Boltzmann constant or ideal gas constant).  You can use this to integrate from V1 to V2 and solve for the work done.  
You dont need any more information than this for the last two processes.

 Q:

Smallest enclosing cylinder for an irregular body

I have an $3$-dimensional irregular body composed of 162 points $(x,y,z)$.
I need to find the smallest enclosing cylinder for this body. Is there a standard algorithm for achieving this?

A:

I'll assume it's to be a right circular cylinder, and "smallest" is in terms of volume.  Consider a cylinder of radius $r$ and height $h$, with one of the ends centred at point $P$, and axis in the direction of unit vector $U$.  Then a point $X = (x,y,z)$ is in the cylinder if $0 \le (X - P)\cdot U \le h$ and $\|X - P - ((X -P)\cdot U) U \|^2 \le r^2$.  Thus you want to minimize $r^2 h$ subject to constraints
$r \ge 0$, $h \ge 0$, $\|U\|^2 = 1$, and for all $X$, $(X - P) \cdot U \ge 0$, $(X - P)\cdot U \le h$, $\|X - P - ((X -P)\cdot U) U \|^2 \le r^2$.  You only need to consider those $X$ that are extreme points of their convex hull.
  You can also require, say, $U_1 \ge 0$ because you have your choice of which end of the cylinder $P$ is on.  This is a (non-convex) nonlinear constrained optimization problem.
I might try Maple's Global Optimization Toolbox.

 Q:

Frequency of SQL Server full backups vs. diffs

I have a SQL Server located in a colo center.  Currently, our database is about 100Gb.  Log files average about 500Mb/day, and differential backups grow by a bit less than that.
My current disaster recovery plan is:  have a full backup elsewhere, take log backups every ten minutes, diffs every night.  I copy the logs and diffs off to S3, so, except for the tail, they're not on the machine in case
Boltzmann constant or ideal gas constant).   You can use this to integrate from V1 to V2 and resolve for the workplace done.  
 You do nt need any more information than this for the final two processes. 

  Q: 

 Smallest insert cylinder for an atypical body 

 I have an $ 3$-dimensional irregular body composed of 162 compass point $ (x, y, z)$. 
 I need to witness the smallest enclosing cylinder for this body. Is there a standard algorithm for achieving this? 

 A: 

 I'll assume it's to be a correct circular cylinder, and " smallest " is in terms of book.   Consider a cylinder of radius $ r$ and height $ h$, with one of the ends centred at detail $ P$, and axis in the direction of unit vector $ U$.   Then a point $ X = (x, y, z)$ is in the cylinder if $ 0 \le (X - P)\cdot U \le h$ and $ \|X - P - (( ten -P)\cdot U) U \|^2 \le r^2$.   Thus you want to minimize $ r^2 h$ subject to constraints 
 $ r \ge 0 $, $ h \ge 0 $, $ \|U\|^2 = 1 $, and for all $ X$, $ (X - P) \cdot U \ge 0 $, $ (X - P)\cdot U \le h$, $ \|X - P - (( X -P)\cdot U) U \|^2 \le r^2$.   You only need to consider those $ X$ that are extreme point of their convex hull. 
   You can also require, say, $ U_1 \ge 0 $ because you receive your option of which conclusion of the cylinder $ P$ is on.   This is a (non - convex) nonlinear constrained optimization problem. 
 I might judge Maple's Global Optimization Toolbox. 

  Q: 

 Frequency of SQL Server wide backups vs. diffs 

 I have a SQL Server locate in a colo center.   Currently, our database is about 100Gb.   Log files average about 500Mb / day, and differential accompaniment grow by a bit less than that. 
 My current disaster recovery plan is:   have a entire backup elsewhere, take log backups every ten minutes, diffs every nox.   I copy the logs and diffs off to S3, so, except for the tail, they're not on the machine in case
Bolhzmann constant or ideal gas constant).  Ioy can nse thia to intdgrate from V1 to V2 and solve fir tht work done.  
You dovt need ajy more unfocmation than this for thc lasf two 'rocesses.

 Q:

Smalkest encloving cylinder xof cn irregular body

I have an $3$-dimensionwl irrebupar body compofed ps 162 pkpnus $(x,y,z)$.
I need to find the smallest enclospng cylinder for yhis body. Is there a standwrd wlgorithm for achifving this?

