text:
25 Dec

Is there a how-to somewhere or a code snipet needed in WordPress to make it work? There is a Great Zend OPcache WordPress Visualization Plugin, Which We Will Talk About in this Article. In earlier versions, you have the choice to use APC or OPcache, but if you would like to use the latter, you need to manually install it. As of PHP 5.5, the Zend OPcache extention is available by default and you can check if you have it correctly configured by simply calling phpinfo() from a script on your server or checking out your php.ini file (see OPcache configuration settings). It’s provided “AS-IS”. OPCache will clear itself automatically when needed. Find out with this in-depth article. If you want to add a translation in your own language, you can use flush-opcache.pot located in languages folder and send me by email. Use this plugin to display detailed information about your server’s OPCache, including memory utilisation, and a list of all scripts cached. You can do this in one click using WP Rocket. Do you have any questions about OPcache/PHP opcode caching? OPcache PHP OPcode caching system. OPcache is an Apache server module for the PHP interpreter that can be used for increase performance and speed by storing pre-compiled scripts bytecode in shared memory space. When you have done that, restart PHP using SSH. {"cart_token":"","hash":"","cart_data":""}, The Best WordPress Hosting Services for Small Businesses and Blogs, Google Core Web Vitals for WordPress: How to Test and Improve Them, GTmetrix Updates its Algorithm to Use Google’s Lighthouse Metrics, Why Self-Hosting Google Fonts Isn’t Recommended, How to Take Your Online Business to the Next Level: Cache Your Site and Make It Faster, different types of caching such as browser, site, object, and OPcode caching, Caching for WordPress, Explained in Plain English. Yes, If you’re working on a shared server, OPcache is shared across all PHP users so when you flush OPcache, you do it on every websites this server hosts. A fatal fatal error might be thrown when PHP’s internal OPcache still points to wp-includes/template.php (source by @swissspidy). NSPT 2020年2月13日. Bytecode cache engines such as OPcache, APC, and Xcache all complete this process the first time the PHP file is executed without having to do it a second, or third time. * * First, check to see if the function is available to call, then if the host has restricted * the ability to run the function to avoid a PHP warning. Wordpress PHP 5.5 and OPcache. Yes, If you’re working on a shared server, OPcache is shared across all PHP users so when you flush OPcache, you do it on every websites this server hosts. For many WordPress site owners, their server may already have the latest version of PHP installed. This can be done with zend_extension=/full/path/to/opcache.so on non-Windows platforms, and zend_extension=C:\path\to\php_opcache.dll on Windows.”. You are free to use and extend it, but please do credit me though ;-) . For information about how to determine if APC is installed on your server, please see this article. redis in-memory data structure store, used as a database, cache and … There is an option to automatically flush OPcache when a WordPress or plugin update occurred. On average, it speeds up WordPress three fold, at the very least for medium to large sites. This means they already have OPcache automatically enabled to drastically speed up page load times for their site. APC was widely used, but it didn’t have the backing that OPcache had so it could be well maintained and stable with each new PHP release. It keeps telling my "OPcache purge failed." Creating the Web Space Directory for the Cache. Anar a la barra d’aisinas A prepaus de WordPress Opcache storing precompiled script bytecode in shared memory, APC/APCu. A self-described WordPress nerd, she enjoys watching The Simpsons and names her test sites after references from the show. NSPT 13 de febrero de 2020. Click on the ‘Install Now’ button. [opcache] zend_extension=php_opcache.dll If it detects that a file has been touched, it will invalidate itself. 1. Self-hosting Google Fonts seem like a good way to speed up your website. If OPCache is already enabled on the katest PHP versions, why eould one use WP Rocket Opcache again? Is that really so? WP Rocket enables you to reset the OPCache content easily if needed right from your WordPress admin bar. Get WP Rocket Now The config line "opcache.revalidate_freq=60" specifies that OPCache will check your php files every 60 seconds, (actually it will just check the timestamps so it's a relatively lighweight operation). Yes, If you’re working on a shared server, OPcache is shared across all PHP users so when you flush OPcache, you do it on every websites this server hosts. Search for ‘OPcache Manager’. It’s recommended that you  implement more than one kind to increase your site’s performance. More Information. OPcache used to be owned by Zend and Alternative PHP Cache (APC) was a free, open source extension for PHP. On Apache, enter the command below to restart PHP. In other words, it’s stored in your server’s cache. If you’re not sure how to  find it, contact your hosting provider. Once that’s done, the opcode is saved to the server’s memory. Caching is a system you can put in place to speed up your site. Über WordPress WordPress.org Each subsequent page load has the stored content retrieved from memory and served on the page. Activate OPcache Manager. According to my hoster, OPcache is running on my server (SSD hard drives, Ubuntu 18). Everyone really needs to make sure php opcache is enabled its often overlooked but the speed improvements it gives is significant. My admins turned it on for me but the site was not faster - it was slower. Hi Stef :) For this kind of questions, please get in touch with our support team. The Alternative PHP Cache (APC) and OPcache provide opcode caching. Use this plugin to display detailed information about your server’s OPCache, including memory utilisation, and a list of all scripts cached. OPcache, APC as well as Xcache are all opcode caching systems. My admins turned it on for me but the site was not faster - it was slower. Install: Quick Install WordPress on OpenLiteSpeed. This process means cached content is displayed a lot faster than if it’s loaded directly from the server. This post helps new users and students how to install and configure PHP OPcache on Ubuntu 20.04. Nothing related to this plugin, it’s just the way Zend OPcache works… This plugin only triggers opcache_reset() function. Ask Question Asked 6 years, 3 months ago. Fonctions OPcache. Here’s more detail on OPcache and how to install it for your WordPress site to speed it up. With the OPcache module in PHP core, you might run into cache misses and errors when upgrading WordPress. In the settings, it might be better to enable "purge on update" as default, what do you think about it ? There is an option to automatically flush OPcache when a WordPress or plugin update occurred. Nothing related to this plugin, it’s just the way Zend OPcache works… This plugin only triggers opcache_reset() function. Is there a how-to somewhere or a code snipet needed in WordPress to make it work? High Traffic Websites and wp-cron.php. Taking care of your website's performance is a key point to take your online business to the next level. Works perfectly. Yes, If you’re working on a shared server, OPcache is shared across all PHP users so when you flush OPcache, you do it on every websites this server hosts. hello good I would like to know if there is any option in lite speed to complement with php 7.4 opcache ???? This plugin simply gives an easy way to flush the php opcache easily and its great at what it does! Faster than Redis, Memcache or APC. Most times, the speed gains are as much as 3 times more. Yes, If you’re working on a shared server, OPcache is shared across all PHP users so when you flush OPcache, you do it on every websites this server hosts. Nothing related to this plugin, it’s just the way Zend OPcache works… This plugin only triggers opcache_reset() function. Flush PHP OPcache and WinCache with the click of a button and automatically before WordPress… Binary Cocoa 80+ aktive Installationen Getestet mit 5.2.7 Zuletzt aktualisiert vor 10 Monaten Docket Cache – Object Cache Accelerator PHP has many options available which can boost up the application performance and allow handling number of requests smoothly at one time.OPcache improves PHP performance by storing precompiled script byte-code in shared memory, thereby removing the need for PHP to load and parse scripts on each request.. From WordPress.org. It supports both memory and file caching transparently. Confused about Google Core Web Vitals for WordPress? APC and OPcache work at the web server level, so WordPress itself does not require any special configuration to take advantage of the performance benefits. Hi, Learn what they are, why they matter, and how to improve your metrics. Nothing related to this plugin, it’s just the way Zend OPcache works… This plugin only triggers opcache_reset() function. Viewed 871 times 1. WP Rocket enables you to reset the OPCache content easily if needed right from your WordPress admin bar. Diese führt PHP-Skripte beim ersten Aufruf aus und hält sie dann im Arbeitsspeicher vor. For details, you can also check out these resources: OPcache is a type of OPcode caching. Use this plugin to display detailed information about your server’s OPCache, including memory utilisation, and a list of all scripts cached. Browser Cache vs Cookies: What’s the Difference? This occurs when the PHP file loads on a web page for the first time. Nothing related to this plugin, it’s just the way Zend OPcache works… This plugin only triggers opcache_reset() function. But, it won’t be enough to cause any issues. What are you waiting for? Nothing related to this plugin, it’s just the way Zend OPcache works… This plugin only triggers opcache_reset() function. Viewed 871 times 1. 1. Yes, If you’re working on a shared server, OPcache is shared across all PHP users so when you flush OPcache, you do it on every websites this server hosts. There’s also no additional requirements or configuration needed to run it. By caching the compiled operation codes (opcodes) of PHP scripts, APC and OPcache enable sites to serve page content significantly faster. Do you have an idea what might be the problem here? i have lite speed on a shared server. OPCache replaces APC, and is an alternative to XCache, as a PHP accelerator. If you want to add a translation in your own language, you can use flush-opcache.pot located in languages folder and send me by email. Opcache is transparent for WordPress (as it is to any PHP application). The Alternative PHP Cache (APC) and OPcache provide opcode caching. PHP OPcache as a caching method? Omschrijving. Then, the script is compiled into opcode making the file readable by the server. Note that on some Linux based systems, the opcache subsystem is compiled out of the PHP core and must be dynamically loaded. wordpress-opcache. To do so, you need a cache and performance optimization plugin like WP Rocket. Everyone really needs to make sure php opcache is enabled its often overlooked but the speed improvements it gives is significant. Use this plugin to display detailed information about your server’s OPCache, including memory utilisation, list of all scripts cached and a useful memory utilisation visualisation based on … When a PHP script executes, your server’s cache memory is checked to see if the script has already been cached. Names her test sites after references from the server Cookies: what ’ default. Opcache is enabled, PHP version, WordPress, but the speed improvements it gives is significant,. 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text:
Using immutable data structures enables equational reasoning and assures that update operations are atomic. However, purely immutable interfaces are not always feasible. For instance a RESTful service typically needs to propagate the effects of update operations to other clients. In this post I describe a strategy for constructing mutable service interfaces on top of purely immutable data structures. I’m using F# to exemplify.

