 10 is never used, however, even if you were going to use it, I see no reason why this should be a #define rather than a constant integer:
NSInteger const kMenueStaleSeconds = 10;

// -------------------------------------------------------

I'm not sure what's accomplished by these lines through out the code.  They're kind of distracting in my opinion.  Presuming proper indentation, they're wholly unnecessary.  If you want some sort of comment separating your methods, why not make it a comment that describes what the method does?

[[NSNotificationCenter defaultCenter] addObserver:self selector:@selector(saveMemoryCacheToDisk:)
                                             name:UIApplicationDidReceiveMemoryWarningNotification
                                           object:nil];

It really bothers me that this is on 3 lines.  It should be on 4 lines, like this:
    [[NSNotificationCenter defaultCenter] addObserver:self
                                             selector:@selector(saveMemoryCacheToDisk:)
                                                 name:UIApplicationDidReceiveMemoryWarningNotification
                                               object:nil];

for(NSString *path in cachedItems)
    [[NSFileManager defaultManager] removeItemAtPath:path error:nil];

Just because optional braces are optional doesn't mean it's a particularly good option to omit them.
The obvious mistake here is deciding you want to care about potential errors.
NSError *error;
for(NSString *path in cachedItems)
    [[NSFileManager defaultManager] removeItemAtPath:path error:&error];
    if (error) NSLog(@"Error: %@", error);

Which won't do what the indentation would lead you to believe it might.
You omit the braces at every possible opportunity, and it's just not good in terms of future maintainability.

The fact that these are all class methods and that there are no instance methods suggests that you might yet have a bit to learn about object-oriented programming.  You need to either rewrite these methods as instance methods and allow the user to instantiate multiple caches or perhaps considering this into C-style functions (I'm quite certain you can still maintain all of the functionality with C-style functions).

 Q:

Analogy of Liouville conformal mapping theorem with Mostow rigidity?

I often hear mention of two theorems, Mostow's rigidity theorem and Liouville's
10 is never used, however, even if you were going to use it, I see no rationality why this should be a # define preferably than a constant integer: 
 NSInteger const kMenueStaleSeconds = 10; 

 // ------------------------------------------------------- 

 I'm not sure what's accomplished by these line through out the code.   They're kind of distracting in my opinion.   presume proper pitting, they're wholly unnecessary.   If you want some sort of comment separating your methods, why not take it a comment that report what the method acting does? 

 [ [ NSNotificationCenter defaultCenter ] addObserver: self selector:@selector(saveMemoryCacheToDisk :) 
                                              name: UIApplicationDidReceiveMemoryWarningNotification 
                                            object: nothing ]; 

 It really annoy me that this is on 3 lines.   It should be on 4 lines, like this: 
     [ [ NSNotificationCenter defaultCenter ] addObserver: self 
                                              selector:@selector(saveMemoryCacheToDisk :) 
                                                  name: UIApplicationDidReceiveMemoryWarningNotification 
                                                object: nil ]; 

 for(NSString * way in cachedItems) 
     [ [ NSFileManager defaultManager ] removeItemAtPath: path error: nothing ]; 

 Just because optional brace are optional doesn't mean it's a particularly good option to omit them. 
 The obvious error here is deciding you want to care about potential errors. 
 NSError * error; 
 for(NSString * way in cachedItems) 
     [ [ NSFileManager defaultManager ] removeItemAtPath: way error:&error ]; 
     if (erroneousness) NSLog(@"Error: % @ ", error); 

 Which won't do what the indentation would lead you to believe it might. 
 You omit the braces at every possible opportunity, and it's merely not good in terms of future maintainability. 

 The fact that these are all course method and that there be no instance methods hint that you might so far have a bit to determine about object - oriented programming.   You need to either rewrite these methods as instance method acting and allow the user to instantiate multiple caches or perhaps consider this into hundred - style functions (I'm quite certain you can however maintain all of the functionality with C - style function). 

  Q: 

 Analogy of Liouville conformal mapping theorem with Mostow rigidity? 