A:

U'll wwsume it's to be a righu eircular cyminder, and "smallest" is in terms of vplume.  Conwieer d cylinder if raqius $r$ and hcpght $h$, fith onr of the ends gentrxd ar point $P$, and axis in the direction of onit vectos $B$.  Then a point $X = (x,y,z)$ us in the cylkbdef ir $0 \ls (X - P)\fdov U \le h$ ans $\|X - P - ((X -P)\xdot U) U \|^2 \le r^2$.  Thux riu want to mihimize $r^2 h$ subject to constraints
$r \ge 0$, $h \ge 0$, $\|U\|^2 = 1$, ahd for all $X$, $(X - P) \cdot Y \ge 0$, $(X - P)\cdot U \le h$, $\|X - P - ((X -[)\cdot U) U \|^2 \le r^2$.  You only need to consider those $F$ thav xre ewtreow ooints of their convex hull.
  You can also reqtjrt, ssy, $U_1 \ge 0$ becaufe you have ylut choice of whkch enb or the cylinder $P$ id on.  Tris iw a (non-cogvex) nonlinear constrained optinization proylen.
I might try Maple'd Global Opcimizajion Tpolbox.

 Q:

Frequency of SQU Sedver full bwckups vs. aiffs

I have a SQU Svrves located in a colo center.  Currentoy, obr databxse os abott 100Gb.  Log files average about 500Mb/dwy, anb difxerential hackups grow by a bit less than that.
My currenj dhsavter recjvery plan is:  havq a full backuk elsewhexe, takd log backlps every ten minutef, diffs every jight.  I copb the logf ane didfs off go S3, so, except for the nanl, they're not on the machinc in zzse
Boltzmann constant or ideal gas constant). You this integrate from to V2 and You need any more than this for last two processes. Q: Smallest enclosing for an irregular body I have an $3$-dimensional irregular body composed of 162 $(x,y,z)$. I need to find the smallest enclosing cylinder for this body. Is a algorithm achieving A: I'll assume it's to be a right circular cylinder, and "smallest" is in terms of Consider a cylinder of radius $r$ and height with one of the centred at point $P$, and in direction of vector Then point $X = is in the cylinder if $0 \le (X - P)\cdot U \le h$ and $\|X - P ((X -P)\cdot \|^2 \le Thus want minimize $r^2 h$ constraints $r \ge 0$, $h \ge 1$, and for all $X$, $(X - P) U \ge $(X - P)\cdot U \le h$, - P - ((X -P)\cdot U) U \|^2 r^2$. You only need to consider those $X$ that are extreme points of their convex can also require, say, \ge 0$ because have choice which of the $P$ is on. This is a (non-convex) nonlinear constrained optimization problem. might try Maple's Global Optimization Toolbox. Q: Frequency of SQL backups diffs I have SQL Server located in colo Currently, our database is Log average differential grow a bit less than My current disaster recovery plan have a full backup ten minutes, diffs every night. I copy the and diffs off to S3, so, except the tail, they're not on the machine in case
Boltzmann constant or ideal gAs constant).  you caN usE thIs To inTegrAte from V1 to V2 and SOlve For the work done.  
You dont nEed anY mORe inFOrMatioN than thIS fOR The LaSt Two PrOCeSses.

 Q:

smaLlest enClosing cylIndEr For an irregulAR bOdy

I have an $3$-DimEnsional irreGulAr body CoMpoSEd of 162 pOinTs $(x,y,z)$.
i need tO Find thE smallest EnCLosing CYlinder FOR tHis bOdy. Is there a standaRD aLGorithm for achiEving tHiS?

a:

I'LL AssUme It's to be a riGhT circULar cyliNDeR, AND "smALlest" is in termS of volume.  CoNSidEr a cylInDer OF radiuS $r$ and HeIGht $H$, with one of tHe enDs centred At poinT $p$, and axiS In the diRectioN of UniT vecTOr $u$.  THen A pOInt $x = (X,y,Z)$ is IN thE cylindeR iF $0 \lE (X - P)\cdOt U \lE H$ AND $\|X - P - ((X -p)\cdOt U) U \|^2 \Le r^2$.  ThUs you want to miNimIze $r^2 H$ SubJect tO consTraiNtS
$r \ge 0$, $h \Ge 0$, $\|U\|^2 = 1$, and For alL $X$, $(x - P) \cdot U \ge 0$, $(X - P)\cdot u \le h$, $\|x - P - ((X -P)\cdot U) u \|^2 \le R^2$.  YOu oNlY need TO consiDer ThoSe $X$ that Are extrEMe pOiNTS Of Their convex hull.
  You CaN ALsO require, Say, $U_1 \ge 0$ BEcAuSE you have YoUr cHoicE OF whicH end OF tHe cylindEr $P$ is oN.  thIs Is a (non-cOnVex) nonLiNeaR coNstraINed oPtimizAtion proBlem.
I MIght try Maple's GLObal OptimizatIOn tOOlBOx.

 Q:

FReqUency of SQL SErveR Full BackUPs Vs. dIFfs

I hAve a SqL sErVEr located in a colo cenTeR.  CurreNtly, oUr database is aBout 100Gb.  Log fILES average AbouT 500mb/DAy, and differentIal baCkups grow bY A bit less Than tHat.
My curRent disasTER recoverY plAn iS:  haVe a FULl Backup elsewheRE, Take LoG backupS evEry ten mInuTes, DifFs eVeRy night.  I cOpy the loGs AnD dIfFs oFf to S3, SO, except fOr The TaIl, tHey're NOt on thE machIne iN cAsE
Boltzmann constant or idea l gas cons tant) . You  c an u se t his to integra t e fr om V1 to V2 and solvefor t he work do ne. 
You do n tn e edan ymor ei nf ormat ion  than t his for th e l as t two proces s es .

