------+
Generating public/private dsa key pair.
Your identification has been saved in /etc/ssh/ssh_host_dsa_key.
Your public key has been saved in /etc/ssh/ssh_host_dsa_key.pub.
The key fingerprint is:
7e:1c:ce:dc:8a:3a:18:13:5b:34:b5:cf:d9:d1:47:b2 root@machine3.example.com
The key's randomart image is:
+--[ DSA 1024]----+
| .. . .|
| o . . + |
| . .. . E .|
| . . o o . . |
| + S = . |
| + . = o |
| + . * . |
| . . o . |
| .o. . |
+-----------------+
Starting sshd.
FreeBSD does not install a graphical environment by default. Refer to 章 5, X Window 系統 for more information about installing and configuring a graphical window manager.
Proper shutdown of a FreeBSD computer helps protect data and hardware from damage. Do not turn off the power before the system has been properly shut down! If the user is a member of the wheel group, become the superuser by typing su at the command line and entering the root password. Then, type shutdown -p now and the system will shut down cleanly, and if the hardware supports it, turn itself off.
2.9. 疑難排解
This section covers basic installation troubleshooting, such as common problems people have reported.
Check the Hardware Notes (http://www.freebsd.org/releases/index.html) document for the version of FreeBSD to make sure the hardware is supported. If the hardware is supported and lock-ups or other problems occur, build a custom kernel using the instructions in 章 8, 設定 FreeBSD 核心 to add support for devices which are not present in the GENERIC kernel. The default kernel assumes that most hardware devices are in their factory default configuration in terms of IRQs, I/O addresses, and DMA channels. If the hardware has been reconfigured, a custom kernel configuration file can tell FreeBSD where to find things.
注意:
Some installation problems can be avoided or alleviated by updating the firmware on various hardware components, most notably the motherboard. Motherboard firmware is usually referred to as the BIOS. Most motherboard and computer manufacturers have a website for upgrades and upgrade information.
Manufacturers generally advise against upgrading the motherboard BIOS unless there is a good reason for doing so, like a critical update. The upgrade process can go wrong, leaving the BIOS incomplete and the computer inoperative.
If the system hangs while probing hardware during boot, or it behaves strangely during install, ACPI may be the culprit. FreeBSD makes extensive use of the system ACPI service on the i386, amd64, and ia64 platforms to aid in system configuration if it is detected during boot. Unfortunately, some bugs still exist in both the ACPI driver and within system motherboards and BIOS firmware. ACPI can be disabled by setting the hint.acpi.0.disabled hint in the third stage boot loader:
set hint.acpi.0.disabled="1"
This is reset each time the system is booted, so it is necessary to add hint.acpi.0.disabled="1" to the file /boot/loader.conf. More information about the boot loader can be found in 節 12.1, “概述”.
2.10. 使用 Live CD
The welcome menu of bsdinstall, shown in 圖形 2.3, “歡迎選單”, provides a option. This is useful for those who are still wondering whether FreeBSD is the right operating system for them and want to test some of the features before installing.
The following points should be noted before using the :
• To gain access to the system, authentication is required. The username is root and the password is blank.
• As the system runs directly from the installation media, performance will be significantly slower than that of a system installed on a hard disk.
• This option only provides a command prompt and not a graphical interface.
3.1. 概述
• 如何使用 FreeBSD 的虛擬 Console。
• How to create and manage users and groups on FreeBSD.
• UNIX® 檔案權限以及 FreeBSD 檔案標記的運作方式。
• 預設的 FreeBSD 檔案系統配置。
• FreeBSD 的磁碟組織。
• 如何掛載(mount)、卸載(umount)檔案系統。
• 什麼是程序、Daemon 以及 Signal。
• 什麼是 Shell，以及如何變更您預設的登入環境。
• 如何使用基本的文字編輯器。
• 什麼是 Devices 和 Device node 。
• 如何閱讀操作手冊以獲得更多的資訊。
3.2. 虛擬 Console 與終端機
FreeBSD/amd64 (pc3.example.org) (ttyv0)
login:
Shell 中有特殊字元用來表示特殊資料，我們將其稱作 Ｍeta-characters。 其中最常見的 Ｍeta-characters 是 * 字元，它代表了檔名中的任意字元。 Meta-characters 可以用在搜尋檔名，舉例來說，輸入 echo * 會和輸入 ls 得到幾乎相同的結果，這是因為 shell 會將所有符合 * 字元的檔案由 echo 顯示出來。
注意:
有一些 Port 並非由個人維護，而是由 郵遞論壇 維護，只要郵件地址長的像 都是，寄信時記得代入實際的論壇名稱。
尤其是顯示 的 Port 都不是由特定個人維護，該 Ports 的修正與支援來自訂閱該郵遞論壇的一般社群所提供，我們非常歡迎志工參與。
若寄信後沒有取得任何回應，可以依照 撰寫 FreeBSD 問題回報 的說明使用 Bugzilla 提出問題回報。
3. 自行修正看看! Porter's Handbook 中含有 Port 基礎架構的詳細資訊，可提供資訊讓您可修正偶然損壞的 Port 或甚至您可以提交之自己的 Port。
4. 依照 節 4.4, “使用 pkg 管理 Binary 套件” 中的說明安裝 Binary 套件，替代使用 Port 安裝。
5.1. 概述
注意:
• 組成 X Window 系統的各種元件以及它們是如何相互運作。
• 如何安裝並設定 Xorg
• 如何安裝並設定各種視窗管理程式與桌面環境。
• 如何在 Xorg 上使用 TrueType® 字型。
• 如何設定系統以使用圖形化登入 (XDM)。
5.2. 術語
X 伺服器(X Server)
X 最初設計是以網路為中心，採用 client-server 架構。在此架構下 X 伺服器 在有鍵盤、螢幕、滑鼠的電腦上運作。該伺服器負責的工作包含管理顯示、處理來自鍵盤、滑鼠的輸入及來自其他設備(如平板或或影像投影機)的輸入或輸出。這點可能會讓人感到困惑，因為 X 使用的術語與一般的認知剛好相反。 一般認知會以為 X 伺服器 是要在最強悍的主機上執行，而 X 客戶端 才是在桌機上面執行，實際上卻是相反。
X 客戶端(X Client)
X 並不規定螢幕上的視窗該長什麼樣、要如何移動滑鼠指標、 要用什麼鍵來在視窗切換、每個視窗的標題列長相，及是否該有關閉按鈕，等等。事實上，X 把這部分交給所謂的視窗管理程式來管理。可用的視窗管理程式有很多種，每一種視窗管理程式都提供不同的使用介面風格：有些支援虛擬桌面，有些允許自訂組合鍵來管理桌面，有些有 開始 鈕，有些則是可更換佈景主題，可自行安裝新的佈景主題以更換外觀。 視窗管理程式可在 Ports 套件集的 x11-wm 分類找到。
KDEGNOME 會被稱作桌面環境是因為包含了完整常用桌面作業的應用程式，這些應用程式可能包含文書軟體、網頁瀏覽器及遊戲。
5.3. 安裝 Xorg
On FreeBSD, Xorg can be installed as a package or port.
To build and install from the Ports Collection:
# cd /usr/ports/x11/xorg
# make install clean
The binary package can be installed more quickly but with fewer options for customization:
# pkg install xorg
Either of these installations results in the complete Xorg system being installed. This is the best option for most users.
A smaller version of the X system suitable for experienced users is available in x11/xorg-minimal. Most of the documents, libraries, and applications will not be installed. Some applications require these additional components to function.
5.4. Xorg 設定
Warren Block
5.4.1. 快速開始
Xorg supports most common video cards, keyboards, and pointing devices. These devices are automatically detected and do not require any manual configuration.
1. If Xorg has been used on this computer before, move or remove any existing configuration files:
# mv /etc/X11/xorg.conf ~/xorg.conf.etc
# mv /usr/local/etc/X11/xorg.conf ~/xorg.conf.localetc
2. Add the user who will run Xorg to the video or wheel group to enable 3D acceleration when available. To add user jru to whichever group is available:
# pw groupmod video -m jru || pw groupmod wheel -m jru
3. The TWM window manager is included by default. It is started when Xorg starts:
% startx
4. On some older versions of FreeBSD, the system console must be set to vt(4) before switching back to the text console will work properly. See 節 5.4.3, “核心模式設定 (Kernel Mode Setting, KMS)”.
5.4.2. 用來加速影像處理的使用者群組
Access to /dev/dri is needed to allow 3D acceleration on video cards. It is usually simplest to add the user who will be running X to either the video or wheel group. Here, pw(8) is used to add user slurms to the video group, or to the wheel group if there is no video group:
# pw groupmod video -m slurms || pw groupmod wheel -m slurms
5.4.3. 核心模式設定 (Kernel Mode Setting, KMS)
When the computer switches from displaying the console to a higher screen resolution for X, it must set the video output mode. Recent versions of Xorg use a system inside the kernel to do these mode changes more efficiently. Older versions of FreeBSD use sc(4), which is not aware of the KMS system. The end result is that after closing X, the system console is blank, even though it is still working. The newer vt(4) console avoids this problem.
Add this line to /boot/loader.conf to enable vt(4):
kern.vty=vt
5.4.4. 設定檔
5.4.4.1. 目錄
Xorg looks in several directories for configuration files. /usr/local/etc/X11/ is the recommended directory for these files on FreeBSD. Using this directory helps keep application files separate from operating system files.
Storing configuration files in the legacy /etc/X11/ still works. However, this mixes application files with the base FreeBSD files and is not recommended.
5.4.4.2. 單檔或多檔
It is easier to use multiple files that each configure a specific setting than the traditional single xorg.conf. These files are stored in the xorg.conf.d/ subdirectory of the main configuration file directory. The full path is typically /usr/local/etc/X11/xorg.conf.d/.
Examples of these files are shown later in this section.
The traditional single xorg.conf still works, but is neither as clear nor as flexible as multiple files in the xorg.conf.d/ subdirectory.
5.4.5. 顯示卡
Intel®
3D acceleration is supported on most Intel® graphics up to Ivy Bridge (HD Graphics 2500, 4000, and P4000), including Iron Lake (HD Graphics) and Sandy Bridge (HD Graphics 2000).
Driver name: intel
For reference, see https://en.wikipedia.org/wiki/List_of_Intel_graphics_processing_units.
2D and 3D acceleration is supported on Radeon cards up to and including the HD6000 series.
Driver name: radeon
For reference, see https://en.wikipedia.org/wiki/List_of_AMD_graphics_processing_units.
NVIDIA
Several NVIDIA drivers are available in the x11 category of the Ports Collection. Install the driver that matches the video card.
For reference, see https://en.wikipedia.org/wiki/List_of_Nvidia_graphics_processing_units.
Hybrid Combination Graphics
Some notebook computers add additional graphics processing units to those built into the chipset or processor. Optimus combines Intel® and NVIDIA hardware. Switchable Graphics or Hybrid Graphics are a combination of an Intel® or AMD® processor and an AMD® Radeon GPU.
Implementations of these hybrid graphics systems vary, and Xorg on FreeBSD is not able to drive all versions of them.
Some computers provide a BIOS option to disable one of the graphics adapters or select a discrete mode which can be used with one of the standard video card drivers. For example, it is sometimes possible to disable the NVIDIA GPU in an Optimus system. The Intel® video can then be used with an Intel® driver.
BIOS settings depend on the model of computer. In some situations, both GPUs can be left enabled, but creating a configuration file that only uses the main GPU in the Device section is enough to make such a system functional.
Other Video Cards
Drivers for some less-common video cards can be found in the x11-drivers directory of the Ports Collection.
Cards that are not supported by a specific driver might still be usable with the x11-drivers/xf86-video-vesa driver. This driver is installed by x11/xorg. It can also be installed manually as x11-drivers/xf86-video-vesa. Xorg attempts to use this driver when a specific driver is not found for the video card.
x11-drivers/xf86-video-scfb is a similar nonspecialized video driver that works on many UEFI and ARM® computers.
Setting the Video Driver in a File
To set the Intel® driver in a configuration file:
/usr/local/etc/X11/xorg.conf.d/driver-intel.conf
Section "Device"
Identifier "Card0"
Driver "intel"
# BusID "PCI:1:0:0"
EndSection
If more than one video card is present, the BusID identifier can be uncommented and set to select the desired card. A list of video card bus IDs can be displayed with pciconf -lv | grep -B3 display.
To set the Radeon driver in a configuration file:
/usr/local/etc/X11/xorg.conf.d/driver-radeon.conf
Section "Device"
Identifier "Card0"
EndSection
To set the VESA driver in a configuration file:
/usr/local/etc/X11/xorg.conf.d/driver-vesa.conf
Section "Device"
Identifier "Card0"
Driver "vesa"
EndSection
To set the scfb driver for use with a UEFI or ARM® computer:
/usr/local/etc/X11/xorg.conf.d/driver-scfb.conf
Section "Device"
Identifier "Card0"
Driver "scfb"
EndSection
5.4.6. 顯示器
Almost all monitors support the Extended Display Identification Data standard (EDID). Xorg uses EDID to communicate with the monitor and detect the supported resolutions and refresh rates. Then it selects the most appropriate combination of settings to use with that monitor.
Other resolutions supported by the monitor can be chosen by setting the desired resolution in configuration files, or after the X server has been started with xrandr(1).
Using xrandr(1)
Run xrandr(1) without any parameters to see a list of video outputs and detected monitor modes:
% xrandr
Screen 0: minimum 320 x 200, current 3000 x 1920, maximum 8192 x 8192
DVI-0 connected primary 1920x1200+1080+0 (normal left inverted right x axis y axis) 495mm x 310mm
1920x1200 59.95*+
1600x1200 60.00
1280x1024 85.02 75.02 60.02
1280x960 60.00
1152x864 75.00
1024x768 85.00 75.08 70.07 60.00
832x624 74.55
800x600 75.00 60.32
640x480 75.00 60.00
720x400 70.08
DisplayPort-0 disconnected (normal left inverted right x axis y axis)
HDMI-0 disconnected (normal left inverted right x axis y axis)
This shows that the DVI-0 output is being used to display a screen resolution of 1920x1200 pixels at a refresh rate of about 60 Hz. Monitors are not attached to the DisplayPort-0 and HDMI-0 connectors.
Any of the other display modes can be selected with xrandr(1). For example, to switch to 1280x1024 at 60 Hz:
% xrandr --mode 1280x1024 --rate 60
A common task is using the external video output on a notebook computer for a video projector.
The type and quantity of output connectors varies between devices, and the name given to each output varies from driver to driver. What one driver calls HDMI-1, another might call HDMI1. So the first step is to run xrandr(1) to list all the available outputs:
% xrandr
Screen 0: minimum 320 x 200, current 1366 x 768, maximum 8192 x 8192
LVDS1 connected 1366x768+0+0 (normal left inverted right x axis y axis) 344mm x 193mm
1366x768 60.04*+
1024x768 60.00
800x600 60.32 56.25
640x480 59.94
VGA1 connected (normal left inverted right x axis y axis)
1280x1024 60.02 + 75.02
1280x960 60.00
1152x864 75.00
1024x768 75.08 70.07 60.00
832x624 74.55
800x600 72.19 75.00 60.32 56.25
640x480 75.00 72.81 66.67 60.00
720x400 70.08
HDMI1 disconnected (normal left inverted right x axis y axis)
DP1 disconnected (normal left inverted right x axis y axis)
Four outputs were found: the built-in panel LVDS1, and external VGA1, HDMI1, and DP1 connectors.
The projector has been connected to the VGA1 output. xrandr(1) is now used to set that output to the native resolution of the projector and add the additional space to the right side of the desktop:
% xrandr --output VGA1 --auto --right-of LVDS1
--auto chooses the resolution and refresh rate detected by EDID. If the resolution is not correctly detected, a fixed value can be given with --mode instead of the --auto statement. For example, most projectors can be used with a 1024x768 resolution, which is set with --mode 1024x768.
xrandr(1) is often run from .xinitrc to set the appropriate mode when X starts.
Setting Monitor Resolution in a File
To set a screen resolution of 1024x768 in a configuration file:
/usr/local/etc/X11/xorg.conf.d/screen-resolution.conf
Section "Screen"
Identifier "Screen0"
Device "Card0"
SubSection "Display"
Modes "1024x768"
EndSubSection
EndSection
The few monitors that do not have EDID can be configured by setting HorizSync and VertRefresh to the range of frequencies supported by the monitor.
/usr/local/etc/X11/xorg.conf.d/monitor0-freq.conf
Section "Monitor"
Identifier "Monitor0"
HorizSync 30-83 # kHz
VertRefresh 50-76 # Hz
EndSection
5.4.7. 輸入裝置
5.4.7.1. 鍵盤
Keyboard Layout
The standardized location of keys on a keyboard is called a layout. Layouts and other adjustable parameters are listed in xkeyboard-config(7).
A United States layout is the default. To select an alternate layout, set the XkbLayout and XkbVariant options in an InputClass. This will be applied to all input devices that match the class.
This example selects a French keyboard layout with the oss variant.
/usr/local/etc/X11/xorg.conf.d/keyboard-fr-oss.conf
Section "InputClass"
Identifier "KeyboardDefaults"
Driver "keyboard"
MatchIsKeyboard "on"
Option "XkbLayout" "fr"
Option "XkbVariant" "oss"
EndSection
Set United States, Spanish, and Ukrainian keyboard layouts. Cycle through these layouts by pressing Alt+Shift. x11/xxkb or x11/sbxkb can be used for improved layout switching control and current layout indicators.
/usr/local/etc/X11/xorg.conf.d/kbd-layout-multi.conf
Section "InputClass"
Identifier "All Keyboards"
MatchIsKeyboard "yes"
Option "XkbLayout" "us, es, ua"
EndSection
Closing Xorg From the Keyboard
X can be closed with a combination of keys. By default, that key combination is not set because it conflicts with keyboard commands for some applications. Enabling this option requires changes to the keyboard InputDevice section:
/usr/local/etc/X11/xorg.conf.d/keyboard-zap.conf
Section "InputClass"
Identifier "KeyboardDefaults"
Driver "keyboard"
MatchIsKeyboard "on"
Option "XkbOptions" "terminate:ctrl_alt_bksp"
EndSection
5.4.7.2. 滑鼠與指標裝置
Many mouse parameters can be adjusted with configuration options. See mousedrv(4) for a full list.
Mouse Buttons
The number of buttons on a mouse can be set in the mouse InputDevice section of xorg.conf. To set the number of buttons to 7:
/usr/local/etc/X11/xorg.conf.d/mouse0-buttons.conf
Section "InputDevice"
Identifier "Mouse0"
Option "Buttons" "7"
EndSection
5.4.8. 手動設定
In some cases, Xorg autoconfiguration does not work with particular hardware, or a different configuration is desired. For these cases, a custom configuration file can be created.
A configuration file can be generated by Xorg based on the detected hardware. This file is often a useful starting point for custom configurations.
Generating an xorg.conf:
# Xorg -configure
The configuration file is saved to /root/xorg.conf.new. Make any changes desired, then test that file with:
# Xorg -config /root/xorg.conf.new
After the new configuration has been adjusted and tested, it can be split into smaller files in the normal location, /usr/local/etc/X11/xorg.conf.d/.
5.5. 在 Xorg 使用字型
5.5.1. Type1 字型
The default fonts that ship with Xorg are less than ideal for typical desktop publishing applications. Large presentation fonts show up jagged and unprofessional looking, and small fonts are almost completely unintelligible. However, there are several free, high quality Type1 (PostScript®) fonts available which can be readily used with Xorg. For instance, the URW font collection (x11-fonts/urwfonts) includes high quality versions of standard type1 fonts (Times Roman®, Helvetica®, Palatino® and others). The Freefonts collection (x11-fonts/freefonts) includes many more fonts, but most of them are intended for use in graphics software such as the Gimp, and are not complete enough to serve as screen fonts. In addition, Xorg can be configured to use TrueType® fonts with a minimum of effort. For more details on this, see the X(7) manual page or 節 5.5.2, “TrueType® 字型”.
To install the above Type1 font collections from the Ports Collection, run the following commands:
# cd /usr/ports/x11-fonts/urwfonts
# make install clean
And likewise with the freefont or other collections. To have the X server detect these fonts, add an appropriate line to the X server configuration file (/etc/X11/xorg.conf), which reads:
FontPath "/usr/local/share/fonts/urwfonts/"
Alternatively, at the command line in the X session run:
% xset fp+ /usr/local/share/fonts/urwfonts
% xset fp rehash
This will work but will be lost when the X session is closed, unless it is added to the startup file (~/.xinitrc for a normal startx session, or ~/.xsession when logging in through a graphical login manager like XDM). A third way is to use the new /usr/local/etc/fonts/local.conf as demonstrated in 節 5.5.3, “反鋸齒字型”.
5.5.2. TrueType® 字型
Xorg has built in support for rendering TrueType® fonts. There are two different modules that can enable this functionality. The freetype module is used in this example because it is more consistent with the other font rendering back-ends. To enable the freetype module just add the following line to the "Module" section of /etc/X11/xorg.conf.
Load "freetype"
Now make a directory for the TrueType® fonts (for example, /usr/local/share/fonts/TrueType) and copy all of the TrueType® fonts into this directory. Keep in mind that TrueType® fonts cannot be directly taken from an Apple® Mac®; they must be in UNIX®/MS-DOS®/Windows® format for use by Xorg. Once the files have been copied into this directory, use mkfontdir to create a fonts.dir, so that the X font renderer knows that these new files have been installed. mkfontdir can be installed as a package:
# pkg install mkfontdir
Then create an index of X font files in a directory:
# cd /usr/local/share/fonts/TrueType
# mkfontdir
Now add the TrueType® directory to the font path. This is just the same as described in 節 5.5.1, “Type1 字型”:
% xset fp+ /usr/local/share/fonts/TrueType
% xset fp rehash
or add a FontPath line to xorg.conf.
Now Gimp, Apache OpenOffice, and all of the other X applications should now recognize the installed TrueType® fonts. Extremely small fonts (as with text in a high resolution display on a web page) and extremely large fonts (within StarOffice) will look much better now.
5.5.3. 反鋸齒字型
All fonts in Xorg that are found in /usr/local/share/fonts/ and ~/.fonts/ are automatically made available for anti-aliasing to Xft-aware applications. Most recent applications are Xft-aware, including KDE, GNOME, and Firefox.
In order to control which fonts are anti-aliased, or to configure anti-aliasing properties, create (or edit, if it already exists) the file /usr/local/etc/fonts/local.conf. Several advanced features of the Xft font system can be tuned using this file; this section describes only some simple possibilities. For more details, please see fonts-conf(5).
This file must be in XML format. Pay careful attention to case, and make sure all tags are properly closed. The file begins with the usual XML header followed by a DOCTYPE definition, and then the <fontconfig> tag:
<?xml version="1.0"?>
<!DOCTYPE fontconfig SYSTEM "fonts.dtd">
<fontconfig>
As previously stated, all fonts in /usr/local/share/fonts/ as well as ~/.fonts/ are already made available to Xft-aware applications. If you wish to add another directory outside of these two directory trees, add a line similar to the following to /usr/local/etc/fonts/local.conf:
<dir>/path/to/my/fonts</dir>
After adding new fonts, and especially new font directories, you should run the following command to rebuild the font caches:
# fc-cache -f
Anti-aliasing makes borders slightly fuzzy, which makes very small text more readable and removes staircases from large text, but can cause eyestrain if applied to normal text. To exclude font sizes smaller than 14 point from anti-aliasing, include these lines:
<match target="font">
<test name="size" compare="less">
<double>14</double>
</test>
<edit name="antialias" mode="assign">
<bool>false</bool>
</edit>
</match>
<match target="font">
<test name="pixelsize" compare="less" qual="any">
<double>14</double>
</test>
<edit mode="assign" name="antialias">
<bool>false</bool>
</edit>
</match>
Spacing for some monospaced fonts may also be inappropriate with anti-aliasing. This seems to be an issue with KDE, in particular. One possible fix for this is to force the spacing for such fonts to be 100. Add the following lines:
<match target="pattern" name="family">
<test qual="any" name="family">
<string>fixed</string>
</test>
<edit name="family" mode="assign">
<string>mono</string>
</edit>
</match>
<match target="pattern" name="family">
<test qual="any" name="family">
<string>console</string>
</test>
<edit name="family" mode="assign">
<string>mono</string>
</edit>
</match>
(this aliases the other common names for fixed fonts as "mono"), and then add:
<match target="pattern" name="family">
<test qual="any" name="family">
<string>mono</string>
</test>
<edit name="spacing" mode="assign">
<int>100</int>
</edit>
</match>
Certain fonts, such as Helvetica, may have a problem when anti-aliased. Usually this manifests itself as a font that seems cut in half vertically. At worst, it may cause applications to crash. To avoid this, consider adding the following to local.conf:
<match target="pattern" name="family">
<test qual="any" name="family">
<string>Helvetica</string>
</test>
<edit name="family" mode="assign">
<string>sans-serif</string>
</edit>
</match>
Once you have finished editing local.conf make sure you end the file with the </fontconfig> tag. Not doing this will cause your changes to be ignored.
Finally, users can add their own settings via their personal .fonts.conf files. To do this, each user should simply create a ~/.fonts.conf. This file must also be in XML format.
One last point: with an LCD screen, sub-pixel sampling may be desired. This basically treats the (horizontally separated) red, green and blue components separately to improve the horizontal resolution; the results can be dramatic. To enable this, add the line somewhere in local.conf:
<match target="font">
<test qual="all" name="rgba">
<const>unknown</const>
</test>
<edit name="rgba" mode="assign">
<const>rgb</const>
</edit>
</match>
注意:
Depending on the sort of display, rgb may need to be changed to bgr, vrgb or vbgr: experiment and see which works best.
5.6. X 顯示管理程式
Contributed by .
Xorg provides an X Display Manager, XDM, which can be used for login session management. XDM provides a graphical interface for choosing which display server to connect to and for entering authorization information such as a login and password combination.
This section demonstrates how to configure the X Display Manager on FreeBSD. Some desktop environments provide their own graphical login manager. Refer to 節 5.7.1, “GNOME” for instructions on how to configure the GNOME Display Manager and 節 5.7.2, “KDE” for instructions on how to configure the KDE Display Manager.
5.6.1. 設定 XDM
To install XDM, use the x11/xdm package or port. Once installed, XDM can be configured to run when the machine boots up by editing this entry in /etc/ttys:
ttyv8 "/usr/local/bin/xdm -nodaemon" xterm off secure
Change the off to on and save the edit. The ttyv8 in this entry indicates that XDM will run on the ninth virtual terminal.
The XDM configuration directory is located in /usr/local/lib/X11/xdm. This directory contains several files used to change the behavior and appearance of XDM, as well as a few scripts and programs used to set up the desktop when XDM is running. 表格 5.1, “XDM 設定檔” summarizes the function of each of these files. The exact syntax and usage of these files is described in xdm(1).
XaccessThe protocol for connecting to XDM is called the X Display Manager Connection Protocol (XDMCP) This file is a client authorization ruleset for controlling XDMCP connections from remote machines. By default, this file does not allow any remote clients to connect.
XresourcesThis file controls the look and feel of the XDM display chooser and login screens. The default configuration is a simple rectangular login window with the hostname of the machine displayed at the top in a large font and Login: and Password: prompts below. The format of this file is identical to the app-defaults file described in the Xorg documentation.
