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Floating point – proof that a guard digit has limited the deduction error

I have read what every computer scientist should know about floating point arithmetic, which is extremely interesting. However, I have some difficulty understanding the proof of Theorem 9 (page 33).

First a pretty trivial question. If the formula (15) $ say:
$$ y – bar {y} lt ( beta – 1) ( beta ^ {- p} + dots + beta ^ {- p-k}) $$
Should not it be? $ le $ instead of $ lt $or did I miss something?

More importantly, I do not understand why it says so if $ x- bar {y} lt $ 1, then $ delta = 0 $, How can there be no rounding error?

Then it means:
$$ x – y ge 1.0 – 0. overbrace {0 dots 0} ^ k overbrace { rho dots rho} ^ k ; textrm {with} ; rho = beta – 1 $$

Why is that? The difference can not be arbitrarily small or even $ 0 $?

And overall, correct me if I'm wrong, but the guard digit just saves the day when the input floats $ x $ and $ y $ are the exact numbers we want to subtract. If they are the well-rounded result of another calculation, there can still be a catastrophic cancellation. The guard digit would only bring the calculated value into the correct range.

Metrics – Why Can not a Tor Node Be a Guard and an Exit Node at the Same Time?

Because protective relays (also called infeed relays) can never be output relays.

If you use a proxy or VPN, you have some anonymity, but also a single point of failure.
If somebody compromises your machine when forwarding, it knows your IP address and the IP address of your destination.

Tor protects against this by interposing at least 3 proxies (relays):

You---[ Tor 1 (entry) ]-[ Tor 2 (middle) ]-[ Tor 3 (exit) ]--Aim

Relay 1 knows who you are, but not where you are going.

Relay 2 only knows where it should be forwarded in the network.

Relay 3 knows where you are going, but not who you are.

In this way, an attacker looking at the network can not easily see where he is
You see where the input node sends its data or where the output node receives its data.

So if you try to separate things so much, the two most sensitive relays, retracting and extending, can not be run on the same machine.

dnd 5e – Can a sorcerer's arcane sentry guard only absorb damage from a projected guard attack?

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Give Tyco nozzles the original prices for contractors

In times of social development, the topic of safety and life safety is increasingly being improved. Accordingly, the topic FPF is focused. However, with the current market disruption: rampant false nozzles, different prices, … Contractors are difficult to find a reputable provider. Come to us: Traders who specialize in delivering sprinkler sprinklers to contractors at original prices – An Phat Technology and Trading Development Company Limited.
A phat is a true distributor of Tyco nozzles with various types such as sprinkler sprinkler heads, sprinkler nozzles down, horizontal sprinkler nozzles, ceiling nozzles and nozzles. For a variety of models, make sure you meet all the features of the protected area.
A Phat product portfolio includes:

1. Standard sprinkler
This is a series of jets that meet the requirements of public areas that are less dangerous, such as restaurants, hotels, banks, shops …
Their maximum working pressure is normally 12.1 bar (175 psi) with a low average injection coefficient of K = 2.8 to K = 8.0

2. Dry nozzle for cold storage
This type of antifreeze nozzle is named after its name in high-risk environments. Dry jets are often installed in systems without water in the pipeline. Only when a fire is detected, the fire extinguishing system is activated, the valve system releases water and allows water to get into the nozzle. Open fire work.
Their maximum working pressure is normally 12.1 bar (175 psi) with an average injection factor of K = 5.6 to K = 16.8.
In addition, this nozzle line is usually coated with a coating or rust-resistant wax to serve corrosive environments.

3. Nozzles for warehouses
The warehouse spray series is designed for the protection of warehouses, large warehouses or high storage shelves. In addition, they are also used in underground firefighting applications.
Their maximum working pressure is normally 12.1 bar (175 psi) with a high injection coefficient between K = 5.6 and K = 25.2.
Nozzles usually have a protective frame or shield that acts as a trigger to prevent collisions and to activate them early in a fire.