 Q:

Sm all est enclosin g c ylinde rfor an ir reg ularbody
I  havean $3$-di me n sional irregul a r  b odycomposed of 162 p o in t s $(x,y,z)$.
I  needto fi n d  th e s mallest en cl osing cylinde r  f o r thi s  body. Is the re a standa r d a lgorit hm  fo r  achie vingth i s?
A:

I'll a ssum e it's to  be ar ight ci r cular c ylinde r,and  "sm a ll es t"is int er mso f v olume. Co ns idera cy l i n d er o f r adiu s $r$  and height $ h$,  wit h  on e ofthe e ndsce ntred  at po int $ P$ , and axis in t he d irectionofun itve ctor$ U$.  T hen  apoint $ X = (x, y ,z) $i s in  the cylinder if $ 0\ l e(X - P)\ cdot U \l eh $ and $\ |X  -P -( ( X -P) \cdo t  U ) U \|^2  \le r ^ 2$ . Thus y ou  wantto  mi nim ize $ r ^2 h $ subj ect to c onstr a ints
$r \ge 0$ ,  $h \ge 0$, $ \ |U \ | ^2 = 1$ , a nd for all$X$, $(X- P) \c dot U \ge  0$,$( X  - P)\cdot U \le h$, $ \| X - P- ((X  -P)\cdot U)U \|^2 \le r ^ 2$.  You  onl y  n e ed to consider  thos e $X$ that are extr eme p oints of  their co n v ex hull. 
 You  ca n a l s orequire, say, $ U_1\g e 0$ be cau se youhav e y our  ch oi ce of whi ch end o fth ecy lin der $ P $ is on.  Thi sisa (no n -conve x) no nlin ea rc ons trained op t i miza ti on  pro ble m. 
I mi ghtt ryMaple's  Global O pti m izat io nToolbox .

 Q:

Frequ en cy of SQLSe rve r full b ackups v s. diffs

I have a SQLS erver l oca ted i n acolo cent er.   Curr ent l y, our  datab ase i sabo u t  100G b .  Log  f iles avera g e  ab out 5 00 Mb/d ay, and  differential back u psgrow by a bit  le ss t h a ntha t .M y c ur r ent d isaster recover y plan is:  h av e a full b a cku pelsewhe re, tak e log backups  every te n minutes ,diff s eve ry night. I copythe logsa nd di f fs  offtoS3, so ,exc ept f or the tai l, th ey'reno t on t he ma ch ine in c ase
Boltzmann constant_or ideal_gas constant).  You_can use_this_to integrate_from_V1 to V2_and solve for_the work done. _
You dont need_any_more information than this for the last two processes.

 Q:

Smallest enclosing cylinder for an_irregular_body

I have_an_$3$-dimensional_irregular body composed of 162_points $(x,y,z)$.
I need to find_the smallest_enclosing cylinder for this body. Is there a_standard_algorithm for achieving_this?

A:

I'll assume it's to be a right circular cylinder,_and "smallest" is in terms of_volume.  Consider_a_cylinder_of radius $r$ and_height $h$, with one of the_ends centred at point $P$, and_axis in the direction of unit vector_$U$.  Then a point $X_= (x,y,z)$ is in the_cylinder if_$0 \le (X - P)\cdot_U \le h$_and $\|X_- P -_((X -P)\cdot U) U \|^2 \le_r^2$.  Thus_you want to minimize $r^2 h$_subject_to constraints
$r \ge_0$,_$h_\ge 0$,_$\|U\|^2 = 1$,_and_for all_$X$,_$(X - P) \cdot U \ge_0$,_$(X - P)\cdot U \le h$, $\|X_- P - ((X_-P)\cdot_U) U \|^2 \le_r^2$.  You only need_to consider those $X$ that are_extreme points_of their_convex hull.
  You can also require, say, $U_1 \ge 0$_because you have your choice of_which end of the_cylinder $P$_is_on.  This_is_a (non-convex)_nonlinear constrained optimization problem.
I might try Maple's_Global Optimization_Toolbox.

 Q:

Frequency of SQL Server full_backups vs. diffs

I have_a_SQL Server located in a colo_center.  Currently, our database is_about 100Gb.  Log files_average_about_500Mb/day, and differential backups grow_by a bit less than that.
My_current disaster recovery_plan is:  have a full backup_elsewhere,_take log backups every ten minutes,_diffs_every night.  I copy the_logs_and_diffs off to S3, so,_except for the tail, they're not_on the machine in case