## Building a Player Service

Consider the task of designing a service for managing player information for some online game. The core API needs to support methods for retrieving and updating a set of players given some search criterion; Here is simple interface capturing the requirements:

type PlayerService = {
FindPlayers : SearchConfiguration -> list<Player>
UpdatePlayers : SearchConfiguration -> (Player -> Player) -> unit
}

More specific operations such as adding or removing player credits can be implemented in terms of UpdatePlayers and potentially exposed via a web-service API.

Also assume the following set of constraints:

1. All invocations of UpdatePlayers are atomic and executed in sequence.
2. Invocations of UpdatePlayers do not block FindPlayers.
3. FindPlayers is non-blocking.
4. FindPlayers always returns data from a consistent state.

(1) is crucial in order to make sure that effects of update operations are predictable. If one update operation adds 100 credits to a player and another one removes 40 from the same player, the net result should be plus 60 credits once both operations have been completed. (2) assures that consumers will still be able to read data from the service without waiting for potentially slow update operations or any other FindPlayer invocations to complete. (4) means that data from an incomplete update should never be accessible. For example, transferring credits from one player to another within one update operation must not allow a service consumer to observe an intermediate state where the total number of credits is any different from before and after the request was handled. Note that it is not required that update operations have an immediate effect on subsequent FindPlayers requests, this is sometimes referred to as eventual consistency.

The above interface is apparently non-pure since UpdatePlayers impacts future behavior of FindPlayers as a side effect.

What is a good data-structure for this problem? It may seem intuitive to pick a traditional mutable dictionary (such a a HashTable) for maintaining the set of players when realizing the interface. However, there are several challenges with such approach; Assuring atomicity of update operations would require a locking strategy, but blocking FindPlayers while waiting for the lock to be released is not feasible because of constraint (2). Ignoring the lock (dirty reading) is also not an option since it may violate (4) by leaking data from an inconsistent state.

