DM-3475 Synthesized
UHF Data Module
Technical Manual
Part Number: 242-3475-XXX
DM-3475 Synthesized UHF Data Module
Technical Manual
001-3475-201 January 2004
2004 by Dataradio COR Ltd.
About Dataradio
Dataradio is the leading designer and manufacturer of
PRACTICE MIDTERM 1 - UIUC MATH 453
NICOLAS ROBLES
1. Problems that can be done up to Wed 9
Exercise 1.1. State and prove Euclids theorem on divisibility. State, but not prove, the extension
to the general case.
Exercise 1.2. State and prove the Fundamenta
HOMEWORK SHEET 3 SOLUTIONS - UIUC MATH 453
NICOLAS ROBLES
Exercise 0.1. Let a and b be positive integers.
(1) The cases a = 1 or b = 1 are straightforward. If a > 1 and b > 1, the desired result follows
from Proposition (1.17) (the one immediately after t
HOMEWORK SHEET 7 - UIUC MATH 453
NICOLAS ROBLES
Exercise 0.1. Let n N. Define an arithmetic function by (1) = 1 and (n) = 2r where r is
the number of distinct prime numbers in the prime factorization of n.
a) Prove that is multiplicative but not completel
HOMEWORK SHEET 6 - UIUC MATH 453
NICOLAS ROBLES
Exercise 0.1. Determine (with a proof or a counterexample) whether each of the arithmetic
functions below is completely multiplicative, multiplicative or both. Here k is a fixed real number.
a) f (n) = kn,
b
HOMEWORK SHEET 4 - UIUC MATH 453
NICOLAS ROBLES
1. Warm up
Exercise 1.1. Let n be an odd integer not divisible by 3. Prove that n2 1 mod 24.
Exercise 1.2. Let a, b Z with a b mod m. If n is a positive integer, prove that an
bn mod m.
Exercise 1.3. Find a
HOMEWORK SHEET 8 - UIUC MATH 453
NICOLAS ROBLES
Exercise 0.1. Let n N. Prove that
n
(n!) X 1
.
n!
i
i=1
Exercise 0.2. Let n1 , n2 , , nm be distinct even perfect numbers. Prove that
(n1 n2 nm ) = 2m1 (n1 )(n2 ) (nm ).
Exercise 0.3. We begin with the follo
HOMEWORK SHEET 5 SOLUTIONS - UIUC MATH 453
NICOLAS ROBLES
Exercise 0.1. The system is solved as follows:
2 2 1 mod 3,
3 2 = 6 1 mod 5,
5 3 = 15 1 mod 7, so
so 2x 1 mod 3
so 3x 2 mod 5
5x 4 mod 7 iff
iff x 2 mod 3.
iff x 4 mod 5.
x 12 5 mod 7.
This means t
HOMEWORK SHEET 10 - UIUC MATH 453
NICOLAS ROBLES
Exercise 0.1. Find the order of 3 modulo 13.
Exercise 0.2. Solve the following.
a) Let m be a positive integer and let a and b be integers relatively prime to m with (expm a, expm b) =
1. Then prove that ex
ADDITIONAL NOTES 4 - UIUC MATH 453
NICOLAS ROBLES
The essence of the theorem of Fermat (and that of Euler, since it generalizes it) is as follows.
Recall that the Euler totient function (n) is the function that counts the number of numbers
1 k n that are
HOMEWORK SHEET 10 - UIUC MATH 453
NICOLAS ROBLES
Exercise 0.1. The answer is 3.
Exercise 0.2. As follows.
a) Let expm a = x, expm a = y and expm a = xy = z. Since (ab)xy = (ax )y (by )x 1 mod m,
we have z|xy, by the theorems of the course. Next,
1 (ab)z (
INTRO TO CULTURAL ANTHROPOLOGY - MEDICAL ANTHROPOLOGY
I. Medical Anthropology
- anthropologists have realized that beliefs in illness often have both a biological and social
basis and must understand both to most effectively treat patients
- have develope
APPENDIX B
RESEARCH PROJECT INSTRUCTIONS PLUS REFERENCING INFORMATION
General Project Instructions
The research project is worth 100 points and 13% of your final grade. It is due by 11:55 pm CDT on
Sunday July 31st but will be accepted late up to 11:55 pm
The Violence in Our Heads - NYTimes.com
September 19, 2013
The Violence in Our Heads
By T. M. LUHRMANN
STANFORD, Calif. THE specter of violence caused by mental illness keeps raising its head. The
Newtown, Conn., school killer may have suffered from the t
IEEE TRANSACTIONS ON EDUCATION, VOL. 46, NO. 3, AUGUST 2003
313
Understanding and Measuring Circular Polarization
Bee Yen Toh, Member, IEEE, Robert Cahill, and Vincent F. Fusco, Senior Member, IEEE
AbstractMany modern satellite and terrestrial point-to-po
Ansoft High Frequency Structure Simulator
Tutorial
The Dipole Antenna
April 2004
Introduction
In this tutorial, a dipole antenna will be constructed and analyzed using
the HFSS simulation software by Ansoft. The example will illustrate both the
simplicity
The information contained in this document is subject to change without notice.
