Messages

1

History of Mathematics / Biography: Arthur Cayley

« on: August 05, 2013, 01:40:45 PM »

ARTHUR CAYLEY (1821–1895) was an English mathematician who was instrumental in developing the theory of matrices. He was the first to use a single symbol such as A to represent a matrix, thereby introducing the idea that a matrix is a single entity rather than just a collection of numbers. Cayley practiced law until the age of 42, but his primary interest from adolescence was mathematics, and he published almost 200 articles on the subject in his spare time. In 1863 he accepted a professorship in mathematics at Cambridge, where he taught until his death. Cayley’s work on matrices was of purely theoretical interest in his day, but in the 20th century many of his results found application in physics, the social sciences, business, and other fields. One of the most common uses of matrices today is in computers, where matrices are employed for data storage, error correction, image manipulation, and many other purposes. These applications have made matrix algebra more useful than ever.

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Applied Maths / Mathematics and the Modern World 4. Unbreakable Codes

« on: August 03, 2013, 12:30:06 PM »

If you read spy novels, you know about secret codes and how the hero “breaks” the code. Today secret codes have a much more common use. Most of the information that is stored on computers is coded to prevent unauthorized use. For example, your banking records, medical records, and school records are coded. Many cellular and cordless phones code the signal carrying your voice so that no one can listen in. Fortunately, because of recent advances in mathematics, today’s codes are “unbreakable.” Modern codes are based on a simple principle: Factoring is much harder than multiplying. For example, try multiplying 78 and 93; now try factoring 9991. It takes a long time to factor 9991 because it is a product of two primes 97 and 103, so to factor it, we have to find one of these primes. Now imagine trying to factor a number N that is the product of two primes p and q, each about 200 digits long. Even the fastest computers would take many millions of years to factor such a number! But the same computer would take less than a second to multiply two such numbers. This fact was used by Ron Rivest, Adi Shamir, and Leonard Adleman in the 1970s to devise the RSA code. Their code uses an extremely large number to encode a message but requires us to know its factors to decode it. As you can see, such a code is practically unbreakable. The RSA code is an example of a “public key encryption” code. In such codes, anyone can code a message using a publicly known procedure based on N, but to decode the message, they must know p and q, the factors of N. When the RSA code was developed, it was thought that a carefully selected 80-digit number would provide an unbreakable code. But interestingly, recent advances in the study of factoring have made much larger numbers necessary.

Reference

J. Stewart, L. Redlin, S. Watson Algebra and Trigonometry 3rd ed. Brooks/Cole 2012

3

Applied Maths / Mathematics and the Modern World 3. Automotive Design

« on: August 03, 2013, 12:08:50 PM »

Automotive Design

Computer-aided design (CAD) has completely changed the way in which car companies design and manufacture cars. Before the 1980s automotive engineers would build a full-scale “nuts and bolts” model of a proposed new car; this was really the only way to tell whether the design was feasible. Today automotive engineers build a mathematical model, one that exists only in the memory of a computer. The model incorporates all the main design features of the car. Certain polynomial curves, called splines, are used in shaping the body of the car. The resulting “mathematical car” can be tested for structural stability, handling, aerodynamics, suspension response, and more. All this testing is done before a prototype is built. As you can imagine, CAD saves car manufacturers millions of dollars each year. More importantly, CAD gives automotive engineers far more flexibility in design; desired changes can be created and tested within seconds. With the help of computer graphics, designers can see how good the “mathematical car” looks before they build the real one. Moreover, the mathematical car can be viewed from any perspective; it can be moved, rotated, or seen from the inside. These manipulations of the car on the computer monitor translate mathematically into solving large systems of linear equations.

4

Applied Maths / Re: Importance of Complex Numbers

« on: August 03, 2013, 11:49:44 AM »

Complex numbers are important in various aspects. This numbers always have been remaining curious to the mathematicians.

