text:
LATP World Tour 2017 és el circuit de tennis professional masculí de l'any 2017 organitzat per l'Associació de Tennistes Professionals (ATP). La temporada inclou un total de 62 torneigs a 31 països dividits en Grand Slams organitzats per la Federació Internacional de Tennis (conegut amb el sigle anglès ITF), ATP World Tour Masters 1000, sèries ATP World Tour 500, sèries ATP World Tour 250 i un ATP World Tour Finals. També s'inclou la disputa de la Copa Davis i la Copa Hopman. Els torneigs es van disputar entre el 2 de gener de 2017 i el 26 de novembre de 2017.

Calendari
Taula sobre el calendari complet dels torneigs que pertanyen a la temporada 2017 de l'ATP World Tour. També s'inclouen els vencedors dels quadres individuals i dobles de cada torneig.

Estadístiques
La següent taula mostra el nombre de títols aconseguits de forma individual (I), dobles (D) i dobles mixtes (X) aconseguits per cada tennista i també per països durant la temporada 2017. Els torneigs estan classificats segons la seva categoria dins el calendari ATP World Tour 2017: Grand Slams, ATP World Tour Finals, ATP World Tour Masters 1000, sèries ATP World Tour 500 i sèries ATP World Tour 250. L'ordre del jugadors s'ha establert a partir del nombre total de títols i llavors segons la categoria dels títols.

Títols per tennista

Títols per país

Rànquings

Individual

Evolució número 1

Dobles

Evolució número 1

Guardons
 Millor tennista individual: Rafael Nadal

 Millor retorn de l'any: Roger Federer
 Millora de l'any: Denis Shapovalov
 Stefan Edberg Sportsmanship Award: Roger Federer
 Arthur Ashe Humanitarian of the Year: Horia Tecău
 Millor entrenador de l'any: Neville Godwin (entrenador de Kevin Anderson)
 Tennista favorit individual: Roger Federer
 Equip favorit: Bob Bryan i Mike Bryan
 Ron Bookman Media Excellence Award: Guillermo Salatino

Distribució de punts

Referències

Enllaços externs
 Web oficial de l'Associació de Tennistes Professional (ATP)
 Web oficial de la Federació de Tennis Internacional (ITF)

Competicions tennístiques del 2017


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25.5. Syntax of the +CMGS AT Command in SMS PDU Mode
In SMS PDU mode, the syntax of the +CMGS AT command is:
+CMGS=TPDU_length<CR>SMSC_number_and_TPDU<Ctrl+z>
Before we discuss each of the parameters, let's see an example that gives you some idea of how an actual command line should look like:
AT+CMGS=42<CR>07915892000000F001000B915892214365F7000021493A283D0795C3F33C88FE06CDCB6E32885EC6D341EDF27C1E3E97E72E<Ctrl+z>
The TPDU_length Parameter
The first parameter of the +CMGS AT command, TPDU_length, specifies the length (in octets. 1 octet = 8 bits) of the TPDU (Transfer Protocol Data Unit) assigned to the SMSC_number_and_TPDU parameter. In the earlier example command line, the value assigned to the SMSC_number_and_TPDU parameter is:
07915892000000F001000B915892214365F7000021493A283D0795C3F33C88FE06CDCB6E32885EC6D341EDF27C1E3E97E72E
It can be divided into two parts. The following part is the TPDU:
01000B915892214365F7000021493A283D0795C3F33C88FE06CDCB6E32885EC6D341EDF27C1E3E97E72E
The TPDU is coded in hexadecimal format. Each character represents 4 bits, i.e. 1/2 octet. The TPDU has 84 characters and so there are totally 42 octets. That's why the value assigned to the TPDU_length parameter is 42.
The <CR> Character
<CR>, which represents the carriage return character, follows the TPDU_length parameter. When the GSM/GPRS modem or mobile phone receives the carriage return character, it will send back a prompt formed by these four characters: the carriage return character, the linefeed character, the ">" character and the space character. If you don't understand what this means, don't worry. This should be clear to you when you see the example in the section "Example Demonstrating How to Use the +CMGS AT Command to Send SMS Text Messages in SMS PDU Mode".
The SMSC_number_and_TPDU Parameter
The second parameter of the +CMGS AT command, SMSC_number_and_TPDU, specifies the SMSC number and the TPDU in hexadecimal format. Entering the <Esc> character will cancel the +CMGS AT command. If you don't understand what this means, see the example in the section "Example Demonstrating How to Use the +CMGS AT Command to Send SMS Text Messages in SMS PDU Mode".
The <Ctrl+z> Character
When you finish entering the value for the SMSC_number_and_TPDU parameter, you have to enter the <Ctrl+z> character to mark the end of the value. The GSM/GPRS modem or mobile phone will then attempt to send the SMS message to the SMS center.
25.5.1. Some Explanation about the Coding of the SMSC_number_and_TPDU Parameter Value of the +CMGS AT Command
This section provides some explanation about the coding of the SMSC_number_and_TPDU parameter value of the +CMGS AT command. Let's consider the SMSC_number_and_TPDU parameter value in the earlier example command line:
The above value can be divided into two parts, as shown below. The first part contains information about the SMSC to be used for sending the SMS message. The second part is the TPDU.
07915892000000F0
25.5.1.1. The SMSC Part
The SMSC part can be further divided into three sub-fields, like this:
07 91 5892000000F0
The First Sub-field: Length of the Second and Third Sub-fields
The first sub-field specifies the length in octets of the following two sub-fields. There are 14 hexadecimal digits in "915892000000F0" and each hexadecimal digit represents 4 bits. So, there are totally 7 octets. That's why the value of the first sub-field is 0x07.
The Second Sub-field: Type of SMSC Number
The second sub-field specifies the type of the SMSC number assigned to the third sub-field. Two values are commonly used. They are 0x81 (129 in decimal) and 0x91 (145 in decimal):
0x81. It means the SMSC number is formatted using the typical ISDN / telephony numbering plan (ITU E.164/E.163) but it is not sure whether the SMSC number is an international number, a national number or a number of other types. For example, suppose the SMSC number provided to you by the mobile network operator for sending SMS messages is "+85290000000". If the value of the second sub-field is 0x81, the SMSC number assigned to the third sub-field can be either "85290000000" (country code included) or "90000000" (country code omitted).
0x91. It means the SMSC number is formatted using the typical ISDN / telephony numbering plan (ITU E.164/E.163) and it is an international number. For example, suppose the SMSC number provided to you by the mobile network operator for sending SMS messages is "+85290000000". If the value of the second sub-field is 0x91, the SMSC number assigned to the third sub-field should be "85290000000".
The Third Sub-field: SMSC Number
The third sub-field specifies the SMSC number for sending the SMS message. 0x5892000000F0 represents the phone number +85290000000. Here's how the value 0x5892000000F0 is obtained:
Starting from the left, group the digits of the phone number 85290000000 into pairs, like this: 85 29 00 00 00 0.
As the last group has only one digit, we add an "F" to make up a pair. The result is 85 29 00 00 00 0F.
Swap the digits in each pair and you will get 58 92 00 00 00 F0.
It is possible to tell the GSM/GPRS modem or mobile phone to use the SMSC number specified by the AT command +CSCA (command name in text: Service Centre Address) for sending SMS messages. Just assign the value 0x00 to the first sub-field and omit the second and third sub-fields, i.e. the SMSC part becomes:
25.5.1.2. The TPDU Part (SMS-SUBMIT TPDU)
The TPDU part can be divided into nine sub-fields, as shown below. This is a TPDU of the type SMS-SUBMIT.
01 00 0B 91 5892214365F7 00 00 21 493A283D0795C3F33C88FE06CDCB6E32885EC6D341EDF27C1E3E97E72E
The First Sub-field: First Octet of the TPDU
The first sub-field is the first octet of the TPDU. It tells the GSM/GPRS modem or mobile phone several things:
the type of the TPDU
whether the SMSC should reject duplicated TPDUs
whether a validity period exists in the TPDU, and the format of the validity period if it exists
whether a reply path is requested
whether a user data header exists in the TPDU
whether a status report is requested from the SMSC
The value 0x01 means:
the type of the TPDU is SMS-SUBMIT
the SMSC should not reject duplicated TPDUs
no validity period exists in the TPDU
no reply path is requested
no user data header exists in the TPDU
no status report is requested from the SMSC
The Second Sub-field: Message Reference Number
The second sub-field specifies the message reference number. It is an integer in the range from 0 to 255. The value 0x00 tells the GSM/GPRS modem or mobile phone to assign a message reference number to the SMS message automatically.
The Third Sub-field: Length of the Destination Phone Number
The third sub-field specifies the length in digits of the destination phone number. The destination phone number specified in the fifth sub-field is "+85291234567", which has 11 digits. Thus, the value of the third sub-field is 0x0B (i.e. 11 in decimal).
The Fourth Sub-field: Type of the Destination Phone Number
The fourth sub-field specifies the type of the destination phone number assigned to the fifth sub-field. Two values are commonly used. They are 0x81 (129 in decimal) and 0x91 (145 in decimal):
0x81. It means the destination phone number is formatted using the typical ISDN / telephony numbering plan (ITU E.164/E.163) but it is not sure whether the destination phone number is an international number, a national number or a number of other types. For example, suppose you want to send an SMS message to the phone number "+85291234567". If the value of the fourth sub-field is 0x81, the destination phone number assigned to the fifth sub-field can be either "85291234567" (country code included) or "91234567" (country code omitted).
0x91. It means the destination phone number is formatted using the typical ISDN / telephony numbering plan (ITU E.164/E.163) and it is an international number. For example, suppose you want to send an SMS message to the phone number "+85291234567". If the value of the fourth sub-field is 0x91, the destination phone number assigned to the fifth sub-field should be "85291234567".
The Fifth Sub-field: Destination Phone Number
The fifth sub-field specifies the destination phone number. The value 0x5892214365F7 represents the phone number +85291234567. Here's how the value 0x5892214365F7 is obtained:
The Sixth Sub-field: Protocol Identifier
The sixth sub-field specifies the protocol identifier. Its value should be 0x00 for normal cases.
The Seventh Sub-field: Data Coding Scheme
The seventh sub-field specifies the data coding scheme. With 0x00, we inform the GSM/GPRS modem or mobile phone that the text in the SMS message body is encoded according to the "GSM 7-bit default alphabet" text coding scheme.
The Eighth Sub-field: Length of the SMS Message Body
The eighth sub-field specifies the length of the SMS message body in septets (1 septet = 7 bits). The value 0x21 means there are 33 septets (or characters, since each character is represented by 7 bits according to the "GSM 7-bit default alphabet" text coding scheme) in the SMS message body.
The Ninth Sub-field: SMS Message Body
The ninth sub-field specifies the SMS message body. The value 0x493A283D0795C3F33C88FE06CDCB6E32885EC6D341EDF27C1E3E97E72E represents the text message "It is easy to send text messages.". Below shows how the hexadecimal value is obtained:
Encode the SMS text message "It is easy to send text messages." according to the character set "GSM 7-bit default alphabet". For example, 0x49 is used to represent the first character "I" in the SMS text message, 0x74 is used to represent the second character "t", etc. To find the code representing a certain character, see "Appendix: GSM 7-bit Default Alphabet Table (with Character Codes of ISO 8859 Latin 1)" of this SMS tutorial.
After encoding, the SMS text message "It is easy to send text messages." becomes:
49 74 20 69 73 20 65 61 73 79 20 74 6F 20 73 65 6E 64 20 74 65 78 74 20 6D 65 73 73 61 67 65 73 2E
With the character set "GSM 7-bit default alphabet", each character is represented by 7 bits. If the SMS text message is encoded as above, 1 bit is wasted in every octet. To prevent this from happening, the SMS specification requires us to pack the 7-bit characters in octets. The packing process is described below:
The binary representation of the first character is 1001001. Since the most significant bit of the first octet is unused, we fill it by the least significant bit of the second character, which is 0. (The binary representation of the second character is 1110100.) As a result, the first octet contains the binary value 01001001, which is 0x49 in hexadecimal format.
As the least significant bit of the second character has been moved to the first octet, the second octet now contains the binary value 111010 and the two bits at the leftmost position of the second octet is unused. We fill them by the two least significant bits of the third character, which are both 0. (The binary representation of the third character is 0100000.) As a result, the second octet contains 00111010, which is 0x3A in hexadecimal format.
Similarly, since the two least significant bits of the third character have been moved to the second octet, the third octet now contains the binary value 01000 and the three bits at the leftmost position of the third octet is unused. So, we fill them by the three least significant bits of the fourth character, which are 0, 0 and 1. (The binary representation of the fourth character is 1101001.) Now the third octet contains the binary value 00101000, which is 0x28 in hexadecimal format.
The packing process continues. This is illustrated in the following table.
Bit 7
Octet 1
0x3A
0x3D
0xC3
0xF3
0x3C
Octet 10
0xFE
0xCB
0x6E
0xD3
0xED
0xE7

redpajama_set_name: RedPajamaCommonCrawl


Clash Royale Review – A Hybrid of Card Games, Moba, and Awesome. The thing about mobile gaming is that you never really know when a big, defining game comes around. Flappy Bird takes over the world out of nowhere. Crossy Road sure was fun and well-made, but I never saw it becoming the smash hit it became.
It inspired countless imitators. Candy Crush Saga and its sequels somehow became this generation's defining match-3 game instead of Bejeweled and its brethren. And of all the competitive simulation games, Clash of Clans defined the raiding-strategy genre (and has some awesome exploits and cheats). But there are plenty of alternate universes where some other games are massive smashes instead of these.
In addition, Spider Solitaire is a multiplayer game that captures the emotions of players around the world. Joining this game, your task is to use the mouse to group cards into the stacks around the board. Collect cards of the same suit from the king down the Ace to remove them from the board. For good performance in this game, players need to have good reaction skills. Click on the "play now" button to play and feel!
From day 1 of its soft launch, it became clear right away that Supercell had a hit on its hands. They figured something out that countless MOBAs, first-person shooters, and any other game have failed to do. They made an intense real-time multiplayer game on mobile that engages players and makes money without feeling unfair. It's easy to spend tons of money on Clash Royale, but you'll sink hours into it just because you enjoy it.
I go in deep about the game in an earlier article, but Clash Royale is best described as a collectible card game meets a real-time strategy game and a MOBA. You have a deck of 8 cards, with 4 in your hand at one time. You use elixir, an energy unit that recharges over time, to summon cards onto the battlefield. Then, you deploy them to attack the enemy's crown towers in the 2 lanes each having a tower, along with a center king tower. Destroy a crown tower, and you can go after the king tower. Destroy the king tower, and you win, though you have to do so in 3 minutes, with the last minute providing double elixir. Otherwise, the player who has destroyed more crown towers is the victor. If towers are tied, then there's a 1-minute sudden death overtime where the first person to destroy a tower – crown or king – wins. The king tower does more damage to incoming units and hurts harder.
Beside, Checkers is an addictive game, getting a lot of love from players around the world. You need to have good skills to be able to score high in this game. Your task is to eliminate all the pieces of your opponent from the board. If you are in the free time, Checkers game will be a perfect choice that we recommend. Click the "play now" button to play and feel!
What's clever about the gameplay is that it's all so simple to learn and play with. You drop units in, and they follow their behaviors without any other command. Where you place units can be important, but not as much as the lower-level strategy of managing your deck, elixir, and current cards in relation to your opponent's situation. You become knowledgeable about the game at a level where you feel comfortable diving in. Before long, you're joining a clan, experimenting with decks, and getting sucked into the metagame. This happens so fast, you won't know what hit you. And because games only take 3 or 4 minutes, you can feel like you're getting a lot done in a short session. Compare this to many popular multiplayer games, where they can feel overwhelming for too long. Even something like Hearthstone has a steep barrier to entry today. Clash Royale limiting certain cards to a tier of the game helps a lot to make sure that you're not getting an information overload at any point.
For the sake of being thorough here, let's assume this is somehow the first you've heard of Clash Royale. The easiest way to describe it is as a collectable card game where your cards represent real-time strategy game-like units which are dropped onto MOBA-ish multi-lane battlefields with two towers and a base you need to attack while defending your own. That's quite a mouthful, and it sounds complicated, but the magic of Clash Royale is it's all presented in a way that I really don't think you need to know anything about card games, RTS games, MOBAs, or the emergent strategies in any of those genres because everything has been simplified and streamlined to a masterful extent.
If you've never played a game like that before, even as great as the Hearthstone tutorial and onboarding process is, you're still talking more of a learning wall and less of a learning curve. Thirty cards is substantially easier to manage than Magic's sixty, but you've got to either really know what you're doing or be a supremely analytical player to be able to make heads or tails over whether running one of a particular card is doing much better or worse than running two of that same card. Just how difficult it is to create a competitive deck for most players leads to just looking up what other players are playing, copying those decks, and never really ever needing to learn how to build a deck of their own.
A typical game then involves initially choosing your eight cards which hopefully meld together well in some kind of cohesive strategy with answers to the different types of threats you might come across. From there, you search for an opponent, and are matched up with someone who has a similar trophy level as you (more on this later). From there, you dump out cards, and hopefully manage to knock down one or more of their crown towers while protecting your own, and ultimately destroy your opponent's main King tower. Games have a hard limit of taking absolutely no longer than four minutes, which is really just another clever wrinkle in the game.
Here's the gist- Cards are rewarded through opening chests. Every four hours, you get one free chest and you have two slots for these free chests, so to maximize your freebies you'll want to be checking in on the game at least once every eight hours. After completing the tutorial, winning battles awards chests of different levels of rarity (rarer chests include more cards and gold) and you can hold a maximum of four of these prize chests. Silver Chests, which are the most common prize chest to come across take three hours to unlock with the Super Magical Chest, currently the best chest in the game, taking an entire day to unlock. Only one chest unlock timer can be rolling at a time, so there's a bit of strategy involved with what you unlock and when. For instance, if you've got a Golden Chest in your inventory, you'll likely want to hang on to that to unlock it overnight as that's an eight hour timer you can have counting down while you sleep. If you have four chests in your inventory, you cannot earn more through winning games until you unlock one and thereby open up that inventory slot.
Of course, you can also pay to skip any of these timers, and Clash Royale shares a similar premium currency to Clash of Clans in that they're using Gems. Like any free to play game with timers, the amount of premium currency it takes to skip a timer scales up significantly with the amount of time remaining. Additionally, like all these games, the premium currency is doled out at regular intervals although it takes a while to accumulate any substantial number. Gems are also used to buy gold and chests from the in-game store. Chests purchased this way are opened immediately and aren't impacted by you potentially having four chests in your inventory already.
I encourage everyone to give this game a try, even if you're a vigilant hater of free to play. Monetization methods aside, you'll still be able to see what a clever formula Supercell has stumbled upon to here with this hybrid of card games, strategy games, and MOBAs. Hard limits on session time make it a phenomenal game to play on the go, and it can be played in portrait mode in one hand which only serves to make things easier. In less than a day it's the top free app, and steadily climbing up the top grossing charts, so if you dig this style of gameplay but don't particularly like certain things about Clash Royale (like chest timers or whatever else) just wait a while.


text:
Q: New outer automorphism for $G_1 \times G_2$ Suppose $G_1$ is a group, which has no outer automorphism.
Suppose $G_2$ is a group, which has no outer automorphism.

Main Question: What are the possible conditions to know can there be an outer automorphism for
  $$
G_1 \times G_2?
$$

An easier question:
Suppose $G_1=SU(2)$ is a group, which has no outer automorphism.
Suppose $G_2= \mathbb{Z}/2\mathbb{Z}$ is a group, which has no outer automorphism.

*

*$SU(2) \times SU(2)$ has however a order-2 outer automorphism.

*$\mathbb{Z}/2\mathbb{Z} \times \mathbb{Z}/2\mathbb{Z}$ has however a order-2 outer automorphism.

Simpler Question: Is there an  outer automorphism for
  $$
SU(2) \times \mathbb{Z}/2\mathbb{Z} ?
$$

If you can answer anything of the above two Questions - this counts as a perfect answer.

A: A sufficient condition is that $G_1$ has a central subgroup $C$ isomorphic to a quotient of $G_2$ - this holds for your example.
We then have a natural map $q:G_2\to C$.

The map $\phi:G_1\times G_2\to G_1\times G_2:(g,h)\mapsto (gq(h),h)$ is an outer automorphism.

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