SOME USEFUL ENGINEERING BOOKS

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FUNDAMENTALS OF IMAGE PROCESSING

Modern digital technology has made it possible to manipulate multi-dimensional signals with systems that range from simple digital circuits to advanced parallel computers. The goal of this manipulation can be divided into three categories:

* Image Processing image in -> image out

* Image Analysis image in -> measurements out

* Image Understanding image in -> high-level description out

We will focus on the fundamental concepts of image processing. Space does not permit us to make more than a few introductory remarks about image analysis. Image understanding requires an approach that differs fundamentally from the theme of this book. Further, we will restrict ourselves to two-dimensional (2D) image processing although most of the concepts and techniques that are to be described can be extended easily to three or more dimensions. Readers interested in either greater detail than presented here or in other aspects of image processing are referred to

We begin with certain basic definitions. An image defined in the "real world" is considered to be a function of two real variables, for example, a(x,y) with a as the amplitude (e.g. brightness) of the image at the real coordinate position (x,y). An image may be considered to contain sub-images sometimes referred to as regions-of-interest, ROIs, or simply regions. This concept reflects the fact that images frequently contain collections of objects each of which can be the basis for a region. In a sophisticated image processing system it should be possible to apply specific image processing operations to selected regions. Thus one part of an image (region) might be processed to suppress motion blur while another part might be processed to improve color rendition.

The amplitudes of a given image will almost always be either real numbers or integer numbers. The latter is usually a result of a quantization process that converts a continuous range (say, between 0 and 100%) to a discrete number of levels. In certain image-forming processes, however, the signal may involve photon counting which implies that the amplitude would be inherently quantized. In other image forming procedures, such as magnetic resonance imaging, the direct physical measurement yields a complex number in the form of a real magnitude and a real phase. For the remainder of this book we will consider amplitudes as reals or integers unless otherwise indicated.

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who is Bhaskara I???

Bhaskara I was an Indian mathematician of the 7th century, who probably lived between c.600- c.680. He was most likely the first to use a circle for the zero in the Hindu-Arabic decimal system, and while commenting on Aryabhata's work, he evaluated an extraordinary rational approximation of the sine function. There is very little information about Bhaskara's life. He is said to be born near Saurashtra in Gujarat and died in Ashmaka. He was educated by his father in astronomy. He is considered to be a follower of Aryabhata I and one of the most renowned scholars of Aryabhata's astronomical school. Bhaskara I wrote two treatises, the Mahabhaskariya and the Laghubhaskariya. He also wrote commentaries on the work of Aryabhata I entitled Aryabhatiyabhasya. The Mahabhaskariya comprises of eight chapters dealing with mathematical astronomy. The book deals with topics such as: the longitudes of the planets; association of the planets with each other and also with the bright stars; the lunar crescent; solar and lunar eclipses; and rising and setting of the planets. Bhaskara I suggested a formula which was astonishingly accurate value of Sine. The formula is: sin x = 16x (p - x)/[5p2 - 4x (p - x)]

Bhaskara I wrote the Aryabhatiyabhasya in 629,, which is a commentary on the Aryabhatiya written by Aryabhata I. Bhaskara I commented only on the 33 verses of Aryabhatiya which is about mathematical astronomy and discusses the problems of the first degree of indeterminate equations and trigonometric formula. While discussing about Aryabhatiya he discussed about cyclic quadrilateral. He was the first mathematician to discuss about quadrilaterals whose four sides are not equal with none of the opposite sides parallel.

For many centuries, the approximate value of p was considered v10. But Bhaskara I did not accept this value and believed that p had an irrational value which later proved to be true. Some of the contributions of Bhaskara I to mathematics are: numbers and symbolism, the categorization of mathematics, the names and solution of the first degree equations, quadratic equations, cubic equations and equations which have more than one unknown value, symbolic algebra, the algorithm method to solve linear indeterminate equations which was later suggested by Euclid, and formulated certain tables for solving equations that occurred in astronomy.

Biography
We know little about Bhāskara's life. Presumably he was born in Kerala. His astronomical education was given by his father. Bhaskara is considered the most important scholar of Aryabhata's astronomical school. He and Brahmagupta are the most renowned Indian mathematicians who made considerable contributions to the study of fractions.