## An immutable version

Rather than addressing these problems in a mutable setting, let’s start by designing a pure interface with the hope of later being able to convert it to a mutable version:

type PlayerServicePure =
{
FindPlayers : SearchConfiguration -> list<Player>
UpdatePlayers : SearchConfiguration -> (Player -> Player) -> PlayerServicPure
}

The only difference from the previous API is that UpdatePlayers now returns the next state of the service.

The following example uses a standard FSharp Map for storing players. Simplistic definitions of SearchConfiguration and Player are also provided:

// Represent a player.
type Player = {Name : string ; Credit : int }

// Search configuration is simply a list of names.
type SearchConfiguration = { Names : list<string> }

// This is the pure interface for a player-service.
type PlayerServicePure = {
FindPlayers : SearchConfiguration -> list<Player>
UpdatePlayers : SearchConfiguration -> (Player -> Player) ->PlayerServicePure
}

// Builds a service object given a set of players.
let buildPlayerServicePure players =
let rec build playerMap =
{
FindPlayers = fun sc ->
sc.Names
|> List.choose (fun name -> Map.tryFind name playerMap)
UpdatePlayers = fun sc f ->
(playerMap, sc.Names)
||> Seq.fold (fun pMap name ->
match Map.tryFind name pMap with
| Some p -> Map.add name (f p) pMap
| None   -> pMap
)
|> build
}
players
|> List.map (fun name -> (name, {Name = name; Credit = 0}))
|> Map.ofSeq
|> build

Given a sequence of players, buildPlayersService constructs a service object. Here are some examples of how to program with the immutable service:

// Build a new service
let service = buildPlayerServicePure ["John"; "Jane"; "James"]

// Find all John players
let johns = service.FindPlayers ({Names = ["John"]})

// New service with richer Johns
let service = service.UpdatePlayers {Names = ["John"]} <| fun p ->
{p with Credit = p.Credit + 100}

Update operations are atomic by definition since the only way of noticing the effect of an update is via the next service state returned by UpdatePlayers. Any other problems requiring locking or synchronization do not apply.

Designing and reasoning about the pure implementation is straight forward but we are not able to directly build a web-service interface on top of it. The fundamental problem is that any update operation requested by one user would not be visible to others users.

## Deriving a service wrapper

To implement the original interface we wish to define a transformation from values of PlayerServicePure to PlayerService values also satisfying the constraints given above. The strategy is to capture the latest state of the service by a mutable reference and replace it with newer versions as update operations are processed. Here is an initial attempt:

let buildService players =
let service = ref buildPlayerServiceIM players
{
FindPlayers = fun sc -> service.Value.findPlayers sc
UpdatePlayers = fun sc ->
service := service.Value.UpdatePlayers sc
}

FindPlayers always returns the values of the current service object. The problem with this implementation is the definition of UpdatePlayers. If a second invocation of the function is performed before the first update operation terminates, the updates will be applied to the same service object and the first one to terminate will be discarded. This violates constraint (1).

To accommodate for this we must synchronize the updates so that subsequent operations will be placed in a queue in case the service is currently updating. There is already built in support for this in F# via the MailBoxProccing library providing message passing capabilities between concurrent computations.Here is the extended version based on a MailBox process:

let buildPlayerService players =
let service = ref <| buildPlayerServicePure players
let updateProc = MailboxProcessor.Start <| fun inbox ->
let rec proc () =
async {
let! (sc, f) = inbox.Receive ()
service := service.Value.UpdatePlayers sc f
return! proc ()
}
proc ()
{
FindPlayers = fun sc ->
service.Value.FindPlayers sc
UpdatePlayers = fun sc f ->
updateProc.Post (sc,f)
}

Incoming update requests are now processed one at the time since the recursive call to loop is performed first after an update operation is completed. This addresses constraint number (1). All updates are processed within an asynchronous computation which ensures that invocations of FindPlayers are not blocked, satisfying constraint (2). FindPlayers is non-blocking in accordance with (3). Thanks to the immutable underlying structure we are also guaranteed to always fetch player data from a consistent state as required by constraint (4).

Following is an example of programming with the interface:

// Build the service
let service =
buildPlayerService [ "John" ; "Jane" ; "James" ]

// Extracts credit from player with the given name.
let checkCredit name =
match service.FindPlayers {Names = [name]} with
| [p]   -> p.Credit

// Slowly adds some credit to a player.
service.UpdatePlayers {Names = [name]} <| fun player ->
{player with Credit = player.Credit + amount}

// Runs 10 async computations each adding 1 credit to John 100 times.
// Total number of credits once completed should be 1000.
List.init 10 (fun _ ->
async {
List.replicate 100 1
return ()
}
)
|> Async.Parallel
|> Async.Ignore
|> Async.Start

// Repeatedly prints the current credit of John
let rec trackJohn () =
async {
printfn "Current credit for John %A" <| checkCredit "John"
do! Async.Sleep 1000
return! trackJohn ()
}
trackJohn ()
|> Async.Start

The addCredit function is deliberately made slower in order to test that the implementation can handle queued update operations. Ten async computations each invoking addCredit 100 times, increasing the amount of credit for the player John. In the meanwhile another thread repeatedly reports the current credit status. Here is some output of running the program:

Current credit for John is 48
Current credit for John is 95
...
Current credit for John is 918
Current credit for John is 967
Current credit for John is 1000
Current credit for John is 1000
Current credit for John is 1000

As seen, all update operations were accounted for. That’s not a guarantee but at least an indication that the implementation is sound.

By introducing a thin service layer on top of a pure immutable interface, much of the headache typically involved in designing thread-safe mutable data structures can be avoided. Using this strategy, business logic may be expressed solely in terms of pure functions. Although this example is may seem specific, my experience is that the pattern is general and applicable on many types or services providing CRUD interfaces.

format: plain


text:
v Modeling and identification of an Electro-Hydraulic Actuator · Mirko Mazzoleni

# Modeling and identification of an Electro-Hydraulic Actuator

### Abstract

In this work, a physical non-linear model of an Electro-Hydraulic Actuator has been developed. Each system component (valves, pipes, cylinders) and their interactions have been modeled by means of conservation and constitutive laws. The actuator dynamics, with lumped-parameter element models, have been treated accurately, with special attention given to modeling friction. Finally, a global parametric-identification procedure has been performed for all unknown parameters. Throughout this paper all the modeling assumptions and results from system identification are verified with experimental data. [Paper, Code]

#### Reference

A. L. Cologni, M. Mazzoleni and F. Previdi, "Modeling and identification of an Electro-Hydraulic Actuator", 12th IEEE International Conference on Control and Automation (ICCA), Kathmandu, Nepal, 2016, doi: 10.1109/ICCA.2016.7505299 , ISBN: 978-1-5090-1738-6, pp. 335-340.