In our college mathematics probably we all have learned about the imaginary number i. We were simply introduced i as a number.

Is it a number?

What kind of number is i ?

Where does the name imaginary come from?

Is it really an imaginary number? If yes then how did this number get involved into the real mathematics?

Can imaginary number do the same thing or different thing as real number do or more?

British mathematical physicist Roger Penrose calls i magic number. What is magical about i?

To explore this readers are requested to visit the following link

http://forum.daffodilvarsity.edu.bd/index.php?topic=7876.0

5

Applied Maths / Re: Mathematics and the Modern World 2. Computers

« on: May 25, 2013, 06:40:27 PM »

In reply to msu_math

Author replies that one should not consider mathematicians as our bosses. They are people with beautiful minds seeking the ultimate truth of the nature.

6

Applied Maths / Re: Some Well known differential Equation

« on: May 25, 2013, 06:37:19 PM »

Dear M. Parvin,

Your compilation is good. As you might have noticed that your post is quite difficult to read for computer font problem. It will be better to re-post it.

Thanks.

7

Applied Maths / Mathematics and the Modern World 2. Computers

« on: May 18, 2013, 03:00:22 PM »

For centuries machines have been designed to perform specific tasks. For example, a washing machine washes clothes, a weaving machine weaves cloth, an adding machine adds numbers, and so on. The computer has changed all that.
     The computer is a machine that does nothing—until it is given instructions on what to do. So your computer can play games, draw pictures, or calculate π to a million decimal places; it all depends on what program (or instructions) you give the computer. The computer can do all this because it is able to accept instructions and logically change those instructions based on incoming data. This versatility makes computers useful in nearly every aspect of human endeavor.
     The idea of a computer was described theoretically in the 1940's by the mathematician Allan Turing in what he called a universal machine. In 1945 the mathematician John Von Neumann, extending Turing’s ideas, built one of the first electronic computers.
          Mathematicians continue to develop new theoretical bases for the design of computers. The heart of the computer is the “chip,” which is capable of processing logical instructions. To get an idea of the chip’s complexity, consider that the Pentium chip has over 3.5 million logic circuits!

Alan Turing (1912-1954)

John von Neumann with the stored-program computer at the Institute for Advanced Study, Princeton, New Jersey, in 1945.

Further reading

Saba Fatema Alan Turing: The Master of Code Breaking http://forum.daffodilvarsity.edu.bd/index.php?topic=9702.msg38548#msg38548

8

Applied Maths / Mathematics and the Modern World Changing Words, Sound, and Pictures into Number

« on: May 15, 2013, 05:02:05 PM »

Pictures, sound, and text are routinely transmitted from one place to another via the Internet, fax machines, or modems. How can such things be transmitted through telephone wires? The key to doing this is to change them into numbers or bits (the digits 0 or 1). It’s easy to see how to change text to numbers. For example, we could use the correspondence

A = 00000001, B = 00000010, C = 00000011, D = 00000100, E = 00000101,

and so on. The word “BED” then becomes

000000100000010100000100

.
By reading the digits in groups of eight, it is possible to translate this number back to the word “BED.”

     Changing sound to bits is more complicated. A sound wave can be graphed on an oscilloscope or a computer. The graph is then broken down mathematically into simpler components corresponding to the different frequencies of the original sound. (A branch of mathematics called Fourier analysis is used here.) The intensity of each component is a number, and the original sound can be reconstructed from these numbers. For example, music is stored on a CD as a sequence of bits; it may look like 101010001010010100101010 10000010 11110101000101011.... (One second of music requires 1.5 million bits!) The CD player reconstructs the music from the numbers on the CD.

    Changing pictures into numbers involves expressing the color and brightness of each dot (or pixel) into a number. This is done very efficiently using a branch of mathematics called wavelet theory. The FBI uses wavelets as a compact way to store the millions of fingerprints they need on file.

