an ugly mind

plz im writing an article about this and i want to know the chances of an MSc holders to become members of faculty staffs in respected colleges and universities and if there are pronounced professors who doesnt hold PhD

for the formula

1/ {1+j Q [(f/v) - (v/f)]}

is approximated as follows( for Q high compared with unity)

a) 1/{1+ j 2 Q ( f - v ) / v } for f>0

b) 1/{1+ j 2 Q ( f + v ) v } for f<0

notes:

1) this equation is from

Haykin, Simon. "Communication system", 3rd Ed. John Wiley & Sons, INC. 1994. page292, ch 4, ex 19.

2) j stands for sqrt(-1)

3) in the book v is written as f sub c

please details of the procedure

the most popular ways

I nead a preciseadress please

I am an electrical engineer with M. Sc. I studied calculas, engineering analysis numerical methods, probability and statistics, operation research and many math topics at engineering college. then i joined math department for three years. the new subjects where finite math ,foundations, linear algebra, abstract algebra, real analysis.

I was brilliant in all those subjects

I couldint continue my formalstudy. the remaining subject where topology, differential eqn theory, functional analysis and complex analysis.

Now I am trying to study the remaining subjects my selfwithout a professor. I have difficulity in constructing proofs or solving exercises. In fact i never liked proofs. should i continue my effort or stop to do somthing else.

this mean that the neibourhood of zero is zero, doesnt it ruin the basis of real analysis. is still there any meaning of infinismally small. what is about epsilon scattering every where in proofs. shouldnot it have any value less than 0.00...1

a) Let I be the set of decimals of the form 0.d1d2......( numbers are subscripts) construct a one to one function from I to I x I ( I cross I).

b) find either an onto function from I to IxI or a one to one function for IxI to I.

c) do I and IxI have the same cardinality

help please,

source:

excercise 2.1.3 , pp34, intr to real analysis, Micheal Schramm

Why (in real analysis texts), it is assumed to be a obvious that 0.5 is equal to 0.4999.... . i find them different. help please to this paradox.

I never sean any western society. My experience is from books literature and movies, The western society and some ex commuist countries were someday respecting virginity and put the faithfulness to spouse in a holly atitude. even the sea clothes were (in 20ths)covering body more than now if they still cover any thing. The movies and media show husbands and wifes who behave normally toward cheating. " she:sorry dear i felt lonely and it was a party and we drunk much i will never do it again. he: promise?". even many cases where people marry with 4 children. when did this starts and why. is it good or bad and how. is it a benifiet or a price paid for the modern life style

I never visited usa but from the movies and even educational programs like Dr phil or reality tv shows I concluded this. Is it true. and to any extent. I mean can sombody live in Usa without using them or hearing them. i mean words like f.u. son of -----, pasta---, kick my ------, fu--ing mother and more. does these words still have an insulting and impolite nature or they are became somthing else because of widespread usage. I saw also that it is not good to say them in front of women and children. Is there any rejection or refusal to use them in public.

all the acounts loging in frm my computer suffer from the same problem. besides it is not usefull to set invisible to the source accounts. the message starts with an icon (flower).and contains random letters and ends with a URL link. It starts when I was logging in an one of the acounts asked for my contact list but a declined the order. I send offline messages to that acount and another one. the next time I find many offline msgs from 2 account that I send them offline messages the last session. what is the problem and what to do please help.