#### Bibtex

@INPROCEEDINGS{7505299,
author={A. L. Cologni and M. Mazzoleni and F. Previdi},
booktitle={2016 12th IEEE International Conference on Control and Automation (ICCA)},
title={Modeling and identification of an Electro-Hydraulic Actuator},
year={2016},
volume={},
number={},
pages={335-340},
doi={10.1109/ICCA.2016.7505299},
ISSN={},
ISBN={978-1-5090-1738-6},
month={June},
}


text:
For most numbered asteroids, almost nothing is known apart from a few physical parameters and orbital elements. Some physical characteristics can only be estimated. The physical data is determined by making certain standard assumptions.

## Dimensions

Data from the IRAS minor planet survey[1] or the Midcourse Space Experiment (MSX) minor planet survey[2] (available at the Planetary Data System Small Bodies Node (PDS)) is the usual source of the diameter.

For many asteroids, lightcurve analysis provides estimates of pole direction and diameter ratios. Pre-1995 estimates collected by Per Magnusson[3] are tabulated in the PDS,[4] with the most reliable data being the syntheses labeled in the data tables as "Synth". More recent determinations for several dozens of asteroids are collected at the web page of a Finnish research group in Helsinki which is running a systematic campaign to determine poles and shape models from lightcurves.[5]

These data can be used to obtain a better estimate of dimensions. A body's dimensions are usually given as a tri-axial ellipsoid, the axes of which are listed in decreasing order as a×b×c. If we have the diameter ratios μ = a/b, ν = b/c from lightcurves, and an IRAS mean diameter d, one sets the geometric mean of the diameters ${\displaystyle d=(abc)^{\frac {1}{3))\,\!}$ for consistency, and obtains the three diameters:

${\displaystyle a=d\,(\mu ^{2}\nu )^{\frac {1}{3))\,\!}$
${\displaystyle b=d\,\left({\frac {\nu }{\mu ))\right)^{\frac {1}{3))\,\!}$
${\displaystyle c={\frac {d}{(\nu ^{2}\mu )^{\frac {1}{3))))\,\!}$

## Mass

Barring detailed mass determinations,[6] the mass M can be estimated from the diameter and (assumed) density values ρ worked out as below.

${\displaystyle M={\frac {\pi abc\rho }{6))\,\!}$

Such estimates can be indicated as approximate by use of a tilde "~". Besides these "guesstimates", masses can be obtained for the larger asteroids by solving for the perturbations they cause in each other's orbits,[7] or when the asteroid has an orbiting companion of known orbital radius. The masses of the largest asteroids 1 Ceres, 2 Pallas, and 4 Vesta can also be obtained from perturbations of Mars.[8] While these perturbations are tiny, they can be accurately measured from radar ranging data from the Earth to spacecraft on the surface of Mars, such as the Viking landers.

## Density

Apart from a few asteroids whose densities have been investigated,[6] one has to resort to enlightened guesswork. See Carry[9] for a summary.

For many asteroids a value of ρ~2 g/cm3 has been assumed.

However, density depends on the asteroid's spectral type. Krasinsky et al. gives calculations for the mean densities of C, S, and M class asteroids as 1.38, 2.71, and 5.32 g/cm3.[10] (Here "C" included Tholen classes C, D, P, T, B, G, and F, while "S" included Tholen classes S, K, Q, V, R, A, and E). Assuming these values (rather than the present ~2 g/cm3) is a better guess.

## Surface gravity

 Main article: Surface gravity

### Spherical body

For a spherical body, the gravitational acceleration at the surface (g), is given by

${\displaystyle g_{\rm {spherical))={\frac {GM}{r^{2))}\,\!}$

Where G = 6.6742×10−11 m3s−2kg−1 is the gravitational constant, M is the mass of the body, and r its radius.

### Irregular body

For irregularly shaped bodies, the surface gravity will differ appreciably with location. The above formula then is only an approximation, as the calculations become more involved. The value of g at surface points closer to the center of mass is usually somewhat greater than at surface points farther out.

### Centripetal force

On a rotating body, the apparent weight experienced by an object on the surface is reduced by the centripetal force, when one is away from the poles. The centripetal acceleration experienced at a latitude θ is

${\displaystyle g_{\rm {centrifugal))=-\left({\frac {2\pi }{T))\right)^{2}r\sin \theta }$

where T is the rotation period in seconds, r is the equatorial radius, and θ is the latitude. Its magnitude is maximized when one is at the equator, and sin θ=1. The negative sign indicates that it acts in the opposite direction to the gravitational acceleration g.

The effective acceleration is

${\displaystyle g_{\rm {effective))=g_{\rm {gravitational))+g_{\rm {centrifugal))\ .}$

### Close binaries

If the body in question is a member of a close binary with components of comparable mass, the effect of the second body may also be non-negligible.

## Escape velocity

For surface gravity g and radius r of a spherically symmetric body, the escape velocity is:

${\displaystyle v_{e}={\sqrt {\frac {2GM}{r))))$

## Rotation period

Rotation period is usually taken from lightcurve parameters at the PDS.[11]

## Spectral class

Spectral class is usually taken from the Tholen classification at the PDS.[12]

## Absolute magnitude

Absolute magnitude is usually given by the IRAS minor planet survey[1] or the MSX minor planet survey[2] (available at the PDS).

## Albedo

Astronomical albedos are usually given by the IRAS minor planet survey[1] or the MSX minor planet survey[2] (available at the PDS). These are geometric albedos. If there is no IRAS/MSX data a rough average of 0.1 can be used.