9

Mathematics / Algebra

« on: May 14, 2013, 06:20:28 PM »

Algebra

Algebra is a branch of mathematics that uses variables to solve equations. When solving an algebraic problem, at least one variable will be unknown. Using the numbers and expressions that are given, the unknown variable(s) can be determined.

Early Algebra

The history of algebra began in ancient Egypt and Babylon. The Rhind Papyrus, which dates to 1650 B.C.E., provides insight into the types of problems being solved at that time.

Portion of Rhind Papyrus

The Babylonians are credited with solving the first quadratic equation. Clay tablets that date to between 1800 and 1600 B.C.E. have been found that show evidence of a procedure similar to the quadratic equation. The Babylonians were also the first people to solve indeterminate equations, in which more than one variable is unknown. The Greek mathematician Diophantus continued the tradition of the ancient Egyptians and Babylonians into the common era. Diophantus is considered the “father of algebra,” and he eventually furthered the discipline with his book Arithmetica. In the book he gives many solutions to very difficult indeterminate equations. It is important to note that, when solving equations, Diophantus was satisfied with any positive number whether it was a whole number or not. By the ninth century, an Egyptian mathematician, Abu Kamil, had stated and proved the basic laws and identities of algebra. In addition, he had solved many problems that were very complicated for his time.

Medieval Algebra

During medieval times, Islamic mathematicians made great strides in algebra. They were able to discuss high powers of an unknown variable and could work out basic algebraic polynomials. All of this was done without using modern symbolism. In addition, Islamic mathematicians also demonstrated knowledge of the binomial theorem.

Modern Algebra

An important development in algebra was the introduction of symbols for the unknown in the sixteenth century. As a result of the introduction of symbols, Book III of La géometrie by René Descartes strongly resembles a modern algebra text. Descartes’s most significant contribution to algebra was his development of analytical algebra. Analytical algebra reduces the solution of geometric problems to a series of algebraic ones. In 1799, German mathematician Carl Friedrich Gauss was able to prove Descartes’s theory that every polynomial equation has at least one root in the complex plane. Following Gauss’s discovery, the focus of algebra began to shift from polynomial equations to studying the structure of abstract mathematical systems. The study of the quaternion became extensive during this period. The study of algebra went on to become more interdisciplinary as people realized that the fundamental principles could be applied to many different disciplines. Today, algebra continues to be a branch of mathematics that people apply to a wide range of topics.

René Descartes (1596-1650)

Carl Friedrich Gauss (1777-1855)

Current Status of Algebra

Today, algebra is an important day-to-day tool; it is not something that is only used in a math course. Algebra can be applied to all types of real-world situations. For example, algebra can be used to figure out how many right answers a person must get on a test to achieve a certain grade. If it is known what percent each question is worth, and what grade is desired, then the unknown variable is how many right answers one must get to reach the desired grade. Not only is algebra used by people all the time in routine activities, but many professions also use algebra just as often. When companies figure out budgets, algebra is used. When stores order products, they use algebra. These are just two examples, but there are countless others. Just as algebra has progressed in the past, it will continue to do so in the future. As it is applied to more disciplines, it will continue to evolve to better suit peoples’ needs. Although algebra may be something not everyone enjoys, it is one branch of mathematics that is impossible to ignore.

10

Science Discussion Forum / Re: "Googol"

« on: May 06, 2013, 06:37:14 PM »

Author could refer the interested reader to the interesting book "Mathematics and the Imagination" by Edward Kasner and James R. Newman published in 1949 for further details.

And in response to the reply of Rafiqul Alam Rubel present author says that the post initiated by S. Fatema was not  about "Google" but the number "Googol" from where the name of the popular search engine comes from.

11

Science Discussion Forum / Neils Henrik Abel Father of Group theory

« on: April 23, 2013, 05:01:24 PM »

Niels Henrik Abel (1802–1829) Norwegian Algebra Born on August 5, 1802.

