1. What types of programs are usually used to generate Vector Graphics? You can draw it or you can use Adobe Illustrator. 2. What are Vector Graphics composed of? Pixels
3. Does scaling a Vector drawing harm it? No. It will keep the quality the same. 4. Do Vector drawings support photographic images well? Yes. 5. _____ format is the only Vector Graphics are normally saved as. EPS. 6. What type of design is Vector Graphics ideal for? Logo Designs. 7. How are Raster Graphic Images created? Digital image capture devices. 8. What are Raster Graphics made of? Grid or a bitmap.

9. Are Raster Graphic affected by scaling? Yes. The quality becomes worse and the pixels are larger, creating a blurry image. 10. What are pixels? Squares containing image parts that are on a X and Y axis on a screen. 11. Describe the difference between the enlargements of the Raster Graphic and the Vector Graphic? Vector graphics are not affected by scaling as the Raster graphics are.

* http://www.thelogofactory.com/library/articles/format.html 12. What file extensions are usually associated with Vector Graphics? PMS. 13. Explain how Vector Graphics are like rubber bands and a peg board. There are points that you can connect to each different dot. And there are lines on each side of a middle line for the outer edge of what word or image you’re trying to create. 14. Every Vector shape can be filled with a different __________.

* http://www.fieggen.com/ian/g_formats.htm
15. What is the best example of a bitmap graphic?
16. (Scroll way down – to “Common Graphic File Formats”) What are the 2 important things to remember about GIF? 17. What are the typical uses for GIF?
18. What was JPG...

...Vector graphics is the use of geometrical primitives such as points, lines, curves, and shapes or polygon(s), which are all based on mathematical expressions, to represent images in computer graphics. "Vector", in this context, implies more than a straight line.
Vector graphics are based on images made up of vectors (also called paths, or strokes) which lead through locations called control points. Each of these points has a definite position on the x and y axes of the work plan. Each point, as well, is a variety of database, including the location of the point in the work space and the direction of the vector (which is what defines the direction of the track). Each track can be assigned a color, a shape, a thickness and also a fill. This does not affect the size of the files in a substantial way because all information resides in the structure; it describes how to draw the vector.
____________________
Home > vector graphics
vector graphics
Same as object-oriented graphics, refers to software and hardware that use geometrical formulas to represent images. The other method for representing graphical images is through bit maps, in which the image is composed of a pattern of dots. This is sometimes called raster graphics. Programs that enable you to create and manipulate vector graphics are called draw programs, whereas...

...Computer as a tool
Nicholas O. Williams
Raster Images vs. Vector Images
Assignment: Discuss the differences, advantages and disadvantages.
There are two major types of images used by graphic design programs, they are called
Vector and Raster images. This paper will seek to highlight the many differences, advantages
and disadvantages respectively.
Raster images are complex renderings made up of
thousands of little dots or pixels. The word raster has its
origin in Latin which means ‘rake’ and has come to refer to
a rectangular pixilated grid. Photograph editors like Adobe
Photoshop, Corel Photo-Paint, Corel Paint Shop Pro and
The GIMP are great to manipulate each pixel. Many will
argue that this type of graphic deals more practically for
photo-realistic images. Raster graphics depend highly on
resolution when resized noticeable amounts of quality will
be removed from the image.
One solution to this is to ensure the image is created at high resolution. An image at a
minimum of 300dpi will resize quite well and keep fairly good clarity however this trait allows it
to contrast with the capabilities of Vector graphics. A vector image is one that is constructed by
paths, each containing a mathematical formula which instructs the path to assume a certain form
and what colours to emit. Vector graphics are mainly used...

...Calculus in 3D Geometry, Vectors, and Multivariate Calculus Zbigniew H. Nitecki
Tufts University
August 19, 2012
ii
This work is subject to copyright. It may be copied for non-commercial purposes.
Preface
The present volume is a sequel to my earlier book, Calculus Deconstructed: A Second Course in First-Year Calculus, published by the Mathematical Association in 2009. I have used versions of this pair of books for severel years in the Honors Calculus course at Tufts, a two-semester “boot camp” intended for mathematically inclined freshmen who have been exposed to calculus in high school. The ﬁrst semester of this course, using the earlier book, covers single-variable calculus, while the second semester, using the present text, covers multivariate calculus. However, the present book is designed to be able to stand alone as a text in multivariate calculus. The treatment here continues the basic stance of its predecessor, combining hands-on drill in techniques of calculation with rigorous mathematical arguments. However, there are some diﬀerences in emphasis. On one hand, the present text assumes a higher level of mathematical sophistication on the part of the reader: there is no explicit guidance in the rhetorical practices of mathematicians, and the theorem-proof format is followed a little more brusquely than before. On the other hand, the material being developed here is unfamiliar territory, for the intended audience, to a far greater degree...

...MIchael Driesen
Mrs. Rozell
Math 10H
17 December 2011
Vectors
Math is everywhere. No matter which way you look at it, it’s there. It is especially present in science. Most people don’t notice it, they have to look closer to find out what it is really made of. A component in math that is very prominent in science is the vector. What is a vector? A vector is a geometric object that has both a magnitude and a direction. A good example of a vector is wind. 30 MPH north. It has both magnitude,(in this case speed) and direction. Vectors have specific properties that make them very useful in real life applications. Through the use of these special objects, many advancements in the fields of math and science are available.
Representations
Vectors can sometimes be hidden behind basic objects. They are usually represented with an arrow on top of its starting point and terminal point, as shown here: The most common form of vector is the bound vector. All that means is that the starting point of the vector is the origin, or (0,0). The bound vector goes from the origin to it’s terminal point, which in this case can be (3,4). An easy way to write this
is A = (3,4), where A is the vector. On a graph, it looks like this:
That applies for two-dimensional vectors. Three dimensional...