Representation of numbers
Bhaskara's probably most important mathematical contribution concerns the representation of numbers in a positional system. The first positional representations were known to Indian astronomers about 500. However, the numbers were not written in figures, but in words or allegories, and were organized in verses. For instance, the number 1 was given as moon, since it exists only once; the number 2 was represented by wings, twins, or eyes, since they always occur in pairs; the number 5 was given by the (5) senses. Similar to our current decimal system, these words were aligned such that each number assigns the factor of the power of ten corresponding to its position, only in reverse order: the higher powers were right from the lower ones. For example,

1052 = wings senses void moon.
Why did the Indian scientists use words instead of the already known Brahmi numerals? The texts were written in Sanskrit, the "language of the gods", which played a similar role as Latin in Europe, the spoken languages were quite different dialects. Presumably, the Brahmi numerals which were used in every-day life were regarded as too vulgar for the gods (Ifrah 2000, p. 431).

About 510, Aryabhata used a different method ("Aryabhata cipher") assigning syllables to the numbers. His number system has the basis 100, and not 10 (Ifrah 2000, p. 449). In his commentary to Aryabhata's Aryabhatiya in 629, Bhaskara modified this system to a true positional system with the base 10, containing a zero. He used properly defined words for the numbers, began with the ones, then writes the tens, etc. For instance, he wrote the number 4,320,000 as

viyat ambara akasha sunya yama rama veda
sky atmosphere ether void primordial couple (Yama & Yami) Rama Veda
0 0 0 0 2 3 4

His system is truly positional, since the same words representing, e.g. the number 4 (like veda), can also be used to represent the values 40 or 400 (van der Waerden 1966, p. 90). Quite remarkably, he often explains a number given in this system, using the formula ankair api ("in figures this reads"), by repeating it written with the first nine Brahmi numerals, using a small circle for the zero (Ifrah 2000, p. 415). Contrary to his word number system, however, the figures are written in descending valuedness from left to right, exactly as we do it today. Therefore, at least since 629 the decimal system is definitely known to the Indian scientists. Presumably, Bhaskara did not invent it, but he was the first having no compunctions to use the Brahmi numerals in a scientific contribution in Sanskrit.

The first, however, to compute with the zero as a number and to know negative numbers, was Bhaskara's contemporary Brahmagupta.

[edit] Further contributions
Bhaskara wrote three astronomical contributions. In 629 he commented the Aryabhatiya, written in verses, about mathematical astronomy. The comments referred exactly to the 33 verses dealing with mathematics. There he considered variable equations and trigonometric formulae.

His work Mahabhaskariya divides into eight chapters about mathematical astronomy. In chapter 7, he gives a remarkable approximation formula for sinx, that is

which he assigns to Aryabhata. It reveals a relative error of less than 1.9% (the greatest deviation at x = 0). Moreover, relations between sine and cosine, as well as between the sine of an angle , or to the sine of an angle are given. Parts of Mahabhaskariya were later translated into Arabic.

Bhaskara already dealt with the assertion: If p is a prime number, then 1 + (p − 1)! is divisible by p. It was proved later by Al-Haitham, also mentioned by Fibonacci, and is now known as Wilson's theorem.

Moreover, Bhaskara stated theorems about the solutions of today so called Pell equations. For instance, he posed the problem: "Tell me, O mathematician, what is that square which multiplied by 8 becomes - together with unity - a square?" In modern notation, he asked for the solutions of the Pell equation 8x2 + 1 = y2. It has the simple solution x = 1, y = 3, or shortly (x,y) = (1,3), from which further solutions can be constructed, e.g., (x,y) = (6,17).