Tyco nozzles for bearings have a long reach

4. The spray head has a wide cover
This is the copper spray line with a long range of up to 392, which is used to protect dangerous environments at low or normal levels such as restaurants, hotels, offices. Some types are used instead of sprinkler nozzles pointing up or down if the structure of the structure does not reach the pipe on the ceiling.
Their maximum working pressure is normally 12.1 bar (175 psi) with a high injection coefficient between K = 5.6 and K = 25.2.
To meet the aesthetic demands of a range of buildings, Tyco has launched a range of products with a wide range of flat or negative flat plate nozzles and an effective fire fighting concept. does not cause any loss of beauty.

5. Nozzles for residential areas
It is often referred to as an aesthetic spray line. The nozzle of this line normally has a maximum working pressure of 12,1 bar (175 psi) with a low injection coefficient of K = 3.0 to K = 6.9.

Tyco residential sprinkler jets

They have been specially developed for residential areas such as houses, apartments, hostels, hotels with high heat sensitivity and water release properties, which have been specially developed to combat fires and to increase capacity. Canopy residents

6. nozzles for special areas
In FPF work, some specialized areas such as psychiatric institutes, prisons, reeducation camps and refurbishment are relatively difficult to plan, install and operate the system to ensure healing. Firing Effectively Because every item here is in danger of becoming a weapon for individuals to attack others and hurt themselves.
To understand this challenge, Tyco has launched a special sprinkler line that is often installed in a flat design in a ceiling or wall whose color matches the color of the protected area. If you successfully complete your firefighting tasks, you can avoid the risk of damage.
Their maximum working pressure is normally 12.1 bar (175 psi) with an average injection coefficient between K = 4.2 and K = 8.0

7. Open the nozzle
This is a nozzle line without heat sensors used in foam fire and membrane fire extinguishing systems.
Their maximum working pressure is normally 12.1 bar (175 psi) with separate purge design and outlet speed.

Tyco sprinkler nozzles

Depending on the intended use. Some nozzles are coated with a rust-proofing coating or wax to serve corrosive environments.

Above you can find a list of fire extinguisher products from An Phat. For the selection of the equipment and your suppliers we would like to send you the price list of the Tyco sprinkler nozzles.

Under the motto of long-term cooperation based on product quality and prestige, we look forward to working with customers. Please contact a phat if you need advice and offer!


dnd 5e – If someone charms a Disenchanter and then damages his Arcane Guard, does the spell cast end?

There is a certain amount of DM discretion here, but I would say yes in most cases. As quoted in the question, Charm person ends up when

you or your companions something harmful to the goal

In D & D 5e, words mean what they mean in plain language. "Harmful" means in plain text: "cause or likely cause damage." Even if the Arcane Guard's attack is completely blocked (or missing), he was probably "at the time he was tried to cause damage."

Another reference to the use of the spell will be found later in its description.

The enchanting creature regards you as a friendly acquaintance.

If you do anything that makes it impossible for you to reasonably consider yourself a friendly acquaintance, the spell ends (probably – again at the discretion of DM).

Identity Guard Review and Best Identity Theft Protection – Social Media Marketing (SMM)

No identity theft is the best identity theft protection and identity guard in the modern world today. A late guest of the Identity Theft Resource Center (ITRC) presented a report on therapeutic identity theft fraud that prevented him from filling his own required medication. The ITRC is a charity that forwards free administrations to those involved in identity fraud. Take a look at the website and see the best reviews about Identity Guard:

Windows Credential Guard protects credentials, but not remote access with the same credentials?

I wonder what the real purpose is to protect credentials through Windows Credential Guard (WCG) when malicious administrators can access them cached Credentials (i.e., those not protected by WCG) and request WCG to issue a remote login token to effectively access a critical remote system, as if the "real" credentials (which are stored in WCG)?

AFAIK, while WCG protects credentials (for PtH and the like), does not protect it access which can be retrieved with the same credentials (for example, remote login to a system).

Can someone explain / explain this? Many Thanks