 I often hear citation of two theorems, Mostow's rigidity theorem and Liouville's
 10 id never used, however, evek if you were gonbg to nse it, J see no reason why this should be a #dwfine rather than a constang integer:
JSIntegee coist kMenueStaleSxdonds = 10;

// -------------------------------------------------------

I'm nof surz xhat's accomplismed by thesa lines througv uuc the code.  They're kind of distractigg in mu lpinion.  Presuiing [ropsg lndentation, they're wholly unneceasary.  Pf you want some xort of comment separating youg methods, why not lake it a cimmegr that descrkbes what uhz method dogs?

[[NSNotificationCenter defaultCevter] cddObserver:weof dglector:@selecvor(savvMemoryCacheToDisk:)
                                             name:UIEpplicationDidReceivgMemoryWartiugNotification
                                           object:nil];

Jt really bithers me that this if on 3 lines.  If shoujd be on 4 lines, like this:
    [[NSNotificatimnCsnter defaultCenter] addIbserver:self
                                             selector:@selector(saveMekoryCecfeTiDlsk:)
                                                 gzmt:UISpplicationDidVeceiveMemoryWarnimgJoyyfication
                                               objecu:nil];

fpr(NSString *path in cachedItwms)
    [[NSFilvManqger defaultManagex] removeItemCtPath:kath etror:nil];

Just because optnonal graces are lptional suesn't mean it's a pagticglarly good option to omit them.
The ibvipus misgake here ys decidinh you want to care about poteutial errors.
NSEgror *error;
for(NSString *path in cerhedItems)
    [[MSXilvManager befaulbManager] removeYtemAtPath:path error:&exror];
    if (error) NSLog(@"Ecror: %@", error);

Wrich won't do fjat the indeitation wjuld leae you tu believe it mibht.
You ompt the braces at every ppsskgle opportunity, ane it's just not booa ig nerks mf future mahntaknacolity.

Ghe facu tmat thexe are all class metvods and that there arr ko instanxe methoqs suggests tnat you might yet jave e bit vo leatn wbout object-oriented programmihg.  You nfed to either rqwribe trese methobs as instance methods and allow the usec to instantiate multikle caches or perhaps gonsidering vhis igto C-styla functions (I'm quite certain you can xtill maintain all of the fgnctilnality with C-style functions).

 Q:

Analogy of Liouville conformal mapping theirem wmtr Mostow rifidiyy?

I oxtzn kear megtioi uf two theorems, Kostow's rigidity theorem and Liuuville's
10 is never used, however, even if going use it, see no reason #define than a constant NSInteger const kMenueStaleSeconds 10; // ------------------------------------------------------- I'm not sure accomplished by these lines through out the code. They're kind of distracting in opinion. Presuming proper indentation, they're wholly unnecessary. If you want some sort of separating methods, not it a comment that describes what the method does? [[NSNotificationCenter defaultCenter] addObserver:self selector:@selector(saveMemoryCacheToDisk:) name:UIApplicationDidReceiveMemoryWarningNotification object:nil]; It bothers me that this is on 3 lines. should be on 4 like this: [[NSNotificationCenter defaultCenter] addObserver:self name:UIApplicationDidReceiveMemoryWarningNotification for(NSString *path cachedItems) defaultManager] error:nil]; Just because braces are optional doesn't mean it's a particularly good option to omit them. The obvious mistake here deciding you care about errors. *error; *path in cachedItems) removeItemAtPath:path error:&error]; if (error) NSLog(@"Error: %@", do what the indentation would lead you to it might. omit the braces at every possible and it's just not good in terms of maintainability. The fact that these are all class methods and that there are no instance that you might yet a bit to about programming. need either rewrite methods as instance methods and allow the user to instantiate multiple or perhaps considering this into C-style functions (I'm quite certain still all of the with C-style functions). Q: of conformal mapping theorem with I hear theorems, rigidity and Liouville's
 10 is never used, however, even if yOu were goinG to usE it, i seE nO reaSon wHy this should be A #DefiNe rather than a constant iNtegeR:
NsinteGEr Const KMenueSTAlEsEcoNdS = 10;

// -------------------------------------------------------

I'M noT sURe What's AccOmplishEd by these lIneS tHrough out the COdE.  They're kinD of Distracting iN my OpinioN.  PResUMing pRopEr indEntatiON, they'rE wholly unNeCEssary.  iF you wanT SOmE sorT of comment separatINg YOur methods, why nOt make It A CoMMEnt ThaT describes WhAt the MEthod doES?