[edit] References
H.-W. Alten, A. Djafari Naini, M. Folkerts, H. Schlosser, K.-H. Schlote, H. Wußing: 4000 Jahre Algebra. Springer-Verlag Berlin Heidelberg 2003 [ISBN 3-540-43554-9], §3.2.1
S. Gottwald, H.-J. Ilgauds, K.-H. Schlote (Hrsg.): Lexikon bedeutender Mathematiker. Verlag Harri Thun, Frankfurt a. M. 1990 [ISBN 3-8171-1164-9]
G. Ifrah: The Universal History of Numbers. John Wiley & Sons, New York 2000 [ISBN 0-471-39340-1]
B. van der Waerden: Erwachende Wissenschaft. Ägyptische, babylonische und griechische Mathematik. Birkäuser-Verlag Basel Stuttgart 1966

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Choosing a Used Car That's Good on Gas

Choosing a Used Car That's Good on Gas
Buying a car is a major commitment, both for financial and environmental reasons. If you are like many people nowadays, you are searching for ways to save money on weekly purchases like groceries, transportation and gas. You may be searching for a used car that's good on gas, but you are not sure what kind of car to choose. Here are some tips to help you select a used car that's economical on fuel:
Look for enough car for your average daily needs.
When choosing a used car, it's important to keep in mind what you will be using the car for on a daily basis. Will you be transporting just yourself to and from work or will this be a family vehicle that requires more room for passengers? If you use your vehicle for your business or you need to be able to carry special equipment around such as for your job or a handicapped member of your family, what kind of vehicle can accommodate these needs? You wouldn't buy a two door sedan instead of a mid-size car just because it was better on gas, then attempt to cram your family of five inside would you? This gives you a good place to start when evaluating used cars for usefulness and economy. Choose a car that will give you maximum usage in an engine and body size that works for your average needs.
Consider the savings now or later.
Before you select a car for your family needs, you may want to consider how saving money on a purchase based on the age of the car versus the longer-term fuel and environmental savings that newer models may have. For example, if you were able to save $5,000 USD now on a used car that's five years old, but that didn't have the features that a one year old used car may have, such as a hybrid engine or a higher mileage rating, is it more important for you to have the immediate savings now or enjoy a greater savings over time? Because you will probably be driving your more economical used car for a few years, you may want to think about the savings over that time period instead of just buying it to save a little money now.
Read the reviews and get more information about the used car.
When you start looking at used cars, you may find that you are overwhelmed with all the features and benefits of the cars themselves. It may be difficult to know which one to choose. One great way to make your decision easier is by reading automotive reviews about the cars that you are considering. Evaluate the different models based on the quality of the materials used to manufacture the car, the user reviews and ratings and then the gas mileage ratings. Just because you can buy a used car with better gas mileage for a lower price, doesn't mean it's a better value. You can save yourself a considerable amount of money if you carefully consider any mechanical or user issues each car may have.

block hole

In general relativity, a black hole is a region of space in which the gravitational field is so powerful that nothing, including light, can escape its pull. The black hole has a one-way surface, called an event horizon, into which objects can fall, but out of which nothing can come. It is called "black" because it absorbs all the light that hits it, reflecting nothing, just like a perfect blackbody in thermodynamics. Quantum analysis of black holes shows them to possess a temperature and Hawking radiation.

Despite its invisible interior, a black hole can reveal its presence through interaction with other matter. A black hole can be inferred by tracking the movement of a group of stars that orbit a region in space which looks empty. Alternatively, one can see gas falling into a relatively small black hole, from a companion star. This gas spirals inward, heating up to very high temperature and emitting large amounts of radiation that can be detected from earthbound and earth-orbiting telescopes. Such observations have resulted in the scientific consensus that, barring a breakdown in our understanding of nature, black holes do exist in our universe.

In general relativity, a black hole is a region of space in which the gravitational field is so powerful that nothing, including light, can escape its pull. The black hole has a one-way surface, called an event horizon, into which objects can fall, but out of which nothing can come. It is called "black" because it absorbs all the light that hits it, reflecting nothing, just like a perfect blackbody in thermodynamics. Quantum analysis of black holes shows them to possess a temperature and Hawking radiation.