XserversThe list of local and remote displays the chooser should provide as login choices.
XsessionDefault session script for logins which is run by XDM after a user has logged in. Normally each user will have a customized session script in ~/.xsession that overrides this script
Xsetup_*Script to automatically launch applications before displaying the chooser or login interfaces. There is a script for each display being used, named Xsetup_*, where * is the local display number. Typically these scripts run one or two programs in the background such as xconsole.
xdm-configGlobal configuration for all displays running on this machine.
xdm-errorsContains errors generated by the server program. If a display that XDM is trying to start hangs, look at this file for error messages. These messages are also written to the user's ~/.xsession-errors on a per-session basis.
xdm-pidThe running process ID of XDM.
5.6.2. 設定遠端存取
By default, only users on the same system can login using XDM. To enable users on other systems to connect to the display server, edit the access control rules and enable the connection listener.
To configure XDM to listen for any remote connection, comment out the DisplayManager.requestPort line in /usr/local/lib/X11/xdm/xdm-config by putting a ! in front of it:
! SECURITY: do not listen for XDMCP or Chooser requests
! Comment out this line if you want to manage X terminals with xdm
DisplayManager.requestPort: 0
Save the edits and restart XDM. To restrict remote access, look at the example entries in /usr/local/lib/X11/xdm/Xaccess and refer to xdm(1) for further information.
5.7. 桌面環境
Contributed by .
This section describes how to install three popular desktop environments on a FreeBSD system. A desktop environment can range from a simple window manager to a complete suite of desktop applications. Over a hundred desktop environments are available in the x11-wm category of the Ports Collection.
5.7.1. GNOME
GNOME is a user-friendly desktop environment. It includes a panel for starting applications and displaying status, a desktop, a set of tools and applications, and a set of conventions that make it easy for applications to cooperate and be consistent with each other. More information regarding GNOME on FreeBSD can be found at http://www.FreeBSD.org/gnome. That web site contains additional documentation about installing, configuring, and managing GNOME on FreeBSD.
This desktop environment can be installed from a package:
# pkg install gnome3
To instead build GNOME from ports, use the following command. GNOME is a large application and will take some time to compile, even on a fast computer.
# cd /usr/ports/x11/gnome3
# make install clean
GNOME requires /proc to be mounted. Add this line to /etc/fstab to mount this file system automatically during system startup:
proc /proc procfs rw 0 0
GNOME uses D-Bus and HAL for a message bus and hardware abstraction. These applications are automatically installed as dependencies of GNOME. Enable them in /etc/rc.conf so they will be started when the system boots:
dbus_enable="YES"
hald_enable="YES"
After installation, configure Xorg to start GNOME. The easiest way to do this is to enable the GNOME Display Manager, GDM, which is installed as part of the GNOME package or port. It can be enabled by adding this line to /etc/rc.conf:
gdm_enable="YES"
It is often desirable to also start all GNOME services. To achieve this, add a second line to /etc/rc.conf:
gnome_enable="YES"
GDM will start automatically when the system boots.
A second method for starting GNOME is to type startx from the command-line after configuring ~/.xinitrc. If this file already exists, replace the line that starts the current window manager with one that starts /usr/local/bin/gnome-session. If this file does not exist, create it with this command:
% echo "exec /usr/local/bin/gnome-session" > ~/.xinitrc
A third method is to use XDM as the display manager. In this case, create an executable ~/.xsession:
% echo "#!/bin/sh" > ~/.xsession
% echo "exec /usr/local/bin/gnome-session" >> ~/.xsession
% chmod +x ~/.xsession
5.7.2. KDE
KDE is another easy-to-use desktop environment. This desktop provides a suite of applications with a consistent look and feel, a standardized menu and toolbars, keybindings, color-schemes, internationalization, and a centralized, dialog-driven desktop configuration. More information on KDE can be found at http://www.kde.org/. For FreeBSD-specific information, consult http://freebsd.kde.org.
To install the KDE package, type:
# pkg install x11/kde4
To instead build the KDE port, use the following command. Installing the port will provide a menu for selecting which components to install. KDE is a large application and will take some time to compile, even on a fast computer.
# cd /usr/ports/x11/kde4
# make install clean
KDE requires /proc to be mounted. Add this line to /etc/fstab to mount this file system automatically during system startup:
proc /proc procfs rw 0 0
KDE uses D-Bus and HAL for a message bus and hardware abstraction. These applications are automatically installed as dependencies of KDE. Enable them in /etc/rc.conf so they will be started when the system boots:
dbus_enable="YES"
hald_enable="YES"
The installation of KDE includes the KDE Display Manager, KDM. To enable this display manager, add this line to /etc/rc.conf:
kdm4_enable="YES"
A second method for launching KDE is to type startx from the command line. For this to work, the following line is needed in ~/.xinitrc:
exec /usr/local/bin/startkde
A third method for starting KDE is through XDM. To do so, create an executable ~/.xsession as follows:
% echo "#!/bin/sh" > ~/.xsession
% echo "exec /usr/local/bin/startkde" >> ~/.xsession
% chmod +x ~/.xsession
Once KDE is started, refer to its built-in help system for more information on how to use its various menus and applications.
5.7.3. Xfce
Xfce is a desktop environment based on the GTK+ toolkit used by GNOME. However, it is more lightweight and provides a simple, efficient, easy-to-use desktop. It is fully configurable, has a main panel with menus, applets, and application launchers, provides a file manager and sound manager, and is themeable. Since it is fast, light, and efficient, it is ideal for older or slower machines with memory limitations. More information on Xfce can be found at http://www.xfce.org.
To install the Xfce package:
# pkg install xfce
Alternatively, to build the port:
# cd /usr/ports/x11-wm/xfce4
# make install clean
Unlike GNOME or KDE, Xfce does not provide its own login manager. In order to start Xfce from the command line by typing startx, first add its entry to ~/.xinitrc:
% echo "exec /usr/local/bin/startxfce4 --with-ck-launch" > ~/.xinitrc
An alternate method is to use XDM. To configure this method, create an executable ~/.xsession:
% echo "#!/bin/sh" > ~/.xsession
% echo "exec /usr/local/bin/startxfce4 --with-ck-launch" >> ~/.xsession
% chmod +x ~/.xsession
5.8. 安裝 Compiz Fusion
One way to make using a desktop computer more pleasant is with nice 3D effects.
Installing the Compiz Fusion package is easy, but configuring it requires a few steps that are not described in the port's documentation.
5.8.1. 設定 FreeBSD nVidia 驅動程式
Desktop effects can cause quite a load on the graphics card. For an nVidia-based graphics card, the proprietary driver is required for good performance. Users of other graphics cards can skip this section and continue with the xorg.conf configuration.
To determine which nVidia driver is needed see the FAQ question on the subject.
Having determined the correct driver to use for your card, installation is as simple as installing any other package.
For example, to install the latest driver:
# pkg install x11/nvidia-driver
The driver will create a kernel module, which needs to be loaded at system startup. Add the following line to /boot/loader.conf:
nvidia_load="YES"
注意:
To immediately load the kernel module into the running kernel by issuing a command like kldload nvidia, however it has been noted that the some versions of Xorg will not function properly if the driver is not loaded at boot time. After editing /boot/loader.conf, a reboot is recommended.
With the kernel module loaded, you normally only need to change a single line in xorg.conf to enable the proprietary driver:
Find the following line in /etc/X11/xorg.conf:
Driver "nv"
and change it to:
Driver "nvidia"
Start the GUI as usual, and you should be greeted by the nVidia splash. Everything should work as usual.
5.8.2. 設定 xorg.conf 來啟動桌面特效
To enable Compiz Fusion, /etc/X11/xorg.conf needs to be modified:
Add the following section to enable composite effects:
Section "Extensions"
Option "Composite" "Enable"
EndSection
Locate the Screen section which should look similar to the one below:
Section "Screen"
Identifier "Screen0"
Device "Card0"
Monitor "Monitor0"
...
and add the following two lines (after Monitor will do):
DefaultDepth 24
Option "AddARGBGLXVisuals" "True"
Locate the Subsection that refers to the screen resolution that you wish to use. For example, if you wish to use 1280x1024, locate the section that follows. If the desired resolution does not appear in any subsection, you may add the relevant entry by hand:
SubSection "Display"
Viewport 0 0
Modes "1280x1024"
EndSubSection
A color depth of 24 bits is needed for desktop composition, change the above subsection to:
SubSection "Display"
Viewport 0 0
Depth 24
Modes "1280x1024"
EndSubSection
Finally, confirm that the glx and extmod modules are loaded in the Module section:
Section "Module"
...
The preceding can be done automatically with x11/nvidia-xconfig by running (as root):
# nvidia-xconfig --add-argb-glx-visuals
# nvidia-xconfig --composite
# nvidia-xconfig --depth=24
5.8.3. 安裝與設定 Compiz Fusion
Installing Compiz Fusion is as simple as any other package:
# pkg install x11-wm/compiz-fusion
When the installation is finished, start your graphic desktop and at a terminal, enter the following commands (as a normal user):
% compiz --replace --sm-disable --ignore-desktop-hints ccp &
% emerald --replace &
Your screen will flicker for a few seconds, as your window manager (e.g. Metacity if you are using GNOME) is replaced by Compiz Fusion. Emerald takes care of the window decorations (i.e. close, minimize, maximize buttons, title bars and so on).
You may convert this to a trivial script and have it run at startup automatically (e.g. by adding to Sessions in a GNOME desktop):
#! /bin/sh
compiz --replace --sm-disable --ignore-desktop-hints ccp &
emerald --replace &
Save this in your home directory as, for example, start-compiz and make it executable:
% chmod +x ~/start-compiz
Then use the GUI to add it to Startup Programs (located in System, Preferences, Sessions on a GNOME desktop).
To actually select all the desired effects and their settings, execute (again as a normal user) the Compiz Config Settings Manager:
% ccsm
注意:
In GNOME, this can also be found in the System, Preferences menu.
If you have selected gconf support during the build, you will also be able to view these settings using gconf-editor under apps/compiz.
5.9. 疑難排解
If the mouse does not work, you will need to first configure it before proceeding. In recent Xorg versions, the InputDevice sections in xorg.conf are ignored in favor of the autodetected devices. To restore the old behavior, add the following line to the ServerLayout or ServerFlags section of this file:
Option "AutoAddDevices" "false"
Input devices may then be configured as in previous versions, along with any other options needed (e.g., keyboard layout switching).
注意:
As previously explained the hald daemon will, by default, automatically detect your keyboard. There are chances that your keyboard layout or model will not be correct, desktop environments like GNOME, KDE or Xfce provide tools to configure the keyboard. However, it is possible to set the keyboard properties directly either with the help of the setxkbmap(1) utility or with a hald's configuration rule.
For example if, one wants to use a PC 102 keys keyboard coming with a french layout, we have to create a keyboard configuration file for hald called x11-input.fdi and saved in the /usr/local/etc/hal/fdi/policy directory. This file should contain the following lines:
<?xml version="1.0" encoding="iso-8859-1"?>
<deviceinfo version="0.2">
<device>
<match key="info.capabilities" contains="input.keyboard">
<merge key="input.x11_options.XkbModel" type="string">pc102</merge>
<merge key="input.x11_options.XkbLayout" type="string">fr</merge>
</match>
</device>
</deviceinfo>
If this file already exists, just copy and add to your file the lines regarding the keyboard configuration.
You will have to reboot your machine to force hald to read this file.
It is possible to do the same configuration from an X terminal or a script with this command line:
% setxkbmap -model pc102 -layout fr
/usr/local/share/X11/xkb/rules/base.lst lists the various keyboard, layouts and options available.
The xorg.conf.new configuration file may now be tuned to taste. Open the file in a text editor such as emacs(1) or ee(1). If the monitor is an older or unusual model that does not support autodetection of sync frequencies, those settings can be added to xorg.conf.new under the "Monitor" section:
Section "Monitor"
Identifier "Monitor0"
VendorName "Monitor Vendor"
ModelName "Monitor Model"
HorizSync 30-107
VertRefresh 48-120
EndSection
Most monitors support sync frequency autodetection, making manual entry of these values unnecessary. For the few monitors that do not support autodetection, avoid potential damage by only entering values provided by the manufacturer.
X allows DPMS (Energy Star) features to be used with capable monitors. The xset(1) program controls the time-outs and can force standby, suspend, or off modes. If you wish to enable DPMS features for your monitor, you must add the following line to the monitor section:
Option "DPMS"
While the xorg.conf.new configuration file is still open in an editor, select the default resolution and color depth desired. This is defined in the "Screen" section:
Section "Screen"
Identifier "Screen0"
Device "Card0"
Monitor "Monitor0"
DefaultDepth 24
SubSection "Display"
Viewport 0 0
Depth 24
Modes "1024x768"
EndSubSection
EndSection
The DefaultDepth keyword describes the color depth to run at by default. This can be overridden with the -depth command line switch to Xorg(1). The Modes keyword describes the resolution to run at for the given color depth. Note that only VESA standard modes are supported as defined by the target system's graphics hardware. In the example above, the default color depth is twenty-four bits per pixel. At this color depth, the accepted resolution is 1024 by 768 pixels.
Finally, write the configuration file and test it using the test mode given above.
注意:
One of the tools available to assist you during troubleshooting process are the Xorg log files, which contain information on each device that the Xorg server attaches to. Xorg log file names are in the format of /var/log/Xorg.0.log. The exact name of the log can vary from Xorg.0.log to Xorg.8.log and so forth.
If all is well, the configuration file needs to be installed in a common location where Xorg(1) can find it. This is typically /etc/X11/xorg.conf or /usr/local/etc/X11/xorg.conf.
# cp xorg.conf.new /etc/X11/xorg.conf
The Xorg configuration process is now complete. Xorg may be now started with the startx(1) utility. The Xorg server may also be started with the use of xdm(1).
5.9.1. 設定 Intel® i810 繪圖晶片組
Configuration with Intel® i810 integrated chipsets requires the agpgart AGP programming interface for Xorg to drive the card. See the agp(4) driver manual page for more information.
This will allow configuration of the hardware as any other graphics board. Note on systems without the agp(4) driver compiled in the kernel, trying to load the module with kldload(8) will not work. This driver has to be in the kernel at boot time through being compiled in or using /boot/loader.conf.
5.9.2. 加入寬螢幕平板顯示器到設定檔
This section assumes a bit of advanced configuration knowledge. If attempts to use the standard configuration tools above have not resulted in a working configuration, there is information enough in the log files to be of use in getting the setup working. Use of a text editor will be necessary.
Current widescreen (WSXGA, WSXGA+, WUXGA, WXGA, WXGA+, et.al.) formats support 16:10 and 10:9 formats or aspect ratios that can be problematic. Examples of some common screen resolutions for 16:10 aspect ratios are:
• 2560x1600
• 1920x1200
• 1680x1050
• 1440x900
• 1280x800
At some point, it will be as easy as adding one of these resolutions as a possible Mode in the Section "Screen" as such:
Section "Screen"
Identifier "Screen0"
Device "Card0"
Monitor "Monitor0"
DefaultDepth 24
SubSection "Display"
Viewport 0 0
Depth 24
Modes "1680x1050"
EndSubSection
EndSection
Xorg is smart enough to pull the resolution information from the widescreen via I2C/DDC information so it knows what the monitor can handle as far as frequencies and resolutions.
If those ModeLines do not exist in the drivers, one might need to give Xorg a little hint. Using /var/log/Xorg.0.log one can extract enough information to manually create a ModeLine that will work. Simply look for information resembling this:
(II) MGA(0): Supported additional Video Mode:
(II) MGA(0): clock: 146.2 MHz Image Size: 433 x 271 mm
(II) MGA(0): h_active: 1680 h_sync: 1784 h_sync_end 1960 h_blank_end 2240 h_border: 0
(II) MGA(0): v_active: 1050 v_sync: 1053 v_sync_end 1059 v_blanking: 1089 v_border: 0
(II) MGA(0): Ranges: V min: 48 V max: 85 Hz, H min: 30 H max: 94 kHz, PixClock max 170 MHz
This information is called EDID information. Creating a ModeLine from this is just a matter of putting the numbers in the correct order:
ModeLine <name> <clock> <4 horiz. timings> <4 vert. timings>
So that the ModeLine in Section "Monitor" for this example would look like this:
Section "Monitor"
Identifier "Monitor1"
VendorName "Bigname"
ModelName "BestModel"
ModeLine "1680x1050" 146.2 1680 1784 1960 2240 1050 1053 1059 1089
Option "DPMS"
EndSection
Now having completed these simple editing steps, X should start on your new widescreen monitor.
5.9.3. Compiz Fusion 疑難排解
5.9.3.1. I have installed Compiz Fusion, and after running the commands you mention, my windows are left without title bars and buttons. What is wrong?
5.9.3.2. When I run the command to start Compiz Fusion, the X server crashes and I am back at the console. What is wrong?
5.9.3.1. I have installed Compiz Fusion, and after running the commands you mention, my windows are left without title bars and buttons. What is wrong? You are probably missing a setting in /etc/X11/xorg.conf. Review this file carefully and check especially the DefaultDepth and AddARGBGLXVisuals directives. 5.9.3.2. When I run the command to start Compiz Fusion, the X server crashes and I am back at the console. What is wrong? If you check /var/log/Xorg.0.log, you will probably find error messages during the X startup. The most common would be:(EE) NVIDIA(0): Failed to initialize the GLX module; please check in your X (EE) NVIDIA(0): log file that the GLX module has been loaded in your X (EE) NVIDIA(0): server, and that the module is the NVIDIA GLX module. If (EE) NVIDIA(0): you continue to encounter problems, Please try (EE) NVIDIA(0): reinstalling the NVIDIA driver.This is usually the case when you upgrade Xorg. You will need to reinstall the x11/nvidia-driver package so glx is built again.
部 II. 一般作業
• 介紹給您常見且實用的桌面應用軟體：瀏覽器、辦工工具、文件閱覽程式等。
• 介紹給您眾多 FreeBSD 上可用的多媒體工具。
• 解釋如何編譯量身訂做的 FreeBSD 核心以增加額外系統功能的流程。
• 詳細描述列印系統，包含桌上型印表機及網路印表機的設定。
• 展示給您看如何在您的 FreeBSD 系統中執行 Linux 應用軟體。
6.2. 瀏覽器
KDEGNOME 桌面環境都有提供自有的 HTML 瀏覽器。請參考 節 5.7, “桌面環境” 來了解更多有關如何設定完整桌面環境的資訊。
Firefox有 FreeBSD 、 Linux® 及在地化版本
Opera有 FreeBSD 、 Linux® 版本
Konqueror需要 KDE 程式庫
Chromium需要 Gtk+ 程式庫
6.2.1. Firefox
Firefox 是一套已完整植到 FreeBSD 的開放源始碼瀏覽器，它具備符合 HTML 標準的顯示引擎、頁籤瀏覽、彈出視窗封鎖、擴充套件、強化安全性及其他更多功能。Firefox 的基礎使用了 Mozilla 的程式庫。
# pkg install firefox
# pkg install firefox-esr
# cd /usr/ports/www/firefox
# make install clean
6.2.1.1. Firefox 與 Java™ 附加元件
# cd /usr/ports/java/icedtea-web
# make install clean
If the browser is unable to find the plugin, each user will have to run the following command and relaunch the browser:
% ln -s /usr/local/lib/IcedTeaPlugin.so \
$HOME/.mozilla/plugins/ 6.2.1.2. Firefox 與 Adobe® Flash® 附加元件 FreeBSD 並沒有原生的 Adobe® Flash® 附加原件。雖然如此，仍可以使用軟體包裝程式來執行 Linux® 版本 的附加元件。該包裝程式也提供其他瀏覽器附加元件的支援，如 RealPlayer®。 要安裝並開啟此附加元件，可執行以下步驟： 1. 自 Port 安裝 www/nspluginwrapper ，受到授權條款的限制，該套件無 Binary 版本。此 Port 需安裝 emulators/linux_base-c6 2. 自 Port 安裝 www/linux-c6-flashplugin11 ，受到授權條款的限制，該套件無 Binary 版本。 3. 第一次使用附加元件前，每位使用者需要先執行： % nspluginwrapper -v -a -i 當附加元件 Port 完成更新並且重新安裝後，每位使用者需要執行： % nspluginwrapper -v -a -u 開啟瀏覽器並在網址列輸入 about:plugins 並按 Enter 鍵，目前可用的附加元件清單中應會顯示該附加元件。 6.2.1.3. Firefox 與 Swfdec Flash® 附加元件 Swfdec is a decoder and renderer for Flash® animations. Swfdec-Mozilla is a plugin for Firefox browsers that uses the Swfdec library for playing SWF files. 要安裝套件可： # pkg install swfdec-plugin If the package is not available, compile and install it from the Ports Collection: # cd /usr/ports/www/swfdec-plugin # make install clean Restart the browser to activate this plugin. 6.2.2. Opera Opera 是個具備完整功能、符合標準且輕量、執行速度快的瀏覽器。 它同時也具備了內建的郵件、新聞閱讀器、IRC 客戶端、RSS/Atom 來源閱讀器等。 可用的版本有兩種原生的 FreeBSD 版本及 Linux® 模擬模式下執行的版本。 以下指令可安裝 FreeBSD Binary 套件版本的 Opera，替換 operalinux-opera 則可改安裝 Linux® 版本。 # pkg install opera 或者，可安裝 Ports 套件集中的版本，以下範例會編譯原生的版本。 # cd /usr/ports/www/opera # make install clean 要安裝 Linux® 則替換 operalinux-opera 要安裝 Adobe® Flash® 附加元件，需先編譯 www/linux-c6-flashplugin11 Port，因受到授權條款限制無法事先做為 Binary 套件。然後安裝 www/opera-linuxplugins。以下範例示範編譯 Port 中的這兩個應用程式。 # cd /usr/ports/www/linux-c6-flashplugin11 # make install clean # cd /usr/ports/www/opera-linuxplugins # make install clean 安裝完成後，開啟瀏覽器檢查附加元件是否存在，在網址列輸入 opera:plugins 並按下 Enter 鍵，便會有清單顯示目前可用的附加元件。 若要安裝 Java 附加元件請依照 節 6.2.1.1, “Firefox 與 Java™ 附加元件” 中的指示。 6.2.3. Konqueror Konqueror 不只是個網頁瀏覽器， 它同時也是檔案管理器和多媒體瀏覽器。它包含在 x11/kde4-baseapps 套件或 Port 中。 Konqueror 使用支援 WebKit 以及它自有的 KTHML。WebKit 是一套被許多現代瀏覽器所使用的繪圖引擎，包含 Chromium。要在 FreeBSD 的 Konqueror 使用 WebKit 需安裝 www/kwebkitpart 套件或 Port。此範例示範使用 Port 編譯： # cd /usr/ports/www/kwebkitpart # make install clean 要啟動 Konqueror 中的 WebKit 點選 SettingsConfigure Konqueror。在 General 設定頁面內點選 Default web browser engine 旁的下拉示選單並變更 KHTMLWebKit Konqueror 也支援 Flash®如何Konqueror 上安裝 Flash® 的說明可參考 http://freebsd.kde.org/howtos/konqueror-flash.php 6.2.4. Chromium Chromium is an open source browser project that aims to build a safer, faster, and more stable web browsing experience. Chromium features tabbed browsing, popup blocking, extensions, and much more. Chromium is the open source project upon which the Google Chrome web browser is based. Chromium can be installed as a package by typing: # pkg install chromium Alternatively, Chromium can be compiled from source using the Ports Collection: # cd /usr/ports/www/chromium # make install clean 注意: The executable for Chromium is /usr/local/bin/chrome, not /usr/local/bin/chromium. 6.2.4.1. Chromium 與 Java™ 附加元件 The installation of Chromium does not include Java™ support. To install Java™ plugin support, follow the instructions in 節 6.2.1.1, “Firefox 與 Java™ 附加元件”. Once Java™ support is installed, start Chromium and enter about:plugins in the address bar. IcedTea-Web should be listed as one of the installed plugins. If Chromium does not display the IcedTea-Web plugin, run the following commands and restart the web browser: # mkdir -p /usr/local/share/chromium/plugins # ln -s /usr/local/lib/IcedTeaPlugin.so \ /usr/local/share/chromium/plugins/ 6.2.4.2. Chromium 與 Adobe® Flash® 附加元件 Configuring Chromium and Adobe® Flash® is similar to the instructions in 節 6.2.1.2, “Firefox 與 Adobe® Flash® 附加元件”. No additional configuration should be necessary, since Chromium is able to use some plugins from other browsers. 6.3. 辦工工具 當開始進行辦公，新的使用者通常會去找好用的辦公室軟體或是好上手的文件處理程式。 雖然有些 桌面環境 像是 KDE 已經提供了辦公軟體組合的套件，FreeBSD 預設未提供任何辦工工具。 不論是否有安裝視窗管理程式，FreeBSD 可安裝多套辦公軟體以及圖型化文件處理程式。 本章節元範如何安裝以下熱門的辦工軟體以及說明該應用程式所需的資源、自 Ports 編譯的時間或者是否有其他主要相依套件。 應用程式名稱所需資源自 Ports 安裝時間主要相依套件 CalligraKDE AbiWordGtk+GNOME The GimpGtk+ Apache OpenOffice非常多JDKMozilla LibreOffice有點多非常多Gtk+KDE/ GNOMEJDK 6.3.1. Calligra The KDE desktop environment includes an office suite which can be installed separately from KDE. Calligra includes standard components that can be found in other office suites. Words is the word processor, Sheets is the spreadsheet program, Stage manages slide presentations, and Karbon is used to draw graphical documents. In FreeBSD, editors/calligra can be installed as a package or a port. To install the package: # pkg install calligra If the package is not available, use the Ports Collection instead: # cd /usr/ports/editors/calligra # make install clean 6.3.2. AbiWord AbiWord 是一個免費的文件處理軟體，外觀和感覺都近似於 Microsoft® Word。 它非常快速，包含了許多功能而且非常容易上手。 AbiWord 可以輸入或輸出許多檔案格式， 包括一些有專利的格式，例如 Microsoft® .rtf 格式。 