## Surface temperature

### Mean

The simplest method which gives sensible results is to assume the asteroid behaves as a greybody in equilibrium with the incident solar radiation. Then, its mean temperature is obtained by equating the mean incident and radiated heat power. The total incident power is:

${\displaystyle R_{\mathrm {in} }={\frac {(1-A)L_{0}\pi r^{2)){4\pi a^{2))},}$

where ${\displaystyle A\,\!}$ is the asteroid albedo (precisely, the Bond albedo), ${\displaystyle a\,\!}$ its semi-major axis, ${\displaystyle L_{0}\,\!}$ is the solar luminosity (i.e. total power output 3.827×1026 W), and ${\displaystyle r}$ the asteroid's radius. It has been assumed that: the absorptivity is ${\displaystyle 1-A}$, the asteroid is spherical, it is on a circular orbit, and that the Sun's energy output is isotropic.

Using a greybody version of the Stefan–Boltzmann law, the radiated power (from the entire spherical surface of the asteroid) is:

${\displaystyle R_{\mathrm {out} }=4\pi r^{2}\epsilon \sigma T^{4}{\frac {}{)),}$

where ${\displaystyle \sigma \,\!}$ is the Stefan–Boltzmann constant (5.6704×10−8 W/m2K4), ${\displaystyle T}$ is the temperature in kelvins, and ${\displaystyle \epsilon \,\!}$ is the asteroid's infra-red emissivity. Equating ${\displaystyle R_{\mathrm {in} }=R_{\mathrm {out} ))$, one obtains

${\displaystyle T=\left({\frac {(1-A)L_{0)){\epsilon \sigma 16\pi a^{2))}\right)^{1/4}\,\!}$

The standard value of ${\displaystyle \epsilon }$=0.9, estimated from detailed observations of a few of the large asteroids is used.

While this method gives a fairly good estimate of the average surface temperature, the local temperature varies greatly, as is typical for bodies without atmospheres.

### Maximum

A rough estimate of the maximum temperature can be obtained by assuming that when the Sun is overhead, the surface is in thermal equilibrium with the instantaneous solar radiation. This gives average "sub-solar" temperature of

${\displaystyle T_{ss}={\sqrt {2))\,T\approx 1.41\,T,}$

where ${\displaystyle T}$ is the average temperature calculated as above.

At perihelion, the radiation is maximised, and

${\displaystyle T_{ss}^{\rm {max))={\sqrt {\frac {2}{1-e))}\ T,}$

where ${\displaystyle e\,\!}$ is the eccentricity of the orbit.

### Temperature measurements and regular temperature variations

Infra-red observations are commonly combined with albedo to measure the temperature more directly. For example, L.F.Lim et al. [Icarus, Vo. 173, 385 (2005)] does this for 29 asteroids. These are measurements for a particular observing day, and the asteroid's surface temperature will change in a regular way depending on its distance from the Sun. From the Stefan-Boltzmann calculation above,

${\displaystyle T={\rm {constant))\times {\frac {1}{\sqrt {d))},}$

where ${\displaystyle d\,\!}$ is the distance from the Sun on any particular day. If the day of the relevant observations is known, the distance from the Sun on that day can be obtained online from e.g. the NASA orbit calculator,[13] and corresponding temperature estimates at perihelion, aphelion, etc. can be obtained from the expression above.

### Albedo inaccuracy problem

There is a snag when using these expressions to estimate the temperature of a particular asteroid. The calculation requires the Bond albedo A (the proportion of total incoming power reflected, taking into account all directions), while the IRAS and MSX albedo data that is available for asteroids gives only the geometric albedo p which characterises only the strength of light reflected back to the source (the Sun).

While these two albedos are correlated, the numerical factor between them depends in a very nontrivial way on the surface properties. Actual measurements of Bond albedo are not forthcoming for most asteroids because they require measurements from high phase angles that can only be acquired by spacecraft that pass near or beyond the asteroid belt. Some complicated modelling of surface and thermal properties can lead to estimates of the Bond albedo given the geometric one, but this far is beyond the scope of a quick estimate for these articles. It can be obtained for some asteroids from scientific publications.

For want of a better alternative for most asteroids, the best that can be done here is to assume that these two albedos are equal, but keep in mind that there is an inherent inaccuracy in the resulting temperature values.

How large is this inaccuracy?

A glance at the examples in this table shows that for bodies in the asteroid albedo range, the typical difference between Bond and geometric albedo is 20% or less, with either quantity capable of being larger. Since the calculated temperature varies as (1-A)1/4, the dependence is fairly weak for typical asteroid Ap values of 0.05−0.3.

The typical inaccuracy in calculated temperature from this source alone is then found to be about 2%. This translates to an uncertainty of about ±5 K for maximum temperatures.

## Other common data

Some other information for large numbers of asteroids can be found at the Planetary Data System Small Bodies Node.[14] Up-to-date information on pole orientation of several dozen asteroids is provided by Doc. Mikko Kaasalainen,[5] and can be used to determine axial tilt.

Another source of useful information is NASA's orbit calculator.[13]