Ansoft makes no warranty of any kind with regard to this material, including,
but not limited to, the implied warranties of merchantability and fitness for a
particular purpos
ADDITIONAL NOTES 1 - UIUC MATH 453
NICOLAS ROBLES
Here are some clarifications of the topics we discussed in class. Some of you were not entirely
familiar with the well-ordering principle which is related to the principle of induction.
The principle of in
HOMEWORK SHEET 4 SOLUTIONS - UIUC MATH 453
NICOLAS ROBLES
Exercise 0.1. The solutions are as follows.
a) Since a2 b2 mod p, we have p|a2 b2 = (a + b)(a b). By Euclids lemma we have that
p|a + b or p|a b from which the result follows.
b) Since a2 a mod p,
HOMEWORK SHEET 9 - UIUC MATH 453
NICOLAS ROBLES
Exercise 0.1. Find all incongruent solutions of each quadratic congruence below.
a) x2 23 mod 77. Hint: consider the congruences x2 23 mod 7 and x2 23 mod 11 and
then use the Chinese Remainder Theorem.
b) x2
Inclusion-Exclusion Principle: Proof by Mathematical Induction
For Dummies
Vita Smid
December 2, 2009
Definition (Discrete Interval). [n] := cfw_1, 2, 3, . . . , n
Theorem (Inclusion-Exclusion Principle). Let A1 , A2 , . . . , An be finite sets. Then
n
\
HOMEWORK SHEET 7 SOLUTIONS - UIUC MATH 453
NICOLAS ROBLES
Exercise 0.1. As follows.
a) Suppose that m and n are relatively prime positive integers. If m = 1 or n = 1 (or both),
then the proof of multiplicative is straightforward. So, let us assume that m
MIDTERM 1 - UIUC MATH 453
SEPTEMBER 16TH, 2015
Name:
This is a closed-book, closed-notes exam. No electronic aids are allowed.
Read each questions carefully. Proof questions should be written out with all the details.
You may use results proven in class
HOMEWORK SHEET 3 - UIUC MATH 453
NICOLAS ROBLES
1. Warm up
These questions are not to be turned in (review of the fundamental theorem of arithmetic). It
is a valuable practice for the final.
Exercise 1.1. Find the greatest common divisor and the least com
HOMEWORK SHEET 1 SOLUTIONS - UIUC MATH 453
NICOLAS ROBLES
Exercise 0.1. The condition is a = b. The sufficiency is straightforward. For the necessity, we
need to recall the definitions of divisibility. Since a|b and b|a, there exist integers c and d for w
ADDITIONAL NOTES 3 - MATH 453
NICOLAS ROBLES
Theorem 0.1 (Inclusion-Exclusion). For any finite sets S1 , S2 , , Sk , we have
[
X
k
k
X
card
Si =
(1)j+1
card(Sl1 Sl2 Slj ),
i=1
j=1
l1 <l2 <lj
where card denotes the cardinality of the set (i.e. the number
MIDTERM 3 - UIUC MATH 453
NOVEMBER 13TH, 2015
Name:
This is a closed-book, closed-notes exam. No electronic aids are allowed.
Read each question carefully. Proof questions should be written out with all the details.
You may use results proven in class,
HOMEWORK SHEET 2 - UIUC MATH 453
NICOLAS ROBLES
1. Warm up
The following are some warm up questions. Not to be turned in.
Exercise 1.1. Find the greatest common divisors below.
a) (21, 28)
b) (32, 56)
c) (58, 63)
d) (0, 113)
Exercise 1.2. Find four intege
MIDTERM 1 - UIUC MATH 453
SEPTEMBER 16TH, 2015
Name:
This is a closed-book, closed-notes exam. No electronic aids are allowed.
Read each questions carefully. Proof questions should be written out with all the details.
You may use results proven in class
HOMEWORK SHEET 9 - UIUC MATH 453
NICOLAS ROBLES
Exercise 0.1. By the early properties of congruences and inspection (no Legendre symbol or
anything), we have that:
a) solutions are x 10, 32, 45, 67 mod 77,
b) this congruence has no solutions.
Exercise 0.2