要安裝 AbiWord Binary 套件，可使用下列指令： # pkg install abiword 若沒有 Binary 套件版本，也可以從 Ports 套件集中編譯安裝： # cd /usr/ports/editors/abiword # make install clean 6.3.3. The GIMP 對於影像的編輯及修改來說，The GIMP 是非常精緻的影像處理軟體。 它可以當作簡單的繪圖軟體或是高品質的相片處理軟體。 它支援為數眾多的外掛程式及指令稿 (script-fu) 介面。 The GIMP 可以讀寫許多檔案格式。 它也支援掃描器和手寫板。 要安裝套件可： # pkg install gimp 或使用 Ports 套件集安裝： # cd /usr/ports/graphics/gimp # make install clean 在 Ports 套件集的 graphics 分類 (freebsd.org/ports/graphics.html) 下也包含了許多 GIMP 相關的附加元件，說明檔及使用手冊。 6.3.4. Apache OpenOffice Apache OpenOffice 是開放原始碼的辦工室軟體，由 Apache Software Foundation's Incubator 底下的團隊所開發。 它包含了所有完整的辦公軟體組合： 文字處理器、試算表、簡報軟體還有繪圖軟體。 除了它的使用者介面非常類似其他的辦公軟體， 他還能夠輸入和輸出許多熱門的檔案格式。 它也包含了不同語言的使用者介面、拼字檢查和字典。 Apache OpenOffice 的文字處理器使用原生的 XML 檔案格式來增加移植性及彈性。 試算表程式支援巨集 (Macro) 功能而且能夠使用外來的資料庫介面。 Apache OpenOffice 已經十分穩定， 並且能夠在 Windows®, Solaris™, Linux®, FreeBSD 及 Mac OS® X 等作業系統上面執行。 想知道更多關於 Apache OpenOffice 的資訊可以在 openoffice.org 網頁上查詢。在 FreeBSD 特定的資訊可參考 porting.openoffice.org/freebsd/ 要安裝 Apache OpenOffice 套件： # pkg install apache-openoffice 當套件安裝完成之後，只要輸入下面的指令就能執行 Apache OpenOffice % openoffice-X.Y.Z 其中 X.Y.Z 是已安裝的 Apache OpenOffice 的版本編號。第一次執行 Apache OpenOffice 會詢問一些問題且會在使用者的家目錄建立一個 .openoffice.org 資料夾。 若無法由套件取得想要的 Apache OpenOffice，仍可選擇從 Port 編譯。 不過必須注意：編譯的過程會需要大量的磁碟空間與時間： # cd /usr/ports/editors/openoffice-4 # make install clean 注意: 如果想要編譯在地化的版本，將前面的指令替換成為： # make LOCALIZED_LANG=your_language install clean 替換 your_language 為正確的語言 ISO 編碼。支援的語言編碼清單在 files/Makefile.localized，位於該 Port 的目錄。 6.3.5. LibreOffice LibreOffice is a free software office suite developed by documentfoundation.org. It is compatible with other major office suites and available on a variety of platforms. It is a rebranded fork of Apache OpenOffice and includes applications found in a complete office productivity suite: a word processor, spreadsheet, presentation manager, drawing program, database management program, and a tool for creating and editing mathematical formulæ. It is available in a number of different languages and internationalization has been extended to interfaces, spell checkers, and dictionaries. The word processor of LibreOffice uses a native XML file format for increased portability and flexibility. The spreadsheet program features a macro language which can be interfaced with external databases. LibreOffice is stable and runs natively on Windows®, Linux®, FreeBSD, and Mac OS® X. More information about LibreOffice can be found at libreoffice.org. To install the English version of the LibreOffice package: # pkg install libreoffice The editors category (freebsd.org/ports/editors.html) of the Ports Collection contains several localizations for LibreOffice. When installing a localized package, replace libreoffice with the name of the localized package. Once the package is installed, type the following command to run LibreOffice: % libreoffice During the first launch, some questions will be asked and a .libreoffice folder will be created in the user's home directory. If the desired LibreOffice package is not available, compiling the port is still an option. However, this requires a lot of disk space and a fairly long time to compile. This example compiles the English version: # cd /usr/ports/editors/libreoffice # make install clean 注意: To build a localized version, cd into the port directory of the desired language. Supported languages can be found in the editors category (freebsd.org/ports/editors.html) of the Ports Collection. 6.4. 文件閱覽程式 Some new document formats have gained popularity since the advent of UNIX® and the viewers they require may not be available in the base system. This section demonstrates how to install the following document viewers: 應用程式名稱所需資源自 Ports 安裝時間主要相依套件 XpdfFreeType gvXaw3d GeeqieGtk+GNOME ePDFViewGtk+ OkularKDE 6.4.1. Xpdf 如果你想要一個小型的 FreeBSD PDF 閱覽軟體， Xpdf 是個輕量級而且有效率的閱覽器。 它只需要非常少的資源而且十分穩定。 它只使用標準的 X 字型且不需要額外的工具包(Toolkit)。 安裝 Xpdf 套件： # pkg install xpdf 若沒有可用的套件版本，可使用 Ports 套件集安裝： # cd /usr/ports/graphics/xpdf # make install clean 完成安裝後，執行 xpdf 並使用滑鼠右鍵開啟選單。 6.4.2. gv gvPostScript® 和 PDF 的閱覽器。 它建構於 ghostview 的基礎上，不過因為使用 Xaw3d 視窗元件工具包，所以外觀看起來比較漂亮。 gv 有許多可設定的功能，比如說紙張方向、紙張大小、縮放比例、和反鋸齒(Anti-aliasing)等。 而且幾乎所有的使用都可以從鍵盤或滑鼠來完成。 安裝 gv 套件： # pkg install gv 若沒有可用的套件版本，可使用 Ports 套件集安裝： # cd /usr/ports/print/gv # make install clean 6.4.3. Geeqie Geeqie 是由已經停止維護的 GQView 專案所衍伸出來的分支，並致力開發新功能並整合已有的修補。Geeqie 是一套影像管理軟體，支援單鍵閱覽檔案、啟動外部編輯器、縮圖預覽等功能。 它也有幻燈片模式及一些基本的檔案操作的功能，能輕鬆的管理大量影像並找出重複的檔案。 Geeqie 也支援使用全螢幕閱覽以及國際化。 安裝 Geeqie 套件： # pkg install geeqie 若沒有可用的套件版本，可使用 Ports 套件集安裝： # cd /usr/ports/graphics/geeqie # make install clean 6.4.4. ePDFView ePDFView is a lightweight PDF document viewer that only uses the Gtk+ and Poppler libraries. It is currently under development, but already opens most PDF files (even encrypted), save copies of documents, and has support for printing using CUPS. To install ePDFView as a package: # pkg install epdfview 若沒有可用的套件版本，可使用 Ports 套件集安裝： # cd /usr/ports/graphics/epdfview # make install clean 6.4.5. Okular Okular is a universal document viewer based on KPDF for KDE. It can open many document formats, including PDF, PostScript®, DjVu, CHM, XPS, and ePub. To install Okular as a package: # pkg install okular 若沒有可用的套件版本，可使用 Ports 套件集安裝： # cd /usr/ports/graphics/okular # make install clean 6.5. 財務 如果有任何理由你想要在你的 FreeBSD 桌面環境上管理你的個人財務， 這裡有一些功能強大、使用簡單的應用程式可供安裝。 這些財務管理軟體之中有些是相容於流行的 QuickenExcel 文件。 這節涵蓋了下面這些軟體： 應用程式名稱所需資源自 Ports 安裝時間主要相依套件 GnuCashGNOME GnumericGNOME KMyMoneyKDE 6.5.1. GnuCash GnuCashGNOME 團隊努力成果中的一部分， GNOME 團隊主要提供親切而強大的桌面應用程式給終端使用者。使用 GnuCash 可以持續追蹤記錄收入與花費、銀行帳戶以及股票證券等。 它的特性是介面直覺但功能仍非常專業。 GnuCash 提供了智慧的計數器、多階層帳戶系統以及快速鍵及自動完成功能。 它也能分開單一的報表至數個詳細的部份。 GnuCash 也能夠匯入及合併 Quicken QIF 檔案。 它也能處理大部分國際的日期及通用貨幣之格式。 安裝 GnuCash 套件： # pkg install gnucash 若沒有可用的套件版本，可使用 Ports 套件集安裝： # cd /usr/ports/finance/gnucash # make install clean 6.5.2. Gnumeric GnumericGNOME 社群所開發的試算表程式。 它的特點是擁有能夠根據儲存格格式 「猜出」使用者的輸入來自動補齊的系統。 它也能夠匯入許多熱門的檔案格式，像是 Excel, Lotus 1-2-3 以及 Quattro Pro。 它有大量內建的函數而且能夠使用常用的儲存格格式，像是：數字、貨幣、日期、時間及其他格式等。 安裝 Gnumeric 套件： # pkg install gnumeric 若沒有可用的套件版本，可使用 Ports 套件集安裝： # cd /usr/ports/math/gnumeric # make install clean 6.5.3. KMyMoney KMyMoney is a personal finance application created by the KDE community. KMyMoney aims to provide the important features found in commercial personal finance manager applications. It also highlights ease-of-use and proper double-entry accounting among its features. KMyMoney imports from standard Quicken QIF files, tracks investments, handles multiple currencies, and provides a wealth of reports. To install KMyMoney as a package: # pkg install kmymoney-kde4 若沒有可用的套件版本，可使用 Ports 套件集安裝： # cd /usr/ports/finance/kmymoney-kde4 # make install clean 章 7. 多媒體 Edited by . 7.1. 概述 FreeBSD 廣泛地支援各種音效卡， 讓您可以享受來自電腦上的高傳真音質(Hi-Fi)， 此外還包括了錄製和播放 MPEG Audio Layer 3 (MP3)、 Waveform Audio File (WAV)、Ogg Vorbis 以及其他許多種格式聲音的能力。同時 FreeBSD Ports 套件集也包含了許多可讓您可以錄音、編修音效以及控制 MIDI 配備的應用程式。 FreeBSD 也能播放一般的視訊檔和 DVD。 FreeBSD Ports 套件集中含有可編碼、轉換以及播放格種影像媒體的應用程式。 本章會說明如何設定 FreeBSD 上的音效卡、影像播放器、電視卡及掃描器。同時會說明有那些應用程式可以使用這些裝置。 讀完這章，您將了解： • 設定 FreeBSD 上的音效卡。 • 音效設定疑難排解。 • 播放、錄製 MP3 及其他聲音檔案格式。 • FreeBSD 系統播放影像的準備工具。 • 播放 DVD.mpg.avi 檔。 • 擷取(Rip) CDDVD的內容至檔案。 • 設定電視卡。 • 在 FreeBSD 安裝 MythTV 。 • 設定影像掃描機。 在開始閱讀這章之前，您需要︰ 7.2. 設定音效卡 Contributed by . Enhanced by . 開始設定之前，必須先知道你的音效卡型號、晶片為何。 FreeBSD 支援許多種音效卡，請檢查支援的音效硬體表 Hardware Notes，以確認你的音效卡是否支援以及如何在 FreeBSD 上驅動。 要使用音效裝置，必須要載入正確的驅動程式才行。最簡單方式就是以 kldload(8) 來載入核心模組。以下範例示範載入 Intel 規格內建的音效晶片驅動程式。 # kldload snd_hda 要開機時自動載入驅動程式，需將驅動程式加到 /boot/loader.conf 檔，以此驅動程式為例： snd_hda_load="YES" 其他可用的音效卡模組清單列於 /boot/defaults/loader.conf。當不確認要使用何種驅動程式時，可載入 snd_driver 模組： # kldload snd_driver 它是 metadriver 會載入所有最通用的音效驅動程式並且用來加速尋找正確的驅動程式。也可以把 metadriver 加入 /boot/loader.conf 檔來載入所有音效驅動程式。 要知道載入 snd_driver metadriver 後使用了那個音效卡驅動程式，請輸入 cat /dev/sndstat 7.2.1. 設定自訂核心支援音效 This section is for users who prefer to statically compile in support for the sound card in a custom kernel. For more information about recompiling a kernel, refer to 章 8, 設定 FreeBSD 核心. When using a custom kernel to provide sound support, make sure that the audio framework driver exists in the custom kernel configuration file: device sound Next, add support for the sound card. To continue the example of the built-in audio chipset based on the Intel specification from the previous section, use the following line in the custom kernel configuration file: device snd_hda Be sure to read the manual page of the driver for the device name to use for the driver. Non-PnP ISA sound cards may require the IRQ and I/O port settings of the card to be added to /boot/device.hints. During the boot process, loader(8) reads this file and passes the settings to the kernel. For example, an old Creative SoundBlaster® 16 ISA non-PnP card will use the snd_sbc(4) driver in conjunction with snd_sb16. For this card, the following lines must be added to the kernel configuration file: device snd_sbc device snd_sb16 If the card uses the 0x220 I/O port and IRQ 5, these lines must also be added to /boot/device.hints: hint.sbc.0.at="isa" hint.sbc.0.port="0x220" hint.sbc.0.irq="5" hint.sbc.0.drq="1" hint.sbc.0.flags="0x15" The syntax used in /boot/device.hints is described in sound(4) and the manual page for the driver of the sound card. The settings shown above are the defaults. In some cases, the IRQ or other settings may need to be changed to match the card. Refer to snd_sbc(4) for more information about this card. 7.2.2. 測試音效 After loading the required module or rebooting into the custom kernel, the sound card should be detected. To confirm, run dmesg | grep pcm. This example is from a system with a built-in Conexant CX20590 chipset: pcm0: <NVIDIA (0x001c) (HDMI/DP 8ch)> at nid 5 on hdaa0 pcm1: <NVIDIA (0x001c) (HDMI/DP 8ch)> at nid 6 on hdaa0 pcm2: <Conexant CX20590 (Analog 2.0+HP/2.0)> at nid 31,25 and 35,27 on hdaa1 The status of the sound card may also be checked using this command: # cat /dev/sndstat FreeBSD Audio Driver (newpcm: 64bit 2009061500/amd64) Installed devices: pcm0: <NVIDIA (0x001c) (HDMI/DP 8ch)> (play) pcm1: <NVIDIA (0x001c) (HDMI/DP 8ch)> (play) pcm2: <Conexant CX20590 (Analog 2.0+HP/2.0)> (play/rec) default The output will vary depending upon the sound card. If no pcm devices are listed, double-check that the correct device driver was loaded or compiled into the kernel. The next section lists some common problems and their solutions. If all goes well, the sound card should now work in FreeBSD. If the CD or DVD drive is properly connected to the sound card, one can insert an audio CD in the drive and play it with cdcontrol(1): % cdcontrol -f /dev/acd0 play 1 警告: Audio CDs have specialized encodings which means that they should not be mounted using mount(8). Various applications, such as audio/workman, provide a friendlier interface. The audio/mpg123 port can be installed to listen to MP3 audio files. Another quick way to test the card is to send data to /dev/dsp: % cat filename > /dev/dsp where filename can be any type of file. This command should produce some noise, confirming that the sound card is working. 注意: The /dev/dsp* device nodes will be created automatically as needed. When not in use, they do not exist and will not appear in the output of ls(1). 7.2.3. 疑難排解音效 表格 7.1, “常見錯誤訊息” lists some common error messages and their solutions: 表格 7.1. 常見錯誤訊息 錯誤解決方式 sb_dspwr(XX) timed out The I/O port is not set correctly. bad irq XX The IRQ is set incorrectly. Make sure that the set IRQ and the sound IRQ are the same. xxx: gus pcm not attached, out of memory There is not enough available memory to use the device. xxx: can't open /dev/dsp! Type fstat | grep dsp to check if another application is holding the device open. Noteworthy troublemakers are esound and KDE's sound support. Modern graphics cards often come with their own sound driver for use with HDMI. This sound device is sometimes enumerated before the sound card meaning that the sound card will not be used as the default playback device. To check if this is the case, run dmesg and look for pcm. The output looks something like this: ... hdac0: HDA Driver Revision: 20100226_0142 hdac1: HDA Driver Revision: 20100226_0142 hdac0: HDA Codec #0: NVidia (Unknown) hdac0: HDA Codec #1: NVidia (Unknown) hdac0: HDA Codec #2: NVidia (Unknown) hdac0: HDA Codec #3: NVidia (Unknown) pcm0: <HDA NVidia (Unknown) PCM #0 DisplayPort> at cad 0 nid 1 on hdac0 pcm1: <HDA NVidia (Unknown) PCM #0 DisplayPort> at cad 1 nid 1 on hdac0 pcm2: <HDA NVidia (Unknown) PCM #0 DisplayPort> at cad 2 nid 1 on hdac0 pcm3: <HDA NVidia (Unknown) PCM #0 DisplayPort> at cad 3 nid 1 on hdac0 hdac1: HDA Codec #2: Realtek ALC889 pcm4: <HDA Realtek ALC889 PCM #0 Analog> at cad 2 nid 1 on hdac1 pcm5: <HDA Realtek ALC889 PCM #1 Analog> at cad 2 nid 1 on hdac1 pcm6: <HDA Realtek ALC889 PCM #2 Digital> at cad 2 nid 1 on hdac1 pcm7: <HDA Realtek ALC889 PCM #3 Digital> at cad 2 nid 1 on hdac1 ... In this example, the graphics card (NVidia) has been enumerated before the sound card (Realtek ALC889). To use the sound card as the default playback device, change hw.snd.default_unit to the unit that should be used for playback: # sysctl hw.snd.default_unit=n where n is the number of the sound device to use. In this example, it should be 4. Make this change permanent by adding the following line to /etc/sysctl.conf: hw.snd.default_unit=4 7.2.4. 使用多個音效來源 Contributed by . It is often desirable to have multiple sources of sound that are able to play simultaneously. FreeBSD uses Virtual Sound Channels to multiplex the sound card's playback by mixing sound in the kernel. Three sysctl(8) knobs are available for configuring virtual channels: # sysctl dev.pcm.0.play.vchans=4 # sysctl dev.pcm.0.rec.vchans=4 # sysctl hw.snd.maxautovchans=4 This example allocates four virtual channels, which is a practical number for everyday use. Both dev.pcm.0.play.vchans=4 and dev.pcm.0.rec.vchans=4 are configurable after a device has been attached and represent the number of virtual channels pcm0 has for playback and recording. Since the pcm module can be loaded independently of the hardware drivers, hw.snd.maxautovchans indicates how many virtual channels will be given to an audio device when it is attached. Refer to pcm(4) for more information. 注意: The number of virtual channels for a device cannot be changed while it is in use. First, close any programs using the device, such as music players or sound daemons. The correct pcm device will automatically be allocated transparently to a program that requests /dev/dsp0. 7.2.5. 設定混音器頻道的預設值 Contributed by . The default values for the different mixer channels are hardcoded in the source code of the pcm(4) driver. While sound card mixer levels can be changed using mixer(8) or third-party applications and daemons, this is not a permanent solution. To instead set default mixer values at the driver level, define the appropriate values in /boot/device.hints, as seen in this example: hint.pcm.0.vol="50" This will set the volume channel to a default value of 50 when the pcm(4) module is loaded. 7.3. MP3 音樂 Contributed by . This section describes some MP3 players available for FreeBSD, how to rip audio CD tracks, and how to encode and decode MP3s. 7.3.1. MP3 播放器 A popular graphical MP3 player is XMMS. It supports Winamp skins and additional plugins. The interface is intuitive, with a playlist, graphic equalizer, and more. Those familiar with Winamp will find XMMS simple to use. On FreeBSD, XMMS can be installed from the multimedia/xmms port or package. The audio/mpg123 package or port provides an alternative, command-line MP3 player. Once installed, specify the MP3 file to play on the command line. If the system has multiple audio devices, the sound device can also be specifed: # mpg123 -a /dev/dsp1.0 Foobar-GreatestHits.mp3 High Performance MPEG 1.0/2.0/2.5 Audio Player for Layers 1, 2 and 3 version 1.18.1; written and copyright by Michael Hipp and others free software (LGPL) without any warranty but with best wishes Playing MPEG stream from Foobar-GreatestHits.mp3 ... MPEG 1.0 layer III, 128 kbit/s, 44100 Hz joint-stereo Additional MP3 players are available in the FreeBSD Ports Collection. 7.3.2. 擷取 CD 音軌 Before encoding a CD or CD track to MP3, the audio data on the CD must be ripped to the hard drive. This is done by copying the raw CD Digital Audio (CDDA) data to WAV files. The cdda2wav tool, which is installed with the sysutils/cdrtools suite, can be used to rip audio information from CDs. With the audio CD in the drive, the following command can be issued as root to rip an entire CD into individual, per track, WAV files: # cdda2wav -D 0,1,0 -B In this example, the -D 0,1,0 indicates the SCSI device 0,1,0 containing the CD to rip. Use cdrecord -scanbus to determine the correct device parameters for the system. To rip individual tracks, use -t to specify the track: # cdda2wav -D 0,1,0 -t 7 To rip a range of tracks, such as track one to seven, specify a range: # cdda2wav -D 0,1,0 -t 1+7 To rip from an ATAPI (IDE) CDROM drive, specify the device name in place of the SCSI unit numbers. For example, to rip track 7 from an IDE drive: # cdda2wav -D /dev/acd0 -t 7 Alternately, dd can be used to extract audio tracks on ATAPI drives, as described in 節 17.5.5, “複製音樂 CD. 7.3.3. MP3 編碼與解碼 Lame is a popular MP3 encoder which can be installed from the audio/lame port. Due to patent issues, a package is not available. The following command will convert the ripped WAV file audio01.wav to audio01.mp3: # lame -h -b 128 --tt "Foo Song Title" --ta "FooBar Artist" --tl "FooBar Album" \ --ty "2014" --tc "Ripped and encoded by Foo" --tg "Genre" audio01.wav audio01.mp3 The specified 128 kbits is a standard MP3 bitrate while the 160 and 192 bitrates provide higher quality. The higher the bitrate, the larger the size of the resulting MP3. The -h turns on the higher quality but a little slower mode. The options beginning with --t indicate ID3 tags, which usually contain song information, to be embedded within the MP3 file. Additional encoding options can be found in the lame manual page. In order to burn an audio CD from MP3s, they must first be converted to a non-compressed file format. XMMS can be used to convert to the WAV format, while mpg123 can be used to convert to the raw Pulse-Code Modulation (PCM) audio data format. To convert audio01.mp3 using mpg123, specify the name of the PCM file: # mpg123 -s audio01.mp3 > audio01.pcm To use XMMS to convert a MP3 to WAV format, use these steps: 過程 7.1. Converting to WAV Format in XMMS 1. Launch XMMS. 2. Right-click the window to bring up the XMMS menu. 3. Select Preferences under Options. 4. Change the Output Plugin to Disk Writer Plugin. 5. Press Configure. 6. Enter or browse to a directory to write the uncompressed files to. 7. Load the MP3 file into XMMS as usual, with volume at 100% and EQ settings turned off. 8. Press Play. The XMMS will appear as if it is playing the MP3, but no music will be heard. It is actually playing the MP3 to a file. 9. When finished, be sure to set the default Output Plugin back to what it was before in order to listen to MP3s again. Both the WAV and PCM formats can be used with cdrecord. When using WAV files, there will be a small tick sound at the beginning of each track. This sound is the header of the WAV file. The audio/sox port or package can be used to remove the header: % sox -t wav -r 44100 -s -w -c 2 track.wav track.raw Refer to 節 17.5, “建立與使用 CD 媒體” for more information on using a CD burner in FreeBSD. 7.4. 影片播放 Contributed by . Before configuring video playback, determine the model and chipset of the video card. While Xorg supports a wide variety of video cards, not all provide good playback performance. To obtain a list of extensions supported by the Xorg server using the card, run xdpyinfo while Xorg is running. It is a good idea to have a short MPEG test file for evaluating various players and options. Since some DVD applications look for DVD media in /dev/dvd by default, or have this device name hardcoded in them, it might be useful to make a symbolic link to the proper device: # ln -sf /dev/cd0 /dev/dvd Due to the nature of devfs(5), manually created links will not persist after a system reboot. In order to recreate the symbolic link automatically when the system boots, add the following line to /etc/devfs.conf: link cd0 dvd DVD decryption invokes certain functions that require write permission to the DVD device. To enhance the shared memory Xorg interface, it is recommended to increase the values of these sysctl(8) variables: kern.ipc.shmmax=67108864 kern.ipc.shmall=32768 7.4.1. 偵測影像處理能力 There are several possible ways to display video under Xorg and what works is largely hardware dependent. Each method described below will have varying quality across different hardware. Common video interfaces include: 1. Xorg: normal output using shared memory. 2. XVideo: an extension to the Xorg interface which allows video to be directly displayed in drawable objects through a special acceleration. This extension provides good quality playback even on low-end machines. The next section describes how to determine if this extension is running. 3. SDL: the Simple Directmedia Layer is a porting layer for many operating systems, allowing cross-platform applications to be developed which make efficient use of sound and graphics. SDL provides a low-level abstraction to the hardware which can sometimes be more efficient than the Xorg interface. On FreeBSD, SDL can be installed using the devel/sdl20 package or port. 4. DGA: the Direct Graphics Access is an Xorg extension which allows a program to bypass the Xorg server and directly alter the framebuffer. Because it relies on a low level memory mapping, programs using it must be run as root. The DGA extension can be tested and benchmarked using dga(1). When dga is running, it changes the colors of the display whenever a key is pressed. To quit, press q. 5. SVGAlib: a low level console graphics layer. 7.4.1.1. XVideo To check whether this extension is running, use xvinfo: % xvinfo XVideo is supported for the card if the result is similar to: X-Video Extension version 2.2 screen #0 Adaptor #0: "Savage Streams Engine" number of ports: 1 port base: 43 operations supported: PutImage supported visuals: depth 16, visualID 0x22 depth 16, visualID 0x23 number of attributes: 5 "XV_COLORKEY" (range 0 to 16777215) client settable attribute client gettable attribute (current value is 2110) "XV_BRIGHTNESS" (range -128 to 127) client settable attribute client gettable attribute (current value is 0) "XV_CONTRAST" (range 0 to 255) client settable attribute client gettable attribute (current value is 128) "XV_SATURATION" (range 0 to 255) client settable attribute client gettable attribute (current value is 128) "XV_HUE" (range -180 to 180) client settable attribute client gettable attribute (current value is 0) maximum XvImage size: 1024 x 1024 Number of image formats: 7 id: 0x32595559 (YUY2) guid: 59555932-0000-0010-8000-00aa00389b71 bits per pixel: 16 number of planes: 1 type: YUV (packed) id: 0x32315659 (YV12) guid: 59563132-0000-0010-8000-00aa00389b71 bits per pixel: 12 number of planes: 3 type: YUV (planar) id: 0x30323449 (I420) guid: 49343230-0000-0010-8000-00aa00389b71 bits per pixel: 12 number of planes: 3 type: YUV (planar) id: 0x36315652 (RV16) guid: 52563135-0000-0000-0000-000000000000 bits per pixel: 16 number of planes: 1 type: RGB (packed) depth: 0 red, green, blue masks: 0x1f, 0x3e0, 0x7c00 id: 0x35315652 (RV15) guid: 52563136-0000-0000-0000-000000000000 bits per pixel: 16 number of planes: 1 type: RGB (packed) depth: 0 red, green, blue masks: 0x1f, 0x7e0, 0xf800 id: 0x31313259 (Y211) guid: 59323131-0000-0010-8000-00aa00389b71 bits per pixel: 6 number of planes: 3 type: YUV (packed) id: 0x0 guid: 00000000-0000-0000-0000-000000000000 bits per pixel: 0 number of planes: 0 type: RGB (packed) depth: 1 red, green, blue masks: 0x0, 0x0, 0x0 The formats listed, such as YUV2 and YUV12, are not present with every implementation of XVideo and their absence may hinder some players. If the result instead looks like: X-Video Extension version 2.2 screen #0 no adaptors present XVideo is probably not supported for the card. This means that it will be more difficult for the display to meet the computational demands of rendering video, depending on the video card and processor. 7.4.2. 可處理影像的 Ports 與套件 This section introduces some of the software available from the FreeBSD Ports Collection which can be used for video playback. 