Niels Abel might have been one of the great mathematicians of the 19th century had he not died of tuberculosis at age 26. He is remembered, and honored, in mathematics for putting an end to the three-century-long search for a solution by radicals of the quintic equation. His theoretical work in the topics of group theory and algebra paved the way for continued significant research in these areas.
          Abel’s short life was dominated by poverty, chiefly due to the severe economic hardships his homeland of Norway endured after the Napoleonic wars, exacerbated by difficult family circumstances. A schoolteacher, thankfully, recognized Abel’s talent for mathematics as a young student and introduced him to the works of Leonhard Euler, Joseph-Louis Lagrange, and other great mathematicians. He also helped raise money to have Abel attend university and continue his studies. Abel entered the University of Christiania in the city of Christiania (present-day Oslo), Norway, in 1821.
          During his final year of study, Abel began working on the solution of quintic equations (fifth-degree polynomial equations) by radicals. Although scholars for a long time knew general formulae for solving for quadratic, cubic, and quartic equations using nothing more than basic arithmetical operations on the coefficients that appear in the equation, no one had yet found a similar formula for solving quintics. In 1822 Abel believed he had produced one. He shared the details of his method with the Danish mathematician Ferdinand Degen in hopes of having the work published by the Royal Society of Copenhagen. Degen had trouble following the logic behind Abel’s approach and asked for a numerical illustration of his method. While trying to produce a numerical example, Abel found an error in his paper that eventually led him to understand the reason why general solutions to fifth- and higher-degree equations are impossible. Abel published this phenomenal discovery in 1825 in a self-published pamphlet “Mémoire sur les équations algébriques où on démontre l’impossibilité de la résolution de l’équation générale ducinquième degré” (Memoir on the impossibility of algebraic solutions to the general equations of the fifth degree), which he later presented as a series of seven papers in the newly established Journal for Pure and Applied Mathematics (commonly known as Crelle’s Journal for its German founder August Leopold Crelle). At first, reaction to this work was slow, but as the reputation of the journal grew, more and more scholars took note of the paper, and news of Abel’s accomplishment began to spread across Europe. A few years later Abel was honored with a professorship at the University of Berlin. Unfortunately, Abel had contracted tuberculosis by this time, and he died on April 6, 1829, a few days before receiving the letter of notification.
          In 1830 the Paris Academy awarded Abel, posthumously, the Grand Prix for his outstanding work. Although Abel did not write in terms of the modern-day concepts of group theory, mathematicians call groups satisfying the commutative property “Abelian groups” in his honor. In 2002, on the bicentenary of his birth, the Norwegian Academy of Science and Letters created a new mathematics prize, the Abel Prize, similar to the Nobel Prize, to be awarded annually.
          Research in the field of commutative algebra continues today using the approach developed by Abel during his short life. His influence on the development of Abstract Algebra is truly significant.

Related post
http://forum.daffodilvarsity.edu.bd/index.php?topic=9210.0

12

Science Discussion Forum / Professor Stephen W. Hawking The Man of Singularity

« on: April 20, 2013, 08:09:58 PM »

Professor Stephen W. Hawking (at home)

Stephen Hawking is a theoretical physicist recognized for his groundbreaking scientific work concerning the relationship between black holes and the beginning of the universe. He studies the basic physical laws governing the universe in an effort to understand how the universe began. Hawking uses complex mathematical models to explore his ideas and develop his scientific theories. He believes anyone can understand the basic ideas of his research and endeavors to share his excitement about science with anyone who is interested, regardless of academic background. He is the author of several books written for nonscientists explaining the concepts of his research on black holes and the universe. His best-selling book A Brief History of Time, first published in 1988, sold over 9 million copies as of 2010 and is published in more than 30 languages. His personal story is also a human interest story. At the age of 21, while attending Cambridge University, Hawking was diagnosed with amyotrophic lateral sclerosis (ALS), also known as “motor neuron disease.” This degenerative disease affects voluntary muscle coordination. ALS does not affect brain function and Hawking is able to continue working in spite of the disabling effects of the disease. His confinement to a motorized wheelchair, his use of a computer-generated voice synthesizer, and his many appearances in the media have made Hawking one of the most recognized scientists around the world.
         

