Register to reply

Question on meaning of some symbols

by yungman
Tags: meaning, symbols
Share this thread:
yungman
#1
Sep26-10, 12:32 PM
P: 3,898
I don't know the meaning of these:


1) [tex]sup_{B_\delta}|f(x,y)| [/tex]

Where [itex]B_\delta [/itex] is the ball of radius [itex]\delta[/itex].

2) [tex]\int \int _{R^2 \B _{\delta} } f(xy)dxdy[/tex]

I don't know what is [itex]R^2 [/itex]\B[itex] _{\delta} [/itex]

Please read my latex because the symbol really don't show correctly.
Phys.Org News Partner Science news on Phys.org
New type of solar concentrator desn't block the view
Researchers demonstrate ultra low-field nuclear magnetic resonance using Earth's magnetic field
Asian inventions dominate energy storage systems
Landau
#2
Sep26-10, 03:06 PM
Sci Advisor
P: 905
1) The supremum of {|f(x,y)|} where (x,y) ranges over the ball centered at 0 of radius delta: |(x,y)|=sqrt(x^2+y^2)<delta.

2) the plane R^2 without the ball centered at 0 of radius delta, i.e. \ (in Latex: "\backslash") means 'complement' or 'set difference'. So it consists of pairs (x,y) of real numbers such that |(x,y)|=sqrt(x^2+y^2)>=delta.
yungman
#3
Sep27-10, 12:20 AM
P: 3,898
Quote Quote by Landau View Post
1) The supremum of {|f(x,y)|} where (x,y) ranges over the ball centered at 0 of radius delta: |(x,y)|=sqrt(x^2+y^2)<delta.

2) the plane R^2 without the ball centered at 0 of radius delta, i.e. \ (in Latex: "\backslash") means 'complement' or 'set difference'. So it consists of pairs (x,y) of real numbers such that |(x,y)|=sqrt(x^2+y^2)>=delta.
Thanks for you reply, so for

1) Is the upper bound of |f(x,y)| in the ball.

2) Is the whole 2D plane minus the circle center at 0 with radius [itex]\delta[/itex]

Landau
#4
Sep27-10, 06:43 AM
Sci Advisor
P: 905
Question on meaning of some symbols

Quote Quote by yungman View Post
1) Is the upper bound of |f(x,y)| in the ball.
The least upper bound, a.k.a. the supremum ;)
2) Is the whole 2D plane minus the circle center at 0 with radius [itex]\delta[/itex]
Yes.
HallsofIvy
#5
Sep27-10, 08:09 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,491
Quote Quote by yungman View Post
Thanks for you reply, so for

1) Is the upper bound of |f(x,y)| in the ball.
No. There is no such thing as "the" upper bound of a set of numbers. If a set has an upper bound, then it has an infinite number of upper bounds. This is the least upper bound- the smallest number in the set of all upper bounds.

2) Is the whole 2D plane minus the circle center at 0 with radius [itex]\delta[/itex]


Register to reply

Related Discussions
E2 - p2c2 = m2c4 - Meaning of symbols Special & General Relativity 31
Question about christoffel symbols Advanced Physics Homework 2
Question about the contracted Christoffel Symbols General Physics 7
Symbols on Div/Curl Question Calculus & Beyond Homework 3
Need help with physics symbols in question Introductory Physics Homework 5