7.4.2.1. MPlayer 與 MEncoder MPlayer is a command-line video player with an optional graphical interface which aims to provide speed and flexibility. Other graphical front-ends to MPlayer are available from the FreeBSD Ports Collection. MPlayer can be installed using the multimedia/mplayer package or port. Several compile options are available and a variety of hardware checks occur during the build process. For these reasons, some users prefer to build the port rather than install the package. When compiling the port, the menu options should be reviewed to determine the type of support to compile into the port. If an option is not selected, MPlayer will not be able to display that type of video format. Use the arrow keys and spacebar to select the required formats. When finished, press Enter to continue the port compile and installation. By default, the package or port will build the mplayer command line utility and the gmplayer graphical utility. To encode videos, compile the multimedia/mencoder port. Due to licensing restrictions, a package is not available for MEncoder. The first time MPlayer is run, it will create ~/.mplayer in the user's home directory. This subdirectory contains default versions of the user-specific configuration files. This section describes only a few common uses. Refer to mplayer(1) for a complete description of its numerous options. To play the file testfile.avi, specify the video interfaces with -vo, as seen in the following examples: % mplayer -vo xv testfile.avi % mplayer -vo sdl testfile.avi % mplayer -vo x11 testfile.avi # mplayer -vo dga testfile.avi # mplayer -vo 'sdl:dga' testfile.avi It is worth trying all of these options, as their relative performance depends on many factors and will vary significantly with hardware. To play a DVD, replace testfile.avi with dvd://N -dvd-device DEVICE, where N is the title number to play and DEVICE is the device node for the DVD. For example, to play title 3 from /dev/dvd: # mplayer -vo xv dvd://3 -dvd-device /dev/dvd 注意: The default DVD device can be defined during the build of the MPlayer port by including the WITH_DVD_DEVICE=/path/to/desired/device option. By default, the device is /dev/cd0. More details can be found in the port's Makefile.options. To stop, pause, advance, and so on, use a keybinding. To see the list of keybindings, run mplayer -h or read mplayer(1). Additional playback options include -fs -zoom, which engages fullscreen mode, and -framedrop, which helps performance. Each user can add commonly used options to their ~/.mplayer/config like so: vo=xv fs=yes zoom=yes mplayer can be used to rip a DVD title to a .vob. To dump the second title from a DVD: # mplayer -dumpstream -dumpfile out.vob dvd://2 -dvd-device /dev/dvd The output file, out.vob, will be in MPEG format. Anyone wishing to obtain a high level of expertise with UNIX® video should consult mplayerhq.hu/DOCS as it is technically informative. This documentation should be considered as required reading before submitting any bug reports. Before using mencoder, it is a good idea to become familiar with the options described at mplayerhq.hu/DOCS/HTML/en/mencoder.html. There are innumerable ways to improve quality, lower bitrate, and change formats, and some of these options may make the difference between good or bad performance. Improper combinations of command line options can yield output files that are unplayable even by mplayer. Here is an example of a simple copy: % mencoder input.avi -oac copy -ovc copy -o output.avi To rip to a file, use -dumpfile with mplayer. To convert input.avi to the MPEG4 codec with MPEG3 audio encoding, first install the audio/lame port. Due to licensing restrictions, a package is not available. Once installed, type: % mencoder input.avi -oac mp3lame -lameopts br=192 \ -ovc lavc -lavcopts vcodec=mpeg4:vhq -o output.avi This will produce output playable by applications such as mplayer and xine. input.avi can be replaced with dvd://1 -dvd-device /dev/dvd and run as root to re-encode a DVD title directly. Since it may take a few tries to get the desired result, it is recommended to instead dump the title to a file and to work on the file. 7.4.2.2. xine 影像播放器 xine is a video player with a reusable base library and a modular executable which can be extended with plugins. It can be installed using the multimedia/xine package or port. In practice, xine requires either a fast CPU with a fast video card, or support for the XVideo extension. The xine video player performs best on XVideo interfaces. By default, the xine player starts a graphical user interface. The menus can then be used to open a specific file. Alternatively, xine may be invoked from the command line by specifying the name of the file to play: % xine -g -p mymovie.avi Refer to xine-project.org/faq for more information and troubleshooting tips. 7.4.2.3. Transcode 工具 Transcode provides a suite of tools for re-encoding video and audio files. Transcode can be used to merge video files or repair broken files using command line tools with stdin/stdout stream interfaces. In FreeBSD, Transcode can be installed using the multimedia/transcode package or port. Many users prefer to compile the port as it provides a menu of compile options for specifying the support and codecs to compile in. If an option is not selected, Transcode will not be able to encode that format. Use the arrow keys and spacebar to select the required formats. When finished, press Enter to continue the port compile and installation. This example demonstrates how to convert a DivX file into a PAL MPEG-1 file (PAL VCD): % transcode -i input.avi -V --export_prof vcd-pal -o output_vcd % mplex -f 1 -o output_vcd.mpg output_vcd.m1v output_vcd.mpa The resulting MPEG file, output_vcd.mpg, is ready to be played with MPlayer. The file can be burned on a CD media to create a video CD using a utility such as multimedia/vcdimager or sysutils/cdrdao. In addition to the manual page for transcode, refer to transcoding.org/cgi-bin/transcode for further information and examples. 7.5. 電視卡 Original contribution by . Enhanced and adapted by . 電視卡(TV card)可以讓您用電腦來看無線、有線電視節目。許多卡都是透過 RCA 或 S-video 輸入端子來接收視訊，而且有些卡還可接收 FM 廣播的功能。 FreeBSD 可透過 bktr(4) 驅動程式，來支援 PCI 介面的電視卡，只要這些卡使用的是 Brooktree Bt848/849/878/879 或 Conexant CN-878/Fusion 878a 視訊擷取晶片。此外，要再確認哪些卡上所附的選台功能是否有支援，可以參考 bktr(4) 說明，以查看所支援的硬體清單。 7.5.1. 載入驅動程式 要用電視卡的話，就要載入 bktr(4) 驅動程式，這個可以透過在 /boot/loader.conf 檔加上下面這一行就可以了： bktr_load="YES" 或者可以將電視卡支援靜態編譯到自訂的核心當中，若要這麼做則可在自訂核心設定檔加入以下行： device bktr device iicbus device iicbb device smbus 之所以要加上這些額外的驅動程式，是因為卡的各組成部分都是透過 I2C 匯流排而相互連接的。接下來，請編譯、安裝新的核心 。 要測試調諧器 (Tuner) 是否被正確的偵測，請先重新啟動系統。電視卡應該會出現在開機訊息檔中，如同此範例： bktr0: <BrookTree 848A> mem 0xd7000000-0xd7000fff irq 10 at device 10.0 on pci0 iicbb0: <I2C bit-banging driver> on bti2c0 iicbus0: <Philips I2C bus> on iicbb0 master-only iicbus1: <Philips I2C bus> on iicbb0 master-only smbus0: <System Management Bus> on bti2c0 bktr0: Pinnacle/Miro TV, Philips SECAM tuner. 該訊息會依硬體不同而有所不同。若必要，可以使用 sysctl(8) 系統偵測的參數或者自訂核心設定選項。例如要強制使用 Philips SECAM 調諧器則可加入下列行至自訂核心設定檔： options OVERRIDE_TUNER=6 或使用 sysctl(8) # sysctl hw.bt848.tuner=6 請參考 bktr(4) 查看 sysctl(8) 可用的參數說明及核心選項。 7.5.2. 好用的應用程式 To use the TV card, install one of the following applications: • multimedia/fxtv provides TV-in-a-window and image/audio/video capture capabilities. • multimedia/xawtv is another TV application with similar features. • audio/xmradio provides an application for using the FM radio tuner of a TV card. More applications are available in the FreeBSD Ports Collection. 7.5.3. 疑難排解 If any problems are encountered with the TV card, check that the video capture chip and the tuner are supported by bktr(4) and that the right configuration options were used. For more support or to ask questions about supported TV cards, refer to the freebsd-multimedia mailing list. 7.6. MythTV MythTV is a popular, open source Personal Video Recorder (PVR) application. This section demonstrates how to install and setup MythTV on FreeBSD. Refer to mythtv.org/wiki for more information on how to use MythTV. MythTV requires a frontend and a backend. These components can either be installed on the same system or on different machines. The frontend can be installed on FreeBSD using the multimedia/mythtv-frontend package or port. Xorg must also be installed and configured as described in 章 5, X Window 系統. Ideally, this system has a video card that supports X-Video Motion Compensation (XvMC) and, optionally, a Linux Infrared Remote Control (LIRC)-compatible remote. To install both the backend and the frontend on FreeBSD, use the multimedia/mythtv package or port. A MySQL™ database server is also required and should automatically be installed as a dependency. Optionally, this system should have a tuner card and sufficient storage to hold recorded data. 7.6.1. 硬體 MythTV uses Video for Linux (V4L) to access video input devices such as encoders and tuners. In FreeBSD, MythTV works best with USB DVB-S/C/T cards as they are well supported by the multimedia/webcamd package or port which provides a V4L userland application. Any Digital Video Broadcasting (DVB) card supported by webcamd should work with MythTV. A list of known working cards can be found at wiki.freebsd.org/WebcamCompat. Drivers are also available for Hauppauge cards in the multimedia/pvr250 and multimedia/pvrxxx ports, but they provide a non-standard driver interface that does not work with versions of MythTV greater than 0.23. Due to licensing restrictions, no packages are available and these two ports must be compiled. The wiki.freebsd.org/HTPC page contains a list of all available DVB drivers. 7.6.2. 設定 MythTV 後端 To install MythTV using the port: # cd /usr/ports/multimedia/mythtv # make install Once installed, set up the MythTV database: # mysql -uroot -p < /usr/local/share/mythtv/database/mc.sql Then, configure the backend: # mythtv-setup Finally, start the backend: # echo 'mythbackend_enable="YES"' >> /etc/rc.conf # service mythbackend start 7.7. 影像掃描器 Written by . In FreeBSD, access to image scanners is provided by SANE (Scanner Access Now Easy), which is available in the FreeBSD Ports Collection. SANE will also use some FreeBSD device drivers to provide access to the scanner hardware. FreeBSD supports both SCSI and USB scanners. Depending upon the scanner interface, different device drivers are required. Be sure the scanner is supported by SANE prior to performing any configuration. Refer to http://www.sane-project.org/sane-supported-devices.html for more information about supported scanners. This chapter describes how to determine if the scanner has been detected by FreeBSD. It then provides an overview of how to configure and use SANE on a FreeBSD system. 7.7.1. 檢查掃描器 The GENERIC kernel includes the device drivers needed to support USB scanners. Users with a custom kernel should ensure that the following lines are present in the custom kernel configuration file: device usb device uhci device ohci device ehci To determine if the USB scanner is detected, plug it in and use dmesg to determine whether the scanner appears in the system message buffer. If it does, it should display a message similar to this: ugen0.2: <EPSON> at usbus0 In this example, an EPSON Perfection® 1650 USB scanner was detected on /dev/ugen0.2. If the scanner uses a SCSI interface, it is important to know which SCSI controller board it will use. Depending upon the SCSI chipset, a custom kernel configuration file may be needed. The GENERIC kernel supports the most common SCSI controllers. Refer to /usr/src/sys/conf/NOTES to determine the correct line to add to a custom kernel configuration file. In addition to the SCSI adapter driver, the following lines are needed in a custom kernel configuration file: device scbus device pass Verify that the device is displayed in the system message buffer: pass2 at aic0 bus 0 target 2 lun 0 pass2: <AGFA SNAPSCAN 600 1.10> Fixed Scanner SCSI-2 device pass2: 3.300MB/s transfers If the scanner was not powered-on at system boot, it is still possible to manually force detection by performing a SCSI bus scan with camcontrol: # camcontrol rescan all Re-scan of bus 0 was successful Re-scan of bus 1 was successful Re-scan of bus 2 was successful Re-scan of bus 3 was successful The scanner should now appear in the SCSI devices list: # camcontrol devlist <IBM DDRS-34560 S97B> at scbus0 target 5 lun 0 (pass0,da0) <IBM DDRS-34560 S97B> at scbus0 target 6 lun 0 (pass1,da1) <AGFA SNAPSCAN 600 1.10> at scbus1 target 2 lun 0 (pass3) <PHILIPS CDD3610 CD-R/RW 1.00> at scbus2 target 0 lun 0 (pass2,cd0) Refer to scsi(4) and camcontrol(8) for more details about SCSI devices on FreeBSD. 7.7.2. SANE 設定 The SANE system is split in two parts: the backends (graphics/sane-backends) and the frontends (graphics/sane-frontends or graphics/xsane). The backends provide access to the scanner. Refer to http://www.sane-project.org/sane-supported-devices.html to determine which backend supports the scanner. The frontends provide the graphical scanning interface. graphics/sane-frontends installs xscanimage while graphics/xsane installs xsane. After installing the graphics/sane-backends port or package, use sane-find-scanner to check the scanner detection by the SANE system: # sane-find-scanner -q found SCSI scanner "AGFA SNAPSCAN 600 1.10" at /dev/pass3 The output should show the interface type of the scanner and the device node used to attach the scanner to the system. The vendor and the product model may or may not appear. 注意: Some USB scanners require firmware to be loaded. Refer to sane-find-scanner(1) and sane(7) for details. Next, check if the scanner will be identified by a scanning frontend. The SANE backends include scanimage which can be used to list the devices and perform an image acquisition. Use -L to list the scanner devices. The first example is for a SCSI scanner and the second is for a USB scanner: # scanimage -L device snapscan:/dev/pass3' is a AGFA SNAPSCAN 600 flatbed scanner # scanimage -L device 'epson2:libusb:/dev/usb:/dev/ugen0.2' is a Epson GT-8200 flatbed scanner In this second example, 'epson2:libusb:/dev/usb:/dev/ugen0.2' is the backend name (epson2) and /dev/ugen0.2 is the device node used by the scanner. If scanimage is unable to identify the scanner, this message will appear: # scanimage -L No scanners were identified. If you were expecting something different, check that the scanner is plugged in, turned on and detected by the sane-find-scanner tool (if appropriate). Please read the documentation which came with this software (README, FAQ, manpages). If this happens, edit the backend configuration file in /usr/local/etc/sane.d/ and define the scanner device used. For example, if the undetected scanner model is an EPSON Perfection® 1650 and it uses the epson2 backend, edit /usr/local/etc/sane.d/epson2.conf. When editing, add a line specifying the interface and the device node used. In this case, add the following line: usb /dev/ugen0.2 Save the edits and verify that the scanner is identified with the right backend name and the device node: # scanimage -L device 'epson2:libusb:/dev/usb:/dev/ugen0.2' is a Epson GT-8200 flatbed scanner Once scanimage -L sees the scanner, the configuration is complete and the scanner is now ready to use. While scanimage can be used to perform an image acquisition from the command line, it is often preferable to use a graphical interface to perform image scanning. The graphics/sane-frontends package or port installs a simple but efficient graphical interface, xscanimage. Alternately, xsane, which is installed with the graphics/xsane package or port, is another popular graphical scanning frontend. It offers advanced features such as various scanning modes, color correction, and batch scans. Both of these applications are usable as a GIMP plugin. 7.7.3. 掃描器權限 In order to have access to the scanner, a user needs read and write permissions to the device node used by the scanner. In the previous example, the USB scanner uses the device node /dev/ugen0.2 which is really a symlink to the real device node /dev/usb/0.2.0. The symlink and the device node are owned, respectively, by the wheel and operator groups. While adding the user to these groups will allow access to the scanner, it is considered insecure to add a user to wheel. A better solution is to create a group and make the scanner device accessible to members of this group. This example creates a group called usb: # pw groupadd usb Then, make the /dev/ugen0.2 symlink and the /dev/usb/0.2.0 device node accessible to the usb group with write permissions of 0660 or 0664 by adding the following lines to /etc/devfs.rules: [system=5] add path ugen0.2 mode 0660 group usb add path usb/0.2.0 mode 0666 group usb Finally, add the users to usb in order to allow access to the scanner: # pw groupmod usb -m joe For more details refer to pw(8). 章 8. 設定 FreeBSD 核心 8.1. 概述 核心 (Kernel) 是 FreeBSD 作業系統最重要的部份之一。它負責記憶體管理、安全控管、網路、硬碟存取等等。 儘管目前 FreeBSD 大多可以用動態設定， 但有時仍需要設定並編譯自訂的核心。 讀完這章，您將了解︰ • 何時需要編譯自訂核心。 • 如何取得硬體資訊。 • 如何量身訂做核心設定檔。 • 如何使用核心設定檔來建立並編譯新的核心。 • 如何安裝新的核心。 • 發生錯誤時如何排除問題。 所有在本章所列出的指令均應以 root 來執行。 8.2. 為何要編譯自訂的核心? 早期的 FreeBSD 的核心 (Kernel) 被戲稱為 “巨石”。因為當時的核心是一個非常大的程式，且只支援固定的硬體裝置，如果您想改變核心的設定，就必須編譯一個新核心並重新開機，才能使用。 現在，大多數在 FreeBSD 核心的功能已採用模組 (Module) 的方式包裝，可以依據需求動態在核心載入或卸載。 這使得核心能夠快速採用新硬體環境的新功能，就叫做模組化核心 (Modular Kernel)。 儘管如此，還是有一些功能因使用到靜態的核心設定須要編譯，因為這些功能與核心緊密結合，無法將做成可動態載入的模組。且部份強調安全性的環境會盡量避免載入與卸載核心模組，且只要將需要的功能靜態的編譯到核心當中。 編譯自訂的核心幾乎是每位進階的 BSD 使用者所必須經歷的過程。儘管這項工作可能比較耗時，但在 FreeBSD 的使用上會有許多好處。 跟必須支援大多數各式硬體的 GENERIC 核心相比的話， 自訂的核心可以更『體貼』，只支援『自己硬體』的部分就好。 自訂核心有許多項優點，如︰ • 加速開機，因為自訂的核心只需要偵測您系統上存在的硬體，所以讓啟動所花的過程更流暢快速。 • 減少記憶體使用，自訂的核心通常會比 GENERIC 核心使用更少的記憶體，這很重要，因為核心必須一直存放在實體記憶體內，會讓其他應用程式無法使用。因此，自訂核心對於記憶體較小的系統來說，發揮很大的作用。 • 支援額外的硬體，自訂的核心可以增加一些 GENERIC 核心沒有提供的硬體支援。 Before building a custom kernel, consider the reason for doing so. If there is a need for specific hardware support, it may already exist as a module. Kernel modules exist in /boot/kernel and may be dynamically loaded into the running kernel using kldload(8). Most kernel drivers have a loadable module and manual page. For example, the ath(4) wireless Ethernet driver has the following information in its manual page: Alternatively, to load the driver as a module at boot time, place the following line in loader.conf(5): if_ath_load="YES" Adding if_ath_load="YES" to /boot/loader.conf will load this module dynamically at boot time. In some cases, there is no associated module in /boot/kernel. This is mostly true for certain subsystems. 8.3. 偵測系統硬體 在編輯核心設定檔之前，建議先調查清楚機器各項硬體資訊。在雙作業系統的環境，也可透過其他作業系統來了解目前機器上的硬體資訊。 舉例來說，Microsoft® 的 裝置管理員 (Device Manager) 內會有目前已安裝的硬體資訊。 注意: 某些版本的 Microsoft® Windows® 會有系統 (System) 圖示可用來進入 裝置管理員 若 FreeBSD 是唯一安裝的作業系統，則可使用 dmesg(8) 來查看開時時系統偵測到的硬體資訊 。FreeBSD 上大多硬體驅動程式都有操作手冊會列出支援的硬體。例如，以下幾行是說 psm(4) 驅動程式偵測到了一隻滑鼠： psm0: <PS/2 Mouse> irq 12 on atkbdc0 psm0: [GIANT-LOCKED] psm0: [ITHREAD] psm0: model Generic PS/2 mouse, device ID 0 因為該硬體存在，此驅動程式便不應該從自訂核心設定檔中移除。 dmesg 輸出的結果未顯示開機偵測硬體的部份，則可改閱讀 /var/run/dmesg.boot 檔案的內容。 另外，也可以透過 pciconf(8) 工具可用來查詢硬體資訊，該工具會列出更詳細的硬體資訊如： % pciconf -lv ath0@pci0:3:0:0: class=0x020000 card=0x058a1014 chip=0x1014168c rev=0x01 hdr=0x00 vendor = 'Atheros Communications Inc.' device = 'AR5212 Atheros AR5212 802.11abg wireless' class = network subclass = ethernet 以上輸出資訊說明 ath 驅動程式已經找到一個無線乙太網路裝置。 man(1) 指令加上 -k 參數，可提供有用的資訊，例如，列出有包含指定關鍵字的手冊頁面清單： # man -k Atheros ath(4) - Atheros IEEE 802.11 wireless network driver ath_hal(4) - Atheros Hardware Access Layer (HAL) 準備好硬體清單之後，參考該清單來確認已安裝的硬體驅動程式在編輯自訂核心設定時沒有被移除。 8.4. 設定檔 為了要建立自訂核心設定檔並編譯自訂核心，必須先安裝完整的 FreeBSD 原始碼樹。 /usr/src/ 目錄不存在或者是空的，代表尚未安裝。原始碼可以使用 Subversion 並依據 節 A.3, “使用 Subversion 中的操作說明來安裝。 完成原始碼完成後，需檢查 /usr/src/sys 內的檔案。該目錄內包含數個子目錄，這些子目錄中包了支援的硬體架構 (Architecture) 如下：amd64, i386, ia64, pc98, powerpc 以及 sparc64。在指定架構目錄中的內容只對該架構有效，其餘部份的程式碼與硬體架構無關，可通用所有平台。每個支援的硬體架構中會有 conf 子目錄，裡面含有供該架構使用的 GENERIC 核心設定檔。 請不要直接對 GENERIC 檔案做編輯。複製該檔案為另一個名稱，並對複製出來的檔案做編輯，習慣上檔名會全部使用大寫字元。當維護多台安裝不同的硬體的 FreeBSD 機器時，將檔名後方加上機器的主機名稱 (Host name) 是個不錯的方法。以下範例使用 amd64 架構的 GENERIC 設定檔建立了一個複本名稱為 MYKERNEL # cd /usr/src/sys/amd64/conf # cp GENERIC MYKERNEL 現在可以使用任何 ASCII 文字編輯器來自訂 MYKERNEL。預設的編輯器為 vi，在 FreeBSD 也內建一個易於初學者使用的編輯器叫做 ee 核心設定檔的格式很簡單，每一行會含有代表裝置 (Device) 或子系統 (Subsystem) 的關鍵字、參數以及簡短的說明。任何在 # 符號之後的文字會被當做註解並且略過。要移除核心對某個裝置或子系統的支援，僅需要在代表該裝置或子系統的行前加上 # 符號。請不要在您還不了解用途的行前加上或移除 # 符號。 警告: 移除對裝置或選項的支援很容易會造成核心損壞。例如，若從核心設定檔 ata(4) 驅動程式，那麼使用 ATA 磁碟驅動程式的系統便會無法開機。因此當您不確定時，請在核心保留該項目的支援。 除了在設定檔中提供的簡短說明之外，尚有其他的說明在 NOTES 檔案中，可在與該架構 GENERIC 相同的目錄底下找到。要查看所有架構通用的選項，請參考 /usr/src/sys/conf/NOTES 提示: 當完成自訂的核心設定檔，請備份到 /usr/src 位置之外。 或者，將核心設定檔放在其他地方，然後建立一個符號連結 (Symbolic link) 至該檔案： # cd /usr/src/sys/amd64/conf # mkdir /root/kernels # cp GENERIC /root/kernels/MYKERNEL # ln -s /root/kernels/MYKERNEL 設定檔中可以使用 include 指令 (Directive)。該指令可以引用其他設定檔到目前的設定檔，這讓只需根據現有檔案設定做些微調整時更簡單。若只有少量的額外選項或驅動程式需要設定，該指令可引用 GENERIC 並設定額外增加的選項，如範例所示： include GENERIC ident MYKERNEL options IPFIREWALL options DUMMYNET options IPFIREWALL_DEFAULT_TO_ACCEPT options IPDIVERT 使用此方法，設定檔只含有與 GENERIC 核心不同的部份。當升級有新功能加入 GENERIC 時，也可一併引用，除非特別使用 nooptionsnodevice 選項來排除設定。更詳細的設定檔指令及其說明可在 config(5) 找到。 注意: 要產生含有所有可用選項的設定檔，可以 root 執行以下指令： # cd /usr/src/sys/arch/conf && make LINT 8.5. 編譯與安裝自訂核心 完成自訂設定檔的編輯並儲存之後，便可依據以下步驟編譯核心的原始碼： 過程 8.1. 編譯核心 1. 切換至此目錄： # cd /usr/src 2. 指定自訂核心設定檔的名稱來編譯新的核心： # make buildkernel KERNCONF=MYKERNEL 3. 安裝使用指定核心設定檔所編譯的新核心。此指令將會複製新核心到 /boot/kernel/kernel 並將舊核心備份到 /boot/kernel.old/kernel # make installkernel KERNCONF=MYKERNEL 4. 關機並重新開機載入新的核心，若發生錯誤請參考 無法使用核心開機 預設在自訂核心編譯完成後，所有核心模組也同被重新編譯。要快速更新核心或只編譯自訂的模組，需在開始編譯之前先編輯 /etc/make.conf 例如，使用以下變數可指定要編譯的模組清單來替代預設編譯所有模組的設定： MODULES_OVERRIDE = linux acpi 或者，可使用以下變數來從編譯程序中排除要編譯的模組： WITHOUT_MODULES = linux acpi sound 尚有其他可用的變數，請參考 make.conf(5) 取得詳細資訊。 8.6. 如果發生錯誤 當編譯自訂核心時可能發生以下四種類型的問題： config 失敗 config 失敗，會列出不正確的行號。使用以下訊息為例子，需要與 GENERICNOTES 比對來確認第 17 行輸入的內容正確： config: line 17: syntax error make 失敗 make 失敗，通常是因為核心設定檔未提供足夠的資訊讓 config 找到問題。請仔細檢查設定檔，若仍不清楚問題，請寄發電子郵件給 FreeBSD general questions mailing list 並附上核心設定檔。 無法使用核心開機 若新核心無法開機或無法辨識裝置並不要恐慌！幸好，FreeBSD 有良好的機制可以從不相容的核心復原。只需要在 FreeBSD 開機載入程式 (Boot loader) 選擇要用來開機的核心便可，當系統開機選單出現時選擇 Escape to a loader prompt 選項，並在指令提示後輸入 boot kernel.old 或替換為任何其他已經知道可以正常開機的核心名稱。 使用好的核心開機之後，檢查設定檔並嘗試再編譯一次。/var/log/messages 是有用的資源，它在每次成功開機時會記錄核心訊息。同樣的，dmesg(8) 也會印出自本次開機後的核心訊息。 注意: 在排除核心問題時，請確定留有 GENERIC 的複本，或者其他已知可以運作的核心，並使用不同的名稱來確保下次編譯時不會被刪除，這很重要，因此每當新的核心被安裝之後，kernel.old 都會被最後安裝的核心覆寫，有可能會無法開機。盡快，透過重新命名將可運作的核心目錄移動到目前運作的核心目錄。 # mv /boot/kernel /boot/kernel.bad # mv /boot/kernel.good /boot/kernel 核心可運作，但 ps(1) 無法運作 若核心版本與系統工具所編譯的版本不同，例如，有一個核心使用 -CURRENT 的原始碼編譯並安裝在 -RELEASE 的系統上，許多系統狀態指令如 ps(1)vmstat(8) 將會無法運作。要修正此問題，請使用與核心相同版本的原始碼樹 (Source tree) 重新編譯並安裝 World。使用與作業系統其他部份版本不同的核心永遠不會是個好主意。 章 9. 列印 Originally contributed by . Putting information on paper is a vital function, despite many attempts to eliminate it. Printing has two basic components. The data must be delivered to the printer, and must be in a form that the printer can understand. 9.1. 快速開始 Basic printing can be set up quickly. The printer must be capable of printing plain ASCII text. For printing to other types of files, see 節 9.5.3, “過濾器”. 1. Create a directory to store files while they are being printed: # mkdir -p /var/spool/lpd/lp # chown daemon:daemon /var/spool/lpd/lp # chmod 770 /var/spool/lpd/lp 2. As root, create /etc/printcap with these contents: lp:\ :lp=/dev/unlpt0:\ :sh:\ :mx#0:\ :sd=/var/spool/lpd/lp:\ :lf=/var/log/lpd-errs: This line is for a printer connected to a USB port.For a printer connected to a parallel or “printer” port, use::lp=/dev/lpt0:\For a printer connected directly to a network, use::lp=:rm=network-printer-name:rp=raw:\Replace network-printer-name with the DNS host name of the network printer. 3. Enable lpd by editing /etc/rc.conf, adding this line: lpd_enable="YES" Start the service: # service lpd start Starting lpd. 4. Print a test: # printf "1. This printer can print.\n2. This is the second line.\n" | lpr 提示: If both lines do not start at the left border, but stairstep instead, see 節 9.5.3.1, “避免在純文字印表機階梯狀列印”. Text files can now be printed with lpr. Give the filename on the command line, or pipe output directly into lpr. % lpr textfile.txt % ls -lh | lpr 9.2. 印表機連線 Printers are connected to computer systems in a variety of ways. Small desktop printers are usually connected directly to a computer's USB port. Older printers are connected to a parallel or printer port. Some printers are directly connected to a network, making it easy for multiple computers to share them. A few printers use a rare serial port connection. FreeBSD can communicate with all of these types of printers. USB USB printers can be connected to any available USB port on the computer. When FreeBSD detects a USB printer, two device entries are created: /dev/ulpt0 and /dev/unlpt0. Data sent to either device will be relayed to the printer. After each print job, ulpt0 resets the USB port. Resetting the port can cause problems with some printers, so the unlpt0 device is usually used instead. unlpt0 does not reset the USB port at all. Parallel (IEEE-1284) The parallel port device is /dev/lpt0. This device appears whether a printer is attached or not, it is not autodetected. Vendors have largely moved away from these legacy ports, and many computers no longer have them. Adapters can be used to connect a parallel printer to a USB port. With such an adapter, the printer can be treated as if it were actually a USB printer. Devices called print servers can also be used to connect parallel printers directly to a network. Serial (RS-232) Serial ports are another legacy port, rarely used for printers except in certain niche applications. Cables, connectors, and required wiring vary widely. For serial ports built into a motherboard, the serial device name is /dev/cuau0 or /dev/cuau1. Serial USB adapters can also be used, and these will appear as /dev/cuaU0. Several communication parameters must be known to communicate with a serial printer. The most important are baud rate or BPS (Bits Per Second) and parity. Values vary, but typical serial printers use a baud rate of 9600 and no parity. Network Network printers are connected directly to the local computer network. The DNS hostname of the printer must be known. If the printer is assigned a dynamic address by DHCP, DNS should be dynamically updated so that the host name always has the correct IP address. Network printers are often given static IP addresses to avoid this problem. Most network printers understand print jobs sent with the LPD protocol. A print queue name can also be specified. Some printers process data differently depending on which queue is used. For example, a raw queue prints the data unchanged, while the text queue adds carriage returns to plain text. Many network printers can also print data sent directly to port 9100. 