...
1a. h=-4.9t^2+450
1b. h(t)=-4.9t^2+450
(h(2)-h(0))/(2-0)
((-4.9(〖2)〗^2+450)-(-4.9(0)^2+450))/2
=(430.4-450)/2
=-19.6
∴The average velocity for the first two seconds was 19.6 metres per second.
c. i)
i)
=
=-24.5
∴ The average velocity from is 24.5 metres/s.
ii)
= -14.7
iii)
= -12.25
∴ The average velocity from is 12.25 metres/s.
d) Instantaneous velocity at 1s:
=-9.8
∴ The instantaneous velocity at 1s is 9.8 metres/s.
2a)
=
=
=
=
=
b)
=
∴ The average rate of change from is -0.4g/s.
C)
∴The instantaneous rate at t = 2 seconds is -1.6g/s
3)
b)
=
=
=22
∴ from seconds the car moves at an average of 22m/s
c)
t=4
=
=16
∴ The instantaneous rate at 4s is 16m/s
4a) In order to determine the instantaneous rate of change of a function using the methods discussed in this lesson, we would use the formula where h will approach 0, and the closer it gets to 0 the more accurate our answer will be.
4b)
∴
=1
Therefore, = 1
5a)
Therefore the instantaneous rate at x=2 is 0.
5b)
Therefore at t=4 the instantaneous rate is 0 and the particle is at rest.
6a)
Rate of change is positive when:
Rate of change in negative when:
6b)
Rate of change is 0 when:
X=-1, x=1
6c)
Local Maximum: (-1,2)
Local Minimum: (1,-2)...

...
Vector Autoregressions
By: James H. Stock and Mark W. Watson
A Critique Paper presented to
The Faculty of the School of Economics
De La Salle University - Manila
In partial fulfillment
Of the course requirements in
Advanced Econometrics (ECOMET2)
3rd Term, AY 2014 - 2015
Submitted to:
Dr. Cesar C. Rufino
Submitted by:
Arjonillo Jr., Rabboni Francis K.
11148624
V25
March 4, 2015
James H. Stock and Mark W. Watson are both professors in Political Economy and Econometrics respectively. They assess the competence of VARs or Vector Autogregressions on the four macroeconomic tasks, which are data description, forecasting, structural inference and policy analysis. In the 1970’s, these four tasks were used with a variety of techniques and models but were somewhat inefficient and unreliable by the time the inflationary chaos of the 1970’s set in.
In 1980, a man named Christopher Sims presented his own macroeconomic framework: vector autoregressions or VARs. According to Sims, the VAR is an n equation, n variable linear model wherein each of the variables are explained by its own lagged values including past and current values of the remaining n-1 variables. This is obviously a level up at that time from a univariate autoregression in which from the term “uni” means having one equation and one variable linear model. According to Sims, this simple framework provides a systematic way to capture rich dynamics in...

...Mehran University College
Of Engineering & Technology,
Khairpur Mir’s
VECTOR GROUPS
ENGR. AHSANULLAH MEMON
LECTURER
DEPARTMENT OF ELECTRICAL ENGINEERING MUCET KHAIRPUR MIRS
ZIGZAG CONNECTION OF TRANSFORMER
The zigzag connection of tranformer is also called the
interconnected star connection.
This connection has some of the features of the Y and
the ∆ connections, combining the advantages of both.
The zigzag transformer contains six coils on three
cores.
Its applications are for the deviation of a neutral
connection from an ungrounded 3-phase system and
the grounding of that neutral to an earth reference
point and harmonics mitigation.
It can cancel triplet (3rd, 9th, 15th, 21st, etc.)
harmonic currents.
INTRODUCTION
Secondary voltage waveforms are in phase
with the primary waveforms.
When two transformers are connected in
parallel, their phase shifts must be identical; if
not, a short circuit will occur when the
transformers are energized.”
When two transformers are connected in
parallel, their phase shifts must be identical; if
not, a short circuit will occur when the
transformers are energized.”
Vector Group of Transformer
The three phase transformer windings can be connected several
ways. Based on the windings’ connection, the vector group of
the transformer is determined.
The transformer vector group is indicated on the Name Plate of
transformer by the manufacturer.
The...

...The outcome at any stage depends only on the outcome of the previous stage. (c.) The probabilities are constant over time. If x0 is a vector which represents the initial state of a system, then there is a matrix M such that the state of the system after one iteration is given by the vector M x0 . Thus we get a chain of state vectors: x0 , M x0 , M 2 x0 , . . . where the state of the system after n iterations is given by M n x0 . Such a chain is called a Markov chain and the matrix M is called a transition matrix. The state vectors can be of one of two types: an absolute vector or a probability vector. An absolute vector is a vector whose entries give the actual number of objects in a give state, as in the ﬁrst example. A probability vector is a vector where the entries give the percentage (or probability) of objects in a given state. We will take all of our state vectors to be probability vectors from now on. Note that the entries of a probability vector add up to 1.
1
Note b =
Theorem 3. Let M be the transition matrix of a Markov process such that M k has only positive entries for some k. Then there exists a unique probability vector xs such that M xs = xs . Moreover limk→∞ M k x0 = xs for any initial state probability vector x0 . The vector xs...