Despite its invisible interior, a black hole can reveal its presence through interaction with other matter. A black hole can be inferred by tracking the movement of a group of stars that orbit a region in space which looks empty. Alternatively, one can see gas falling into a relatively small black hole, from a companion star. This gas spirals inward, heating up to very high temperature and emitting large amounts of radiation that can be detected from earthbound and earth-orbiting telescopes. Such observations have resulted in the scientific consensus that, barring a breakdown in our understanding of nature, black holes do exist in our universe.

astrology

Astrology (from Greek ἄστρον, astron, "constellation, star"; and -λογία, -logia, "the study of") is a group of systems, traditions, and beliefs which hold that the relative positions of celestial bodies and related details can provide information about personality, human affairs, and other terrestrial matters. A practitioner of astrology is called an astrologer. Scientists consider astrology a pseudoscience or superstition.^[1][2][3][4]

Numerous traditions and applications employing astrological concepts have arisen since its earliest recorded beginnings in the 3rd millennium BC. Astrology has played an important role in the shaping of culture, early astronomy, the Vedas,^[5] the Bible,^[6] and various disciplines throughout history. In fact, astrology and astronomy were often indistinguishable before the modern era, with the desire for predictive and divinatory knowledge one of the primary motivating factors for astronomical observation. Astronomy began to diverge from astrology after a period of gradual separation from the Renaissance up until the 18th century. Eventually, astronomy distinguished itself as the scientific study of astronomical objects and phenomena without regard to the astrological understandings of these phenomena.

Astrologers believe that the movements and positions of celestial bodies either directly influence life on Earth or correspond to events experienced on a human scale.^[7] Modern astrologers define astrology as a symbolic language,^[8][9][10] an art form, or a form of divination.^[11][12] Despite differences in definitions, a common assumption of astrology is that celestial placements can aid in the interpretation of past and present events and in the prediction of the future.

shopping

For those who find making their gifts list for the holidays a very exciting activity, good for you. Those who find it less than an appealing bustle don't fret. Many share your sentiment. The problem with making a list is that it seems to become never ending especially when you decide on checking it twice. Okay, you're no good ol' Saint Nick but hey, this is only looking at it with a bird's eye view. What you don't know is that buying the gifts could actually cause a bigger headache than the preparing of the list.
Who wants to wallow in the stress brought by holiday gift-giving? Holidays need not always put you in a major state of panic. Here's how to breeze through the holiday season with these tips on buying gifts.
1. Say no to a rigid gift list.
This doesn't mean that when you arrive on a situation like when you get to see a "spunkier" Ipod when you originally thought of giving out a Walkman, you'll always give in. The thing is that you should be open to alternatives with your choice of gifts. You might as wel, jot down all the possible options on that gift on your list in case you're having a hard time looking for it.

2. Nifty over Hefty.
An expensive price tag does not necessarily mean a perfect gift. What is more appreciated is creativity and when someone puts in genuine effort. Your budget does not have to suffer so much during the holidays. Doing your homework will get you a long, long way.

3. Doing some favor is a labor of love.
Instead of material presents, an act of kindness can very well serve as a very valuable holiday gift. One may run errands or do things like babysit for a busy aunt, cook dinner for a couple, or do a car wash. Of course, just don't forget to do this for free. One more thing, you can also do this goodie-two-shoes stuff not only for your family and friends but also for those less-fortunate.

4. Techie not Newbie.
For those who are still thinking that the Internet is only a mirage of the future, please wake up. You're so late! Online shopping is one of the many conveniences the Internet offers. Just click the mouse and voila! Before you are a wide array of brands and pricelists for your choice of gifts. Amazon.com, EBay, and Overstock.com are just a few of the best web sites that can help you in this endeavor. Just remember to provide ample time for delivery.

5. Comfort Zone.
During the commotion from shopping for holiday gifts, it's wise to wear your most comfortable outfits. This will make it easier for you to rummage through shelves of stuffs and will make scurrying not much of a hassle.
6. Early Bird Gets the Most Appreciation
Yes, there's still no better way of dealing with this gift-buying problem but to do it ahead of time. Creating your list about two months before the "season to be jolly" will help a lot in downsizing the hassles of this activity. Some can even go the length of preparing for it at least three months before the holidays.
Some people never have to worry about buying for gifts. Can you imagine having a closet of stuff always ready to be given out for various occasions? Yes, these cases exist. But you don't have to really succumb to such almost-paranoid acts. Following the simple but noble tips above will do. About the Author
David Arnold Livingston does all his gift shopping online without stress and recommends the gift directory:
http://www.rggift.com/