       

            Born January 8, 1942, in Oxford, England, Hawking realized at a young age that he wanted to study science. He attended Oxford University and planned to study mathematics, but chose to study physics because the university did not have a program in mathematics. After completing his studies at Oxford, Hawking earned a Ph.D. in cosmology from Cambridge University. While working as a research associate at Cambridge, Hawking became interested in the study of black holes and the history of the universe. In his dissertation, Hawking theoretically proved that the universe began as a single point of infinite density, known as a “singularity.” As a theoretical physicist, Hawking relies on mathematical models to describe and build scientific theory, which can then be supported or refuted through observation. In particular, Hawking applies known mathematics to study particular objects in the universe, called “black holes,” and to study the universe itself. His work concerning the origins of the universe is built from the mathematical model of the general theory of relativity. This theory, developed by Albert Einstein and published in 1915, describes gravity in terms of its geometric relationship to space and time. Using the mathematics of general relativity, Hawking demonstrated that the equations imply the universe had a beginning as a singularity. This moment at the beginning of the universe is known as the “Big Bang.” However, theoretical physicists such as Hawking have been unable to determine the precise conditions that enable the Big Bang to occur because the mathematics of time and space become undefined at the point of a singularity. Singularities also occur when stars collapse under their own gravitational force and become black holes. Applying the mathematics of general relativity, Hawking also demonstrated that time should come to an end inside a black hole, although the equations are again undefined at the point of a singularity. His research into the structure of black holes further led to his development of a theoretical model concerning radiation emitted from black holes, which is known as “Hawking radiation.” Hawking states he has always been intrigued by life’s big questions and wants to find scientific answers to those questions. His extensive work in the mathematical exploration of black holes and the structure of the universe has led to profound insights in the fields of theoretical physics and cosmology. Among his many academic honors and awards, he held the prestigious Lucasian Chair of Mathematics at Cambridge University from 1979 to 2009, a post once held by Isaac Newton. He continues to work toward his goal of achieving a complete understanding of the universe and why it exists as it does. He and other theoretical physicists are searching for mathematical models to combine quantum mechanics (the study of subatomic particles) and general relativity. He claims that he does not particularly enjoy working with complex mathematical equations because he does not find them intuitive. Rather, he thinks about his ideas geometrically by envisioning mental pictures and visual images. It is these mental pictures and images he uses to try to convey his theoretical ideas. Since writing A Brief History of Time, he has continued his efforts to share his ideas and has written several books for the nonscientist, including Black Holes and Baby Universes and Other Essays and The Universe in a Nutshell.

          He had a guest appearance on an episode of the television series ‘Star Trek: The Next Generation’, playing poker with Data, Albert Einstein, and Isaac Newton in the episode ‘Descent, Part I’. The animated television series ‘The Simpsons’ has occasionally featured him in episodes.

Useful WebPages
Stephen Hawking official page
http://www.hawking.org.uk/
Stephen Hawking – Wikipedia
http://en.wikipedia.org/wiki/Stephen_Hawking
Science Kids – Stephen Hawking
http://www.sciencekids.co.nz/sciencefacts/scientists/stephenhawking.html

Further Reading
Hawking, S. Black Holes and Baby Universes and Other Essays. New York: Bantam, 1993.
Hawking, S. A Brief History of Time. New York: Bantam, 1988.
Hawking, S. God Created the Integers: The Mathematical Breakthroughs That Changed History. New York: Running Press, 2007.
Hawking, S. The Universe in a Nutshell. New York: Bantam, 2001.

