Homothetic functions yog qhov sib npaug ntawm homogeneous functions homogeneous functions Nyob rau hauv lej, homogeneous muaj nuj nqi yog ib tug nrog multiplicative scaling cwj pwm: yog tag nrho nws cov lus sib cav yog multiplied los ntawm ib yam, ces nws tus nqi yog multiplied by qee lub zog ntawm qhov xwm txheej no thiab txhua tus lej tiag. hu ua degree ntawm homogeneity. https://en.wikipedia.org › wiki › Homogeneous_function
homogeneous muaj nuj nqi - Wikipedia
. Homothetic muaj nuj nqi. … A function f: C → R yog homothetic yog rau txhua x, y ∈ C thiab t > 0, f(x) ≥ f(y) yog thiab tsuas yog f(tx) ≥ f(ty). Ib qho txiaj ntsig ntawm kev txhais ntawm homotheticity yog f yog sib npaug rau g txhais los ntawm g(x)=f(tx).
Puas yog homothetic?
Ib txoj haujlwm yog homothetic yog tias nws yog kev hloov pauv monotonic ntawm homogenous muaj nuj nqi(nco ntsoov tias qhov haujlwm thib ob tsis tas yuav ua homogenous nws tus kheej). This is homogenous, since f(tx, ty)=(tx)a(ty)b=ta+bxayb=ta+bf(x,y).
Koj qhia li cas yog tias nyiam yog homothetic?
Tam sim no peb hais tias kev nyiam kev sib raug zoo yog homothetic yog rau ob pob x thiab y xws li x ∼ y, ces αx ∼ αy rau ib qho α > 0 cov lus nug, uas tseem nyuaj dua. nyiam kev sib raug zoo º yog homothetic yog thiab tsuas yog tias nws tuaj yeem sawv cev los ntawm cov khoom siv hluav taws xob uas yog homogeneous ntawm qib ib.
Koj txhais li cas los ntawm homothetic function?
Nyob rau hauv lej, homothetic muaj nuj nqi yog a monotonic transformation ntawm ib tug muaj nuj nqi uas yog homogeneous; Txawm li cas los xij, txij li kev siv hluav taws xob ua haujlwm tsuas yog txhais tau los ntawm kev hloov pauv monotonic zuj zus, muaj qhov sib txawv me me ntawm ob lub tswv yim hauv cov neeg siv khoom txoj kev xav.
Thaum cov khoom muaj nuj nqi yog homothetic?
A homogeneous ntau lawm muaj nuj nqi kuj yog homothetic-hloov, nws yog ib qho tshwj xeeb ntawm homothetic ntau lawm functions. Nyob rau hauv daim duab 8.26, ntau lawm muaj nuj nqi yog homogeneous yog, ntxiv rau, peb muaj f(tL, tK)=t Q qhov twg t yog tus lej tiag tiag, thiab n yog qib ntawm homogeneity.