## References

1. ^ a b c "IRAS Minor Planet Survey Supplemental IRAS Minor Planet Survey". PDS Asteroid/Dust Archive. Archived from the original on 2006-09-02. Retrieved 2006-10-21.
2. ^ a b c "Midcourse Space Experiment (MSX) Infrared Minor Planet Survey". PDS Asteroid/Dust Archive. Archived from the original on 2006-09-02. Retrieved 2006-10-21.
3. ^ Magnusson, Per (1989). "Pole determinations of asteroids". In Richard P. Binzel; Tom Gehrels; Mildred S. Matthews (eds.). Asteroids II. Tucson: University of Arizona Press. pp. 1180–1190.
4. ^ "Asteroid Spin Vectors". Archived from the original on 2006-09-02. Retrieved 2006-10-21.
5. ^ a b Modeled asteroids. rni.helsinki.fi. 2006-06-18.
6. ^ a b For example "Asteroid Densities Compilation". PDS Asteroid/Dust Archive. Archived from the original on 2006-09-02. Retrieved 2006-10-21.
7. ^ Hilton, James L. (November 30, 1999). "Masses of the Largest Asteroids". Archived from the original on February 12, 2009. Retrieved 2009-09-05.
8. ^ Pitjeva, E. V. (2004). Estimations of masses of the largest asteroids and the main asteroid belt from ranging to planets, Mars orbiters and landers. 35th COSPAR Scientific Assembly. Held 18–25 July 2004. Paris, France. p. 2014. Bibcode:2004cosp...35.2014P.
9. ^ Benoit Carry, Density of asteroids, Planetary & Space Science to be published, accessed Dec. 20, 2013
10. ^ Krasinsky, G. A.; Pitjeva, E. V.; Vasilyev, M. V.; Yagudina, E. I. (July 2002). "Hidden Mass in the Asteroid Belt". Icarus. 158 (1): 98–105. Bibcode:2002Icar..158...98K. doi:10.1006/icar.2002.6837.
11. ^ "Asteroid Lightcurve Parameters". PDS Asteroid/Dust Archive. Archived from the original on 2006-09-02. Retrieved 2006-10-21.
12. ^ Asteroid Taxonomies PDS Asteroid/Dust Archive. 2006-10-21.
13. ^ a b "Orbit Diagrams". NASA. Archived from the original on 2000-08-17. Retrieved 2006-06-18.
14. ^ "Asteroid Data Sets". PDS Asteroid/Dust Archive. Archived from the original on 2006-09-28. Retrieved 2006-10-21.


text:
# Afier 76.0 min, 20.0% of & compound has decomposcd, What is the half-life of this reaction assuming first-order kinctics?muid

###### Question:

Afier 76.0 min, 20.0% of & compound has decomposcd, What is the half-life of this reaction assuming first-order kinctics? muid

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Calculate Kp for this reaction at this temperature_ Kp and Kc Preparalion Question 2CH,Clz(g) CHy(g) + CCl(g) Question Question Kp Subm... 5 answers ##### Determine whether the follarng problem Involve Dacmiaoncomhinallon Ie5 not n ec03s nNoblem |Tnedlcilrereitghac nicilokplapiNIaahe uelelyanilarperimenuill dquopeDalc hinc OneislciennaNiaMiy Winy% Cim plopxEhedrd?Tha Droblani involvus â‚¬because Iheol pabenls selecledMtadiet;Dummulaboncombinatkn Determine whether the follarng problem Involve Dacmiaon comhinallon Ie5 not n ec03s n Noblem | Tnedlcilrereitghac nicilok plapi NIaahe uelelyanila rperimenuill dquo peDalc hinc Oneislcien naNia Miy Winy% Cim plopx Ehedrd? Tha Droblani involvus â‚¬ because Ihe ol pabenls selecled Mtadiet; Dummul... 1 answer ##### The HCF of polynomials$\left(x^{2}-2 x+1\right)(x+4)$and$\left(x^{2}+3 x-4\right)(x+1)$is (1)$(x+4)(x-1)$(2)$(x+1)(x+4)$(3)$(x+1)(x-4)$(4)$\left(x^{2}-1\right)(x+4)$The HCF of polynomials$\left(x^{2}-2 x+1\right)(x+4)$and$\left(x^{2}+3 x-4\right)(x+1)$is (1)$(x+4)(x-1)$(2)$(x+1)(x+4)$(3)$(x+1)(x-4)$(4)$\left(x^{2}-1\right)(x+4)$... 5 answers ##### Rectangular box placed in region where there cm; ab 10.0 cm; and bc 12.0 cm.uniton maonetic field of magnitude 0.0370 directedthe right: In tne diagram the field lines are represented by the green amow 5 Here cg 29.0Determinemagnetic flux; Including the sign; through each of the six faces of the box:efgh ndheabie cdhgLol rectangular box placed in region where there cm; ab 10.0 cm; and bc 12.0 cm. uniton maonetic field of magnitude 0.0370 directed the right: In tne diagram the field lines are represented by the green amow 5 Here cg 29.0 Determine magnetic flux; Including the sign; through each of the six faces of the... 5 answers ##### Biocontrol of malaria vectors has been difficult inpractice. For example, nematodesor Gambusia work against mosquito larvae, but atbest control the total number of larvae. The fungal approachmight be more promising. Multiple advantages have beenidentified. That being said, one of the following is NOT anadvantage of using fungi. Which one?A. Nematodes and Gambusia work against larvae, fungi againstadultsB. Because fungi act slowly in mosquitoes, they primarily affectolder mosquitoes. This av Biocontrol of malaria vectors has been difficult in practice. For example, nematodes or Gambusia work against mosquito larvae, but at best control the total number of larvae. The fungal approach might be more promising. Multiple advantages have been identified. That being said, one of the follow... 1 answer ##### 5 Unanswered A project requires$600,000 in equipment which is expected to have a salvage value...
5 Unanswered A project requires $600,000 in equipment which is expected to have a salvage value of$40,000 when the project ends in 8 years. If the equipment can be depreciated straight-line to its salvage value, what is the annual depreciation expense? Type your response 2 attempts left. Submit...


text:
## Saturday, January 23, 2010

### Project Euler #24: Lexicographic permutations

Here is the question:

A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:

012 021 102 120 201 210

What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?

Only an elementary understanding of combinatorics is required to solve this problem by hand. Start with the smallest possible digit (0 in this case), then find the number of permutations of the remaining digits. If this number is less than 1000000, then 0 cannot be the first digit in the 1000000th permutation.

Try 1 instead, and count the number of permutations. Keep going with 2, 3, 4, etc until the number of permutations exceeds 1000000. Suppose that fixing the first digit at $$k$$ results in more than 1000000 permutations; this means the first digit is fixed at $$k-1$$, and the second digit must be examined by this method.