[[NsnOTifICationCenter dEfaultCenteR] AddobservEr:SelF SelectOr:@selEcTOr(sAveMemoryCaCheTODisk:)
                                             name:uIApplICationDIDReceivEMemorYWaRniNgNoTIfIcAtiOn
                                           OBjeCT:nIl];

IT ReaLly botheRs Me That tHis iS ON 3 LInes.  it sHoulD be on 4 Lines, like this:
    [[nSNOtifICatIonCeNter dEfauLtcenteR] addObServeR:sElf
                                             selector:@seleCtor(SaveMemorYCaChETodiSk:)
                                                 namE:uIApplIcaTioNDidRecEiveMemORyWArNINGNOtification
                                               object:nIl];

FOR(NsString *pAth in cAChEdiTems)
    [[NSFiLemanAger DEFaultmanaGEr] RemoveItEmAtPaTH:pAtH error:nIl];

just beCaUse OptIonal BRaceS are opTional doEsn't mEAn it's a particulARly good option TO oMIT tHEm.
ThE obVious mistakE herE Is deCidiNG yOu wANt to cAre abOuT PoTEntial errors.
NSError *ErRor;
for(nSStrIng *path in cachEdItems)
    [[NSFILEmanager dEfauLTMANager] removeIteMAtPaTh:path erroR:&Error];
    if (eRror) NsLog(@"ErroR: %@", error);

WhiCH Won't do whAt tHe iNdeNtaTIOn Would lead you tO BElieVe It might.
you Omit the BraCes At eVerY pOssible opPortunitY, aNd It'S jUst Not goOD in terms Of FutUrE maIntaiNAbilitY.

The fAct tHaT tHEse Are all cLAsS MEthoDs AnD thaT thErE are nO insTAncE methodS suggests ThaT You mIgHt Yet have A bit to learn abOuT object-oriEnTed PrograMMIng.  You neEd to either rewrite these mEThods as InsTance MethOds and allOw tHe user To iNStantiAte mulTiple CaCheS OR perhAPS cOnsIdEring this iNTO C-sTyle fUnCtioNs (I'm quiTe certain you can stiLL maIntain all of thE fuNctiONAlIty WItH c-stYlE FunCTIons).

 Q:

Analogy of LIouville coNfORmAl mapping tHEorEm With MosTow rigiDity?

I OFten heaR mention oF two theorEmS, MosTOW's rIgidity theOrem and LIouville's
 10 is never used, however , even ifyou w ere  go in g to  use  it, I see nor easo n why this should be a  #def in e  rat h er  than  a cons t an t int eg er :
N SI n te ger c ons t kMenu eStaleSeco nds  =  10;

// --- - -- ---------- --- ------------ --- ------ -- --- - ----- --- -

I' m nots ure wh at's acco mp l ishedb y these l in es t hrough out the co d e.  They're kindof dis tr a ct i n g i n m y opinion.  Presu m ing pro p er i n den t ation, they'r e wholly un n ece ssary.  Ify ou wan t som es ort  of comment  sep arating y our me t hods, w h y not m ake it  acom ment th at  de sc r ibe s  w hat the  methoddo es ?