9.2.1. 摘要 Wired network connections are usually the easiest to set up and give the fastest printing. For direct connection to the computer, USB is preferred for speed and simplicity. Parallel connections work but have limitations on cable length and speed. Serial connections are more difficult to configure. Cable wiring differs between models, and communication parameters like baud rate and parity bits must add to the complexity. Fortunately, serial printers are rare. 9.3. 常見的頁面描述語言 Data sent to a printer must be in a language that the printer can understand. These languages are called Page Description Languages, or PDLs. ASCII Plain ASCII text is the simplest way to send data to a printer. Characters correspond one to one with what will be printed: an A in the data prints an A on the page. Very little formatting is available. There is no way to select a font or proportional spacing. The forced simplicity of plain ASCII means that text can be printed straight from the computer with little or no encoding or translation. The printed output corresponds directly with what was sent. Some inexpensive printers cannot print plain ASCII text. This makes them more difficult to set up, but it is usually still possible. PostScript® PostScript® is almost the opposite of ASCII. Rather than simple text, a PostScript® program is a set of instructions that draw the final document. Different fonts and graphics can be used. However, this power comes at a price. The program that draws the page must be written. Usually this program is generated by application software, so the process is invisible to the user. Inexpensive printers sometimes leave out PostScript® compatibility as a cost-saving measure. PCL (Printer Command Language) PCL is an extension of ASCII, adding escape sequences for formatting, font selection, and printing graphics. Many printers provide PCL5 support. Some support the newer PCL6 or PCLXL. These later versions are supersets of PCL5 and can provide faster printing. Host-Based Manufacturers can reduce the cost of a printer by giving it a simple processor and very little memory. These printers are not capable of printing plain text. Instead, bitmaps of text and graphics are drawn by a driver on the host computer and then sent to the printer. These are called host-based printers. Communication between the driver and a host-based printer is often through proprietary or undocumented protocols, making them functional only on the most common operating systems. 9.3.1. 轉換 PostScript® 至其他 PDL Many applications from the Ports Collection and FreeBSD utilities produce PostScript® output. This table shows the utilities available to convert that into other common PDLs: 表格 9.1. 輸出 PDL 格式 Output PDLGenerated By說明 PCL or PCL5print/ghostscript9-sDEVICE=ljet4 for monochrome, -sDEVICE=cljet5 for color PCLXL or PCL6print/ghostscript9-sDEVICE=pxlmono for monochrome, -sDEVICE=pxlcolor for color ESC/P2print/ghostscript9-sDEVICE=uniprint XQXprint/foo2zjs 9.3.2. 摘要 For the easiest printing, choose a printer that supports PostScript®. Printers that support PCL are the next preferred. With print/ghostscript, these printers can be used as if they understood PostScript® natively. Printers that support PostScript® or PCL directly almost always support direct printing of plain ASCII text files also. Line-based printers like typical inkjets usually do not support PostScript® or PCL. They often can print plain ASCII text files. print/ghostscript supports the PDLs used by some of these printers. However, printing an entire graphic-based page on these printers is often very slow due to the large amount of data to be transferred and printed. Host-based printers are often more difficult to set up. Some cannot be used at all because of proprietary PDLs. Avoid these printers when possible. Descriptions of many PDLs can be found at http://www.undocprint.org/formats/page_description_languages. The particular PDL used by various models of printers can be found at http://www.openprinting.org/printers. 9.4. 直接列印 For occasional printing, files can be sent directly to a printer device without any setup. For example, a file called sample.txt can be sent to a USB printer: # cp sample.txt /dev/unlpt0 Direct printing to network printers depends on the abilities of the printer, but most accept print jobs on port 9100, and nc(1) can be used with them. To print the same file to a printer with the DNS hostname of netlaser: # nc netlaser 9100 < sample.txt 9.5. LPD (行列式印表機 Daemon) Printing a file in the background is called spooling. A spooler allows the user to continue with other programs on the computer without waiting for the printer to slowly complete the print job. FreeBSD includes a spooler called lpd(8). Print jobs are submitted with lpr(1). 9.5.1. 初始設定 A directory for storing print jobs is created, ownership is set, and the permissions are set to prevent other users from viewing the contents of those files: # mkdir -p /var/spool/lpd/lp # chown daemon:daemon /var/spool/lpd/lp # chmod 770 /var/spool/lpd/lp Printers are defined in /etc/printcap. An entry for each printer includes details like a name, the port where it is attached, and various other settings. Create /etc/printcap with these contents: lp:\ :lp=/dev/unlpt0:\ :sh:\ :mx#0:\ :sd=/var/spool/lpd/lp:\ :lf=/var/log/lpd-errs: The name of this printer. lpr(1) sends print jobs to the lp printer unless another printer is specified with -P, so the default printer should be named lp. The device where the printer is connected. Replace this line with the appropriate one for the connection type shown here. Connection TypeDevice Entry in /etc/printcap USB :lp=/dev/unlpt0:\ This is the non-resetting USB printer device. If problems are experienced, use ulpt0 instead, which resets the USB port on each use. Parallel :lp=/dev/lpt0:\ Network For a printer supporting the LPD protocol: :lp=:rm=network-printer-name:rp=raw:\ For printers supporting port 9100 printing: :lp=9100@network-printer-name:\ For both types, replace network-printer-name with the DNS host name of the network printer. Serial :lp=/dev/cuau0:br=9600:pa=none:\ These values are for a typical serial printer connected to a motherboard serial port. The baud rate is 9600, and no parity is used. Suppress the printing of a header page at the start of a print job. Do not limit the maximum size of a print job. The path to the spooling directory for this printer. Each printer uses its own spooling directory. The log file where errors on this printer will be reported. After creating /etc/printcap, use chkprintcap(8) to test it for errors: # chkprintcap Fix any reported problems before continuing. Enable lpd(8) in /etc/rc.conf: lpd_enable="YES" Start the service: # service lpd start 9.5.2. 使用 lpr(1) 列印 Documents are sent to the printer with lpr. A file to be printed can be named on the command line or piped into lpr. These two commands are equivalent, sending the contents of doc.txt to the default printer: % lpr doc.txt % cat doc.txt | lpr Printers can be selected with -P. To print to a printer called laser: % lpr -Plaser doc.txt 9.5.3. 過濾器 The examples shown so far have sent the contents of a text file directly to the printer. As long as the printer understands the content of those files, output will be printed correctly. Some printers are not capable of printing plain text, and the input file might not even be plain text. Filters allow files to be translated or processed. The typical use is to translate one type of input, like plain text, into a form that the printer can understand, like PostScript® or PCL. Filters can also be used to provide additional features, like adding page numbers or highlighting source code to make it easier to read. The filters discussed here are input filters or text filters. These filters convert the incoming file into different forms. Use su(1) to become root before creating the files. Filters are specified in /etc/printcap with the if= identifier. To use /usr/local/libexec/lf2crlf as a filter, modify /etc/printcap like this: lp:\ :lp=/dev/unlpt0:\ :sh:\ :mx#0:\ :sd=/var/spool/lpd/lp:\ :if=/usr/local/libexec/lf2crlf:\ :lf=/var/log/lpd-errs: if= identifies the input filter that will be used on incoming text. 提示: The backslash line continuation characters at the end of the lines in printcap entries reveal that an entry for a printer is really just one long line with entries delimited by colon characters. An earlier example can be rewritten as a single less-readable line: lp:lp=/dev/unlpt0:sh:mx#0:sd=/var/spool/lpd/lp:if=/usr/local/libexec/lf2crlf:lf=/var/log/lpd-errs: 9.5.3.1. 避免在純文字印表機階梯狀列印 Typical FreeBSD text files contain only a single line feed character at the end of each line. These lines will stairstep on a standard printer: A printed file looks like the steps of a staircase scattered by the wind A filter can convert the newline characters into carriage returns and newlines. The carriage returns make the printer return to the left after each line. Create /usr/local/libexec/lf2crlf with these contents: #!/bin/sh CR=$'\r'
/usr/bin/sed -e "s/$/${CR}/g"
Set the permissions and make it executable:
# chmod 555 /usr/local/libexec/lf2crlf
Modify /etc/printcap to use the new filter:
:if=/usr/local/libexec/lf2crlf:\
Test the filter by printing the same plain text file. The carriage returns will cause each line to start at the left side of the page.
9.5.3.2. 使用 print/enscript 在 PostScript® 印表機美化純文字內容
GNU Enscript converts plain text files into nicely-formatted PostScript® for printing on PostScript® printers. It adds page numbers, wraps long lines, and provides numerous other features to make printed text files easier to read. Depending on the local paper size, install either print/enscript-letter or print/enscript-a4 from the Ports Collection.
Create /usr/local/libexec/enscript with these contents:
#!/bin/sh
/usr/local/bin/enscript -o -
Set the permissions and make it executable:
# chmod 555 /usr/local/libexec/enscript
Modify /etc/printcap to use the new filter:
:if=/usr/local/libexec/enscript:\
Test the filter by printing a plain text file.
9.5.3.3. 列印 PostScript® 到 PCL 印表機
Many programs produce PostScript® documents. However, inexpensive printers often only understand plain text or PCL. This filter converts PostScript® files to PCL before sending them to the printer.
Install the Ghostscript PostScript® interpreter, print/ghostscript9, from the Ports Collection.
Create /usr/local/libexec/ps2pcl with these contents:
#!/bin/sh
/usr/local/bin/gs -dSAFER -dNOPAUSE -dBATCH -q -sDEVICE=ljet4 -sOutputFile=- -
Set the permissions and make it executable:
# chmod 555 /usr/local/libexec/ps2pcl
PostScript® input sent to this script will be rendered and converted to PCL before being sent on to the printer.
Modify /etc/printcap to use this new input filter:
:if=/usr/local/libexec/ps2pcl:\
Test the filter by sending a small PostScript® program to it:
% printf "%%\!PS \n /Helvetica findfont 18 scalefont setfont \
72 432 moveto (PostScript printing successful.) show showpage \004" | lpr
9.5.3.4. 智慧過濾器
A filter that detects the type of input and automatically converts it to the correct format for the printer can be very convenient. The first two characters of a PostScript® file are usually %!. A filter can detect those two characters. PostScript® files can be sent on to a PostScript® printer unchanged. Text files can be converted to PostScript® with Enscript as shown earlier. Create /usr/local/libexec/psif with these contents:
#!/bin/sh
#
# psif - Print PostScript or plain text on a PostScript printer
#
first_two_chars=expr "$first_line" : '$$..$$' case "$first_two_chars" in
%!)
# %! : PostScript job, print it.
echo "$first_line" && cat && exit 0 exit 2 ;; *) # otherwise, format with enscript ( echo "$first_line"; cat ) | /usr/local/bin/enscript -o - && exit 0
exit 2
;;
esac
Set the permissions and make it executable:
# chmod 555 /usr/local/libexec/psif
Modify /etc/printcap to use this new input filter:
:if=/usr/local/libexec/psif:\
Test the filter by printing PostScript® and plain text files.
9.5.3.5. 其他智慧過濾器
Writing a filter that detects many different types of input and formats them correctly is challenging. print/apsfilter from the Ports Collection is a smart magic filter that detects dozens of file types and automatically converts them to the PDL understood by the printer. See http://www.apsfilter.org for more details.
9.5.4. 多序列
The entries in /etc/printcap are really definitions of queues. There can be more than one queue for a single printer. When combined with filters, multiple queues provide users more control over how their jobs are printed.
As an example, consider a networked PostScript® laser printer in an office. Most users want to print plain text, but a few advanced users want to be able to print PostScript® files directly. Two entries can be created for the same printer in /etc/printcap:
textprinter:\
:lp=9100@officelaser:\
:sh:\
:mx#0:\
:sd=/var/spool/lpd/textprinter:\
:if=/usr/local/libexec/enscript:\
:lf=/var/log/lpd-errs:
psprinter:\
:lp=9100@officelaser:\
:sh:\
:mx#0:\
:sd=/var/spool/lpd/psprinter:\
:lf=/var/log/lpd-errs:
Documents sent to textprinter will be formatted by the /usr/local/libexec/enscript filter shown in an earlier example. Advanced users can print PostScript® files on psprinter, where no filtering is done.
This multiple queue technique can be used to provide direct access to all kinds of printer features. A printer with a duplexer could use two queues, one for ordinary single-sided printing, and one with a filter that sends the command sequence to enable double-sided printing and then sends the incoming file.
9.5.5. 監視與控制列印
Several utilities are available to monitor print jobs and check and control printer operation.
9.5.5.1. lpq(1)
lpq(1) shows the status of a user's print jobs. Print jobs from other users are not shown.
Show the current user's pending jobs on a single printer:
% lpq -Plp
Rank Owner Job Files Total Size
1st jsmith 0 (standard input) 12792 bytes
Show the current user's pending jobs on all printers:
% lpq -a
lp:
Rank Owner Job Files Total Size
1st jsmith 1 (standard input) 27320 bytes
laser:
Rank Owner Job Files Total Size
1st jsmith 287 (standard input) 22443 bytes
9.5.5.2. lprm(1)
lprm(1) is used to remove print jobs. Normal users are only allowed to remove their own jobs. root can remove any or all jobs.
Remove all pending jobs from a printer:
# lprm -Plp -
dfA002smithy dequeued
cfA002smithy dequeued
dfA003smithy dequeued
cfA003smithy dequeued
dfA004smithy dequeued
cfA004smithy dequeued
Remove a single job from a printer. lpq(1) is used to find the job number.
% lpq
Rank Owner Job Files Total Size
1st jsmith 5 (standard input) 12188 bytes
% lprm -Plp 5
dfA005smithy dequeued
cfA005smithy dequeued
9.5.5.3. lpc(8)
lpc(8) is used to check and modify printer status. lpc is followed by a command and an optional printer name. all can be used instead of a specific printer name, and the command will be applied to all printers. Normal users can view status with lpc(8). Only class="username">root can use commands which modify printer status.
Show the status of all printers:
% lpc status all
lp:
queuing is enabled
printing is enabled
1 entry in spool area
printer idle
laser:
queuing is enabled
printing is enabled
1 entry in spool area
waiting for laser to come up
Prevent a printer from accepting new jobs, then begin accepting new jobs again:
# lpc disable lp
lp:
queuing disabled
# lpc enable lp
lp:
queuing enabled
Stop printing, but continue to accept new jobs. Then begin printing again:
# lpc stop lp
lp:
printing disabled
# lpc start lp
lp:
printing enabled
daemon started
Restart a printer after some error condition:
# lpc restart lp
lp:
no daemon to abort
printing enabled
daemon restarted
Turn the print queue off and disable printing, with a message to explain the problem to users:
# lpc down lp Repair parts will arrive on Monday
lp:
printer and queuing disabled
status message is now: Repair parts will arrive on Monday
Re-enable a printer that is down:
# lpc up lp
lp:
printing enabled
daemon started
See lpc(8) for more commands and options.
9.5.6. 分享印表機
Printers are often shared by multiple users in businesses and schools. Additional features are provided to make sharing printers more convenient.
9.5.6.1. 別名
The printer name is set in the first line of the entry in /etc/printcap. Additional names, or aliases, can be added after that name. Aliases are separated from the name and each other by vertical bars:
lp|repairsprinter|salesprinter:\
Aliases can be used in place of the printer name. For example, users in the Sales department print to their printer with
% lpr -Psalesprinter sales-report.txt
Users in the Repairs department print to their printer with
% lpr -Prepairsprinter repairs-report.txt
All of the documents print on that single printer. When the Sales department grows enough to need their own printer, the alias can be removed from the shared printer entry and used as the name of a new printer. Users in both departments continue to use the same commands, but the Sales documents are sent to the new printer.
9.5.6.2. 頁首
It can be difficult for users to locate their documents in the stack of pages produced by a busy shared printer. Header pages were created to solve this problem. A header page with the user name and document name is printed before each print job. These pages are also sometimes called banner or separator pages.
Enabling header pages differs depending on whether the printer is connected directly to the computer with a USB, parallel, or serial cable, or is connected remotely over a network.
Header pages on directly-connected printers are enabled by removing the :sh:\ (Suppress Header) line from the entry in /etc/printcap. These header pages only use line feed characters for new lines. Some printers will need the /usr/share/examples/printing/hpif filter to prevent stairstepped text. The filter configures PCL printers to print both carriage returns and line feeds when a line feed is received.
Header pages for network printers must be configured on the printer itself. Header page entries in /etc/printcap are ignored. Settings are usually available from the printer front panel or a configuration web page accessible with a web browser.
9.5.7. 參考文獻
Example files: /usr/share/examples/printing/.
The 4.3BSD Line Printer Spooler Manual, /usr/share/doc/smm/07.lpd/paper.ascii.gz.
Manual pages: printcap(5), lpd(8), lpr(1), lpc(8), lprm(1), lpq(1).
9.6. 其他列印系統
Several other printing systems are available in addition to the built-in lpd(8). These systems offer support for other protocols or additional features.
9.6.1. CUPS (Common UNIX® Printing System)
CUPS is a popular printing system available on many operating systems. Using CUPS on FreeBSD is documented in a separate article:../../../../doc/en_US.ISO8859-1/articles/cups
9.6.2. HPLIP
Hewlett Packard provides a printing system that supports many of their inkjet and laser printers. The port is print/hplip. The main web page is at http://hplipopensource.com/hplip-web/index.html. The port handles all the installation details on FreeBSD. Configuration information is shown at http://hplipopensource.com/hplip-web/install/manual/hp_setup.html.
9.6.3. LPRng
LPRng was developed as an enhanced alternative to lpd(8). The port is sysutils/LPRng. For details and documentation, see http://www.lprng.com/.
章 10. Linux® Binary 相容性
Restructured and parts updated by .
Originally contributed by and .
10.1. 概述
FreeBSD 提供和 32 位元 Linux® Binary 的相容性，允許使用者在 FreeBSD 不需要修改就可以安裝和執行大部份 32 位元 Linux® Binary。 曾經有報告指出，在某些情況下，32 位元 Linux® Binary 在 FreeBSD 的表現比在 Linux® 好。
• 如何在 FreeBSD 系統啟用 Linux® Binary 相容模式。
• 如何安裝其他的 Linux® 共用程式庫。
• 如何在 FreeBSD 系統安裝 Linux® 應用程式。
• 在 FreeBSD 中 Linux® 相容性的實作細節。
10.2. 設定 Linux® Binary 相容性
Linux® 程式庫預設並不會安裝，且並不會開啟 Linux® Binary 相容性。 Linux® 程式庫可以手動安裝或是從 FreeBSD Ports 套件集安裝。
# kldload linux
% kldstat
1 2 0xc0100000 16bdb8 kernel
7 1 0xc24db000 d000 linux.ko
# printf "compat.linux.osrelease=2.6.18\n" >> /etc/sysctl.conf
# sysctl compat.linux.osrelease=2.6.18
# pkg install emulators/linux_base-c6
linux_enable="YES"
10.2.1. 手動安裝其他程式庫
Linux® 系統，可使用 ldd 來找出應用程式需要哪個共用程式庫。 例如，檢查 linuxdoom 需要哪個共用程式庫，在有安裝 DoomLinux® 系統執行這個指令：
% ldd linuxdoom
libXt.so.3 (DLL Jump 3.1) => /usr/X11/lib/libXt.so.3.1.0
libX11.so.3 (DLL Jump 3.1) => /usr/X11/lib/libX11.so.3.1.0
libc.so.4 (DLL Jump 4.5pl26) => /lib/libc.so.4.6.29
/compat/linux/usr/X11/lib/libXt.so.3.1.0
/compat/linux/usr/X11/lib/libXt.so.3 -> libXt.so.3.1.0
/compat/linux/usr/X11/lib/libX11.so.3.1.0
/compat/linux/usr/X11/lib/libX11.so.3 -> libX11.so.3.1.0
/compat/linux/lib/libc.so.4.6.29
/compat/linux/lib/libc.so.4 -> libc.so.4.6.29
Linux® 共用程式庫已經存在，並符合 ldd 輸出結果第一欄的主要修訂版號，則不需要複製該行最後一欄的檔案，使用既有的程式庫應可運作。若有較新的版本建議仍要複製共用程式庫，只要符號連結指向新版的程式庫，舊版便可移除。
/compat/linux/lib/libc.so.4.6.27
/compat/linux/lib/libc.so.4 -> libc.so.4.6.27
ldd 顯示 Binary 需要使用較新的版本：
libc.so.4 (DLL Jump 4.5pl26) -> libc.so.4.6.29
/compat/linux/lib/libc.so.4.6.29
/compat/linux/lib/libc.so.4 -> libc.so.4.6.29
10.2.2. 安裝 Linux® ELF Binary
ELF Binary 有時候需要額外的步驟。當執行無商標 (Unbranded) 的 ELF Binary，會產生錯誤訊息：
% ./my-linux-elf-binary
ELF binary type not known
Abort
% brandelf -t Linux my-linux-elf-binary
10.2.3. 安裝以 Linux® RPM 為基礎的應用程式
# cd /compat/linux
# rpm2cpio < /path/to/linux.archive.rpm | cpio -id
10.2.4. 設定主機名稱解析器
resolv+: "bind" is an invalid keyword resolv+:
"hosts" is an invalid keyword
/compat/linux/etc/host.conf 設定如下：
order hosts, bind
multi on
10.3. 進階主題
This section describes how Linux® binary compatibility works and is based on an email written to FreeBSD chat mailing list by Terry Lambert (Message ID: <199906020108.SAA07001@usr09.primenet.com>).
FreeBSD has an abstraction called an execution class loader. This is a wedge into the execve(2) system call.
Historically, the UNIX® loader examined the magic number (generally the first 4 or 8 bytes of the file) to see if it was a binary known to the system, and if so, invoked the binary loader.
If it was not the binary type for the system, the execve(2) call returned a failure, and the shell attempted to start executing it as shell commands. The assumption was a default of whatever the current shell is.
Later, a hack was made for sh(1) to examine the first two characters, and if they were :\n, it invoked the csh(1) shell instead.
FreeBSD has a list of loaders, instead of a single loader, with a fallback to the #! loader for running shell interpreters or shell scripts.
For the Linux® ABI support, FreeBSD sees the magic number as an ELF binary. The ELF loader looks for a specialized brand, which is a comment section in the ELF image, and which is not present on SVR4/Solaris™ ELF binaries.
For Linux® binaries to function, they must be branded as type Linux using brandelf(1):
# brandelf -t Linux file
When the ELF loader sees the Linux brand, the loader replaces a pointer in the proc structure. All system calls are indexed through this pointer. In addition, the process is flagged for special handling of the trap vector for the signal trampoline code, and several other (minor) fix-ups that are handled by the Linux® kernel module.
The Linux® system call vector contains, among other things, a list of sysent[] entries whose addresses reside in the kernel module.
When a system call is called by the Linux® binary, the trap code dereferences the system call function pointer off the proc structure, and gets the Linux®, not the FreeBSD, system call entry points.
Linux® mode dynamically reroots lookups. This is, in effect, equivalent to the union option to file system mounts. First, an attempt is made to lookup the file in /compat/linux/original-path. If that fails, the lookup is done in /original-path. This makes sure that binaries that require other binaries can run. For example, the Linux® toolchain can all run under Linux® ABI support. It also means that the Linux® binaries can load and execute FreeBSD binaries, if there are no corresponding Linux® binaries present, and that a uname(1) command can be placed in the /compat/linux directory tree to ensure that the Linux® binaries cannot tell they are not running on Linux®.
In effect, there is a Linux® kernel in the FreeBSD kernel. The various underlying functions that implement all of the services provided by the kernel are identical to both the FreeBSD system call table entries, and the Linux® system call table entries: file system operations, virtual memory operations, signal delivery, and System V IPC. The only difference is that FreeBSD binaries get the FreeBSD glue functions, and Linux® binaries get the Linux® glue functions. The FreeBSD glue functions are statically linked into the kernel, and the Linux® glue functions can be statically linked, or they can be accessed via a kernel module.
Technically, this is not really emulation, it is an ABI implementation. It is sometimes called Linux® emulation because the implementation was done at a time when there was no other word to describe what was going on. Saying that FreeBSD ran Linux® binaries was not true, since the code was not compiled in.
部 III. 系統管理
章 11. 設定與調校
Written by .
Based on a tutorial written by .
Also based on tuning(7) written by .
11.1. 概述
• rc.conf 設定的基礎概念及 /usr/local/etc/rc.d 啟動 Script。
• 如何設定並測試網路卡。
• 如何在網路裝置上設定虛擬主機。
• 如何使用在 /etc 中的各種設定檔。
• 如何使用 sysctl(8) 變數調校 FreeBSD。
• 如何調校磁碟效能及修改核心限制。
11.2. 啟動服務
Contributed by .
Many users install third party software on FreeBSD from the Ports Collection and require the installed services to be started upon system initialization. Services, such as mail/postfix or www/apache22 are just two of the many software packages which may be started during system initialization. This section explains the procedures available for starting third party software.
In FreeBSD, most included services, such as cron(8), are started through the system start up scripts.
11.2.1. 延伸應用程式設定
Now that FreeBSD includes rc.d, configuration of application startup is easier and provides more features. Using the key words discussed in 節 11.4, “管理 FreeBSD 中的服務”, applications can be set to start after certain other services and extra flags can be passed through /etc/rc.conf in place of hard coded flags in the start up script. A basic script may look similar to the following:
#!/bin/sh
#
# PROVIDE: utility
# REQUIRE: DAEMON
# KEYWORD: shutdown
. /etc/rc.subr
name=utility
rcvar=utility_enable
command="/usr/local/sbin/utility"
load_rc_config $name # # DO NOT CHANGE THESE DEFAULT VALUES HERE # SET THEM IN THE /etc/rc.conf FILE # utility_enable=${utility_enable-"NO"}
pidfile=${utility_pidfile-"/var/run/utility.pid"} run_rc_command "$1"
This script will ensure that the provided utility will be started after the DAEMON pseudo-service. It also provides a method for setting and tracking the process ID (PID).
This application could then have the following line placed in /etc/rc.conf:
utility_enable="YES"
This method allows for easier manipulation of command line arguments, inclusion of the default functions provided in /etc/rc.subr, compatibility with rcorder(8), and provides for easier configuration via rc.conf.
11.2.2. 使用服務來啟動其他服務
Other services can be started using inetd(8). Working with inetd(8) and its configuration is described in depth in 節 28.2, “inetd 超級伺服器”.
In some cases, it may make more sense to use cron(8) to start system services. This approach has a number of advantages as cron(8) runs these processes as the owner of the crontab(5). This allows regular users to start and maintain their own applications.
The @reboot feature of cron(8), may be used in place of the time specification. This causes the job to run when cron(8) is started, normally during system initialization.
11.3. 設定 cron(8)
Contributed by .
One of the most useful utilities in FreeBSD is cron. This utility runs in the background and regularly checks /etc/crontab for tasks to execute and searches /var/cron/tabs for custom crontab files. These files are used to schedule tasks which cron runs at the specified times. Each entry in a crontab defines a task to run and is known as a cron job.
Two different types of configuration files are used: the system crontab, which should not be modified, and user crontabs, which can be created and edited as needed. The format used by these files is documented in crontab(5). The format of the system crontab, /etc/crontab includes a who column which does not exist in user crontabs. In the system crontab, cron runs the command as the user specified in this column. In a user crontab, all commands run as the user who created the crontab.
User crontabs allow individual users to schedule their own tasks. The root user can also have a user crontab which can be used to schedule tasks that do not exist in the system crontab.
Here is a sample entry from the system crontab, /etc/crontab:
# /etc/crontab - root's crontab for FreeBSD
#
# $FreeBSD: head/zh_TW.UTF-8/books/handbook/book.xml 49235 2016-08-09 03:14:22Z wblock$
#
SHELL=/bin/sh
PATH=/etc:/bin:/sbin:/usr/bin:/usr/sbin
#
#minute hour mday month wday who command
#
*/5 * * * * root /usr/libexec/atrun
Lines that begin with the # character are comments. A comment can be placed in the file as a reminder of what and why a desired action is performed. Comments cannot be on the same line as a command or else they will be interpreted as part of the command; they must be on a new line. Blank lines are ignored. The equals (=) character is used to define any environment settings. In this example, it is used to define the SHELL and PATH. If the SHELL is omitted, cron will use the default Bourne shell. If the PATH is omitted, the full path must be given to the command or script to run. This line defines the seven fields used in a system crontab: minute, hour, mday, month, wday, who, and command. The minute field is the time in minutes when the specified command will be run, the hour is the hour when the specified command will be run, the mday is the day of the month, month is the month, and wday is the day of the week. These fields must be numeric values, representing the twenty-four hour clock, or a *, representing all values for that field. The who field only exists in the system crontab and specifies which user the command should be run as. The last field is the command to be executed. This entry defines the values for this cron job. The */5, followed by several more * characters, specifies that /usr/libexec/atrun is invoked by root every five minutes of every hour, of every day and day of the week, of every month.Commands can include any number of switches. However, commands which extend to multiple lines need to be broken with the backslash “\” continuation character.
11.3.1. 建立使用者的 Crontab
To create a user crontab, invoke crontab in editor mode:
% crontab -e
This will open the user's crontab using the default text editor. The first time a user runs this command, it will open an empty file. Once a user creates a crontab, this command will open that file for editing.
It is useful to add these lines to the top of the crontab file in order to set the environment variables and to remember the meanings of the fields in the crontab:
SHELL=/bin/sh
PATH=/etc:/bin:/sbin:/usr/bin:/usr/sbin
# Order of crontab fields
# minute hour mday month wday command
Then add a line for each command or script to run, specifying the time to run the command. This example runs the specified custom Bourne shell script every day at two in the afternoon. Since the path to the script is not specified in PATH, the full path to the script is given:
0 14 * * * /usr/home/dru/bin/mycustomscript.sh
提示:
Before using a custom script, make sure it is executable and test it with the limited set of environment variables set by cron. To replicate the environment that would be used to run the above cron entry, use:
env -i SHELL=/bin/sh PATH=/etc:/bin:/sbin:/usr/bin:/usr/sbin HOME=/home/dru LOGNAME=dru /usr/home/dru/bin/mycustomscript.sh
The environment set by cron is discussed in crontab(5). Checking that scripts operate correctly in a cron environment is especially important if they include any commands that delete files using wildcards.
When finished editing the crontab, save the file. It will automatically be installed and cron will read the crontab and run its cron jobs at their specified times. To list the cron jobs in a crontab, use this command:
% crontab -l
0 14 * * * /usr/home/dru/bin/mycustomscript.sh
To remove all of the cron jobs in a user crontab:
% crontab -r
remove crontab for dru? y
11.4. 管理 FreeBSD 中的服務
Contributed by .
FreeBSD uses the rc(8) system of startup scripts during system initialization and for managing services. The scripts listed in /etc/rc.d provide basic services which can be controlled with the start, stop, and restart options to service(8). For instance, sshd(8) can be restarted with the following command:
# service sshd restart
This procedure can be used to start services on a running system. Services will be started automatically at boot time as specified in rc.conf(5). For example, to enable natd(8) at system startup, add the following line to /etc/rc.conf:
natd_enable="YES"
If a natd_enable="NO" line is already present, change the NO to YES. The rc(8) scripts will automatically load any dependent services during the next boot, as described below.
Since the rc(8) system is primarily intended to start and stop services at system startup and shutdown time, the start, stop and restart options will only perform their action if the appropriate /etc/rc.conf variable is set. For instance, sshd restart will only work if sshd_enable is set to YES in /etc/rc.conf. To start, stop or restart a service regardless of the settings in /etc/rc.conf, these commands should be prefixed with one. For instance, to restart sshd(8) regardless of the current /etc/rc.conf setting, execute the following command:
# service sshd onerestart
To check if a service is enabled in /etc/rc.conf, run the appropriate rc(8) script with rcvar. This example checks to see if sshd(8) is enabled in /etc/rc.conf:
# service sshd rcvar
# sshd
#
sshd_enable="YES"
# (default: "")
注意:
The # sshd line is output from the above command, not a root console.
To determine whether or not a service is running, use status. For instance, to verify that sshd(8) is running:
# service sshd status
sshd is running as pid 433.
In some cases, it is also possible to reload a service. This attempts to send a signal to an individual service, forcing the service to reload its configuration files. In most cases, this means sending the service a SIGHUP signal. Support for this feature is not included for every service.
The rc(8) system is used for network services and it also contributes to most of the system initialization. For instance, when the /etc/rc.d/bgfsck script is executed, it prints out the following message:
Starting background file system checks in 60 seconds.
This script is used for background file system checks, which occur only during system initialization.
Many system services depend on other services to function properly. For example, yp(8) and other RPC-based services may fail to start until after the rpcbind(8) service has started. To resolve this issue, information about dependencies and other meta-data is included in the comments at the top of each startup script. The rcorder(8) program is used to parse these comments during system initialization to determine the order in which system services should be invoked to satisfy the dependencies.
The following key word must be included in all startup scripts as it is required by rc.subr(8) to enable the startup script:
• PROVIDE: Specifies the services this file provides.
The following key words may be included at the top of each startup script. They are not strictly necessary, but are useful as hints to rcorder(8):
• REQUIRE: Lists services which are required for this service. The script containing this key word will run after the specified services.
• BEFORE: Lists services which depend on this service. The script containing this key word will run before the specified services.
By carefully setting these keywords for each startup script, an administrator has a fine-grained level of control of the startup order of the scripts, without the need for runlevels used by some UNIX® operating systems.
Additional information can be found in rc(8) and rc.subr(8). Refer to this article for instructions on how to create custom rc(8) scripts.
11.4.1. 管理特定系統的設定
The principal location for system configuration information is /etc/rc.conf. This file contains a wide range of configuration information and it is read at system startup to configure the system. It provides the configuration information for the rc* files.
The entries in /etc/rc.conf override the default settings in /etc/defaults/rc.conf. The file containing the default settings should not be edited. Instead, all system-specific changes should be made to /etc/rc.conf.
A number of strategies may be applied in clustered applications to separate site-wide configuration from system-specific configuration in order to reduce administration overhead. The recommended approach is to place system-specific configuration into /etc/rc.conf.local. For example, these entries in /etc/rc.conf apply to all systems:
sshd_enable="YES"
keyrate="fast"
defaultrouter="10.1.1.254"
Whereas these entries in /etc/rc.conf.local apply to this system only:
hostname="node1.example.org"
ifconfig_fxp0="inet 10.1.1.1/8"
Distribute /etc/rc.conf to every system using an application such as rsync or puppet, while /etc/rc.conf.local remains unique.
Upgrading the system will not overwrite /etc/rc.conf, so system configuration information will not be lost.
提示:
Both /etc/rc.conf and /etc/rc.conf.local are parsed by sh(1). This allows system operators to create complex configuration scenarios. Refer to rc.conf(5) for further information on this topic.
11.5. 設定網路介面卡
Contributed by .
11.5.1. 找到正確的驅動程式
First, determine the model of the NIC and the chip it uses. FreeBSD supports a wide variety of NICs. Check the Hardware Compatibility List for the FreeBSD release to see if the NIC is supported.
If the NIC is supported, determine the name of the FreeBSD driver for the NIC. Refer to /usr/src/sys/conf/NOTES and /usr/src/sys/arch/conf/NOTES for the list of NIC drivers with some information about the supported chipsets. When in doubt, read the manual page of the driver as it will provide more information about the supported hardware and any known limitations of the driver.
The drivers for common NICs are already present in the GENERIC kernel, meaning the NIC should be probed during boot. The system's boot messages can be viewed by typing more /var/run/dmesg.boot and using the spacebar to scroll through the text. In this example, two Ethernet NICs using the dc(4) driver are present on the system:
dc0: <82c169 PNIC 10/100BaseTX> port 0xa000-0xa0ff mem 0xd3800000-0xd38
000ff irq 15 at device 11.0 on pci0
miibus0: <MII bus> on dc0
bmtphy0: <BCM5201 10/100baseTX PHY> PHY 1 on miibus0
bmtphy0: 10baseT, 10baseT-FDX, 100baseTX, 100baseTX-FDX, auto
dc1: <82c169 PNIC 10/100BaseTX> port 0x9800-0x98ff mem 0xd3000000-0xd30
000ff irq 11 at device 12.0 on pci0
miibus1: <MII bus> on dc1
bmtphy1: <BCM5201 10/100baseTX PHY> PHY 1 on miibus1
bmtphy1: 10baseT, 10baseT-FDX, 100baseTX, 100baseTX-FDX, auto
dc1: [ITHREAD]
If the driver for the NIC is not present in GENERIC, but a driver is available, the driver will need to be loaded before the NIC can be configured and used. This may be accomplished in one of two ways:
• The easiest way is to load a kernel module for the NIC using kldload(8). To also automatically load the driver at boot time, add the appropriate line to /boot/loader.conf. Not all NIC drivers are available as modules.
• Alternatively, statically compile support for the NIC into a custom kernel. Refer to /usr/src/sys/conf/NOTES, /usr/src/sys/arch/conf/NOTES and the manual page of the driver to determine which line to add to the custom kernel configuration file. For more information about recompiling the kernel, refer to 章 8, 設定 FreeBSD 核心. If the NIC was detected at boot, the kernel does not need to be recompiled.
11.5.1.1. 使用 Windows® NDIS 驅動程式
Unfortunately, there are still many vendors that do not provide schematics for their drivers to the open source community because they regard such information as trade secrets. Consequently, the developers of FreeBSD and other operating systems are left with two choices: develop the drivers by a long and pain-staking process of reverse engineering or using the existing driver binaries available for Microsoft® Windows® platforms.
FreeBSD provides native support for the Network Driver Interface Specification (NDIS). It includes ndisgen(8) which can be used to convert a Windows® XP driver into a format that can be used on FreeBSD. Because the ndis(4) driver uses a Windows® XP binary, it only runs on i386™ and amd64 systems. PCI, CardBus, PCMCIA, and USB devices are supported.
To use ndisgen(8), three things are needed:
1. FreeBSD kernel sources.
2. A Windows® XP driver binary with a .SYS extension.
3. A Windows® XP driver configuration file with a .INF extension.
Download the .SYS and .INF files for the specific NIC. Generally, these can be found on the driver CD or at the vendor's website. The following examples use W32DRIVER.SYS and W32DRIVER.INF.
The driver bit width must match the version of FreeBSD. For FreeBSD/i386, use a Windows® 32-bit driver. For FreeBSD/amd64, a Windows® 64-bit driver is needed.
The next step is to compile the driver binary into a loadable kernel module. As root, use ndisgen(8):
# ndisgen /path/to/W32DRIVER.INF /path/to/W32DRIVER.SYS
This command is interactive and prompts for any extra information it requires. A new kernel module will be generated in the current directory. Use kldload(8) to load the new module:
# kldload ./W32DRIVER_SYS.ko
In addition to the generated kernel module, the ndis.ko and if_ndis.ko modules must be loaded. This should happen automatically when any module that depends on ndis(4) is loaded. If not, load them manually, using the following commands:
# kldload ndis
# kldload if_ndis
The first command loads the ndis(4) miniport driver wrapper and the second loads the generated NIC driver.
Check dmesg(8) to see if there were any load errors. If all went well, the output should be similar to the following:
ndis0: <Wireless-G PCI Adapter> mem 0xf4100000-0xf4101fff irq 3 at device 8.0 on pci1
ndis0: NDIS API version: 5.0
ndis0: 11b rates: 1Mbps 2Mbps 5.5Mbps 11Mbps
ndis0: 11g rates: 6Mbps 9Mbps 12Mbps 18Mbps 36Mbps 48Mbps 54Mbps
From here, ndis0 can be configured like any other NIC.
To configure the system to load the ndis(4) modules at boot time, copy the generated module, W32DRIVER_SYS.ko, to /boot/modules. Then, add the following line to /boot/loader.conf:
W32DRIVER_SYS_load="YES"
11.5.2. 設定網路卡
Once the right driver is loaded for the NIC, the card needs to be configured. It may have been configured at installation time by bsdinstall(8).
To display the NIC configuration, enter the following command:
% ifconfig
dc0: flags=8843<UP,BROADCAST,RUNNING,SIMPLEX,MULTICAST> metric 0 mtu 1500
ether 00:a0:cc:da:da:da
media: Ethernet autoselect (100baseTX <full-duplex>)
status: active
dc1: flags=8802<UP,BROADCAST,RUNNING,SIMPLEX,MULTICAST> metric 0 mtu 1500
ether 00:a0:cc:da:da:db
media: Ethernet 10baseT/UTP
status: no carrier
lo0: flags=8049<UP,LOOPBACK,RUNNING,MULTICAST> metric 0 mtu 16384
options=3<RXCSUM,TXCSUM>
inet6 fe80::1%lo0 prefixlen 64 scopeid 0x4
inet6 ::1 prefixlen 128
nd6 options=3<PERFORMNUD,ACCEPT_RTADV>
In this example, the following devices were displayed:
• dc0: The first Ethernet interface.
• dc1: The second Ethernet interface.
• lo0: The loopback device.
FreeBSD uses the driver name followed by the order in which the card is detected at boot to name the NIC. For example, sis2 is the third NIC on the system using the sis(4) driver.
In this example, dc0 is up and running. The key indicators are:
1. UP means that the card is configured and ready.
2. The card has an Internet (inet) address, 192.168.1.3.
3. It has a valid subnet mask (netmask), where 0xffffff00 is the same as 255.255.255.0.
4. It has a valid broadcast address, 192.168.1.255.
5. The MAC address of the card (ether) is 00:a0:cc:da:da:da.
6. The physical media selection is on autoselection mode (media: Ethernet autoselect (100baseTX <full-duplex>)). In this example, dc1 is configured to run with 10baseT/UTP media. For more information on available media types for a driver, refer to its manual page.
7. The status of the link (status) is active, indicating that the carrier signal is detected. For dc1, the status: no carrier status is normal when an Ethernet cable is not plugged into the card.
If the ifconfig(8) output had shown something similar to:
dc0: flags=8843<BROADCAST,SIMPLEX,MULTICAST> metric 0 mtu 1500
ether 00:a0:cc:da:da:da
media: Ethernet autoselect (100baseTX <full-duplex>)
status: active
it would indicate the card has not been configured.
The card must be configured as root. The NIC configuration can be performed from the command line with ifconfig(8) but will not persist after a reboot unless the configuration is also added to /etc/rc.conf. If a DHCP server is present on the LAN, just add this line:
ifconfig_dc0="DHCP"
Replace dc0 with the correct value for the system.
The line added, then, follow the instructions given in 節 11.5.3, “測試與疑難排解”.
注意:
If the network was configured during installation, some entries for the NIC(s) may be already present. Double check /etc/rc.conf before adding any lines.
In the case, there is no DHCP server, the NIC(s) have to be configured manually. Add a line for each NIC present on the system, as seen in this example:
ifconfig_dc0="inet 192.168.1.3 netmask 255.255.255.0"
ifconfig_dc1="inet 10.0.0.1 netmask 255.255.255.0 media 10baseT/UTP"
Replace dc0 and dc1 and the IP address information with the correct values for the system. Refer to the man page for the driver, ifconfig(8), and rc.conf(5) for more details about the allowed options and the syntax of /etc/rc.conf.
If the network is not using DNS, edit /etc/hosts to add the names and IP addresses of the hosts on the LAN, if they are not already there. For more information, refer to hosts(5) and to /usr/share/examples/etc/hosts.
注意:
If there is no DHCP server and access to the Internet is needed, manually configure the default gateway and the nameserver:
# echo 'defaultrouter="your_default_router"' >> /etc/rc.conf
# echo 'nameserver your_DNS_server' >> /etc/resolv.conf
11.5.3. 測試與疑難排解
Once the necessary changes to /etc/rc.conf are saved, a reboot can be used to test the network configuration and to verify that the system restarts without any configuration errors. Alternatively, apply the settings to the networking system with this command:
# service netif restart
注意:
If a default gateway has been set in /etc/rc.conf, also issue this command:
# service routing restart
Once the networking system has been relaunched, test the NICs.
11.5.3.1. 測試乙太網路卡
To verify that an Ethernet card is configured correctly, ping(8) the interface itself, and then ping(8) another machine on the LAN:
% ping -c5 192.168.1.3
PING 192.168.1.3 (192.168.1.3): 56 data bytes
64 bytes from 192.168.1.3: icmp_seq=0 ttl=64 time=0.082 ms
64 bytes from 192.168.1.3: icmp_seq=1 ttl=64 time=0.074 ms
64 bytes from 192.168.1.3: icmp_seq=2 ttl=64 time=0.076 ms
64 bytes from 192.168.1.3: icmp_seq=3 ttl=64 time=0.108 ms
64 bytes from 192.168.1.3: icmp_seq=4 ttl=64 time=0.076 ms
--- 192.168.1.3 ping statistics ---
5 packets transmitted, 5 packets received, 0% packet loss
round-trip min/avg/max/stddev = 0.074/0.083/0.108/0.013 ms
% ping -c5 192.168.1.2
PING 192.168.1.2 (192.168.1.2): 56 data bytes
64 bytes from 192.168.1.2: icmp_seq=0 ttl=64 time=0.726 ms
64 bytes from 192.168.1.2: icmp_seq=1 ttl=64 time=0.766 ms
64 bytes from 192.168.1.2: icmp_seq=2 ttl=64 time=0.700 ms
64 bytes from 192.168.1.2: icmp_seq=3 ttl=64 time=0.747 ms
64 bytes from 192.168.1.2: icmp_seq=4 ttl=64 time=0.704 ms
--- 192.168.1.2 ping statistics ---
5 packets transmitted, 5 packets received, 0% packet loss
round-trip min/avg/max/stddev = 0.700/0.729/0.766/0.025 ms
To test network resolution, use the host name instead of the IP address. If there is no DNS server on the network, /etc/hosts must first be configured. To this purpose, edit /etc/hosts to add the names and IP addresses of the hosts on the LAN, if they are not already there. For more information, refer to hosts(5) and to /usr/share/examples/etc/hosts.
11.5.3.2. 疑難排解
When troubleshooting hardware and software configurations, check the simple things first. Is the network cable plugged in? Are the network services properly configured? Is the firewall configured correctly? Is the NIC supported by FreeBSD? Before sending a bug report, always check the Hardware Notes, update the version of FreeBSD to the latest STABLE version, check the mailing list archives, and search the Internet.
If the card works, yet performance is poor, read through tuning(7). Also, check the network configuration as incorrect network settings can cause slow connections.
Some users experience one or two device timeout messages, which is normal for some cards. If they continue, or are bothersome, determine if the device is conflicting with another device. Double check the cable connections. Consider trying another card.
To resolve watchdog timeout errors, first check the network cable. Many cards require a PCI slot which supports bus mastering. On some old motherboards, only one PCI slot allows it, usually slot 0. Check the NIC and the motherboard documentation to determine if that may be the problem.
No route to host messages occur if the system is unable to route a packet to the destination host. This can happen if no default route is specified or if a cable is unplugged. Check the output of netstat -rn and make sure there is a valid route to the host. If there is not, read 節 30.2, “通訊閘與路由”.
ping: sendto: Permission denied error messages are often caused by a misconfigured firewall. If a firewall is enabled on FreeBSD but no rules have been defined, the default policy is to deny all traffic, even ping(8). Refer to 章 29, 防火牆 for more information.
Sometimes performance of the card is poor or below average. In these cases, try setting the media selection mode from autoselect to the correct media selection. While this works for most hardware, it may or may not resolve the issue. Again, check all the network settings, and refer to tuning(7).
11.6. 虛擬主機
A common use of FreeBSD is virtual site hosting, where one server appears to the network as many servers. This is achieved by assigning multiple network addresses to a single interface.
A given network interface has one real address, and may have any number of alias addresses. These aliases are normally added by placing alias entries in /etc/rc.conf, as seen in this example:
ifconfig_fxp0_alias0="inet xxx.xxx.xxx.xxx netmask xxx.xxx.xxx.xxx"
Alias entries must start with alias0 using a sequential number such as alias0, alias1, and so on. The configuration process will stop at the first missing number.
The calculation of alias netmasks is important. For a given interface, there must be one address which correctly represents the network's netmask. Any other addresses which fall within this network must have a netmask of all 1s, expressed as either 255.255.255.255 or 0xffffffff.
For example, consider the case where the fxp0 interface is connected to two networks: 10.1.1.0 with a netmask of 255.255.255.0 and 202.0.75.16 with a netmask of 255.255.255.240. The system is to be configured to appear in the ranges 10.1.1.1 through 10.1.1.5 and 202.0.75.17 through 202.0.75.20. Only the first address in a given network range should have a real netmask. All the rest (10.1.1.2 through 10.1.1.5 and 202.0.75.18 through 202.0.75.20) must be configured with a netmask of 255.255.255.255.
The following /etc/rc.conf entries configure the adapter correctly for this scenario:
ifconfig_fxp0="inet 10.1.1.1 netmask 255.255.255.0"
ifconfig_fxp0_alias7="inet 202.0.75.20 netmask 255.255.255.255"
A simpler way to express this is with a space-separated list of IP address ranges. The first address will be given the indicated subnet mask and the additional addresses will have a subnet mask of 255.255.255.255.
ifconfig_fxp0_aliases="inet 10.1.1.1-5/24 inet 202.0.75.17-20/28"
11.7. 設定系統日誌
Contributed by .
Generating and reading system logs is an important aspect of system administration. The information in system logs can be used to detect hardware and software issues as well as application and system configuration errors. This information also plays an important role in security auditing and incident response. Most system daemons and applications will generate log entries.
FreeBSD provides a system logger, syslogd, to manage logging. By default, syslogd is started when the system boots. This is controlled by the variable syslogd_enable in /etc/rc.conf. There are numerous application arguments that can be set using syslogd_flags in /etc/rc.conf. Refer to syslogd(8) for more information on the available arguments.
This section describes how to configure the FreeBSD system logger for both local and remote logging and how to perform log rotation and log management.
11.7.1. 設定本地日誌
The configuration file, /etc/syslog.conf, controls what syslogd does with log entries as they are received. There are several parameters to control the handling of incoming events. The facility describes which subsystem generated the message, such as the kernel or a daemon, and the level describes the severity of the event that occurred. This makes it possible to configure if and where a log message is logged, depending on the facility and level. It is also possible to take action depending on the application that sent the message, and in the case of remote logging, the hostname of the machine generating the logging event.
This configuration file contains one line per action, where the syntax for each line is a selector field followed by an action field. The syntax of the selector field is facility.level which will match log messages from facility at level level or higher. It is also possible to add an optional comparison flag before the level to specify more precisely what is logged. Multiple selector fields can be used for the same action, and are separated with a semicolon (;). Using * will match everything. The action field denotes where to send the log message, such as to a file or remote log host. As an example, here is the default syslog.conf from FreeBSD:
# $FreeBSD: head/zh_TW.UTF-8/books/handbook/book.xml 49235 2016-08-09 03:14:22Z wblock$
#
# Spaces ARE valid field separators in this file. However,
# other *nix-like systems still insist on using tabs as field
# separators. If you are sharing this file between systems, you
# may want to use only tabs as field separators here.
# Consult the syslog.conf(5) manpage.
*.err;kern.warning;auth.notice;mail.crit /dev/console
*.notice;authpriv.none;kern.debug;lpr.info;mail.crit;news.err /var/log/messages
security.* /var/log/security
auth.info;authpriv.info /var/log/auth.log
mail.info /var/log/maillog
lpr.info /var/log/lpd-errs
ftp.info /var/log/xferlog
cron.* /var/log/cron
!-devd
*.=debug /var/log/debug.log
*.emerg *
# uncomment this to log all writes to /dev/console to /var/log/console.log
#console.info /var/log/console.log
# uncomment this to enable logging of all log messages to /var/log/all.log
# touch /var/log/all.log and chmod it to mode 600 before it will work
#*.* /var/log/all.log
# uncomment this to enable logging to a remote loghost named loghost
#*.* @loghost
# uncomment these if you're running inn
# news.crit /var/log/news/news.crit
# news.err /var/log/news/news.err
# news.notice /var/log/news/news.notice
# Uncomment this if you wish to see messages produced by devd
# !devd
# *.>=info
!ppp
*.* /var/log/ppp.log
!*
In this example:
• Line 8 matches all messages with a level of err or higher, as well as kern.warning, auth.notice and mail.crit, and sends these log messages to the console (/dev/console).
• Line 12 matches all messages from the mail facility at level info or above and logs the messages to /var/log/maillog.
• Line 17 uses a comparison flag (=) to only match messages at level debug and logs them to /var/log/debug.log.
• Line 33 is an example usage of a program specification. This makes the rules following it only valid for the specified program. In this case, only the messages generated by ppp are logged to /var/log/ppp.log.
The available levels, in order from most to least critical are emerg, alert, crit, err, warning, notice, info, and debug.
The facilities, in no particular order, are auth, authpriv, console, cron, daemon, ftp, kern, lpr, mail, mark, news, security, syslog, user, uucp, and local0 through local7. Be aware that other operating systems might have different facilities.
To log everything of level notice and higher to /var/log/daemon.log, add the following entry:
daemon.notice /var/log/daemon.log
For more information about the different levels and facilities, refer to syslog(3) and syslogd(8). For more information about /etc/syslog.conf, its syntax, and more advanced usage examples, see syslog.conf(5).
11.7.2. 日誌管理與循環
Log files can grow quickly, taking up disk space and making it more difficult to locate useful information. Log management attempts to mitigate this. In FreeBSD, newsyslog is used to manage log files. This built-in program periodically rotates and compresses log files, and optionally creates missing log files and signals programs when log files are moved. The log files may be generated by syslogd or by any other program which generates log files. While newsyslog is normally run from cron(8), it is not a system daemon. In the default configuration, it runs every hour.
To know which actions to take, newsyslog reads its configuration file, /etc/newsyslog.conf. This file contains one line for each log file that newsyslog manages. Each line states the file owner, permissions, when to rotate that file, optional flags that affect log rotation, such as compression, and programs to signal when the log is rotated. Here is the default configuration in FreeBSD:
# configuration file for newsyslog
# $FreeBSD: head/zh_TW.UTF-8/books/handbook/book.xml 49235 2016-08-09 03:14:22Z wblock$
#
# Entries which do not specify the '/pid_file' field will cause the
# syslogd process to be signalled when that log file is rotated. This
# action is only appropriate for log files which are written to by the
# syslogd process (ie, files listed in /etc/syslog.conf). If there
# is no process which needs to be signalled when a given log file is
# rotated, then the entry for that file should include the 'N' flag.
#
# The 'flags' field is one or more of the letters: BCDGJNUXZ or a '-'.
#
# Note: some sites will want to select more restrictive protections than the
# defaults. In particular, it may be desirable to switch many of the 644
# entries to 640 or 600. For example, some sites will consider the
# contents of maillog, messages, and lpd-errs to be confidential. In the
# future, these defaults may change to more conservative ones.
#
# logfilename [owner:group] mode count size when flags [/pid_file] [sig_num]
/var/log/all.log 600 7 * @T00 J
/var/log/amd.log 644 7 100 * J
/var/log/auth.log 600 7 100 @0101T JC
/var/log/console.log 600 5 100 * J
/var/log/cron 600 3 100 * JC
/var/log/daily.log 640 7 * @T00 JN
/var/log/debug.log 600 7 100 * JC
/var/log/kerberos.log 600 7 100 * J
/var/log/lpd-errs 644 7 100 * JC
/var/log/maillog 640 7 * @T00 JC
/var/log/messages 644 5 100 @0101T JC
/var/log/monthly.log 640 12 * $M1D0 JN /var/log/pflog 600 3 100 * JB /var/run/pflogd.pid /var/log/ppp.log root:network 640 3 100 * JC /var/log/devd.log 644 3 100 * JC /var/log/security 600 10 100 * JC /var/log/sendmail.st 640 10 * 168 B /var/log/utx.log 644 3 * @01T05 B /var/log/weekly.log 640 5 1$W6D0 JN
/var/log/xferlog 600 7 100 * JC
Each line starts with the name of the log to be rotated, optionally followed by an owner and group for both rotated and newly created files. The mode field sets the permissions on the log file and count denotes how many rotated log files should be kept. The size and when fields tell newsyslog when to rotate the file. A log file is rotated when either its size is larger than the size field or when the time in the when field has passed. An asterisk (*) means that this field is ignored. The flags field gives further instructions, such as how to compress the rotated file or to create the log file if it is missing. The last two fields are optional and specify the name of the Process ID (PID) file of a process and a signal number to send to that process when the file is rotated.
For more information on all fields, valid flags, and how to specify the rotation time, refer to newsyslog.conf(5). Since newsyslog is run from cron(8), it cannot rotate files more often than it is scheduled to run from cron(8).
11.7.3. 設定遠端日誌
Contributed by .
Monitoring the log files of multiple hosts can become unwieldy as the number of systems increases. Configuring centralized logging can reduce some of the administrative burden of log file administration.
In FreeBSD, centralized log file aggregation, merging, and rotation can be configured using syslogd and newsyslog. This section demonstrates an example configuration, where host A, named logserv.example.com, will collect logging information for the local network. Host B, named logclient.example.com, will be configured to pass logging information to the logging server.
11.7.3.1. 日誌伺服器設定
A log server is a system that has been configured to accept logging information from other hosts. Before configuring a log server, check the following:
• If there is a firewall between the logging server and any logging clients, ensure that the firewall ruleset allows UDP port 514 for both the clients and the server.
• The logging server and all client machines must have forward and reverse entries in the local DNS. If the network does not have a DNS server, create entries in each system's /etc/hosts. Proper name resolution is required so that log entries are not rejected by the logging server.
On the log server, edit /etc/syslog.conf to specify the name of the client to receive log entries from, the logging facility to be used, and the name of the log to store the host's log entries. This example adds the hostname of B, logs all facilities, and stores the log entries in /var/log/logclient.log.
+logclient.example.com
*.* /var/log/logclient.log
Next, configure /etc/rc.conf:
syslogd_enable="YES"
syslogd_flags="-a logclient.example.com -v -v"
The first entry starts syslogd at system boot. The second entry allows log entries from the specified client. The -v -v increases the verbosity of logged messages. This is useful for tweaking facilities as administrators are able to see what type of messages are being logged under each facility.
Multiple -a options may be specified to allow logging from multiple clients. IP addresses and whole netblocks may also be specified. Refer to syslogd(8) for a full list of possible options.
Finally, create the log file:
# touch /var/log/logclient.log
At this point, syslogd should be restarted and verified:
# service syslogd restart
# pgrep syslog
If a PID is returned, the server restarted successfully, and client configuration can begin. If the server did not restart, consult /var/log/messages for the error.
11.7.3.2. 日誌客戶端設定
A logging client sends log entries to a logging server on the network. The client also keeps a local copy of its own logs.
Once a logging server has been configured, edit /etc/rc.conf on the logging client:
syslogd_enable="YES"
syslogd_flags="-s -v -v"
The first entry enables syslogd on boot up. The second entry prevents logs from being accepted by this client from other hosts (-s) and increases the verbosity of logged messages.
Next, define the logging server in the client's /etc/syslog.conf. In this example, all logged facilities are sent to a remote system, denoted by the @ symbol, with the specified hostname:
*.* @logserv.example.com
After saving the edit, restart syslogd for the changes to take effect:
# service syslogd restart
To test that log messages are being sent across the network, use logger(1) on the client to send a message to syslogd:
# logger "Test message from logclient"
This message should now exist both in /var/log/messages on the client and /var/log/logclient.log on the log server.
11.7.3.3. 日誌伺服器除錯
If no messages are being received on the log server, the cause is most likely a network connectivity issue, a hostname resolution issue, or a typo in a configuration file. To isolate the cause, ensure that both the logging server and the logging client are able to ping each other using the hostname specified in their /etc/rc.conf. If this fails, check the network cabling, the firewall ruleset, and the hostname entries in the DNS server or /etc/hosts on both the logging server and clients. Repeat until the ping is successful from both hosts.
If the ping succeeds on both hosts but log messages are still not being received, temporarily increase logging verbosity to narrow down the configuration issue. In the following example, /var/log/logclient.log on the logging server is empty and /var/log/messages on the logging client does not indicate a reason for the failure. To increase debugging output, edit the syslogd_flags entry on the logging server and issue a restart:
syslogd_flags="-d -a logclient.example.com -v -v"
# service syslogd restart
Debugging data similar to the following will flash on the console immediately after the restart:
logmsg: pri 56, flags 4, from logserv.example.com, msg syslogd: restart
syslogd: restarted
logmsg: pri 6, flags 4, from logserv.example.com, msg syslogd: kernel boot file is /boot/kernel/kernel
Logging to FILE /var/log/messages
syslogd: kernel boot file is /boot/kernel/kernel
cvthname(192.168.1.10)
validate: dgram from IP 192.168.1.10, port 514, name logclient.example.com;
rejected in rule 0 due to name mismatch.
In this example, the log messages are being rejected due to a typo which results in a hostname mismatch. The client's hostname should be logclient, not logclien. Fix the typo, issue a restart, and verify the results:
# service syslogd restart
logmsg: pri 56, flags 4, from logserv.example.com, msg syslogd: restart
syslogd: restarted
logmsg: pri 6, flags 4, from logserv.example.com, msg syslogd: kernel boot file is /boot/kernel/kernel
syslogd: kernel boot file is /boot/kernel/kernel
logmsg: pri 166, flags 17, from logserv.example.com,
msg Dec 10 20:55:02 <syslog.err> logserv.example.com syslogd: exiting on signal 2
cvthname(192.168.1.10)
validate: dgram from IP 192.168.1.10, port 514, name logclient.example.com;
accepted in rule 0.
logmsg: pri 15, flags 0, from logclient.example.com, msg Dec 11 02:01:28 trhodes: Test message 2
Logging to FILE /var/log/logclient.log
Logging to FILE /var/log/messages
At this point, the messages are being properly received and placed in the correct file.
11.7.3.4. 安全注意事項
As with any network service, security requirements should be considered before implementing a logging server. Log files may contain sensitive data about services enabled on the local host, user accounts, and configuration data. Network data sent from the client to the server will not be encrypted or password protected. If a need for encryption exists, consider using security/stunnel, which will transmit the logging data over an encrypted tunnel.
Local security is also an issue. Log files are not encrypted during use or after log rotation. Local users may access log files to gain additional insight into system configuration. Setting proper permissions on log files is critical. The built-in log rotator, newsyslog, supports setting permissions on newly created and rotated log files. Setting log files to mode 600 should prevent unwanted access by local users. Refer to newsyslog.conf(5) for additional information.
11.8. 設定檔
11.8.1. /etc 配置
There are a number of directories in which configuration information is kept. These include:
/etc Generic system-specific configuration information. /etc/defaults Default versions of system configuration files. /etc/mail Extra sendmail(8) configuration and other MTA configuration files. /etc/ppp Configuration for both user- and kernel-ppp programs. /etc/namedb Default location for named(8) data. Normally named.conf and zone files are stored here. /usr/local/etc Configuration files for installed applications. May contain per-application subdirectories. /usr/local/etc/rc.d rc(8) scripts for installed applications. /var/db Automatically generated system-specific database files, such as the package database and the locate(1) database.
11.8.2. 主機名稱
11.8.2.1. /etc/resolv.conf
How a FreeBSD system accesses the Internet Domain Name System (DNS) is controlled by resolv.conf(5).
The most common entries to /etc/resolv.conf are:
nameserver The IP address of a name server the resolver should query. The servers are queried in the order listed with a maximum of three. search Search list for hostname lookup. This is normally determined by the domain of the local hostname. domain The local domain name.
A typical /etc/resolv.conf looks like this:
search example.com
nameserver 147.11.1.11
nameserver 147.11.100.30
注意:
Only one of the search and domain options should be used.
When using DHCP, dhclient(8) usually rewrites /etc/resolv.conf with information received from the DHCP server.
11.8.2.2. /etc/hosts
/etc/hosts is a simple text database which works in conjunction with DNS and NIS to provide host name to IP address mappings. Entries for local computers connected via a LAN can be added to this file for simplistic naming purposes instead of setting up a named(8) server. Additionally, /etc/hosts can be used to provide a local record of Internet names, reducing the need to query external DNS servers for commonly accessed names.
# $FreeBSD: head/zh_TW.UTF-8/books/handbook/book.xml 49235 2016-08-09 03:14:22Z wblock$
#
#
# Host Database
#
# This file should contain the addresses and aliases for local hosts that
# share this file. Replace 'my.domain' below with the domainname of your
# machine.
#
# In the presence of the domain name service or NIS, this file may
# not be consulted at all; see /etc/nsswitch.conf for the resolution order.
#
#
::1 localhost localhost.my.domain
127.0.0.1 localhost localhost.my.domain
#
# Imaginary network.
#10.0.0.2 myname.my.domain myname
#10.0.0.3 myfriend.my.domain myfriend
#
# According to RFC 1918, you can use the following IP networks for
# private nets which will never be connected to the Internet:
#
# 10.0.0.0 - 10.255.255.255
# 172.16.0.0 - 172.31.255.255
# 192.168.0.0 - 192.168.255.255
#
# In case you want to be able to connect to the Internet, you need
# real official assigned numbers. Do not try to invent your own network
# numbers but instead get one from your network provider (if any) or
# from your regional registry (ARIN, APNIC, LACNIC, RIPE NCC, or AfriNIC.)
#
The format of /etc/hosts is as follows:
[Internet address] [official hostname] [alias1] [alias2] ...
For example:
10.0.0.1 myRealHostname.example.com myRealHostname foobar1 foobar2
11.9. 使用 sysctl(8) 調校
sysctl(8) is used to make changes to a running FreeBSD system. This includes many advanced options of the TCP/IP stack and virtual memory system that can dramatically improve performance for an experienced system administrator. Over five hundred system variables can be read and set using sysctl(8).
At its core, sysctl(8) serves two functions: to read and to modify system settings.
% sysctl -a
To read a particular variable, specify its name:
% sysctl kern.maxproc
kern.maxproc: 1044
To set a particular variable, use the variable=value syntax:
# sysctl kern.maxfiles=5000
kern.maxfiles: 2088 -> 5000
Settings of sysctl variables are usually either strings, numbers, or booleans, where a boolean is 1 for yes or 0 for no.
To automatically set some variables each time the machine boots, add them to /etc/sysctl.conf. For more information, refer to sysctl.conf(5) and 節 11.9.1, “sysctl.conf.
11.9.1. sysctl.conf
The configuration file for sysctl(8), /etc/sysctl.conf, looks much like /etc/rc.conf. Values are set in a variable=value form. The specified values are set after the system goes into multi-user mode. Not all variables are settable in this mode.
For example, to turn off logging of fatal signal exits and prevent users from seeing processes started by other users, the following tunables can be set in /etc/sysctl.conf:
# Do not log fatal signal exits (e.g., sig 11)
kern.logsigexit=0
# Prevent users from seeing information about processes that
# are being run under another UID.
security.bsd.see_other_uids=0
11.9.2. 唯讀 sysctl(8)
Contributed by .
In some cases it may be desirable to modify read-only sysctl(8) values, which will require a reboot of the system.
For instance, on some laptop models the cardbus(4) device will not probe memory ranges and will fail with errors similar to:
cbb0: Could not map register memory
device_probe_and_attach: cbb0 attach returned 12
The fix requires the modification of a read-only sysctl(8) setting. Add hw.pci.allow_unsupported_io_range=1 to /boot/loader.conf and reboot. Now cardbus(4) should work properly.
11.10. 調校磁碟
The following section will discuss various tuning mechanisms and options which may be applied to disk devices. In many cases, disks with mechanical parts, such as SCSI drives, will be the bottleneck driving down the overall system performance. While a solution is to install a drive without mechanical parts, such as a solid state drive, mechanical drives are not going away anytime in the near future. When tuning disks, it is advisable to utilize the features of the iostat(8) command to test various changes to the system. This command will allow the user to obtain valuable information on system IO.
11.10.1. Sysctl 變數
11.10.1.1. vfs.vmiodirenable
The vfs.vmiodirenable sysctl(8) variable may be set to either 0 (off) or 1 (on). It is set to 1 by default. This variable controls how directories are cached by the system. Most directories are small, using just a single fragment (typically 1 K) in the file system and typically 512 bytes in the buffer cache. With this variable turned off, the buffer cache will only cache a fixed number of directories, even if the system has a huge amount of memory. When turned on, this sysctl(8) allows the buffer cache to use the VM page cache to cache the directories, making all the memory available for caching directories. However, the minimum in-core memory used to cache a directory is the physical page size (typically 4 K) rather than 512 bytes. Keeping this option enabled is recommended if the system is running any services which manipulate large numbers of files. Such services can include web caches, large mail systems, and news systems. Keeping this option on will generally not reduce performance, even with the wasted memory, but one should experiment to find out.
11.10.1.2. vfs.write_behind
The vfs.write_behind sysctl(8) variable defaults to 1 (on). This tells the file system to issue media writes as full clusters are collected, which typically occurs when writing large sequential files. This avoids saturating the buffer cache with dirty buffers when it would not benefit I/O performance. However, this may stall processes and under certain circumstances should be turned off.
11.10.1.3. vfs.hirunningspace
The vfs.hirunningspace sysctl(8) variable determines how much outstanding write I/O may be queued to disk controllers system-wide at any given instance. The default is usually sufficient, but on machines with many disks, try bumping it up to four or five megabytes. Setting too high a value which exceeds the buffer cache's write threshold can lead to bad clustering performance. Do not set this value arbitrarily high as higher write values may add latency to reads occurring at the same time.
There are various other buffer cache and VM page cache related sysctl(8) values. Modifying these values is not recommended as the VM system does a good job of automatically tuning itself.
11.10.1.4. vm.swap_idle_enabled
The vm.swap_idle_enabled sysctl(8) variable is useful in large multi-user systems with many active login users and lots of idle processes. Such systems tend to generate continuous pressure on free memory reserves. Turning this feature on and tweaking the swapout hysteresis (in idle seconds) via vm.swap_idle_threshold1 and vm.swap_idle_threshold2 depresses the priority of memory pages associated with idle processes more quickly then the normal pageout algorithm. This gives a helping hand to the pageout daemon. Only turn this option on if needed, because the tradeoff is essentially pre-page memory sooner rather than later which eats more swap and disk bandwidth. In a small system this option will have a determinable effect, but in a large system that is already doing moderate paging, this option allows the VM system to stage whole processes into and out of memory easily.
11.10.1.5. hw.ata.wc
Turning off IDE write caching reduces write bandwidth to IDE disks, but may sometimes be necessary due to data consistency issues introduced by hard drive vendors. The problem is that some IDE drives lie about when a write completes. With IDE write caching turned on, IDE hard drives write data to disk out of order and will sometimes delay writing some blocks indefinitely when under heavy disk load. A crash or power failure may cause serious file system corruption. Check the default on the system by observing the hw.ata.wc sysctl(8) variable. If IDE write caching is turned off, one can set this read-only variable to 1 in /boot/loader.conf in order to enable it at boot time.
11.10.1.6. SCSI_DELAY (kern.cam.scsi_delay)
The SCSI_DELAY kernel configuration option may be used to reduce system boot times. The defaults are fairly high and can be responsible for 15 seconds of delay in the boot process. Reducing it to 5 seconds usually works with modern drives. The kern.cam.scsi_delay boot time tunable should be used. The tunable and kernel configuration option accept values in terms of milliseconds and not seconds.
11.10.2. 軟更新
To fine-tune a file system, use tunefs(8). This program has many different options. To toggle Soft Updates on and off, use:
# tunefs -n enable /filesystem
# tunefs -n disable /filesystem
A file system cannot be modified with tunefs(8) while it is mounted. A good time to enable Soft Updates is before any partitions have been mounted, in single-user mode.
Soft Updates is recommended for UFS file systems as it drastically improves meta-data performance, mainly file creation and deletion, through the use of a memory cache. There are two downsides to Soft Updates to be aware of. First, Soft Updates guarantee file system consistency in the case of a crash, but could easily be several seconds or even a minute behind updating the physical disk. If the system crashes, unwritten data may be lost. Secondly, Soft Updates delay the freeing of file system blocks. If the root file system is almost full, performing a major update, such as make installworld, can cause the file system to run out of space and the update to fail.
11.10.2.1. 有關軟更新的更多詳細資訊
Meta-data updates are updates to non-content data like inodes or directories. There are two traditional approaches to writing a file system's meta-data back to disk.
Historically, the default behavior was to write out meta-data updates synchronously. If a directory changed, the system waited until the change was actually written to disk. The file data buffers (file contents) were passed through the buffer cache and backed up to disk later on asynchronously. The advantage of this implementation is that it operates safely. If there is a failure during an update, meta-data is always in a consistent state. A file is either created completely or not at all. If the data blocks of a file did not find their way out of the buffer cache onto the disk by the time of the crash, fsck(8) recognizes this and repairs the file system by setting the file length to 0. Additionally, the implementation is clear and simple. The disadvantage is that meta-data changes are slow. For example, rm -r touches all the files in a directory sequentially, but each directory change will be written synchronously to the disk. This includes updates to the directory itself, to the inode table, and possibly to indirect blocks allocated by the file. Similar considerations apply for unrolling large hierarchies using tar -x.
The second approach is to use asynchronous meta-data updates. This is the default for a UFS file system mounted with mount -o async. Since all meta-data updates are also passed through the buffer cache, they will be intermixed with the updates of the file content data. The advantage of this implementation is there is no need to wait until each meta-data update has been written to disk, so all operations which cause huge amounts of meta-data updates work much faster than in the synchronous case. This implementation is still clear and simple, so there is a low risk for bugs creeping into the code. The disadvantage is that there is no guarantee for a consistent state of the file system. If there is a failure during an operation that updated large amounts of meta-data, like a power failure or someone pressing the reset button, the file system will be left in an unpredictable state. There is no opportunity to examine the state of the file system when the system comes up again as the data blocks of a file could already have been written to the disk while the updates of the inode table or the associated directory were not. It is impossible to implement a fsck(8) which is able to clean up the resulting chaos because the necessary information is not available on the disk. If the file system has been damaged beyond repair, the only choice is to reformat it and restore from backup.
The usual solution for this problem is to implement dirty region logging, which is also referred to as journaling. Meta-data updates are still written synchronously, but only into a small region of the disk. Later on, they are moved to their proper location. Because the logging area is a small, contiguous region on the disk, there are no long distances for the disk heads to move, even during heavy operations, so these operations are quicker than synchronous updates. Additionally, the complexity of the implementation is limited, so the risk of bugs being present is low. A disadvantage is that all meta-data is written twice, once into the logging region and once to the proper location, so performance pessimization might result. On the other hand, in case of a crash, all pending meta-data operations can be either quickly rolled back or completed from the logging area after the system comes up again, resulting in a fast file system startup.
Kirk McKusick, the developer of Berkeley FFS, solved this problem with Soft Updates. All pending meta-data updates are kept in memory and written out to disk in a sorted sequence (ordered meta-data updates). This has the effect that, in case of heavy meta-data operations, later updates to an item catch the earlier ones which are still in memory and have not already been written to disk. All operations are generally performed in memory before the update is written to disk and the data blocks are sorted according to their position so that they will not be on the disk ahead of their meta-data. If the system crashes, an implicit log rewind causes all operations which were not written to the disk appear as if they never happened. A consistent file system state is maintained that appears to be the one of 30 to 60 seconds earlier. The algorithm used guarantees that all resources in use are marked as such in their blocks and inodes. After a crash, the only resource allocation error that occurs is that resources are marked as used which are actually free. fsck(8) recognizes this situation, and frees the resources that are no longer used. It is safe to ignore the dirty state of the file system after a crash by forcibly mounting it with mount -f. In order to free resources that may be unused, fsck(8) needs to be run at a later time. This is the idea behind the background fsck(8): at system startup time, only a snapshot of the file system is recorded and fsck(8) is run afterwards. All file systems can then be mounted dirty, so the system startup proceeds in multi-user mode. Then, background fsck(8) is scheduled for all file systems where this is required, to free resources that may be unused. File systems that do not use Soft Updates still need the usual foreground fsck(8).
The advantage is that meta-data operations are nearly as fast as asynchronous updates and are faster than logging, which has to write the meta-data twice. The disadvantages are the complexity of the code, a higher memory consumption, and some idiosyncrasies. After a crash, the state of the file system appears to be somewhat older. In situations where the standard synchronous approach would have caused some zero-length files to remain after the fsck(8), these files do not exist at all with Soft Updates because neither the meta-data nor the file contents have been written to disk. Disk space is not released until the updates have been written to disk, which may take place some time after running rm(1). This may cause problems when installing large amounts of data on a file system that does not have enough free space to hold all the files twice.
11.11. 調校核心限制
11.11.1. 檔案/程序限制
11.11.1.1. kern.maxfiles
The kern.maxfiles sysctl(8) variable can be raised or lowered based upon system requirements. This variable indicates the maximum number of file descriptors on the system. When the file descriptor table is full, file: table is full will show up repeatedly in the system message buffer, which can be viewed using dmesg(8).
Each open file, socket, or fifo uses one file descriptor. A large-scale production server may easily require many thousands of file descriptors, depending on the kind and number of services running concurrently.
In older FreeBSD releases, the default value of kern.maxfiles is derived from maxusers in the kernel configuration file. kern.maxfiles grows proportionally to the value of maxusers. When compiling a custom kernel, consider setting this kernel configuration option according to the use of the system. From this number, the kernel is given most of its pre-defined limits. Even though a production machine may not have 256 concurrent users, the resources needed may be similar to a high-scale web server.
The read-only sysctl(8) variable kern.maxusers is automatically sized at boot based on the amount of memory available in the system, and may be determined at run-time by inspecting the value of kern.maxusers. Some systems require larger or smaller values of kern.maxusers and values of 64, 128, and 256 are not uncommon. Going above 256 is not recommended unless a huge number of file descriptors is needed. Many of the tunable values set to their defaults by kern.maxusers may be individually overridden at boot-time or run-time in /boot/loader.conf. Refer to loader.conf(5) and /boot/defaults/loader.conf for more details and some hints.
In older releases, the system will auto-tune maxusers if it is set to 0. [2]. When setting this option, set maxusers to at least 4, especially if the system runs Xorg or is used to compile software. The most important table set by maxusers is the maximum number of processes, which is set to 20 + 16 * maxusers. If maxusers is set to 1, there can only be 36 simultaneous processes, including the 18 or so that the system starts up at boot time and the 15 or so used by Xorg. Even a simple task like reading a manual page will start up nine processes to filter, decompress, and view it. Setting maxusers to 64 allows up to 1044 simultaneous processes, which should be enough for nearly all uses. If, however, the proc table full error is displayed when trying to start another program, or a server is running with a large number of simultaneous users, increase the number and rebuild.
注意:
maxusers does not limit the number of users which can log into the machine. It instead sets various table sizes to reasonable values considering the maximum number of users on the system and how many processes each user will be running.
11.11.1.2. kern.ipc.soacceptqueue
The kern.ipc.soacceptqueue sysctl(8) variable limits the size of the listen queue for accepting new TCP connections. The default value of 128 is typically too low for robust handling of new connections on a heavily loaded web server. For such environments, it is recommended to increase this value to 1024 or higher. A service such as sendmail(8), or Apache may itself limit the listen queue size, but will often have a directive in its configuration file to adjust the queue size. Large listen queues do a better job of avoiding Denial of Service (DoS) attacks.
11.11.2. 網路限制
The NMBCLUSTERS kernel configuration option dictates the amount of network Mbufs available to the system. A heavily-trafficked server with a low number of Mbufs will hinder performance. Each cluster represents approximately 2 K of memory, so a value of 1024 represents 2 megabytes of kernel memory reserved for network buffers. A simple calculation can be done to figure out how many are needed. A web server which maxes out at 1000 simultaneous connections where each connection uses a 6 K receive and 16 K send buffer, requires approximately 32 MB worth of network buffers to cover the web server. A good rule of thumb is to multiply by 2, so 2x32 MB / 2 KB = 64 MB / 2 kB = 32768. Values between 4096 and 32768 are recommended for machines with greater amounts of memory. Never specify an arbitrarily high value for this parameter as it could lead to a boot time crash. To observe network cluster usage, use -m with netstat(1).
The kern.ipc.nmbclusters loader tunable should be used to tune this at boot time. Only older versions of FreeBSD will require the use of the NMBCLUSTERS kernel config(8) option.
For busy servers that make extensive use of the sendfile(2) system call, it may be necessary to increase the number of sendfile(2) buffers via the NSFBUFS kernel configuration option or by setting its value in /boot/loader.conf (see loader(8) for details). A common indicator that this parameter needs to be adjusted is when processes are seen in the sfbufa state. The sysctl(8) variable kern.ipc.nsfbufs is read-only. This parameter nominally scales with kern.maxusers, however it may be necessary to tune accordingly.
重要:
Even though a socket has been marked as non-blocking, calling sendfile(2) on the non-blocking socket may result in the sendfile(2) call blocking until enough struct sf_buf's are made available.
11.11.2.1. net.inet.ip.portrange.*
The net.inet.ip.portrange.* sysctl(8) variables control the port number ranges automatically bound to TCP and UDP sockets. There are three ranges: a low range, a default range, and a high range. Most network programs use the default range which is controlled by net.inet.ip.portrange.first and net.inet.ip.portrange.last, which default to 1024 and 5000, respectively. Bound port ranges are used for outgoing connections and it is possible to run the system out of ports under certain circumstances. This most commonly occurs when running a heavily loaded web proxy. The port range is not an issue when running a server which handles mainly incoming connections, such as a web server, or has a limited number of outgoing connections, such as a mail relay. For situations where there is a shortage of ports, it is recommended to increase net.inet.ip.portrange.last modestly. A value of 10000, 20000 or 30000 may be reasonable. Consider firewall effects when changing the port range. Some firewalls may block large ranges of ports, usually low-numbered ports, and expect systems to use higher ranges of ports for outgoing connections. For this reason, it is not recommended that the value of net.inet.ip.portrange.first be lowered.
11.11.2.2. TCP 頻寬延遲乘積
TCP bandwidth delay product limiting can be enabled by setting the net.inet.tcp.inflight.enable sysctl(8) variable to 1. This instructs the system to attempt to calculate the bandwidth delay product for each connection and limit the amount of data queued to the network to just the amount required to maintain optimum throughput.
This feature is useful when serving data over modems, Gigabit Ethernet, high speed WAN links, or any other link with a high bandwidth delay product, especially when also using window scaling or when a large send window has been configured. When enabling this option, also set net.inet.tcp.inflight.debug to 0 to disable debugging. For production use, setting net.inet.tcp.inflight.min to at least 6144 may be beneficial. Setting high minimums may effectively disable bandwidth limiting, depending on the link. The limiting feature reduces the amount of data built up in intermediate route and switch packet queues and reduces the amount of data built up in the local host's interface queue. With fewer queued packets, interactive connections, especially over slow modems, will operate with lower Round Trip Times. This feature only effects server side data transmission such as uploading. It has no effect on data reception or downloading.
Adjusting net.inet.tcp.inflight.stab is not recommended. This parameter defaults to 20, representing 2 maximal packets added to the bandwidth delay product window calculation. The additional window is required to stabilize the algorithm and improve responsiveness to changing conditions, but it can also result in higher ping(8) times over slow links, though still much lower than without the inflight algorithm. In such cases, try reducing this parameter to 15, 10, or 5 and reducing net.inet.tcp.inflight.min to a value such as 3500 to get the desired effect. Reducing these parameters should be done as a last resort only.
11.11.3. 虛擬記憶體
11.11.3.1. kern.maxvnodes
A vnode is the internal representation of a file or directory. Increasing the number of vnodes available to the operating system reduces disk I/O. Normally, this is handled by the operating system and does not need to be changed. In some cases where disk I/O is a bottleneck and the system is running out of vnodes, this setting needs to be increased. The amount of inactive and free RAM will need to be taken into account.
To see the current number of vnodes in use:
# sysctl vfs.numvnodes
vfs.numvnodes: 91349
To see the maximum vnodes:
# sysctl kern.maxvnodes
kern.maxvnodes: 100000
If the current vnode usage is near the maximum, try increasing kern.maxvnodes by a value of 1000. Keep an eye on the number of vfs.numvnodes. If it climbs up to the maximum again, kern.maxvnodes will need to be increased further. Otherwise, a shift in memory usage as reported by top(1) should be visible and more memory should be active.
11.12. 增加交換空間
Sometimes a system requires more swap space. This section describes two methods to increase swap space: adding swap to an existing partition or new hard drive, and creating a swap file on an existing partition.
For information on how to encrypt swap space, which options exist, and why it should be done, refer to 節 17.13, “交換空間加密”.
11.12.1. 使用新硬碟或既有分割區增加交換空間
Adding a new hard drive for swap gives better performance than using a partition on an existing drive. Setting up partitions and hard drives is explained in 節 17.2, “加入磁碟” while 節 2.6.1, “規劃分割區配置” discusses partition layouts and swap partition size considerations.
Use swapon to add a swap partition to the system. For example:
# swapon /dev/ada1s1b
警告:
It is possible to use any partition not currently mounted, even if it already contains data. Using swapon on a partition that contains data will overwrite and destroy that data. Make sure that the partition to be added as swap is really the intended partition before running swapon.
To automatically add this swap partition on boot, add an entry to /etc/fstab:
/dev/ada1s1b none swap sw 0 0
See fstab(5) for an explanation of the entries in /etc/fstab. More information about swapon can be found in swapon(8).
11.12.2. 建立交換檔
These examples create a 64M swap file called /usr/swap0 instead of using a partition.
Using swap files requires that the module needed by md(4) has either been built into the kernel or has been loaded before swap is enabled. See 章 8, 設定 FreeBSD 核心 for information about building a custom kernel.
1. Create the swap file:
# dd if=/dev/zero of=/usr/swap0 bs=1m count=64
2. Set the proper permissions on the new file:
# chmod 0600 /usr/swap0
3. Inform the system about the swap file by adding a line to /etc/fstab:
md99 none swap sw,file=/usr/swap0,late 0 0
The md(4) device md99 is used, leaving lower device numbers available for interactive use.
4. Swap space will be added on system startup. To add swap space immediately, use swapon(8):
# swapon -aL
1. Create the swap file, /usr/swap0:
# dd if=/dev/zero of=/usr/swap0 bs=1m count=64
2. Set the proper permissions on /usr/swap0:
# chmod 0600 /usr/swap0
3. Enable the swap file in /etc/rc.conf:
swapfile="/usr/swap0" # Set to name of swap file
4. Swap space will be added on system startup. To enable the swap file immediately, specify a free memory device. Refer to 節 17.9, “記憶體磁碟” for more information about memory devices.
# mdconfig -a -t vnode -f /usr/swap0 -u 0 && swapon /dev/md0
11.13. 電源與資源管理
Written by and .
It is important to utilize hardware resources in an efficient manner. Power and resource management allows the operating system to monitor system limits and to possibly provide an alert if the system temperature increases unexpectedly. An early specification for providing power management was the Advanced Power Management (APM) facility. APM controls the power usage of a system based on its activity. However, it was difficult and inflexible for operating systems to manage the power usage and thermal properties of a system. The hardware was managed by the BIOS and the user had limited configurability and visibility into the power management settings. The APM BIOS is supplied by the vendor and is specific to the hardware platform. An APM driver in the operating system mediates access to the APM Software Interface, which allows management of power levels.
There are four major problems in APM. First, power management is done by the vendor-specific BIOS, separate from the operating system. For example, the user can set idle-time values for a hard drive in the APM BIOS so that, when exceeded, the BIOS spins down the hard drive without the consent of the operating system. Second, the APM logic is embedded in the BIOS, and it operates outside the scope of the operating system. This means that users can only fix problems in the APM BIOS by flashing a new one into the ROM, which is a dangerous procedure with the potential to leave the system in an unrecoverable state if it fails. Third, APM is a vendor-specific technology, meaning that there is a lot of duplication of efforts and bugs found in one vendor's BIOS may not be solved in others. Lastly, the APM BIOS did not have enough room to implement a sophisticated power policy or one that can adapt well to the purpose of the machine.
The Plug and Play BIOS (PNPBIOS) was unreliable in many situations. PNPBIOS is 16-bit technology, so the operating system has to use 16-bit emulation in order to interface with PNPBIOS methods. FreeBSD provides an APM driver as APM should still be used for systems manufactured at or before the year 2000. The driver is documented in apm(4).
The successor to APM is the Advanced Configuration and Power Interface (ACPI). ACPI is a standard written by an alliance of vendors to provide an interface for hardware resources and power management. It is a key element in Operating System-directed configuration and Power Management as it provides more control and flexibility to the operating system.
This chapter demonstrates how to configure ACPI on FreeBSD. It then offers some tips on how to debug ACPI and how to submit a problem report containing debugging information so that developers can diagnosis and fix ACPI issues.
11.13.1. 設定 ACPI
In FreeBSD the acpi(4) driver is loaded by default at system boot and should not be compiled into the kernel. This driver cannot be unloaded after boot because the system bus uses it for various hardware interactions. However, if the system is experiencing problems, ACPI can be disabled altogether by rebooting after setting hint.acpi.0.disabled="1" in /boot/loader.conf or by setting this variable at the loader prompt, as described in 節 12.2.3, “階段三”.
注意:
ACPI and APM cannot coexist and should be used separately. The last one to load will terminate if the driver notices the other is running.
ACPI can be used to put the system into a sleep mode with acpiconf, the -s flag, and a number from 1 to 5. Most users only need 1 (quick suspend to RAM) or 3 (suspend to RAM). Option 5 performs a soft-off which is the same as running halt -p.
Other options are available using sysctl. Refer to acpi(4) and acpiconf(8) for more information.
11.13.2. 常見問題
ACPI is present in all modern computers that conform to the ia32 (x86), ia64 (Itanium), and amd64 (AMD) architectures. The full standard has many features including CPU performance management, power planes control, thermal zones, various battery systems, embedded controllers, and bus enumeration. Most systems implement less than the full standard. For instance, a desktop system usually only implements bus enumeration while a laptop might have cooling and battery management support as well. Laptops also have suspend and resume, with their own associated complexity.
An ACPI-compliant system has various components. The BIOS and chipset vendors provide various fixed tables, such as FADT, in memory that specify things like the APIC map (used for SMP), config registers, and simple configuration values. Additionally, a bytecode table, the Differentiated System Description Table DSDT, specifies a tree-like name space of devices and methods.
The ACPI driver must parse the fixed tables, implement an interpreter for the bytecode, and modify device drivers and the kernel to accept information from the ACPI subsystem. For FreeBSD, Intel® has provided an interpreter (ACPI-CA) that is shared with Linux® and NetBSD. The path to the ACPI-CA source code is src/sys/contrib/dev/acpica. The glue code that allows ACPI-CA to work on FreeBSD is in src/sys/dev/acpica/Osd. Finally, drivers that implement various ACPI devices are found in src/sys/dev/acpica.
For ACPI to work correctly, all the parts have to work correctly. Here are some common problems, in order of frequency of appearance, and some possible workarounds or fixes. If a fix does not resolve the issue, refer to 節 11.13.4, “取得與回報除錯資訊” for instructions on how to submit a bug report.
11.13.2.1. 滑鼠問題
In some cases, resuming from a suspend operation will cause the mouse to fail. A known work around is to add hint.psm.0.flags="0x3000" to /boot/loader.conf.
11.13.2.2. 待機/喚醒
ACPI has three suspend to RAM (STR) states, S1-S3, and one suspend to disk state (STD), called S4. STD can be implemented in two separate ways. The S4BIOS is a BIOS-assisted suspend to disk and S4OS is implemented entirely by the operating system. The normal state the system is in when plugged in but not powered up is soft off (S5).
Use sysctl hw.acpi to check for the suspend-related items. These example results are from a Thinkpad:
hw.acpi.supported_sleep_state: S3 S4 S5
hw.acpi.s4bios: 0
Use acpiconf -s to test S3, S4, and S5. An s4bios of one (1) indicates S4BIOS support instead of S4 operating system support.
When testing suspend/resume, start with S1, if supported. This state is most likely to work since it does not require much driver support. No one has implemented S2, which is similar to S1. Next, try S3. This is the deepest STR state and requires a lot of driver support to properly reinitialize the hardware.
A common problem with suspend/resume is that many device drivers do not save, restore, or reinitialize their firmware, registers, or device memory properly. As a first attempt at debugging the problem, try:
# sysctl debug.bootverbose=1
# sysctl debug.acpi.suspend_bounce=1
# acpiconf -s 3
This test emulates the suspend/resume cycle of all device drivers without actually going into S3 state. In some cases, problems such as losing firmware state, device watchdog time out, and retrying forever, can be captured with this method. Note that the system will not really enter S3 state, which means devices may not lose power, and many will work fine even if suspend/resume methods are totally missing, unlike real S3 state.
Harder cases require additional hardware, such as a serial port and cable for debugging through a serial console, a Firewire port and cable for using dcons(4), and kernel debugging skills.
To help isolate the problem, unload as many drivers as possible. If it works, narrow down which driver is the problem by loading drivers until it fails again. Typically, binary drivers like nvidia.ko, display drivers, and USB will have the most problems while Ethernet interfaces usually work fine. If drivers can be properly loaded and unloaded, automate this by putting the appropriate commands in /etc/rc.suspend and /etc/rc.resume. Try setting hw.acpi.reset_video to 1 if the display is messed up after resume. Try setting longer or shorter values for hw.acpi.sleep_delay to see if that helps.
Try loading a recent Linux® distribution to see if suspend/resume works on the same hardware. If it works on Linux®, it is likely a FreeBSD driver problem. Narrowing down which driver causes the problem will assist developers in fixing the problem. Since the ACPI maintainers rarely maintain other drivers, such as sound or ATA, any driver problems should also be posted to the freebsd-current list and mailed to the driver maintainer. Advanced users can include debugging printf(3)s in a problematic driver to track down where in its resume function it hangs.
Finally, try disabling ACPI and enabling APM instead. If suspend/resume works with APM, stick with APM, especially on older hardware (pre-2000). It took vendors a while to get ACPI support correct and older hardware is more likely to have BIOS problems with ACPI.
11.13.2.3. 系統無回應
Most system hangs are a result of lost interrupts or an interrupt storm. Chipsets may have problems based on boot, how the BIOS configures interrupts before correctness of the APIC (MADT) table, and routing of the System Control Interrupt (SCI).
Interrupt storms can be distinguished from lost interrupts by checking the output of vmstat -i and looking at the line that has acpi0. If the counter is increasing at more than a couple per second, there is an interrupt storm. If the system appears hung, try breaking to DDB (CTRL+ALT+ESC on console) and type show interrupts.
When dealing with interrupt problems, try disabling APIC support with hint.apic.0.disabled="1" in /boot/loader.conf.
11.13.2.4. 當機
Panics are relatively rare for ACPI and are the top priority to be fixed. The first step is to isolate the steps to reproduce the panic, if possible, and get a backtrace. Follow the advice for enabling options DDB and setting up a serial console in 節 25.6.4, “從序列線路 (Serial Line) 進入 DDB 除錯程式” or setting up a dump partition. To get a backtrace in DDB, use tr. When handwriting the backtrace, get at least the last five and the top five lines in the trace.
Then, try to isolate the problem by booting with ACPI disabled. If that works, isolate the ACPI subsystem by using various values of debug.acpi.disable. See acpi(4) for some examples.
11.13.2.5. 系統在待機或關機後仍開機
First, try setting hw.acpi.disable_on_poweroff="0" in /boot/loader.conf. This keeps ACPI from disabling various events during the shutdown process. Some systems need this value set to 1 (the default) for the same reason. This usually fixes the problem of a system powering up spontaneously after a suspend or poweroff.
11.13.2.6. BIOS 含有有問題的 Bytecode
Some BIOS vendors provide incorrect or buggy bytecode. This is usually manifested by kernel console messages like this:
ACPI-1287: *** Error: Method execution failed [\\_SB_.PCI0.LPC0.FIGD._STA] \\
(Node 0xc3f6d160), AE_NOT_FOUND
Often, these problems may be resolved by updating the BIOS to the latest revision. Most console messages are harmless, but if there are other problems, like the battery status is not working, these messages are a good place to start looking for problems.
11.13.3. 覆蓋預設的 AML
The BIOS bytecode, known as ACPI Machine Language (AML), is compiled from a source language called ACPI Source Language (ASL). The AML is found in the table known as the Differentiated System Description Table (DSDT).
The goal of FreeBSD is for everyone to have working ACPI without any user intervention. Workarounds are still being developed for common mistakes made by BIOS vendors. The Microsoft® interpreter (acpi.sys and acpiec.sys) does not strictly check for adherence to the standard, and thus many BIOS vendors who only test ACPI under Windows® never fix their ASL. FreeBSD developers continue to identify and document which non-standard behavior is allowed by Microsoft®'s interpreter and replicate it so that FreeBSD can work without forcing users to fix the ASL.
To help identify buggy behavior and possibly fix it manually, a copy can be made of the system's ASL. To copy the system's ASL to a specified file name, use acpidump with -t, to show the contents of the fixed tables, and -d, to disassemble the AML:
# acpidump -td > my.asl
Some AML versions assume the user is running Windows®. To override this, set hw.acpi.osname="Windows 2009" in /boot/loader.conf, using the most recent Windows® version listed in the ASL.
Other workarounds may require my.asl to be customized. If this file is edited, compile the new ASL using the following command. Warnings can usually be ignored, but errors are bugs that will usually prevent ACPI from working correctly.
# iasl -f my.asl
Including -f forces creation of the AML, even if there are errors during compilation. Some errors, such as missing return statements, are automatically worked around by the FreeBSD interpreter.
The default output filename for iasl is DSDT.aml. Load this file instead of the BIOS's buggy copy, which is still present in flash memory, by editing /boot/loader.conf as follows:
acpi_dsdt_load="YES"
acpi_dsdt_name="/boot/DSDT.aml"
Be sure to copy DSDT.aml to /boot, then reboot the system. If this fixes the problem, send a diff(1) of the old and new ASL to freebsd-acpi so that developers can work around the buggy behavior in acpica.
11.13.4. 取得與回報除錯資訊
Written by .
With contributions from and .
The ACPI driver has a flexible debugging facility. A set of subsystems and the level of verbosity can be specified. The subsystems to debug are specified as layers and are broken down into components (ACPI_ALL_COMPONENTS) and ACPI hardware support (ACPI_ALL_DRIVERS). The verbosity of debugging output is specified as the level and ranges from just report errors (ACPI_LV_ERROR) to everything (ACPI_LV_VERBOSE). The level is a bitmask so multiple options can be set at once, separated by spaces. In practice, a serial console should be used to log the output so it is not lost as the console message buffer flushes. A full list of the individual layers and levels is found in acpi(4).
Debugging output is not enabled by default. To enable it, add options ACPI_DEBUG to the custom kernel configuration file if ACPI is compiled into the kernel. Add ACPI_DEBUG=1 to /etc/make.conf to enable it globally. If a module is used instead of a custom kernel, recompile just the acpi.ko module as follows:
# cd /sys/modules/acpi/acpi && make clean && make ACPI_DEBUG=1
Copy the compiled acpi.ko to /boot/kernel and add the desired level and layer to /boot/loader.conf. The entries in this example enable debug messages for all ACPI components and hardware drivers and output error messages at the least verbose level:
debug.acpi.layer="ACPI_ALL_COMPONENTS ACPI_ALL_DRIVERS"
debug.acpi.level="ACPI_LV_ERROR"
If the required information is triggered by a specific event, such as a suspend and then resume, do not modify /boot/loader.conf. Instead, use sysctl to specify the layer and level after booting and preparing the system for the specific event. The variables which can be set using sysctl are named the same as the tunables in /boot/loader.conf.
Once the debugging information is gathered, it can be sent to freebsd-acpi so that it can be used by the FreeBSD ACPI maintainers to identify the root cause of the problem and to develop a solution.
注意:
Before submitting debugging information to this mailing list, ensure the latest BIOS version is installed and, if available, the embedded controller firmware version.
When submitting a problem report, include the following information:
• Description of the buggy behavior, including system type, model, and anything that causes the bug to appear. Note as accurately as possible when the bug began occurring if it is new.
• The output of dmesg after running boot -v, including any error messages generated by the bug.
• The dmesg output from boot -v with ACPI disabled, if disabling ACPI helps to fix the problem.
• Output from sysctl hw.acpi. This lists which features the system offers.
• The URL to a pasted version of the system's ASL. Do not send the ASL directly to the list as it can be very large. Generate a copy of the ASL by running this command:
# acpidump -dt > name-system.asl
Substitute the login name for name and manufacturer/model for system. For example, use njl-FooCo6000.asl.
Most FreeBSD developers watch the FreeBSD-CURRENT mailing list, but one should submit problems to freebsd-acpi to be sure it is seen. Be patient when waiting for a response. If the bug is not immediately apparent, submit a PR using send-pr(1). When entering a PR, include the same information as requested above. This helps developers to track the problem and resolve it. Do not send a PR without emailing freebsd-acpi first as it is likely that the problem has been reported before.
11.13.5. 參考文獻
• The FreeBSD ACPI Mailing List Archives (http://lists.freebsd.org/pipermail/freebsd-acpi/)
• The ACPI 2.0 Specification (http://acpi.info/spec.htm)
[2] The auto-tuning algorithm sets maxusers equal to the amount of memory in the system, with a minimum of 32, and a maximum of 384.
12.1. 概述
• FreeBSD 開機系統的元件以及它們如何互動。
• FreeBSD 開機程式中各元件可使用的選項，用來控制開機程序。
• 如何設定自訂的開機啟動畫面 (Splash screen)。
• 設定 Device Hints 的基礎。
• 如何開機進入單人及多人模式以及如何正確關閉 FreeBSD 系統。
12.2. FreeBSD 開機程序
Turning on a computer and starting the operating system poses an interesting dilemma. By definition, the computer does not know how to do anything until the operating system is started. This includes running programs from the disk. If the computer can not run a program from the disk without the operating system, and the operating system programs are on the disk, how is the operating system started?
This problem parallels one in the book The Adventures of Baron Munchausen. A character had fallen part way down a manhole, and pulled himself out by grabbing his bootstraps and lifting. In the early days of computing, the term bootstrap was applied to the mechanism used to load the operating system. It has since become shortened to booting.
On x86 hardware, the Basic Input/Output System (BIOS) is responsible for loading the operating system. The BIOS looks on the hard disk for the Master Boot Record (MBR), which must be located in a specific place on the disk. The BIOS has enough knowledge to load and run the MBR, and assumes that the MBR can then carry out the rest of the tasks involved in loading the operating system, possibly with the help of the BIOS.
注意:
FreeBSD provides for booting from both the older MBR standard, and the newer GUID Partition Table (GPT). GPT partitioning is often found on computers with the Unified Extensible Firmware Interface (UEFI). However, FreeBSD can boot from GPT partitions even on machines with only a legacy BIOS with gptboot(8). Work is under way to provide direct UEFI booting.
The code within the MBR is typically referred to as a boot manager, especially when it interacts with the user. The boot manager usually has more code in the first track of the disk or within the file system. Examples of boot managers include the standard FreeBSD boot manager boot0, also called Boot Easy, and Grub, which is used by many Linux® distributions.
If only one operating system is installed, the MBR searches for the first bootable (active) slice on the disk, and then runs the code on that slice to load the remainder of the operating system. When multiple operating systems are present, a different boot manager can be installed to display a list of operating systems so the user can select one to boot.
The remainder of the FreeBSD bootstrap system is divided into three stages. The first stage knows just enough to get the computer into a specific state and run the second stage. The second stage can do a little bit more, before running the third stage. The third stage finishes the task of loading the operating system. The work is split into three stages because the MBR puts limits on the size of the programs that can be run at stages one and two. Chaining the tasks together allows FreeBSD to provide a more flexible loader.
The kernel is then started and begins to probe for devices and initialize them for use. Once the kernel boot process is finished, the kernel passes control to the user process init(8), which makes sure the disks are in a usable state, starts the user-level resource configuration which mounts file systems, sets up network cards to communicate on the network, and starts the processes which have been configured to run at startup.
This section describes these stages in more detail and demonstrates how to interact with the FreeBSD boot process.
12.2.1. 開機管理程式
The boot manager code in the MBR is sometimes referred to as stage zero of the boot process. By default, FreeBSD uses the boot0 boot manager.
The MBR installed by the FreeBSD installer is based on /boot/boot0. The size and capability of boot0 is restricted to 446 bytes due to the slice table and 0x55AA identifier at the end of the MBR. If boot0 and multiple operating systems are installed, a message similar to this example will be displayed at boot time:
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2016-08-30 01:17:31
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