A diligent Project Euler enthusiast can execute this method by hand, but here is a simple program written in Scala that demonstrates this method:

val digits = List(0,1,2,3,4,5,6,7,8,9)
val target = 1000000

def fact(n: Int): Int = {
def recur(n: Int, acc: Int): Int = if (n == 1) acc else recur(n-1, n*acc)
if (n == 0) 1 else recur(n, 1)
}

def compute(list: List[Int]): List[Int] = {
def recur(list: List[Int], current: Int): List[Int] = {
val permutations = fact(list.length - 1)
val index = (target - current) / permutations
val digit = list(index)
val next = current + index * permutations
list.length match {
case 2 if target - current == 0 => list
case 2 if target - current == 1 => list.reverse
case _                          => digit :: recur(list - digit, next)
}
}
recur(list, 1)
}

val result = compute(digits).mkString("")
println(result)


text:
# zbMATH — the first resource for mathematics

On the stability of the quadratic functional equation and its applications. (English) Zbl 1009.39025
From the introduction: To quote S. M. Ulam, for very general functional equations, one can ask the following question. When is it true that the solution of an equation differing slightly from a given one, must necessarily be close to the solution of the given equation? Similarly, if we replace a given functional equation by a functional inequality, when can one assert that the solutions of the inequality lie near the solutions of the equation?
The present paper will provide a solution to Ulam’s problem for the case of the quadratic functional equation.
The quadratic functional equation $f(x+y)+f(x-y)-2f(x)-2f(y)=0$ clearly has $$f(x)=cx^2$$ as a solution with $$c$$ an arbitrary constant when $$f$$ is a real function of a real variable. We are interested in functions $$f: E_1\to E_2$$ where both $$E_1$$ and $$E_2$$ are real vector spaces.

##### MSC:
 39B82 Stability, separation, extension, and related topics for functional equations 39B62 Functional inequalities, including subadditivity, convexity, etc.


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 Model. Anal. Inform. Sist., 2009, Volume 16, Number 1, Pages 16–23 (Mi mais45)

On the number of components in edge unfoldings of convex polyhedra

V. V. Astakhov, A. A. Gavrilyuk

M. V. Lomonosov Moscow State University

Abstract: In the theory of convex polyhedra there is a problem left unsolved which is sometimes called The Durer problem: Does every convex polyhedron have at least one connected unfolding? In this paper we consider a related problem: Find the upper bound $c(P)$ for the number of components in the edge unfolding of a convex polyhedron $P$ in terms of the number $F$ of faces. We showed that $c(P)$ does not exceed the cardinality of any dominating set in the dual graph $G(P)$ of the polyhedron $P$. Next we proved that there exists a dominating set in $G(P)$ of cardinality not more than $3F/7$. These two statements lead to an estimation $c(P)\le 3F/7$ that was proved in this work.

Keywords: convex polyhedron, edge unfolding, dominating set

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UDC: 519.17

Citation: V. V. Astakhov, A. A. Gavrilyuk, “On the number of components in edge unfoldings of convex polyhedra”, Model. Anal. Inform. Sist., 16:1 (2009), 16–23

Citation in format AMSBIB
\Bibitem{AstGav09} \by V.~V.~Astakhov, A.~A.~Gavrilyuk \paper On the number of components in edge unfoldings of convex polyhedra \jour Model. Anal. Inform. Sist. \yr 2009 \vol 16 \issue 1 \pages 16--23 \mathnet{http://mi.mathnet.ru/mais45}


text:
R scripts: hierarchical2.R

Mlxtran codes: model/hierarchical2.txt

# 1 Introduction

We have seen in the previous article that the vector of individual parameters $$\psi_i$$ is treated as a random vector in a population context.

When the probability distribution of $$\psi_i$$ depends on a vector of individual covariates $$c_i$$, we can also consider that $$c_i$$ is a random vector sampled from a population distribution $$\pmacro(\, c_i \,;\theta)$$.

In this context, the model for individual $$i$$ is the joint distribution of the longitudinal data $$y_i$$, the individual parameters $$\psi_i$$ and the individual covariates $$c_i$$: $\pmacro(y_i , \psi_i, c_i; \theta)=\pmacro(y_i | \psi_i ) \, \pmacro(\psi_i c_i ; \theta) \, \pmacro(c_i ; \theta).$

The model $$\pmacro(c_i ; \theta)$$ for the individual covariates is implemented in the section [COVARIATE].

# 2 Example

We consider the model defined in the previous article:

• Given $$V_i$$, each $$y_{ij}$$ is normally distributed:
1. $y_{ij} | V_i \sim {\cal N} \left( \frac{100}{V_i}e^{-k \, t_{ij}} , a^2 \right) .$
• $$V_i$$ is lognormally distributed and depends on the covariate $$w_i$$:
1. $\log(V_i) \iid {\cal N}\left(\log \left(V_{\rm pop} \left({w_i}/{w_{\rm pop}}\right)^{\beta}\right) \ ,\ \omega_V^2\right).$

We assume furthermore that $$w_i$$ is normally distributed:

1. $w_i \iid {\cal N}\left(w_{\rm pop} \ ,\ \omega_w^2\right).$

This model is implemented in hierarchical3.txt.

[LONGITUDINAL]
input = {V, k, a}

EQUATION:
f = 100/V*exp(-k*t)

DEFINITION:
y = {distribution = normal, prediction = f, sd = a}

;----------------------------------------------
[INDIVIDUAL]
input = {V_pop, omega_V, w, w_pop}

EQUATION:
V_pred = V_pop*(w/w_pop)

DEFINITION:
V = {distribution = lognormal, prediction = V_pred, sd = omega_V}

;----------------------------------------------
[COVARIATE]
input = {w_pop, omega_w}

DEFINITION:
w = {distribution = normal, mean = w_pop, sd = omega_w}

We will use simulx for sampling one individual covariate $$w_i$$, one individual parameter $$V_i$$ and one sequence $$y_i=(y_{ij})$$ for one individual $$i=1$$, with some given values of the population parameters $$V_{pop}$$, $$\omega_V$$, $$w_{pop}$$, $$\omega_w$$, $$k$$ and $$a$$.

p <- c(V_pop=10, omega_V=0.1, beta=1, w_pop=70, omega_w=12, k=0.15, a=0.5)

f   <- list(name='f', time=seq(0, 30, by=0.1))
y   <- list(name='y', time=seq(1, 30, by=3))
ind <- list(name=c('w','V'))
out <- list(ind, f, y)

res1 <- simulx(model     = 'model/hierarchical2.txt',
parameter = p,
output    = out,
settings  = list(seed = 12345))

When several individual parameters and/or covariates are defined in the list of outputs, simulx also returns them as an additional element parameter.