13

Science Discussion Forum / Re: THE DEATH OF A REKNOWNED BANGLADESHI SCIENTIST PROF. JAMAL NAZRUL ISLAM

« on: April 07, 2013, 06:38:30 PM »

I was fortunate to come close to Prof. J.N. Islam during my study BSc (Hons.) and MS in Mathematics at the University of Chittagong, Bangladesh. To show some respect to his scientific career present author have collected his scholarly articles.
For more details one can see the following reference
1. http://en.wikipedia.org/wiki/Jamal_Nazrul_Islam (References are compiled by the present author)
2. http://forum.daffodilvarsity.edu.bd/index.php?topic=12475.0

14

Science Discussion Forum / Professor Dr. Jamal Nazrul Islam (1939-2013)

« on: April 07, 2013, 06:18:50 PM »

LIFE SKETCH

Prof. Dr. Jamal Nazrul Islam

Early Life and Education
Professor Islam was born on 24 February 1939 in Jhenaidah, British India (what is now Bangladesh). He studied at Chittagong Collegiate School, going on to Lawrence College in Marit, West Pakistan where he passed the Senior Cambridge and Senior Cambridge Higher Senior Cambridge exams. He received a Bachelor of science BSc degree from St. Xavier's College, Calcutta St. Xavier's College at the University of Calcutta. Islam took his mathematical tripos and PhD from Trinity College, Cambridge in 1964, followed by a DSc in 1982.

When J.N. Islam got admitted to Chittagong Collegiate School, he was doubly  promoted for his extraordinary result in the admission test. Islam was the only person who studied Mathematics in the Higher Senior Cambridge level which is now GCE Advanced Level in the whole Pakistan. He used to say that “I never used calculator”.

Career At a Glance
In his lifetime Dr. Islam has worked in various institutions over the world.
 
*A post-doctoral fellow of the Department of Physics and Astronomy, University of Maryland, College Park, Maryland (1963-1965).
*Staff member, Institute of Theoretical Astronomy, University of Cambridge, (1967-1971).
*Visiting appointments at the Institute for Advanced Study, Princeton, New Jersey, (1968,1973, 1984).
*Visiting associate at the California Institute of Technology (famously known as CALTECH), (1971-1972).
*Senior research associate in the Department of Astronomy, University of Washington, (1972-1973).
*Lecturer in Applied Mathematics, King’s College London, (1973-1974).
*Fellow of science research council at University College, Cardiff, UK, (1975-1978).
*Lecturer and Reader at the City University, London, UK, (1978-1984).
*Professor and Head of the Department of Mathematics, University of Chittagong
*Professor Emeritus at the University of Chittagong, Bangladesh.
*Member of University Grants Commission (UGC) of Bangladesh.

Research Interests
His research areas include Applied Mathematics, Theoretical Physics, Mathematical Physics, theory of Gravitation, General Relativity, Mathematical Cosmology and Quantum Field Theory. Dr. Islam authored/coauthored/edited more than 50 scientific articles, books and some popular articles published in various prestigious scientific journals. Besides this the books he has written in Bangla are no less important,however. Particularly noteworthy are ''Black Hole'', published from the Bangla Academy, “The Mother Tongue, Scientific Research and other Articles” from Rahat Publishers and “Art, Literature and Society” from Siraj Publishers. The latter two are compilations.
He has participated and organized in several international conferences, seminars, symposia, workshops and meetings both in Bangladesh and in many countries of the world.

Selected Publications
Books Authored/Coauthored/Edited
1. Islam, J.N. (1983): The Ultimate Fate of the Universe. Cambridge University Press, Cambridge, England. ISBN 978-0-521-11312-0. (Digital print version published in 2009).
2. Bonnor, W.B., Islam, J.N., MacCallum, M.A.H. (eds.)(1983): Classical General Relativity: Proceedings of the Conference on Classical (Non-Quantum) General Relativity, Cambridge University Press, Cambridge, England. ISBN 0-521-26747-1.
3. