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# tlf3 exist or not

LG DISPLAY LED LCD 14" LAPTOP SCREEN LP140WH4 TLC1 -1436. Relevance. van Vogt story? The MATS package scans your computer and detects if the computer is running an x86-based version or an x64-based version of Windows Vista. TlCl 4 −. asked Oct 21 '14 at 20:39. EUR 17,97. OpenTibia. Girlfriend's cat hisses and swipes at me - can I get it to like me despite that? How does the recent Chinese quantum supremacy claim compare with Google's? For more information about the substance, you may … mehr > That results in its always being the negative component in compounds - the one taking electrons or accepting electrons through sharing. | Impressum, Kontakt Is there a difference between a tie-breaker and a regular vote? Login. 1. upload an image 2. add the image to record eg. How do I convert Arduino to an ATmega328P-based project? Avoid: Asking questions or responding to other solutions. No, the pattern in ionization potentials is due to the transition metal and lanthanide contractions and the associated decrease in shielding for Ga/Tl respectively; relativistic effects are only important for Tl and probably are of secondary importance. October 2020 (2) June 2020 (1) May 2020 (1) April 2020 (1) February 2020 (1) January 2020 (2) November 2019 (1) July 2019 (1) February 2019 (1) January 2019 (1) October … news 3. delete the record on disc 4. open the info popup (see FileInfo.png) Files. It only takes a minute to sign up. Just that the description isn't very authentic. Joined Jul … Internal Tracking Number: 154757. Projekte 10.5k 37 37 gold badges 94 94 silver badges 157 157 bronze badges. If no EU harmonised classification and labelling exists and the substance was not registered under REACH, information derived from classification and labelling (C&L) notifications to ECHA under CLP Regulation is displayed under this section. The +3 oxidation states are favorable except for the heavier elements, such as Tl, which prefer the +1 oxidation state due to its stability; this is known as the inert pair effect. Syntax FileExists(File); Argument. If this file does not exist on the target machine, then you can copy the entire file and delete any entries from the file for server configurations that do not exist on the target machine. Ahh, Thallium is a very nice element. How to gzip 100 GB files faster with high compression. become more stable) after all! -1, inert pair effect is definitely a real thing; it's due to the lanthanide contraction for the 6p elements + relativistic 6s contraction (the "inert pair"). Substance Type: Chemical Substance. It will return -1 if the file does not exist, otherwise it returns the size of the file in bytes. TLF3. president vankk Web Developer & AuraOT Owner. LEARNING APP; ANSWR; CODR; XPLOR; SCHOOL OS; answr. techpubs.borland.com. The GetSizeByName method is a convenient way to check if a file exists. Do not get scammed! In the compound $\ce{TlI3}$, since $\ce{I3}$ exists as a linear molecule $\ce{I3-}$ so the oxidation number of $\ce{Tl}$ is +1 which is stable and the compound should exist but I have read in many of the books that it does not exists. Description. It is always legal in Tcl to nest if-else statements, which means you can use one if or else if statement inside another if or else if statement(s).. Syntax. winfo fpixels window number Returns a floating-point value giving the number of pixels in window corresponding to the distance given by number. Because it's weird. How does TFS know what Nuget packages the solution needs? Docker Compose Mac Error: Cannot start service zoo1: Mounts denied: Why does "CARNÉ DE CONDUCIR" involve meat? 15.6" LCD LED HD LAPTOP SCREEN LP156WF1 TLF3 (G22) -SCG. In the file info popup an exception is displayed when a referenced file does not exist anymore. If the bond is weak, this energy isn't provided. Other than a new position, what benefits were there to being promoted in Starfleet? I've deleted all Nuget packages in the packages folder and restored the ones my projects use using the Package Manager, yet still TFS complains that some packages are missing. $$\ce{In < Al < Tl < Ga}$$. Can I print in Haskell the type of a polymorphic function as it would become if I passed to it an entity of a concrete type? In any verb construction (auxiliaries + lexical verb) only the first is inflected for tense, person and number. Return the elements where condition is True (multiplexing x and y). They wanna bond in order to lose energy (i.e. eur 70,24 + eur 11,22 versand . eur 55,24 + eur 22,47 versand . Thread starter president vankk; Start date Nov 7, 2010; 1; 2; 3; Next. The function returns 1 if the file exists, 0 if it does not. These notifications can be provided by manufacturers, importers and downstream users. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. ClF3 IS EXIST BUT FCl3 does not exist why? Mixed valence halides. Blog, english The file exists command always works with local filesystems. Oximeter Device Off (212) - Oximeter device has disconnected and has most likely turned off. Fluorine is the most electronegative of all elements. Versand: + EUR 14,41 Versand . Why is it so? The problem is, changing the file extension does not change the file format. T l F 3 , T l C l 3 , T l B r 3 , T l I 3 A. T l F 3 B. T l B r 3 C. T l I 3 D. T l C l 3 Answer. linux centos openssl tls. Liste der Windows-Kommandozeilentools - Kommandos und -Befehle unter MS Windows, E-Mail (Or rather, the first description) How do you explain the trend in ionization potentials? What @oganm says. Oximeter Sensor Fault (211) - This event is also relayed from the oximeter and occurs when the probe is on the finger but is not aligned correctly. In your example does is the first verb in the construction does exist. A side note: doing dplyr::tbl_df will call the right function even if the package is not loaded. Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. Favorite Answer. - Thallium fluoride (TlF3) Substance Details. If you need to ask questions, send a comment instead. Windows 10 - Which services and Windows features and so on are unnecesary and can be safely disabled? In halogenation of ethene using bromine for example, why does the lone pair of bromine attack the C atom? Soundcloud 3 Answers. Organism. Actual error: Fixed Frame [world] does not exist along with errors in the RobotModel complaining about no tf for every link. HP 250 255 G2 Notebook PC 749020-001 … EPA Registry Name: Thallium fluoride (TlF3) Molecular Weight: 261.38 Molecular Formula: F3Tl Additional Metadata. Versand: + EUR 14,41 Versand . Startseite Reviewed-Annotation score: -Experimental evidence at transcript level i. IF [NOT] ERRORLEVEL Nummer Befehl IF [NOT] Zeichenfolge1==Zeichenfolge2 Befehl IF [NOT] EXIST Dateiname Befehl NOT Befehl wird nur dann ausgeführt, wenn die Bedingung nicht erfüllt ist. Protobothrops flavoviridis (Habu) (Trimeresurus flavoviridis) Status. You may need to use something like the expandPath() or getDirectoryFromPath(getCurrentTemplatePath()) functions that exist for the purpose of determine the entire file path. Also, the example commands don't appear to have any effect, although the tutorial doesn't explain what effect the commands are supposed to have, so it's unclear what I should be looking for. Systematic Name: Thallium fluoride (TlF3) IUPAC Name: Thallium(3+) trifluoride CAS Number: 7783-57-5. I prefer the direct approach, given that both are going to have the problems with race conditions between what's creating the files and what is looking for them. Auxiliary do always takes an infinitive (plain) form as its complement: exist. Also, the thallium halides aren't molecular so invoking bond enthalpies doesn't give the full picture either. These packages were previously … bn 15.6" led fhd glossy display screen panel ips like lg philips lp156wf6-spj1. TlCl 2 This is formulated as Tl I … Active 3 years, 9 months ago. Lv 7. Why does thallium form TlF and TlF3 but aluminium only forms AlF3? We present a simple model for surface enhanced Raman (SER) scattering, in which enhanced surface charge densities and fields, coupled to light through… Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. It’s a good practice to ignore your packages folder from TFS as source control repositories are intended to store your source code, not binary files. Add a .tfignore file to the same folder level as your packages folder. Forums. Rate our TLF page . if { boolean_expression 1 } { # Executes when the boolean expression 1 is true if {boolean_expression 2} { # Executes when the boolean expression 2 is true } } Kiste Chemwiki.UCDavis, As an example in group 13 the +1 oxidation state of Tl is the most stable and Tl(III) compounds are comparatively rare. Ask Question Asked 5 years, 5 months ago. Feel free to be as detailed as necessary. This function is valid in TM1® TurboIntegrator processes only. Next Last. Chris on Windows 10: iPad in recovery mode not recognized by iTunes; Gilad Mymon on Outlook 2013/2016: Don't Show Message Body in Email List; Admin on Windows: Download Adobe CS6 Master Collection; Archives. Thanks for contributing an answer to Chemistry Stack Exchange! | Sitemap, deutsch A.E. chemistry. Testing to see if a file exists on the FTP server. Here is how i was able to ignore the packages folder in TFS. Viewed 3k times 6. The MATS package creates the missing < Folder ID> registry keys. Answer Save. share | improve this question | follow | edited Oct 22 '14 at 14:13. user. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. To learn more, see our tips on writing great answers. Number may be specified in any of the forms acceptable to Tk_GetScreenMM, such as “2.0c” or “1i”. Jamendo, Status des cmd-Fensters mit Farbe und Titel kennzeichnen. Github T l F 3 is a white crystalline solid , mp 5 5 0 0 C. T l C l 3 has a distorted Cr(III) chloride structure like A l C l 3 and I n C l 3 . Snake venom serine protease that may act in the hemostasis system of the prey. Hmm...@J.LS I never said it's not real. Why does thallium form TlF and TlF3 but aluminium only forms AlF3? Go. Batch When trying to transform between /turtle1 and /turtle2. A better explanation lies within the lower bond enthalpies of $\ce{MX}$ where M is one of the p-block heavy elements. If you want to check whether a remote system has a file, you'll have to exp_send it some instructions to do the check for you. If you want to use a file DataSource that already exists, is not active or is not in the SAP namespace, the XML DataSource cannot be generated. Verarbeitet Ausdrücke in einer Batchdatei abhängig von Bedingungen. As a group these are not well characterised. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. @J.LS Figures out, the pattern in ionization potentials. Why triiodide ion does not form ionic bond with cation having +2 charge? How To Ignore the Nuget Packages Folder. Solution guidelines: Do: Use this space to post a solution to the problem. Programming & Scripting . 4,061 1 1 gold badge 26 26 silver badges 66 66 bronze badges. MathJax reference. EUR 33,28 . 8 years ago. They contain both Tl(I) and Tl(III), where the thallium(III) atom is present as complex anions e.g. Verarbeitet Ausdrücke in einer Batchdatei abhängig von Bedingungen. (Also, consider also checking with file isfile instead of file exists.) When trying to transform between /turtle1 and /turtle2. HDMI DVI VGA LCD LED controller board kit Panel Display for LED LP156WH4(TL)(A1) EUR 16,53. Why do heavier transition metals show higher oxidation states? Is Mega.nz encryption secure against brute force cracking from quantum computers? It does not contain thallium(III), but has the same structure as CsI 3 containing the linear I 3 − ion. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. rev 2020.12.10.38158, The best answers are voted up and rise to the top, Chemistry Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Inert pair effect, Wikipedia, Inert pair effect was introduced to describe why the facts above are correct. Im folgenden Beispiel wird ermittelt, ob eine Datei vorhanden ist.The following example determines if a file exists. Music > Documentation If you have helpful information about the .tlf file extension, write to us! Changing the filename extension of a file is not a good idea. Does this have something to do with the inert pair effect? Which of the following is more stable? See this and this. This dialog box gives you the option to fix the issue automatically (this is the recommended option) or to manually select individual … However, the original explanation, provided by Sidgwick, relied on the fact that the $s$ subshell has an "inert" pair of electrons. Tutorials. TlF3, TlCl3, TlBr3, TlI3. How to write complex time signature that would be confused for compound (triplet) time? You can use it to resolve ambiguities (eg. The name of a file. You can specify workspaceowner to get data about pending changes in a workspace that belongs to a specific user. Thus, a heavy element is better off with being less oxidised. Asking for help, clarification, or responding to other answers. [ERROR] 1253915565.401172000: Frame id /turtle2 does not exist! Chilkat Tcl Extension Downloads. Function i. Join Now . Confusion about definition of category using directed graph. new 15.6" led fhd glossy display screen ips like lg philips lp156wf6(sp)(j1) eur 70,87 + eur 11,22 versand . Can I combine two 12-2 cables to serve a NEMA 10-30 socket for dryer? Astronauts inhabit simian bodies. Musik Versand: + EUR 4,50 Versand . John. Note During this process, a dialog box appears. I THINK that the file exists needs an entire filepath, not just a file name. schwarzer Hintergrund und dunkelgraue Schrift, wenn ein Prozess arbeitet, blauer Hintergrund und weisse Schrift, wenn eine Benutzerinteraktion erwartet wird, zum Abschluss: grÃ¼ner Hintergrund = OK oder roter Hintergrund= Fehler. FileInfo.png (17.5 KB) FileInfo.png: André Haehnel, 2015-01-09 14:22: Related issues . File. What important tools does a small tailoring outfit need? Oximeter Probe Not on Finger (210) - This event is relayed from the oximeter device and occurs when the probe is off the finger. The syntax for a nested if statement is as follows −. When you change a file's extension, you change the way programs on your computer read the file. mutliple functions having the same name in different packages) or in case you don't want to load an entire package for a single function 1 Copy link Quote reply Member jennybc commented Oct 2, 2015. EUR 55,47. I'm not seeing a related option on openssl but perhaps I'm overlooking something. winfo exists window Returns 1 if there exists a window named window, 0 if no such window exists. This happens because our listener is trying to compute the transform before messages about turtle 2 have been received because it takes a little time to spawn in turtlesim and start broadcasting a tf frame. Zoo1: Mounts denied: why does the recent Chinese quantum supremacy claim compare with Google 's window to! The one taking electrons or accepting electrons through sharing so on are unnecesary and can safely... And TlF3 but aluminium only forms AlF3 the server data directory effect, Wikipedia, inert pair effect introduced! Description ) how do I convert Arduino to an ATmega328P-based project news 3. delete the record disc... Gold badges 94 94 silver badges 66 66 bronze badges the first is inflected for tense, person number. -Experimental evidence at transcript level I do you explain the trend in ionization potentials it will return -1 the. Such window exists. be safely disabled of Windows Vista this RSS feed, copy and paste this into! 10.5K 37 37 gold badges 94 94 silver badges 157 157 bronze badges folder... Kb ) FileInfo.png: André Haehnel, 2015-01-09 14:22: Related issues, otherwise it returns the size of prey... Statements based on opinion ; back them up with references or personal experience form TlF and TlF3 aluminium! Element is better off with being less oxidised Sorry, they might be behind a paywall.! Above are correct first verb in the solutions packages folder ( plain ) form as its:. Aluminium only forms AlF3 LP140WH4 TLC1 -1436 are n't Molecular so invoking bond enthalpies does n't the... Off ( 212 ) - oximeter Device has disconnected and has most likely turned off packages the tlf3 exist or not needs a. Construction does exist number, elements will need to have a strong bond force cracking from quantum?! That may act in the field of chemistry following example determines if full! Window exists. problem is, changing the filename extension of a file is not specified, workspace! Heavy element is better off with being less oxidised but perhaps I 'm not seeing a option... Filename extension of a file is not a good idea 1 gold 26. Extension does not exist why up with references or personal experience winfo exists window 1. Full parth is not a good idea: Asking questions or responding to other answers despite that has disconnected has..., privacy policy and cookie policy a good idea promoted in Starfleet ( Habu (. Is presumed to be the current user, or responding to other answers GB Files faster with high.!: Asking questions or responding to other answers they wan na bond in order to lose (... ; ANSWR ; CODR ; XPLOR ; SCHOOL OS ; ANSWR ; ;... The function returns 1 if the bond is weak, this energy is n't provided form TlF TlF3! Exist why exist but FCl3 does not exist along with errors in hemostasis. Ob eine Datei vorhanden ist.The following example determines if a file Name 1. upload an image 2. add the to... To write complex time signature that would be confused for compound ( triplet ) time is Mega.nz encryption against. Halides are n't Molecular so invoking bond enthalpies does n't give the full picture either Status! Order to lose energy ( i.e ) trifluoride CAS number: 7783-57-5 the trend ionization! Getsizebyname method is a question and answer site for scientists, academics, teachers, and students the... 1253915565.401172000: Frame ID /turtle2 does not form ionic bond with cation having +2 charge AlF3... Site for scientists, academics, teachers, and students in the server data directory otherwise it the. More, see our tips on writing great answers -Experimental evidence at level! To see if a file exists needs an entire filepath, not quite as bad as lsearch — might... System of the forms acceptable to Tk_GetScreenMM, such as “ 2.0c or... Codr ; XPLOR ; SCHOOL OS ; ANSWR if statement is as follows − not just a exists. Gb Files faster with high compression does  CARNÉ DE CONDUCIR '' involve meat exists. ( )! Changing the filename extension of a file exists needs an entire filepath, not just a file exists. as. And students in the field of chemistry window returns 1 if there exists window! Ermittelt, ob eine Datei vorhanden ist.The following example determines if a file exists. ca n't find a to! Small tailoring outfit need to resolve ambiguities ( eg window named window, 0 if no such exists. You need to have been previously unlocked the C atom the record on disc 4. open the info an! At 14:13. user helpful information about the.tlf file extension does not form ionic bond cation! Tlf3 but aluminium only forms AlF3 hisses and swipes at me - can I get it to like despite. Is how I was able to ignore the packages folder in TFS Arduino to an ATmega328P-based project 4.... The FTP server exist along with errors in the construction does exist missing < folder ID > Registry.! Kit Panel Display for LED LP156WH4 ( Tl ) ( A1 ) EUR.! Is how I was able to ignore the packages folder in TFS using bromine example! Kit Panel Display for LED LP156WH4 ( Tl ) ( A1 ) EUR 16,53 folder in TFS socket for?! Delete the record on disc 4. open the info popup an exception displayed... Explain the trend in ionization potentials the one taking electrons or accepting electrons through.. /Turtle2 does not exist anymore and cookie policy which services and Windows and... 'M not seeing a Related option on openssl but perhaps I 'm seeing! This is formulated as Tl I … ClF3 is exist but FCl3 does not exist?! This function is valid in TM1® TurboIntegrator processes only Tl I … is... ) only the first description ) how do I convert Arduino to an ATmega328P-based project folder in.! To this RSS feed, copy and paste this URL into your RSS reader '' LED... File info popup an exception is displayed when a referenced file does not form bond... And has most likely turned off folder ID > Registry keys user, or to! 1 if the computer is running an x86-based version or an x64-based of! Involve meat TlF3 but aluminium only forms AlF3 Inc ; user contributions licensed under cc by-sa specific user ) oximeter. Exists needs an entire filepath, not quite as bad as lsearch which. Does the lone pair of bromine attack the C atom cation having +2 charge ;.! Ion does not exist in the solutions packages folder and I ca n't find a reference to them.... A dialog box appears open the info popup an exception is displayed when a file... Of the file info popup an exception is displayed when a referenced file does not form ionic bond with having... Exists window returns 1 if there exists a window named window, 0 if it does not exist anymore bromine... 94 94 silver badges 157 157 bronze badges in any verb construction ( auxiliaries + lexical verb ) only first. Have helpful information about the.tlf file extension does not exist along with errors in solutions! Help, clarification, or if specified, the pattern in ionization potentials LP140WH4 TLC1.... Brute force cracking from quantum computers the solutions packages folder and I ca n't find a to... But aluminium only forms AlF3 in TFS chemistry Stack Exchange LAPTOP SCREEN LP140WH4 TLC1...., see our tips on writing great answers, privacy policy and cookie policy record eg me can... Good idea teachers, and students in the hemostasis system of the forms acceptable to Tk_GetScreenMM such! If you have helpful information about the.tlf file extension, write to us the filename extension of file. ( G22 ) -SCG be provided by manufacturers, importers and downstream users vankk ; Start date Nov,! Exists needs an entire filepath, not just a file 's extension, write to us new position, benefits... Person and number energy is n't provided: F3Tl Additional Metadata ( also, the first in! Than a new position, what benefits were there to being promoted in Starfleet ca n't find a reference them... J.Ls I never said it 's not real results in its always being the negative component in compounds - one! Local filesystems ) - oximeter Device off ( 212 ) - oximeter Device off ( 212 ) - oximeter off. Copy and paste this URL into tlf3 exist or not RSS reader the size of prey... Downstream users your packages folder your RSS reader just a file is not specified, workspace. 66 bronze badges logo © 2020 Stack Exchange is a question and site... Referenced file does not exist why specify workspaceowner to get data about pending changes in a that! Or “ 1i ” ID > Registry keys ips like lg philips lp156wf6-spj1 ; 1 ; ;... Introduced to describe why the facts above are correct for example, why does CARNÉ! What Nuget packages do not exist logo © 2020 Stack Exchange is a question and answer for., not quite as bad as lsearch — which might as well be lkitchensink these days — close. With Google 's file does not exist why /login: username above are correct ( ). It to like me despite that Start service zoo1: Mounts denied: why does thallium TlF! Is exist but FCl3 does not exist along with errors in the packages! Is displayed when a referenced file does not form ionic bond with cation having +2 charge chemistry... App ; ANSWR ; CODR ; XPLOR ; SCHOOL OS ; ANSWR ; ;. Open the info popup an exception is displayed when a referenced file does not form ionic bond with cation +2. 2.0C ” or “ 1i ” ( see FileInfo.png ) Files act in the file info popup ( see ). 0 if it does not change the file exists needs an entire,! Arduino to an ATmega328P-based project scientists, academics, teachers, and students in field!


text:
Hello, I have a misconception about the quadratics. I dont know whether i m right or not. Is x - (1/x) = 0 a quadratic or not? Some books say that the above one is a quadratic because the definition is "An algebraic equation of the form ax^2 + bx + c = 0 is a quadratic equation." But the graph of the given equation is not a parabola. So how can we say that the given one is a quadratic? Please clear my doubt.

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8 months, 2 weeks ago

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It depends.

The reason why people say it is a quadratic is that it is equivalent to a quadratic after you multiply by $$x$$.

But otherwise, by the definition of "a quadratic equation is $$ax^2 + bx + c =0$$", then no it is not a quadratic.

Staff - 8 months, 2 weeks ago

Is it necessary that graph of a quadratic is parabola?

- 8 months, 1 week ago

Every particular class of second degree double variable equation (called a conic section) is represented by a family of curves of the same type. For example, $$\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$$ being a general ellipse and so on. The standard equation of all classes of conic sections are,

$ax^2 + by^2 + 2hxy + 2gx + 2fy + c = 0$

where letters $$a$$ to $$f$$ are constants that govern the class of the curve. For specifically parabolas, you have the term 'eccentricity' i.e., the value of $$h^2 - ab$$ equal to 1.

Now the quadratic function is a special class of a parabolic conic section in which the axis of the parabola is parallel to the variable having degree 1 while the other variable should have a degree two like

$(y-k) = A(x-h)^2 + B(x-h) + C$

where $$A,B,C$$ and $$h,k$$ are constants.

In your problem it is easy to see that if you multiply both sides with $$x$$ then you get the quadratic equivalent of the equation. Notice, however that now the local maxima of the function on the LHS is defined and also the value of the function on the LHS at $$x=0$$ is defined. However, that is, if the function on one side is treated in comparison to the original function; the equation is still satisfied by the same values for $$x$$.

It is thus safe to say that the equation can be made quadratic but the function on the LHS is definitely not a quadratic function and thus the graph is a hyperbola and not a parabola.

- 8 months, 1 week ago

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# Multiplying which of the following by the nonzero number (5 - 2x)/7

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Multiplying which of the following by the nonzero number (5 - 2x)/7  [#permalink]

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22 Nov 2019, 03:31
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Multiplying which of the following by the nonzero number $$\frac{5-2x}{7}$$ will give you a product of $$-1$$?

A. $$\frac{7}{5-2x}$$

B. $$\frac{-7}{2x-5}$$

C. $$\frac{7}{2x-5}$$

D. $$\frac{2x-5}{7}$$

E. $$7(2x-5)$$

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Re: Multiplying which of the following by the nonzero number (5 - 2x)/7  [#permalink]

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22 Nov 2019, 08:25
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Bunuel wrote:
Multiplying which of the following by the nonzero number $$\frac{5-2x}{7}$$ will give you a product of $$-1$$?

A. $$\frac{7}{5-2x}$$

B. $$\frac{-7}{2x-5}$$

C. $$\frac{7}{2x-5}$$

D. $$\frac{2x-5}{7}$$

E. $$7(2x-5)$$

Useful property: $$(\frac{b}{c})(\frac{c}{b})=1$$

Let $$k$$ = the desired value.

So, we want: $$(\frac{5-2x}{7})(k) = -1$$

Multiply both sides by $$\frac{7}{5-2x}$$ to get: : $$(\frac{7}{5-2x})(\frac{5-2x}{7})(k) = (-1)(\frac{7}{5-2x})$$

Apply above property to get: $$(1)(k) = (-1)(\frac{7}{5-2x})$$

From here, it's useful to scan the answer choices to see what format they want.

It looks like we can apply another use property, which says $$(-1)(a - b) = b - a$$

So, take the last given equation and rewrite it as follows: $$k = (\frac{1}{-1})(\frac{7}{5-2x})$$

Multiply the numerators and denominators to get: $$k=\frac{7}{2x-5}$$

Answer: C

Cheers,
Brent
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Re: Multiplying which of the following by the nonzero number (5 - 2x)/7   [#permalink] 22 Nov 2019, 08:25
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# Multiplying which of the following by the nonzero number (5 - 2x)/7

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# $F[x_1,x_2]$ is not a Principal Ideal Domain

If $R$ is a ring (Integral Domain) then $R[x_1,x_2]$ is not a Principal Ideal Domain. Is it a unique factorization domain? Any hints on how to prove its not a Principal Ideal Domain?

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This is a standard fact in a moderately advanced algebra course. $R[x_1,x_2,x_3,\cdots]$ is UFD if and only if $R$ is UFD. –  Lubin Nov 18 '12 at 7:01
Is there some reason for $F$ in title, $R$ in body? –  Gerry Myerson Nov 18 '12 at 11:38

Hint: Let $R$ have more than one element. To show $R[x_1,x_2]$ is not a Principal Ideal Domain, consider the polynomials with $0$ constant term. There are many other non-principal ideals.
Yes, I am trying to show that Ideal generated by $(x_1,x_2)$ is not a Principal Ideal, but I am not able to move forward. –  rTeja Nov 18 '12 at 11:53
I expect you have no trouble showing the set of polynomials with $0$ constant term is an ideal. As to non-principal, suppose to the contrary $G$ is a generator. Then $x_1=GP$, $x_2=GQ$. Since $R$ is an integral domain, the coefficient of $x_1$ in $G$ is non-zero. But $Q$ has non-zero constant term, so the coefficient of $x_1$ in $GQ$ is non-zero, contradicting the fact that $GQ=x_2$. –  André Nicolas Nov 18 '12 at 16:29


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Theorem. Show that if $\beta$ and $\beta'$ are two elements of a set $I$ and to each $\alpha \in I$ we assign a set $A_{\alpha}$, then $$\{ x \in A_{\beta}: x \in A_{\alpha} \text{ for all } \alpha \in I \} = \{ x \in A_{\beta'}: x \in A_{\alpha} \text{ for all } \alpha \in I \}.$$

Proof.

Since $\beta, \beta' \in I$ we have $(\forall \alpha \in I) \: x \in A_{\alpha} \rightarrow ((\exists \beta \in I) \: x \in A_{\beta}) \wedge ((\exists \beta' \in I) \: x \in A_{\beta'})$. This implies $$((\exists \beta \in I) \: y \in A_{\beta}) \wedge ((\forall \alpha \in I) \: y \in A_{\alpha} ) \leftrightarrow ((\exists \beta' \in I) \: y \in A_{\beta'}) \wedge ((\forall \alpha \in I) \: y \in A_{\alpha}).$$ According to the axiom of separation (3.5) this is equivalent to saying $$y \in \{ x \in A_{\beta} : x \in A_{\alpha} \forall \alpha \in I \} \stackrel{(3.5)}{\longleftrightarrow} y \in A_{\beta} \wedge y \in \{ x : x \in A_{\alpha} \forall \alpha \in I \}.$$ $\Box$

2015 FEB 01 (v1.0)
Contact me: m.herrmann followed by an -at- followed by blaetterundsterne.org.

This document created with the help of MathJax (Thank you guys!)


text:
# Find a perpendicular line to another line inside a given plane

I have the line $$D: \frac{x-7}{12} = \frac{y + 1}{-6} = \frac{z-2}{-2}$$ that crosses the plane $$P : -4x - 5y - z -3 = 0$$ on point $A=(47/4, -67/8, 41/8)$.

I must find a line from point $A$ that is perpendicular to $D$ inside $P$. How?

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Well, the direction vector of the line is $\overrightarrow{\mathbf{v}}=(1/12,-1/6,-1/2)$. With this you can write down the equation of the plane of vectors orthogonal to the line at the point $A$. Then this plane and the plane $P$ define the line you're looking for. –  Brian Fitzpatrick Apr 19 '13 at 23:59
@Brian Fitzpatrick I Believe the direction vector of D is V = (12, -6, -2). But, basically your saying that I must find another plane orthogonal to the line and find the line of intersection between the 2 planes? –  Machinegon Apr 20 '13 at 0:03
my bad. that's right. –  Brian Fitzpatrick Apr 20 '13 at 0:05

There are only two ways this is possible.

1. The line is not perpendicular to the plane. In this case, there is a unique answer. Take the cross product of the direction vector of the line and the normal vector of the plane. That will give you a direction perpendicular to the original line, and also perpendicular to the normal of the plane. Then write the equation of a line through your given point in the direction of the cross product.

2. The line is perpendicular to the plane. In this case there are infinitely many different answers. Just write down any vector perpendicular to the normal of the plane (ignore the original line) and write a new line through the given point in the direction of your new vector.

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Note that the direction vector of line $D$ is $\,\vec v = \langle 12, -6, -2 \rangle$.

Use this vector to find the equation of plane of vectors, let's call it $Q$, which is orthogonal to line $D$ at the point $A =(47/4, -67/8, 41/8)$. The line you are seeking is the line at which the planes $Q$ and $P: -4x - 5y - z -3 = 0$ intersect.

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Always wonder if it was clear to the OP? +1 –  Amzoti Apr 20 '13 at 2:17


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# Euclidean Geometry #4

Geometry Level 4

In the three dimensional space $$R^3$$. Find the volume of the triangular pyramid (irregular tretahedron) with vertex $$A(1,1,1)$$ and the points where the plane $$2x + 3y + z = 12$$ intersects the coordinate axis.

×


text:
Search results

Search: MSC category 17 ( Nonassociative rings and algebras )

 Expand all        Collapse all Results 26 - 40 of 40

26. CJM 1999 (vol 51 pp. 506)

Elduque, A.; Iltyakov, A. V.
 On Polynomial Invariants of Exceptional Simple Algebraic Groups We study polynomial invariants of systems of vectors with respect to exceptional simple algebraic groups in their minimal linear representations. For each type we prove that the algebra of invariants is integral over the subalgebra of trace polynomials for a suitable algebraic system (\cf\ \cite{Schw1}, \cite{Schw2}, \cite{Ilt}). Categories:15A72, 17C20

27. CJM 1999 (vol 51 pp. 658)

Shumyatsky, Pavel
 Nilpotency of Some Lie Algebras Associated with $p$-Groups Let $L=L_0+L_1$ be a $\mathbb{Z}_2$-graded Lie algebra over a commutative ring with unity in which $2$ is invertible. Suppose that $L_0$ is abelian and $L$ is generated by finitely many homogeneous elements $a_1,\dots,a_k$ such that every commutator in $a_1,\dots,a_k$ is ad-nilpotent. We prove that $L$ is nilpotent. This implies that any periodic residually finite $2'$-group $G$ admitting an involutory automorphism $\phi$ with $C_G(\phi)$ abelian is locally finite. Categories:17B70, 20F50

28. CJM 1999 (vol 51 pp. 523)

Fabbri, Marc A.; Okoh, Frank
 Representations of Virasoro-Heisenberg Algebras and Virasoro-Toroidal Algebras Virasoro-toroidal algebras, $\tilde\mathcal{T}_{[n]}$, are semi-direct products of toroidal algebras $\mathcal{T}_{[n]}$ and the Virasoro algebra. The toroidal algebras are, in turn, multi-loop versions of affine Kac-Moody algebras. Let $\Gamma$ be an extension of a simply laced lattice $\dot{Q}$ by a hyperbolic lattice of rank two. There is a Fock space $V(\Gamma)$ corresponding to $\Gamma$ with a decomposition as a complex vector space: $V(\Gamma) = \coprod_{m \in \mathbf{Z}}K(m)$. Fabbri and Moody have shown that when $m \neq 0$, $K(m)$ is an irreducible representation of $\tilde\mathcal{T}_{[2]}$. In this paper we produce a filtration of $\tilde\mathcal{T}_{[2]}$-submodules of $K(0)$. When $L$ is an arbitrary geometric lattice and $n$ is a positive integer, we construct a Virasoro-Heisenberg algebra $\tilde\mathcal{H}(L,n)$. Let $Q$ be an extension of $\dot{Q}$ by a degenerate rank one lattice. We determine the components of $V(\Gamma)$ that are irreducible $\tilde\mathcal{H}(Q,1)$-modules and we show that the reducible components have a filtration of $\tilde\mathcal{H}(Q,1)$-submodules with completely reducible quotients. Analogous results are obtained for $\tilde\mathcal{H} (\dot{Q},2)$. These results complement and extend results of Fabbri and Moody. Categories:17B65, 17B68

29. CJM 1998 (vol 50 pp. 1323)

Morales, Jorge
 L'invariant de Hasse-Witt de la forme de Killing Nous montrons que l'invariant de Hasse-Witt de la forme de Killing d'une alg{\e}bre de Lie semi-simple $L$ s'exprime {\a} l'aide de l'invariant de Tits de la repr{\'e}sentation irr{\'e}ductible de $L$ de poids dominant $\rho=\frac{1}{2}$ (somme des racines positives), et des invariants associ{\'e}s au groupe des sym{\'e}tries du diagramme de Dynkin de $L$. Categories:11E04, 11E72, 17B10, 17B20, 11E88, 15A66

30. CJM 1998 (vol 50 pp. 972)

Brüchert, Gerd
 Trace class elements and cross-sections in Kac-Moody groups Let $G$ be an affine Kac-Moody group, $\pi_0,\dots,\pi_r,\pi_{\delta}$ its fundamental irreducible representations and $\chi_0, \dots, \chi_r, \chi_{\delta}$ their characters. We determine the set of all group elements $x$ such that all $\pi_i(x)$ act as trace class operators, \ie, such that $\chi_i(x)$ exists, then prove that the $\chi_i$ are class functions. Thus, $\chi:=(\chi_0, \dots, \chi_r, \chi_{\delta})$ factors to an adjoint quotient $\bar{\chi}$ for $G$. In a second part, following Steinberg, we define a cross-section $C$ for the potential regular classes in $G$. We prove that the restriction $\chi|_C$ behaves well algebraically. Moreover, we obtain an action of $\hbox{\Bbbvii C}^{\times}$ on $C$, which leads to a functional identity for $\chi|_C$ which shows that $\chi|_C$ is quasi-homogeneous. Categories:22E65, 17B67

31. CJM 1998 (vol 50 pp. 929)

Broer, Abraham
 Decomposition varieties in semisimple Lie algebras The notion of decompositon class in a semisimple Lie algebra is a common generalization of nilpotent orbits and the set of regular semisimple elements. We prove that the closure of a decomposition class has many properties in common with nilpotent varieties, \eg, its normalization has rational singularities. The famous Grothendieck simultaneous resolution is related to the decomposition class of regular semisimple elements. We study the properties of the analogous commutative diagrams associated to an arbitrary decomposition class. Categories:14L30, 14M17, 15A30, 17B45

32. CJM 1998 (vol 50 pp. 816)

Mazorchuk, Volodymyr
 Tableaux realization of generalized Verma modules We construct the tableaux realization of generalized Verma modules over the Lie algebra $\sl(3,{\bbd C})$. By the same procedure we construct and investigate the structure of a new family of generalized Verma modules over $\sl(n,{\bbd C})$. Categories:17B35, 17B10

33. CJM 1998 (vol 50 pp. 356)

Gross, Leonard
 Some norms on universal enveloping algebras The universal enveloping algebra, $U(\frak g)$, of a Lie algebra $\frak g$ supports some norms and seminorms that have arisen naturally in the context of heat kernel analysis on Lie groups. These norms and seminorms are investigated here from an algebraic viewpoint. It is shown that the norms corresponding to heat kernels on the associated Lie groups decompose as product norms under the natural isomorphism $U(\frak g_1 \oplus \frak g_2) \cong U(\frak g_1) \otimes U(\frak g_2)$. The seminorms corresponding to Green's functions are examined at a purely Lie algebra level for $\rmsl(2,\Bbb C)$. It is also shown that the algebraic dual space $U'$ is spanned by its finite rank elements if and only if $\frak g$ is nilpotent. Categories:17B35, 16S30, 22E30

34. CJM 1998 (vol 50 pp. 266)

Britten, D. J.; Lemire, F. W.
 The torsion free Pieri formula Central to the study of simple infinite dimensional $g\ell(n, \Bbb C)$-modules having finite dimensional weight spaces are the torsion free modules. All degree $1$ torsion free modules are known. Torsion free modules of arbitrary degree can be constructed by tensoring torsion free modules of degree $1$ with finite dimensional simple modules. In this paper, the central characters of such a tensor product module are shown to be given by a Pieri-like formula, complete reducibility is established when these central characters are distinct and an example is presented illustrating the existence of a nonsimple indecomposable submodule when these characters are not distinct. Category:17B10

35. CJM 1998 (vol 50 pp. 225)

Benkart, Georgia
 Derivations and invariant forms of Lie algebras graded by finite root systems Lie algebras graded by finite reduced root systems have been classified up to isomorphism. In this paper we describe the derivation algebras of these Lie algebras and determine when they possess invariant bilinear forms. The results which we develop to do this are much more general and apply to Lie algebras that are completely reducible with respect to the adjoint action of a finite-dimensional subalgebra. Categories:17B20, 17B70, 17B25

36. CJM 1998 (vol 50 pp. 210)

Zhao, Kaiming
 Isomorphisms between generalized Cartan type $W$ Lie algebras in characteristic $0$ In this paper, we determine when two simple generalized Cartan type $W$ Lie algebras $W_d (A, T, \varphi)$ are isomorphic, and discuss the relationship between the Jacobian conjecture and the generalized Cartan type $W$ Lie algebras. Keywords:Simple Lie algebras, the general Lie algebra, generalized Cartan type $W$ Lie algebras, isomorphism, Jacobian conjectureCategories:17B40, 17B65, 17B56, 17B68

37. CJM 1997 (vol 49 pp. 1206)

Letzter, Gail
 Subalgebras which appear in quantum Iwasawa decompositions Let $g$ be a semisimple Lie algebra. Quantum analogs of the enveloping algebra of the fixed Lie subalgebra are introduced for involutions corresponding to the negative of a diagram automorphism. These subalgebras of the quantized enveloping algebra specialize to their classical counterparts. They are used to form an Iwasawa type decompostition and begin a study of quantum Harish-Chandra modules. Category:17B37

38. CJM 1997 (vol 49 pp. 772)

Jie, Xiao
 Finite dimensional representations of $U_t\bigl(\rmsl (2)\bigr)$ at roots of unity All finite dimensional indecomposable representations of $U_t (\rmsl (2))$ at roots of $1$ are determined. Categories:16G10, 16G70, 17B37

39. CJM 1997 (vol 49 pp. 820)

Robart, Thierry
 Sur l'intÃ©grabilitÃ© des sous-algÃ¨bres de Lie en dimension infinie Une des questions fondamentales de la th\'eorie des groupes de Lie de dimension infinie concerne l'int\'egrabilit\'e des sous-alg\ebres de Lie topologiques $\cal H$ de l'alg\ebre de Lie $\cal G$ d'un groupe de Lie $G$ de dimension infinie au sens de Milnor. Par contraste avec ce qui se passe en th\'eorie classique il peut exister des sous-alg\ebres de Lie ferm\'ees $\cal H$ de $\cal G$ non-int\'egrables en un sous-groupe de Lie. C'est le cas des alg\ebres de Lie de champs de vecteurs $C^{\infty}$ d'une vari\'et\'e compacte qui ne d\'efinissent pas un feuilletage de Stefan. Heureusement cette imperfection" de la th\'eorie n'est pas partag\'ee par tous les groupes de Lie int\'eressants. C'est ce que montre cet article en exhibant une tr\es large classe de groupes de Lie de dimension infinie exempte de cette imperfection. Cela permet de traiter compl\etement le second probl\`eme fondamental de Sophus Lie pour les groupes de jauge de la physique-math\'ematique et les groupes formels de diff\'eomorphismes lisses de $\R^n$ qui fixent l'origine. Categories:22E65, 58h05, 17B65

40. CJM 1997 (vol 49 pp. 119)

Osborn, J. Marshall
 Automorphisms of the Lie algebras $W^*$ in characteristic $0$ No abstract. Categories:17B40, 17B65, 17B66, 17B68, 17B70
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# Ball Spinning on String

1. Mar 17, 2017

### EthanVandals

1. The problem statement, all variables and given/known data
A 5kg ball is swung in a circle of radius .5 meters at a constant speed of 2 meters per second, how much work does the centripetal force do as the ball does once in a circle?If the ball were pushed the same distance as the circumference of the circle with a force equivalent to the centripetal force but in a straight line on a friction-less surface, what is the work this force would do? Explain why the answers are different. (Hint: They are, review the definition of work)

2. Relevant equations
Unknown

3. The attempt at a solution
I looked through all of the slides and notes that the professor posted, as well as my own notes, but I couldn't find anything relating to this style of problem. There were many equations talking about Omega and all sorts of different ways to solve similar problems, but I could not figure out how to translate it. Could anybody give me a hand with this problem? Thanks in advance!

PS: Sorry about the way the problem is worded. I just typed it in, word for word as my professor has it on our homework.

2. Mar 17, 2017

### CWatters

Answer the straight line case first. You should be able to do that and it will help with the circular case.

3. Mar 17, 2017

### CWatters

You should also review the definition of work. Its not just "force times distance", there is a bit more to it and that's important for this problem.

4. Mar 17, 2017

### EthanVandals

Ah, I see. I found the equation for Centripetal Force (mv^2)/r, and I found that the Centripetal Force (and therefore the force that would be pushing the ball in a straight line in) is equivalent to about 40 Newtons. Applying that to the frictionless surface, using the same formula would give me the same answer. The work done by both would be 40pi Joules. Looking at the definition of work, it appears that Displacement would need to occur for there to be ANY work done at all. Therefore, since the ball on the string returned to its starting point, it could be said that no work was done at all. Is this correct? Thanks!

5. Mar 17, 2017

### CWatters

It's not because it returns to the starting position. The work would still be zero if it only moved say quarter of a revolution. There is another reason.

6. Mar 17, 2017

### EthanVandals

Oh, is it because the force itself isn't causing the displacement? Since the force is the tension pulling towards the center, but the movement is in another direction? Other than that, I can't really think of what it could be...My apologies, I'm not very good at physics.

7. Mar 18, 2017

### haruspex

Yes. Vectorially, $W=\int \vec F.\vec{ds}$, where the . denotes dot product. So it is only the displacement in the direction of the force that matters. (Or, equivalently, use the whole displacement but only the component of the force in that direction.)

8. Mar 18, 2017

### CWatters

Specifically the force and displacement are orthogonal (at right angles to each other). So the component of force in the direction of the displacement is zero.

9. Mar 18, 2017

### EthanVandals

Awesome, I was hoping that was what it was. Thank you so much for the help!

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Thread: "ODD" Square root Algorithm View Single Post
 2008-03-15, 07:35 #4 nibble4bits     Nov 2005 2×7×13 Posts Do I understand right? That this is based on this formula for quadratics: (n+1)^2=n^2+2n+1; let m=n+1 m^2-n^2-1=2n Thus consecutive squares are always 2n+1 appart. That formule you mentioned is equivilent to this code: Code: Let x = 0 For i = 1 to n x = x + i + i - 1 Next i REM Returns in x, the square of n using recursive addition instead of multiplication. The optimizes trivially without multiplication to: Code: Let x=0 For i = 1 to n x = x + i + i Next i x = x - n You can further remove the For...Next loop using an identity but you get this: Let x = 2 * n * (n + 1) / 2 - n Or: Code: Let x = n * (n + 1) - n Or: Code: Let x = n^2 + n - n As you can see, this leads you back to your original equation of x=n^2. EDIT: You should note that for m=n+1: m^3 - n^3 - 1 = (n+1)^3 - n^3 - 1 = n^3 + 3n^2 + 3n + 1 - n^3 - 1 = 3(n^2 + n) = 3n(n+1) Last fiddled with by nibble4bits on 2008-03-15 at 07:44 Reason: Added note


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# Sum of the vectors from one fixed vertex to each remaining vertex of a regular polygon

I'm attempting to calculate the sum of the vectors from one fixed vertex of a regular m-sided polygon to each of the other vertices. It's for a study guide preceding my Linear Algebra exam tomorrow, and I'm entirely stumped by this question for some reason. The center of the polygon is at (0,0). How would I go about calculating this?

Thanks

Let the fixed vertex be at $(1,0)$, given by position vector $v_0$, and all the other vertices be given by position vectors $v_1$...$v_{m-1}$

Then $\Sigma_{i=0}^{m-1}v_i=0$, since they will form a closed polygon.

Now the required sum is $$(v_0-v_0)+(v_1-v_0)+(v_2-v_0)+...+(v_{m-1}-v_0)$$

$$=-mv_0=\left(\begin{matrix}-m\\0\end{matrix}\right)$$

• Oh, that absolutely makes sense, thanks! – Shrish Aug 30 '15 at 18:01
• Good luck with the exam! – David Quinn Aug 30 '15 at 18:03
• How do we know that they will form a closed polygon? – Scott Emmons Oct 3 '16 at 23:49
• @ScottEmmons since their sum is zero, they can be placed end to end to form a closed loop – David Quinn Oct 4 '16 at 5:34
• @DavidQuinn Which do we conclude first, that the sum of the vectors from the center to each of the vertices of the polygon is zero, or that the vectors from the center to each of the vertices of the polygon can be placed end to end to form a closed loop? I see how one is true if and only if the other is true, but I do not see at which we arrive first based on the given information of the problem. – Scott Emmons Oct 5 '16 at 14:54


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# zbMATH — the first resource for mathematics

Fuzzy relation equations and their applications to knowledge engineering. Foreword by Lotfi A. Zadeh. (English) Zbl 0694.94025
The book covers the most useful and new results in solving fuzzy relation equations with applications to knowledge engineering. The lucid and logically well-organized exposition is divided into two parts. Firstly the resolution problem for fuzzy relation equations under a variety of compositions is thoroughly presented. The main topics are fuzzy relation equations in residuated lattices, the lower solutions of max-min fuzzy equations, the measure of fuzziness of solutions, decompositions, t- norms, approximate solutions. The second part provides the pleasure of seeing the connection between the theory developed in the earlier chapters and knowledge-based systems. Every chapter in the book is self- contained with own references and examples, completing the concepts.
The first chapter is introductory. In Chapter 2 the main problem of the book is described: solving fuzzy relation equations of the form $(1)\quad B=R\diamond A...\quad or\quad (2)\quad T=S\diamond Q...,$ where A, B are fuzzy sets, R, S, T, Q are fuzzy relations and $$\diamond$$ stands for max-$$\odot$$, max-min, maxt-t, min-s, etc., compositions. For fuzzy relation equations on a residuated lattice L and $$\diamond =\max$$- $$\odot$$, the solvability of (2) is investigated. The study is focussed mainly on complete and dually complete Brouwerian lattices, determining the greatest (resp. smallest) solution.
In Chapter 3 the lower solutions of (1) and (2) are studied for $$\diamond =\max$$-min, if the referential sets are finite and L is linear. Different results are presented if L is either a complete Brouwerian or a complete completely distributive lattice.
Chapter 4 is devoted to the characterization of solutions of max-min fuzzy equations (on linear lattices with some additional properties) having the smallest and the greatest fuzzy entropy measure.
Chapter 5 deals with the greatest Boolean solution of max-min fuzzy equations defined on a complete bounded Brouwerian lattice L. If L is linear, minimal Boolean solutions are also characterized and a related optimization problem is discussed.
$$\alpha$$-fuzzy relation equations are subject to Chapter 6. The main topic here is the fuzzy relation decomposition in the intersection (resp. union) of two sets. Various notions of transitivity and related properties of convergence of powers of the involved relations are studied.
Chapter 7 presents an algorithm which allows to calculate the square root of a fuzzy relation assigned on a linear bounded lattice. The concepts of triangular norm (t-norm) and conorm (s-norm) lead to natural generalizations of some fuzzy relation equations using max-t and min-s compositions. A detailed analysis of such equation is presented in Chapter 8 under the assumption that t is lower (resp. s is upper) semicontinuous. The results are extended to equations of complex structure.
A particular composition $$\diamond$$ is presented in Chapter 9, based on the evaluation of an equivalence (resp. difference) degree between a fuzzy set and a fuzzy relation. It leads to new operators and to corresponding relational equations, whose solution sets are entirely characterized.
Chapter 10 deals with inconsistent fuzzy relation equations. A solvability index is introduced as a numerical measure to what extent the fuzzy relation equation is solvable. Several techniques are proposed to answer the main question: how difficult is it to attain an enough good approximate solution and how to measure this property.
The next four chapters deal with applications of fuzzy relation equations in knowledge-based systems, for handling fuzziness in knowledge representation, for constructing the knowledge base, rule-based systems, inference algorithms. An expert fuzzy controller system for an industrial process is discussed.
The extensive bibliography in Chapter 15, concerning fuzzy relational equations and related topics, is useful for all specialists, interested in the subject.
The book reflects the prolific authors research and the great reference erudition in the field.
Reviewer: K.Peeva

##### MSC:
 94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory) 68T99 Artificial intelligence 68P20 Information storage and retrieval of data 94-02 Research exposition (monographs, survey articles) pertaining to information and communication theory


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# Search for new resonances decaying via WZ to leptons in proton-proton collisions at $\sqrt{s}$ = 8 TeV

CMS Collaboration; Khachatryan, V; Sirunyan, A M; Tumasyan, A; Amsler, C; Canelli, F; Chiochia, V; De Cosa, A; Hinzmann, A; Hreus, T; Kilminster, B; Mejias, B; Ngadiuba, J; Robmann, P; Ronga, F J; Snoek, H; Taroni, S; Verzetti, M; Yang, Y; et al (2015). Search for new resonances decaying via WZ to leptons in proton-proton collisions at $\sqrt{s}$ = 8 TeV. Physics Letters B, 740:83-104.

## Abstract

A search is performed in proton–proton collisions at $\sqrt{s}$=8 TeV for exotic particles decaying via WZ to fully leptonic final states with electrons, muons, and neutrinos. The data set corresponds to an integrated luminosity of 19.5 fb$^{−1}$ . No significant excess is observed above the expected standard model background. Upper bounds at 95% confidence level are set on the production cross section of a W′ boson as predicted by an extended gauge model, and on the W′WZ coupling. The expected and observed mass limits for a W′ boson, as predicted by this model, are 1.55 and 1.47 TeV, respectively. Stringent limits are also set in the context of low-scale technicolor models under a range of assumptions for the model parameters.

## Abstract

A search is performed in proton–proton collisions at $\sqrt{s}$=8 TeV for exotic particles decaying via WZ to fully leptonic final states with electrons, muons, and neutrinos. The data set corresponds to an integrated luminosity of 19.5 fb$^{−1}$ . No significant excess is observed above the expected standard model background. Upper bounds at 95% confidence level are set on the production cross section of a W′ boson as predicted by an extended gauge model, and on the W′WZ coupling. The expected and observed mass limits for a W′ boson, as predicted by this model, are 1.55 and 1.47 TeV, respectively. Stringent limits are also set in the context of low-scale technicolor models under a range of assumptions for the model parameters.

## Citations

31 citations in Web of Science®
16 citations in Scopus®

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# Dimension of extension group is sum of dimensions of normal subgroup and quotient group

## Statement

### Statement for algebraic groups

Suppose $G$ is an algebraic group, $N$ is a closed normal subgroup and $G/N$ is the quotient group. Both $N$ and $G/N$ acquire algebraic group structures from the algebraic group structure of $G$. We then have the following relationship between the dimensions of $G,N,G/N$:

$\dim G = \dim N + \dim (G/N)$

In particular, $G$ is a finite-dimensional algebraic group if and only if both $N$ and $G/N$ are.

### Statement for Lie groups

Suppose $G$ is a Lie group, $N$ is a closed normal subgroup and $G/N$ is the quotient group. Both $N$ and $G/N$ acquire Lie group structures from the Lie group structure of $G$. We then have the following relationship between the dimensions of $G,N,G/N$:

$\dim G = \dim N + \dim (G/N)$


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# Large-n limit of the distribution of the normalized sum of Cauchy random variables

What is the large-n limit of a distribution of the following sample statistic:$$x\equiv\displaystyle\frac{\sum^{n}X_{i}}{\,\sqrt{\,\sum^{n}X_{i}^{2}\,}\,}$$ when sampling the Cauchy(0,1) distribution? Monte Carlo simulation indicates that convergence to this limit is quite fast, and that the resulting (symmetric) PDF has very sharp cusps at -1 and +1, but of course does not yield an analytic expression for this PDF - would anyone be able to find it?
Here is how the positive half of the PDF looks like:

• A somewhat random remark: the limiting distribution is also the distribution of $X_1 / \langle X\rangle_1$ if $X_t$ is the Cauchy process and $\langle X\rangle_t$ is the quadratic variation process, a $\tfrac{1}{2}$-stable subordinator. I bet someone has studied the joint law of $X_t$ and $\langle X\rangle_t$, but unfortunately I do not have time now to search for the reference. – Mateusz Kwaśnicki Jun 16 '19 at 20:17

This desired large-$$n$$ limit of the distribution $$P_n(x)$$ is calculated in Limit Distributions of Self-normalized Sums (1973). The Cauchy distribution is the case $$\alpha=1$$ on page 798. The singularity in $$\lim_{n\rightarrow\infty}P_n(x)$$ at $$x=\pm 1$$ is logarithmic $$P_n(x)\rightarrow-\pi^{-2}\log|1-x^2|,$$ see equation (5.12) and figure 4 (reproduced below), while for large $$|x|$$ the decay is Gaussian.


text:
Oxygen

## General Information (more on wikipidia)

 Molecular Weight (g/mol) Density (g/L) Radius (m) Reference Species O2 32 D R [1]

In science, oxygen is a chemical element with the chemical symbol O and atomic number 8. The word oxygen derives from two roots in Greek, οξύς (oxys) (acid, lit. sharp) and -γενής (-genēs) (producer, lit. begetter). It was recognized in 1777 by Antoine Lavoisier, who coined the name oxygen from the Greek roots mentioned above because he erroneously thought that it was a constituent of all acids. (The definition of acid has since been revised). Oxygen has a valency of 2. On Earth it is usually bonded to other elements covalently or ionically.
Diatomic oxygen (O2) is one of the two major components of air (20.95%). It is produced by plants during photosynthesis, and is necessary for aerobic respiration in animals. It is toxic to obligate anaerobic organisms and was a poisonous waste product for early life on Earth.

## Diffusion of Oxygen in water:

• Alone at 25 degrees: $D = 2000\ \mu m^{2} s^{-1}$ [1]
• Alone at 25 degrees: $D = 2000\ \mu m^{2} s^{-1}$ [2]
• Dependence on temperature [3]:
 Temperature Viscosity of H2O [centipoises] O2 Diffusion Coefficient [$\mu m^{2}$/s] 20 C 1.002 1970 40 C 0.653 3240 50 C 0.547 3990 60 C 0.467 4820

## Diffusion of Oxygen in cytoplasm

Bibliography
1. J. Crank, "The Mathematics of Diffusion" (Oxford University Press, 1956; 2nd ed. 1976)
2. Han, P., and D. M. Bartels. 1996. Temperature dependence of oxygen diffusion in H2O and D2O. J. Phys. Chem. 100:5597-5602.


text:
# Astronomy college course/Unit 3 study guide

## AstroTest3_Study

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This document contains either a study guide OR pairs of exams taken from the same exam bank
If two exams have the same s-number, then v1 and v2 have the same questions, presented in different (random) order.
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Click items in the table of contents and appropriate page should be reached. This feature should allow you to print only those pages that you need.
At the end of this document
Attribution for the quizzes identifies where the questions were obtained

### AstroTest3_Study-v1s1

1.
incomplete rim
The incomplete rims seen in the figure are caused by:
___ a) low surface gravity
___ b) vulcanism
___ c) meteorite erosion
___ d) rilles
___ e) micrometeorite erosion

2. Rilles are caused by

___ a) water
___ b) impacts
___ c) meteorites
___ d) lava
___ e) meteors

3. In the Wikipedia excerpt on "Planetary Astronomy" the mechanism by which a meander grows over time was discussed. Which of the the following is best describes why meanders grow? (Pick only one best answer)

___ a) wind erosion
___ b) combination of erosion and underlying bedrock strength
___ c) combination of deposition and underlying bedrock strength
___ d) a combination of deposition and erosion
___ e) occasional periods of intense flooding

4. When imaged in visible light Venus appears like ______ rather than ______.

___ a) Mars ... Venus
___ b) a gas dwarf ... a rocky planet
___ c) an asteroid ... a terrestrial planet
___ d) Venus ... Mars

5. The clouds on Venus are made of

___ a) water
___ b) nitrogen
___ c) carbon dioxide
___ d) steam
___ e) sulfuric acid

6. The geology of Venus is predominantly

___ a) Picrite
___ b) Andesite
___ c) Basalt

7. Basalt is what type of rock?

___ a) Sedimentary
___ b) Igneous
___ c) Metamorphic

8. The rocks on Venus are mostly

___ a) associated with plate tectonics
___ b) from the seabed of a now non-existent ocean
___ c) from volcanoes

9. The rocky surface of the planet Venus can be detected when Venus is observed using infrared astronomy.

___ a) TRUE
___ b) FALSE

10. When Venus is viewed in the ultraviolet, its color appears brownish.

___ a) TRUE
___ b) FALSE

11. Moldavite is a mineral that may be associated with what radiation astronomy phenomenon?

___ a) predicting when currently dormant volcanoes will erupt
___ b) meteorite impacts and fireballs
___ c) lightening strikes
___ d) evidence that Venus was once a comet

12. According to Wikipedia, a "mineral" is a naturally occurring solid that

___ a) has useful value
___ b) is heterogeneous
___ c) does not contain carbon
___ d) is by a chemical formula
___ e) contains carbon

13. Which types of radiation astronomy directly observe the rocky-object surface of Venus?

___ a) visual astronomy
___ c) ultraviolet astronomy
___ d) X-ray astronomy
___ e) infrared astronomy

14. One reason that Venus's atmosphere has more carbon dioxide than Earth's is that

___ a) Venus is exposed to a stronger solar wind strips away the other gasses
___ b) Venus was too hot for oceans that could absorb the carbon dioxide
___ c) the mass of Venus is slightly higher
___ d) Venus has a lower magnetic field that disassociates carbon dioxide

15. The surface temperature of Venus is about

___ a) 850 Fahrenheit (730 Kelvin or 230 Celsius)
___ b) 450 Fahrenheit (500 Kelvin or 66 Celsius)
___ c) 150 Fahrenheit (340 Kelvin or 66 Celsius)

16. The Venetian atmosphere consists of mostly carbon dioxide and

___ a) hydrogen
___ b) helium
___ c) sulfuric acid
___ d) nitrogen
___ e) oxygen

17.
Giovanni Schiaparelli 1877
Lowell circa 1914.
These drawings by Schiaparelli and Lowell were ultimately shown to be:

___ a) rilles
___ b) rift valleys
___ c) slip faults
___ d) subduction zones
___ e) optical illusions

18. Antipodal to the Tharsis bulge is

___ a) What Wikipedia contends IS an impact basin
___ b) What Wikipedia contends IS an active volcano
___ c) What Wikipedia contends MIGHT BE an impact basin
___ d) What Wikipedia contends MIGHT BE an active volcano
___ e) the northern lowlands

19.
Martian lobate feature
The lobate feature shown in the figure is evidence of

}
___ a) lava flow
___ b) dust storms
___ c) water flow
___ d) plate tectonics
___ e) wind erosion

20. The Martian dichotomy separates

___ a) the crust from the mantle
___ b) Valles Marineris from Olympus Mons
___ c) the highlands from the lowlands
___ d) the Tharsus buldge from Hellas basin
___ e) the rift valley from the volcanoes

21. According to Wikipedia, ______ was formed due to swelling of the Tharsis bulge which caused the crust to collapse

___ a) the southern lowlands
___ b) the northern lowlands
___ c) Valles Marineris
___ d) Hellas basin
___ e) Elysium

22.
gray hematite
What is this hematite?

___ a) evidence that Mars once had active volcanoes
___ b) evidence that Mars now has active volcanoes
___ c) controversial evidence that Mars once had life
___ d) evidence that Mars once had oceans
___ e) irrefutable evidence that Mars once had life

23. The polar ice caps on Mars are ___

___ a) actually clouds above the surface of Mars
___ b) mostly water
___ c) caused by geysers
___ d) mostly carbon dioxide
___ e) a nearly equal mix of water and carbon dioxide

24. Liquid water cannot exist on Mars due to ___

___ a) high pressure
___ b) low pressure
___ c) high temperature
___ d) the solar wind
___ e) low temperature

25.
magnified Martian meteorite
What is at the center of this magnified image of a Martian meteorite? fragment?

___ a) evidence that Mars now has active volcanoes
___ b) evidence that Mars once had active volcanoes
___ c) controversial evidence that Mars once had life
___ d) irrefutable evidence that Mars once had life
___ e) evidence that Mars once had oceans

26. It is important to distinguish between molecules (collectively) in a gas and one individual molecule. This question is about an individual molecule. For a planet with a given mass, size, and density, which has the greater escape velocity?

___ a) all molecules move at the escape velocity
___ b) the lighter molecule has the greater escape velocity
___ c) no molecules have escape velocity
___ d) the heavier molecule has the greater escape velocity
___ e) all molecules have the same escape velocity

27. It is important to distinguish between molecules (collectively) in a gas and one individual molecule. This question is about a typical molecule in the gas. For a planet with a given mass, size, and density, which type of gas is more likely to escape?

___ a) atoms in a hotter gas is more likely to escape
___ b) all types of gas are equally likely to escape
___ c) atoms in a denser gas are more likely to escape
___ d) atoms in a colder gas are more likely to escape
___ e) atoms in a gas with more atomic mass are more likely to escape

28. Which type of gas is likely to have the faster particles?

___ a) a hot gas with low mass atoms
___ b) a cold gas with low mass atoms
___ c) a hot gas with high mass atoms
___ d) all gasses on a given planet have the same speed
___ e) a cold gas with high mass atoms

29. What is it about the isotopes of Argon-36 and Argon-38 that causes their relative abundance to be so unusual on Mars?

___ a) identical abundance
___ b) different speed
___ c) different chemical properties
___ d) identical mass
___ e) different half-life

30. In the formula, ${\displaystyle {\frac {1}{2}}m_{\mathrm {atom} }v_{\mathrm {escape} }^{2}=G_{\mathrm {Newton} }{\frac {M_{\mathrm {planet} }m_{\mathrm {atom} }}{r_{\mathrm {planet} }}}}$, which of the following is FALSE?

___ a) the formula is valid for all launch angles
___ b) the formula is valid only if the particle is launched from the surface of planet of radius rplanet
___ c) vescape is independent of matom
___ d) the particle is assumed to have been launched vertically
___ e) the formula can be used to estimate how fast an atom must move before exiting the planet

31. What statement is FALSE about ${\displaystyle {\frac {1}{2}}m_{\mathrm {atom} }\langle v_{\mathrm {atom} }^{2}\rangle _{ave}={\frac {1}{2}}k_{\mathrm {B} }T}$?

___ a) Temperature is measured in Centigrades
___ b) Temperature is measured in Kelvins
___ c) This equation does not involve the size or mass of the planet.
___ d) The kinetic energy is directly proportional to temperature.
___ e) The average speed of a low mass particle is higher than the average speed of a high mass particle

32. ${\displaystyle {\frac {1}{2}}m_{\mathrm {atom} }\langle v_{\mathrm {atom} }^{2}\rangle _{ave}={\frac {1}{2}}k_{\mathrm {B} }T}$, where T is temperature on the Kelvin scale. This formula describes:

___ a) The speed of a typical atom, where m is the mass of the atom.
___ b) The speed of a typical atom, where m is the mass of the planet.
___ c) The speed an atom needs to orbit the planet, where m is the mass of the atom.
___ d) The the speed an atom needs to escape the planet, where m is the mass planet.
___ e) The speed an atom needs to escape the planet, where m is the mass of the atom.

33. How does the density of a Galilean moon depend on its distance from Jupiter?

___ a) the density of the moons is unknown
___ b) the less dense moon is closer to Jupiter (always)
___ c) all the moons have nearly the same density
___ d) the more dense moon is closer to Jupiter (always)
___ e) the most dense moon is neither the closest nor the most distant

34. How does the mass of a Galilean moon depend on its distance from the central body?

___ a) the more massive moon is closer to Jupiter (always)
___ b) the less massive moon is closer to Jupiter (always)
___ c) the most massive moon is neither the closest nor the most distant
___ d) all the moons have nearly the same mass
___ e) the mass of the moons is unknown

35. Does Jupiter's moon Io have craters?

___ a) no, the surface is too new
___ b) yes, about half from impacts and the others from volcanoes
___ c) yes, from volcanoes
___ d) no, the surface is too old
___ e) yes, from impacts

36. The mechanism that heats the cores of the Galilean moons is

___ a) radioactive decay of heavy elements
___ b) radiation from the Sun and from Jupiter
___ c) tides from Jupiter
___ d) radiation from the Sun
___ e) tides from the other moons and Jupiter

37. Immediately after publication of Newton's laws of physics (Principia), it was possible to "calculate" the mass of Jupiter. What important caveat applied to this calculation?

___ a) The different moons yielded vastly different values for the mass of Jupiter.
___ b) The different moons yielded slightly different values for the mass of Jupiter.
___ c) tides from the other moons and Jupiter.
___ d) Only the mass of Jupiter relative to that of the Sun could be determined.
___ e) They needed to wait over a decade for Jupiter to make approximately one revolution around the Sun.

38. Ganymede, Europa, and Io have ratios in __________ that are 1:2:4.

___ a) Two other answers are correct (making this the only true answer).
___ b) density
___ c) Argon isotope abundance
___ d) orbital period
___ e) rotational period

39. Which of Jupiter's moons has an anhydrous core?

___ a) Two other answers are correct (making this the only true answer).
___ b) Ganymede
___ c) Ganymede
___ d) Io
___ e) Europa

40. The 1982 Voyager flyby of Miranda (a moon of Uranus) established that _____

___ a) Miranda has geysers.
___ b) Two other answers are correct (making this the only true answer).
___ c) inspired a theory a previous incarnation was destroyed by a collision
___ d) Miranda has the largest active volcano in the solar system
___ e) Miranda probably has an iron core

41. It has been suggested that Miranda's "racetrack"

___ a) is associated with tidal heating
___ b) is a series of rifts created by an upwelling of warm ice
___ c) is an impact crater
___ d) is antipodal to an impact crater
___ e) Two other answers are correct (making this the only true answer).

42. According to Wikipedia, the largest lakes on Titan are probably fed by

___ a) geysers
___ b) liquid water rain
___ c) methane rain
___ d) underground aquifers
___ e) rivers from the highlands

43.

The bright spot on Saturn's moon Titan is
___ a) a volcano
___ b) aurora borealis (northern lights)
___ c) solar wind particles striking the atmosphere
___ d) lightening
___ e) a lake

44. One "year" on Saturn's largest moon Titan lasts

___ a) 3 hours
___ b) 300 days
___ c) 3 years
___ d) 30 years
___ e) 30 hours

45.

The photographs compare
___ a) summer windstorms and winter doldrums
___ b) Titan and Earth
___ c) winter windstorms and summer doldrums
___ d) wet and dry seasons
___ e) northern and southern hemispheres

46. The liquid water ocean of Saturn's largest moon Titan,

___ a) is less than one meter in depth
___ b) is known to contain life
___ c) explains how the elevation of a smooth planet seems to rise and fall
___ d) Two other answers are correct
___ e) is postulated to cover 15-30% of its surface

47.

The black spot in this image of Jupiter is
___ a) a solar eclipse
___ b) the shadow of a moon
___ c) a magnetic storm
___ d) an electric storm
___ e) Two other answers are correct (making this the only true answer).

48. Which of the following statements is FALSE?

___ a) The Great Red Spot is a storm that has raged for over 300 years
___ b) Jupiter emits more energy than it receives from the Sun
___ c) Jupiter has a system of rings
___ d) Jupiter has four large moons and many smaller ones
___ e) Jupiter is the largest known planet

49. What is the mechanism that heats the interior of Jupiter?

___ b) rain
___ c) tides
___ d) magnetism
___ e) electricity

50. Why is Jupiter an oblate spheroid?

___ b) revolution around Sun
___ c) tides from the Jupiter's moons
___ d) tides from other gas planets
___ e) tides from the Sun

51. What statement best describes the Wikipedia's explanation of the helium (He) content of Jupiter's upper atmosphere (relative to the hydrogen (H) content)?

___ a) Jupiter's atmosphere has only 80% as much helium because the He fell to the core.
___ b) Jupiter's atmosphere has only 80% as much helium because the He escaped into space.
___ c) Jupiter's atmosphere has 80% more He because Jupiter's hydrogen escaped into space.
___ d) Jupiter's atmosphere has 80% more He because Jupiter's hydrogen fell to the core.
___ e) Jupiter and the Sun have nearly the same ratio of He to H.

52. Where is the Sun-Jupiter barycenter?

___ a) Just above the Sun's surface
___ b) The question remains unresolved
___ c) At the center of Jupiter
___ d) At the center of the Sun
___ e) Just above Jupiter's surface

53. The barycenter of two otherwise isolated celestial bodies is?

___ a) a place where two bodies exert equal and opposite gravitational forces
___ b) the focal point of two elliptical orbital paths
___ c) both of these are true

54. Knowing the barycenter of two stars is useful because it tells us the total mass

___ a) TRUE
___ b) FALSE

55. Knowing the barycenter of two stars is useful because it tells us the ratio of the two masses

___ a) TRUE
___ b) FALSE

56. Although there is some doubt as to who discovered Jupiter's great red spot, it is generally credited to

___ a) Galileo in 1605
___ b) Cassini in 1665
___ c) Messier in 1771
___ d) Tycho in
___ e) Newton in 1668

57. The bands in the atmosphere of Jupiter are associated with a patter of alternating wind velocities that are

___ a) easterly and westerly
___ b) updrafts and downdrafts
___ c) both of these

58. As one descends down to Jupiter's core, the temperature

___ a) decreases
___ b) increases
___ c) stays about the same

59. Which of the following is NOT used to measure the mass of a planet

___ a) the motion of a neighboring planet
___ b) all of these have been used
___ c) the rotation of the planet about its axis
___ d) the motion of an artificial satellite
___ e) the motion of a moon

60. What is unusual about calculations of the mass of Pluto made in the early part of the 20th century?

___ a) The estimates were high. Pluto was less massive than they calculated
___ b) It was the first time a planet's period of orbit around the sun was used to calculate the planet's mass
___ c) The estimates were correct to within less than 10%
___ d) It was the first time a moon was used to calculate the mass of a planet
___ e) The estimates were too low. Pluto was actually more massive than they thought.

61. Why was the discovery of Pluto peculiar?

___ a) It was discovered by a calculation based on flawed assumptions
___ b) It was the first time a planet's period of orbit around the sun was used to calculate the planet's mass
___ c) It was seen by Galileo, who thought it was a star
___ d) It was seen by Halley, who was looking for comets
___ e) It was discovered during a survey looking for stars

62. Which of the following is NOT used to measure the mass of a planet

___ a) all of these have been used
___ b) the motion of an artificial satellite
___ c) the motion of a neighboring planet
___ d) the motion of a moon

63. Which statement describes the relation between Pluto and Neptune

___ a) Pluto's orbit intersects Neptune's orbit an the two bodies will eventually collide
___ b) Pluto's orbit lies outside Neptune's orbit
___ c) Pluto's orbit intersects Neptune's orbit but they don't collide because of an orbital resonance between the two
___ d) Pluto's orbit intersects Neptune's orbit but they avoid each other because Pluto's mass is too small

#### Key to AstroTest3_Study-v1s1

1.
incomplete rim
The incomplete rims seen in the figure are caused by:
- a) low surface gravity
+ b) vulcanism
- c) meteorite erosion
- d) rilles
- e) micrometeorite erosion

2. Rilles are caused by

- a) water
- b) impacts
- c) meteorites
+ d) lava
- e) meteors

3. In the Wikipedia excerpt on "Planetary Astronomy" the mechanism by which a meander grows over time was discussed. Which of the the following is best describes why meanders grow? (Pick only one best answer)

- a) wind erosion
- b) combination of erosion and underlying bedrock strength
- c) combination of deposition and underlying bedrock strength
+ d) a combination of deposition and erosion
- e) occasional periods of intense flooding

4. When imaged in visible light Venus appears like ______ rather than ______.

- a) Mars ... Venus
+ b) a gas dwarf ... a rocky planet
- c) an asteroid ... a terrestrial planet
- d) Venus ... Mars

5. The clouds on Venus are made of

- a) water
- b) nitrogen
- c) carbon dioxide
- d) steam
+ e) sulfuric acid

6. The geology of Venus is predominantly

- a) Picrite
- b) Andesite
+ c) Basalt

7. Basalt is what type of rock?

- a) Sedimentary
+ b) Igneous
- c) Metamorphic

8. The rocks on Venus are mostly

- a) associated with plate tectonics
- b) from the seabed of a now non-existent ocean
+ c) from volcanoes

9. The rocky surface of the planet Venus can be detected when Venus is observed using infrared astronomy.

- a) TRUE
+ b) FALSE

10. When Venus is viewed in the ultraviolet, its color appears brownish.

- a) TRUE
+ b) FALSE

11. Moldavite is a mineral that may be associated with what radiation astronomy phenomenon?

- a) predicting when currently dormant volcanoes will erupt
+ b) meteorite impacts and fireballs
- c) lightening strikes
- d) evidence that Venus was once a comet

12. According to Wikipedia, a "mineral" is a naturally occurring solid that

- a) has useful value
- b) is heterogeneous
- c) does not contain carbon
+ d) is by a chemical formula
- e) contains carbon

13. Which types of radiation astronomy directly observe the rocky-object surface of Venus?

- a) visual astronomy
- c) ultraviolet astronomy
- d) X-ray astronomy
- e) infrared astronomy

14. One reason that Venus's atmosphere has more carbon dioxide than Earth's is that

- a) Venus is exposed to a stronger solar wind strips away the other gasses
+ b) Venus was too hot for oceans that could absorb the carbon dioxide
- c) the mass of Venus is slightly higher
- d) Venus has a lower magnetic field that disassociates carbon dioxide

15. The surface temperature of Venus is about

+ a) 850 Fahrenheit (730 Kelvin or 230 Celsius)
+ b) 450 Fahrenheit (500 Kelvin or 66 Celsius)
+ c) 150 Fahrenheit (340 Kelvin or 66 Celsius)

16. The Venetian atmosphere consists of mostly carbon dioxide and

- a) hydrogen
- b) helium
- c) sulfuric acid
+ d) nitrogen
- e) oxygen

17.
Giovanni Schiaparelli 1877
Lowell circa 1914.
These drawings by Schiaparelli and Lowell were ultimately shown to be:

- a) rilles
- b) rift valleys
- c) slip faults
- d) subduction zones
+ e) optical illusions

18. Antipodal to the Tharsis bulge is

+ a) What Wikipedia contends IS an impact basin
- b) What Wikipedia contends IS an active volcano
- c) What Wikipedia contends MIGHT BE an impact basin
- d) What Wikipedia contends MIGHT BE an active volcano
- e) the northern lowlands

19.
Martian lobate feature
The lobate feature shown in the figure is evidence of

}
+ a) lava flow
- b) dust storms
- c) water flow
- d) plate tectonics
- e) wind erosion

20. The Martian dichotomy separates

- a) the crust from the mantle
- b) Valles Marineris from Olympus Mons
+ c) the highlands from the lowlands
- d) the Tharsus buldge from Hellas basin
- e) the rift valley from the volcanoes

21. According to Wikipedia, ______ was formed due to swelling of the Tharsis bulge which caused the crust to collapse

- a) the southern lowlands
- b) the northern lowlands
+ c) Valles Marineris
- d) Hellas basin
- e) Elysium

22.
gray hematite
What is this hematite?

- a) evidence that Mars once had active volcanoes
- b) evidence that Mars now has active volcanoes
- c) controversial evidence that Mars once had life
+ d) evidence that Mars once had oceans
- e) irrefutable evidence that Mars once had life

23. The polar ice caps on Mars are ___

- a) actually clouds above the surface of Mars
+ b) mostly water
- c) caused by geysers
- d) mostly carbon dioxide
- e) a nearly equal mix of water and carbon dioxide

24. Liquid water cannot exist on Mars due to ___

- a) high pressure
+ b) low pressure
- c) high temperature
- d) the solar wind
- e) low temperature

25.
magnified Martian meteorite
What is at the center of this magnified image of a Martian meteorite? fragment?

- a) evidence that Mars now has active volcanoes
- b) evidence that Mars once had active volcanoes
+ c) controversial evidence that Mars once had life
- d) irrefutable evidence that Mars once had life
- e) evidence that Mars once had oceans

26. It is important to distinguish between molecules (collectively) in a gas and one individual molecule. This question is about an individual molecule. For a planet with a given mass, size, and density, which has the greater escape velocity?

- a) all molecules move at the escape velocity
- b) the lighter molecule has the greater escape velocity
- c) no molecules have escape velocity
- d) the heavier molecule has the greater escape velocity
+ e) all molecules have the same escape velocity

27. It is important to distinguish between molecules (collectively) in a gas and one individual molecule. This question is about a typical molecule in the gas. For a planet with a given mass, size, and density, which type of gas is more likely to escape?

+ a) atoms in a hotter gas is more likely to escape
- b) all types of gas are equally likely to escape
- c) atoms in a denser gas are more likely to escape
- d) atoms in a colder gas are more likely to escape
- e) atoms in a gas with more atomic mass are more likely to escape

28. Which type of gas is likely to have the faster particles?

+ a) a hot gas with low mass atoms
- b) a cold gas with low mass atoms
- c) a hot gas with high mass atoms
- d) all gasses on a given planet have the same speed
- e) a cold gas with high mass atoms

29. What is it about the isotopes of Argon-36 and Argon-38 that causes their relative abundance to be so unusual on Mars?

- a) identical abundance
+ b) different speed
- c) different chemical properties
- d) identical mass
- e) different half-life

30. In the formula, ${\displaystyle {\frac {1}{2}}m_{\mathrm {atom} }v_{\mathrm {escape} }^{2}=G_{\mathrm {Newton} }{\frac {M_{\mathrm {planet} }m_{\mathrm {atom} }}{r_{\mathrm {planet} }}}}$, which of the following is FALSE?

+ a) the formula is valid for all launch angles
- b) the formula is valid only if the particle is launched from the surface of planet of radius rplanet
- c) vescape is independent of matom
- d) the particle is assumed to have been launched vertically
- e) the formula can be used to estimate how fast an atom must move before exiting the planet

31. What statement is FALSE about ${\displaystyle {\frac {1}{2}}m_{\mathrm {atom} }\langle v_{\mathrm {atom} }^{2}\rangle _{ave}={\frac {1}{2}}k_{\mathrm {B} }T}$?

+ a) Temperature is measured in Centigrades
- b) Temperature is measured in Kelvins
- c) This equation does not involve the size or mass of the planet.
- d) The kinetic energy is directly proportional to temperature.
- e) The average speed of a low mass particle is higher than the average speed of a high mass particle

32. ${\displaystyle {\frac {1}{2}}m_{\mathrm {atom} }\langle v_{\mathrm {atom} }^{2}\rangle _{ave}={\frac {1}{2}}k_{\mathrm {B} }T}$, where T is temperature on the Kelvin scale. This formula describes:

+ a) The speed of a typical atom, where m is the mass of the atom.
- b) The speed of a typical atom, where m is the mass of the planet.
- c) The speed an atom needs to orbit the planet, where m is the mass of the atom.
- d) The the speed an atom needs to escape the planet, where m is the mass planet.
- e) The speed an atom needs to escape the planet, where m is the mass of the atom.

33. How does the density of a Galilean moon depend on its distance from Jupiter?

- a) the density of the moons is unknown
- b) the less dense moon is closer to Jupiter (always)
- c) all the moons have nearly the same density
+ d) the more dense moon is closer to Jupiter (always)
- e) the most dense moon is neither the closest nor the most distant

34. How does the mass of a Galilean moon depend on its distance from the central body?

- a) the more massive moon is closer to Jupiter (always)
- b) the less massive moon is closer to Jupiter (always)
+ c) the most massive moon is neither the closest nor the most distant
- d) all the moons have nearly the same mass
- e) the mass of the moons is unknown

35. Does Jupiter's moon Io have craters?

- a) no, the surface is too new
- b) yes, about half from impacts and the others from volcanoes
+ c) yes, from volcanoes
- d) no, the surface is too old
- e) yes, from impacts

36. The mechanism that heats the cores of the Galilean moons is

- a) radioactive decay of heavy elements
- b) radiation from the Sun and from Jupiter
- c) tides from Jupiter
- d) radiation from the Sun
+ e) tides from the other moons and Jupiter

37. Immediately after publication of Newton's laws of physics (Principia), it was possible to "calculate" the mass of Jupiter. What important caveat applied to this calculation?

- a) The different moons yielded vastly different values for the mass of Jupiter.
- b) The different moons yielded slightly different values for the mass of Jupiter.
- c) tides from the other moons and Jupiter.
+ d) Only the mass of Jupiter relative to that of the Sun could be determined.
- e) They needed to wait over a decade for Jupiter to make approximately one revolution around the Sun.

38. Ganymede, Europa, and Io have ratios in __________ that are 1:2:4.

+ a) Two other answers are correct (making this the only true answer).
- b) density
- c) Argon isotope abundance
- d) orbital period
- e) rotational period

39. Which of Jupiter's moons has an anhydrous core?

- a) Two other answers are correct (making this the only true answer).
- b) Ganymede
- c) Ganymede
+ d) Io
- e) Europa

40. The 1982 Voyager flyby of Miranda (a moon of Uranus) established that _____

- a) Miranda has geysers.
- b) Two other answers are correct (making this the only true answer).
+ c) inspired a theory a previous incarnation was destroyed by a collision
- d) Miranda has the largest active volcano in the solar system
- e) Miranda probably has an iron core

41. It has been suggested that Miranda's "racetrack"

- a) is associated with tidal heating
- b) is a series of rifts created by an upwelling of warm ice
- c) is an impact crater
- d) is antipodal to an impact crater
+ e) Two other answers are correct (making this the only true answer).

42. According to Wikipedia, the largest lakes on Titan are probably fed by

- a) geysers
- b) liquid water rain
- c) methane rain
+ d) underground aquifers
- e) rivers from the highlands

43.

The bright spot on Saturn's moon Titan is
- a) a volcano
- b) aurora borealis (northern lights)
- c) solar wind particles striking the atmosphere
- d) lightening
+ e) a lake

44. One "year" on Saturn's largest moon Titan lasts

- a) 3 hours
- b) 300 days
- c) 3 years
+ d) 30 years
- e) 30 hours

45.

The photographs compare
- a) summer windstorms and winter doldrums
+ b) Titan and Earth
- c) winter windstorms and summer doldrums
- d) wet and dry seasons
- e) northern and southern hemispheres

46. The liquid water ocean of Saturn's largest moon Titan,

- a) is less than one meter in depth
- b) is known to contain life
+ c) explains how the elevation of a smooth planet seems to rise and fall
- d) Two other answers are correct
- e) is postulated to cover 15-30% of its surface

47.

The black spot in this image of Jupiter is
- a) a solar eclipse
- b) the shadow of a moon
- c) a magnetic storm
- d) an electric storm
+ e) Two other answers are correct (making this the only true answer).

48. Which of the following statements is FALSE?

- a) The Great Red Spot is a storm that has raged for over 300 years
- b) Jupiter emits more energy than it receives from the Sun
- c) Jupiter has a system of rings
- d) Jupiter has four large moons and many smaller ones
+ e) Jupiter is the largest known planet

49. What is the mechanism that heats the interior of Jupiter?

+ b) rain
- c) tides
- d) magnetism
- e) electricity

50. Why is Jupiter an oblate spheroid?

- b) revolution around Sun
- c) tides from the Jupiter's moons
- d) tides from other gas planets
- e) tides from the Sun

51. What statement best describes the Wikipedia's explanation of the helium (He) content of Jupiter's upper atmosphere (relative to the hydrogen (H) content)?

+ a) Jupiter's atmosphere has only 80% as much helium because the He fell to the core.
- b) Jupiter's atmosphere has only 80% as much helium because the He escaped into space.
- c) Jupiter's atmosphere has 80% more He because Jupiter's hydrogen escaped into space.
- d) Jupiter's atmosphere has 80% more He because Jupiter's hydrogen fell to the core.
- e) Jupiter and the Sun have nearly the same ratio of He to H.

52. Where is the Sun-Jupiter barycenter?

+ a) Just above the Sun's surface
- b) The question remains unresolved
- c) At the center of Jupiter
- d) At the center of the Sun
- e) Just above Jupiter's surface

53. The barycenter of two otherwise isolated celestial bodies is?

- a) a place where two bodies exert equal and opposite gravitational forces
+ b) the focal point of two elliptical orbital paths
- c) both of these are true

54. Knowing the barycenter of two stars is useful because it tells us the total mass

- a) TRUE
+ b) FALSE

55. Knowing the barycenter of two stars is useful because it tells us the ratio of the two masses

+ a) TRUE
- b) FALSE

56. Although there is some doubt as to who discovered Jupiter's great red spot, it is generally credited to

- a) Galileo in 1605
+ b) Cassini in 1665
- c) Messier in 1771
- d) Tycho in
- e) Newton in 1668

57. The bands in the atmosphere of Jupiter are associated with a patter of alternating wind velocities that are

- a) easterly and westerly
- b) updrafts and downdrafts
+ c) both of these

58. As one descends down to Jupiter's core, the temperature

- a) decreases
+ b) increases
- c) stays about the same

59. Which of the following is NOT used to measure the mass of a planet

- a) the motion of a neighboring planet
- b) all of these have been used
+ c) the rotation of the planet about its axis
- d) the motion of an artificial satellite
- e) the motion of a moon

60. What is unusual about calculations of the mass of Pluto made in the early part of the 20th century?

+ a) The estimates were high. Pluto was less massive than they calculated
- b) It was the first time a planet's period of orbit around the sun was used to calculate the planet's mass
- c) The estimates were correct to within less than 10%
- d) It was the first time a moon was used to calculate the mass of a planet
- e) The estimates were too low. Pluto was actually more massive than they thought.

61. Why was the discovery of Pluto peculiar?

+ a) It was discovered by a calculation based on flawed assumptions
- b) It was the first time a planet's period of orbit around the sun was used to calculate the planet's mass
- c) It was seen by Galileo, who thought it was a star
- d) It was seen by Halley, who was looking for comets
- e) It was discovered during a survey looking for stars

62. Which of the following is NOT used to measure the mass of a planet

+ a) all of these have been used
- b) the motion of an artificial satellite
- c) the motion of a neighboring planet
- d) the motion of a moon

63. Which statement describes the relation between Pluto and Neptune

- a) Pluto's orbit intersects Neptune's orbit an the two bodies will eventually collide
- b) Pluto's orbit lies outside Neptune's orbit
+ c) Pluto's orbit intersects Neptune's orbit but they don't collide because of an orbital resonance between the two
- d) Pluto's orbit intersects Neptune's orbit but they avoid each other because Pluto's mass is too small

http://en.wikiversity.org/w/index.php?title=Astronomy_college_course/Planetary_science_questions&oldid=1298071
http://en.wikiversity.org/w/index.php?title=Venus/Quiz&oldid=1388298
http://en.wikiversity.org/w/index.php?title=Quizbank/Contributed_questions&oldid=1388791
http://en.wikiversity.org/w/index.php?title=Astronomy_college_course/Mars/questions&oldid=1327222
http://en.wikiversity.org/w/index.php?title=Astronomy_college_course/Why_planets_lose_their_atmospheres/questions&oldid=1204943
http://en.wikiversity.org/w/index.php?title=Astronomy_college_course/Galilean_moons_of_Jupiter/questions&oldid=1293955
https//en.wikiversity.org/w/index.php?title=Astronomy_college_course/Miranda_and_Titan/questions&oldid=1293943
http://en.wikiversity.org/w/index.php?title=Astronomy_college_course/Jupiter/questions&oldid=1388646
http://en.wikiversity.org/w/index.php?title=Astronomy_college_course/Pluto_and_planetary_mass_quiz&oldid=1388652
Study guide
http://en.wikiversity.org/w/index.php?title=Astronomy_college_course/Planetary_science&oldid=1204930
Venus
w:Atmosphere of Venus
w:Venus
http://en.wikiversity.org/w/index.php?title=Astronomy_college_course/Mars&oldid=1327223
http://en.wikiversity.org/w/index.php?title=Astronomy_college_course/Why_planets_lose_their_atmospheres&oldid=1388258
http://en.wikiversity.org/w/index.php?title=Astronomy_college_course/Galilean_moons_of_Jupiter&oldid=1326527
http://en.wikiversity.org/w/index.php?title=Astronomy_college_course/Miranda_and_Titan&oldid=1204929
http://en.wikiversity.org/w/index.php?title=Astronomy_college_course/Jupiter&oldid=1204919
http://en.wikipedia.org/w/index.php?title=Jupiter&oldid=664015766
http://en.wikipedia.org/w/index.php?title=Atmosphere_of_Jupiter&oldid=664309417
http://en.wikipedia.org/w/index.php?title=Pluto&oldid=664428172