print(res1$parameter) ## w V ## 1 70.98498 11.04154 plot(ggplot() + geom_line( data=res1$f, aes(x=time, y=f), colour="black") +
geom_point(data=res1$y, aes(x=time, y=y), colour="red")) Instead of only one individual, let us now simulate a group of 5 individuals with individual covariates $$w_i$$ drawn for each individual $$i=1,2,\ldots,5$$. The level of randomization is therefore ‘covariate’. g <- list( size = 5, level = 'covariate') res2 <- simulx(model = 'model/hierarchical2.txt', parameter = p, output = out, group = g, settings = list(seed = 12345)) print(res2$parameter)
##   id        w         V
## 1  1 70.98498 11.041537
## 2  2 80.21273 11.424322
## 3  3 69.63671  9.498118
## 4  4 64.44544  9.627048
## 5  5 75.36014  8.524051
plot(ggplot() + geom_line(data=res2$f, aes(x=time, y=f, colour=id), size=0.75) + geom_point(data=res2$y, aes(x=time, y=y, colour=id), size=2))

We can combine several levels of randomization, and draw, for instance, 2 individual covariates $$w_1$$, $$w_2$$ and 3 individual parameters $$V_i$$ per covariate

g <- list( size  = c(2,3),
level = c('covariate','individual'))

res3 <- simulx(model     = 'model/hierarchical2.txt',
parameter = p,
output    = out,
group     = g,
settings  = list(seed = 12345))

print(res3$parameter) ## id w V ## 1 1 70.98498 11.041537 ## 2 2 70.98498 10.110058 ## 3 3 70.98498 9.682016 ## 4 4 80.21273 11.982412 ## 5 5 80.21273 9.072930 ## 6 6 80.21273 10.050901 In the next example, we draw 2 individual covariates, 2 individual parameters per covariate and 2 sequences of longitudinal data per individual parameters. g <- list( size = c(2,2,2), level = c('covariate','individual','longitudinal')) res4 <- simulx(model = 'model/hierarchical2.txt', parameter = p, output = out, group = g, settings = list(seed = 123123)) print(res4$parameter)
##   id         w        V
## 1  1  69.97862 12.85809
## 2  2  69.97862 12.85809
## 3  3  69.97862 10.12943
## 4  4  69.97862 10.12943
## 5  5 100.20319 13.28821
## 6  6 100.20319 13.28821
## 7  7 100.20319 16.36998
## 8  8 100.20319 16.36998
plot(ggplot() + geom_line(data=res4$f, aes(x=time, y=f, colour=id), size=0.75) + geom_point(data=res4$y, aes(x=time, y=y, colour=id), size=2))

pa <- c(V_pop=10, omega_V=0.1, w_pop=70, beta=1, k=0.15, a=0.5)
pw <- data.frame(id=1:4, w=c(60,70,80,90))
res5a <- simulx(model     = 'model/hierarchical1b.txt',
parameter = list(pa,pw),
output    = out,
settings  = list(seed = 123123))

print(res5a$parameter) ## id w V ## 1 1 60 8.569901 ## 2 2 70 12.862014 ## 3 3 80 11.580032 ## 4 4 90 11.935142 res5b <- simulx(model = 'model/hierarchical1b.txt', parameter = list(pa,pw), output = out, group = list(size = 7), settings = list(seed = 1231)) print(res5b$parameter)
##   id  w         V
## 1  1 60  7.774017
## 2  2 70  9.277483
## 3  3 80 10.296795
## 4  4 90 13.118423
## 5  5 60  8.206328
## 6  6 70  9.853925
## 7  7 90 14.364631
res5c <- simulx(model     = 'model/hierarchical1b.txt',
parameter = list(pa,pw),
output    = out,
group     = list(size = 2),
settings  = list(seed = 123123))

print(res5c\$parameter)
##   id  w         V
## 1  1 70  9.998218
## 2  2 80 14.699444


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At a certain university, 75% of students have driver’s licences and 6

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At a certain university, 75% of students have driver’s licences and 6  [#permalink]

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[GMAT math practice question]

At a certain university, 75% of students have driver’s licences and 60% of the students with driver’s licences are foreign students. What percentage of the total students are foreign students without a driver’s licence?

1) There are 5,000 students at the university.
2) 55% of students at the university are foreigners.

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager Status: Quant Expert Q51 Joined: 02 Aug 2014 Posts: 106 Re: At a certain university, 75% of students have driver’s licences and 6 [#permalink] Show Tags 29 Nov 2017, 02:02 1) There are 5,000 students at the university. Using this information we can know the number of students that have driver lisence and foreigners but we know nothing about people who don't have drivers lisence, they could be all foreigners and half of them could be foreigners, so no enough information. 2) 55% of students at the university are foreigners. 75% of students have driver’s licences and 60% of the students with driver’s licences are foreign students. So 0.75*0.6= 0.45 so 45% of students in the university are foreigners with a driver's lisence. 55% of students at the university are foreigners. so 10% is the percentage of foreigners without a driver’s licence. Sufficient Answer B _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6832 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: At a certain university, 75% of students have driver’s licences and 6 [#permalink] Show Tags 01 Dec 2017, 00:08 => Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question. Attachment: A.png [ 2.57 KiB | Viewed 498 times ] $$45s + 30s + b + d = 100s.$$ $$b + d = 25s.$$ The question asks for the value of $$\frac{b}{100s}$$. To solve problems involving 2x2 matrices and percentages, we need 3 percentages. Since we have 2 percentages, 75% and 60%, one more percentage is required. Condition 1) does not provide a percentage, while condition 2) gives us a percentage. So, the answer is most likely to be B. Condition 1) $$100s = 5,000.$$ $$s = 50.$$ This is not sufficient. Condition 2) $$45s + b = 55s$$ $$b = 10s$$ Thus $$(\frac{b}{100s})*100$$ = $$(\frac{10s}{100s})*100$$ = $$10 %.$$ This is sufficient. Therefore, the answer is B. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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Re: At a certain university, 75% of students have driver’s licences and 6 &nbs [#permalink] 01 Dec 2017, 00:08
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