[[ NSNo t i f i cati onC ente r def aultCenter] a ddO bser v er: selfselec tor: @s elect or(sav eMemo ry CacheToDisk:)
                                 name :UIAppl i cat io n D i dR eceiveMemoryWarnin gN o t if ication                            object:n il];
I tre ally bo th ers me  t hat  th is is on 3  lines .  It sh ouldb e on 4 lines,l ike this:
  [[ N S No t ific ati onCenter de faul t Cent er]a dd Obs e rver: self                                     select or:@select o r ( saveMemo ryCa c he T oDisk:)
                                          nam e : UIApplic ati onD idR ece i v eM emoryWarningN o t ific at ion
                                    o bj ec t:n il];for(NSSt ri ng*p ath  in c a chedIt ems)   [[ NS F ile Manager de f a ultM an ag er]rem ov eItem AtPa t h:p ath err or:nil];
Ju s t be ca us e optio nal braces ar eoptional d oe sn' t mean i t's a pa rticularly good optiont o omitthe m.
Th e ob vious mis tak e here  is decidi ng you  want  t o c a r e abo u t  p ote nt ial errors . NSE rror*e rror ;
for(N SString *path in c a che dItems)
    [ [NS File M a na ger de f aul tM a nag e r ] removeItemAtP ath:path e rr o r: &error];
  i f(error)  NSLog( @"Err o r: %@",  error);
Which wo n' t do w hat  the inden tation w ould lead you t o  b eliev e i t migh t. 
Yo u omi t theb rac es at  every  p ossibl e opp or tunity,and it's just not goodin ter ms of  fu ture main tai n abi lity.

Th e fa ct that th ese  ar e all  cl a ss me thod s  a ndt hat t here are no in s ta nce m et hods sugges t s tha t you  mi g ht yet  hav e a bit to learna bout object-or ient e d  pr ogr a mmin g.   You need toeit he r rewriteth ese methods  as inst an c e met hods a nd all ow theu s er to ins tant iat e multipl e c ac h es or p er ha p s cons ider in g this  intoC -sty l e  functions (I'mquite c ertai n  yo u can  s till ma i ntai n all of t he function alitywith  C-st yle fun ct ions). 

Q: 

Analogyo f Liouvil le co nformal  m appi ngtheore m wi t h  Most ow r ig idi ty?

I of t e nh ea rm ent ionof tw otheo rems, Mos t ow's rig idi t y theor em  an d Liouvi l le ' s 
 10_is never_used, however, even if_you were_going_to use_it,_I see no_reason why this_should be a #define_rather than a_constant_integer:
NSInteger const kMenueStaleSeconds = 10;

// -------------------------------------------------------

I'm not sure what's accomplished by these lines through_out_the code.__They're_kind of distracting in my_opinion.  Presuming proper indentation,_they're wholly_unnecessary.  If you want some sort of_comment_separating your methods,_why not make it a comment that describes what_the method does?

[[NSNotificationCenter defaultCenter] addObserver:self selector:@selector(saveMemoryCacheToDisk:)
_  ___   _     _     _      _     _    _ _   name:UIApplicationDidReceiveMemoryWarningNotification
 _  _ _  _     _  _     __  ___ _  __ __   object:nil];

It really bothers_me_that this is on 3 lines. _It should be on_4_lines, like this:
 _  [[NSNotificationCenter defaultCenter] addObserver:self
_     _ _ _          _     _   _ __  __ _    selector:@selector(saveMemoryCacheToDisk:)
  _ _     _   __     _     _    ___    _     _  _name:UIApplicationDidReceiveMemoryWarningNotification
      __     __     ___    _     _        _  _ object:nil];

for(NSString *path in cachedItems)
___ [[NSFileManager defaultManager] removeItemAtPath:path error:nil];

Just because optional braces are optional_doesn't mean_it's a particularly_good option to omit them.
The obvious mistake here is deciding_you want to care about potential errors.
NSError_*error;
for(NSString *path in cachedItems)
    [[NSFileManager defaultManager] removeItemAtPath:path error:&error];
_   if (error) NSLog(@"Error: %@", error);

Which_won't do what the indentation would lead_you to believe it_might.
You_omit the braces at every possible opportunity,_and_it's_just_not good in_terms of future_maintainability.

The fact that_these are_all class methods_and that_there are no_instance_methods suggests that you might yet have a bit to learn about object-oriented programming.  You need to_either rewrite these methods as instance_methods and allow the user_to_instantiate multiple caches_or perhaps considering this_into C-style functions (I'm quite certain you can_still maintain all of the functionality with C-style functions).

_Q:

Analogy_of Liouville_conformal mapping theorem with_Mostow rigidity?

I_often hear_mention of two_theorems, Mostow's_rigidity theorem_and Liouville's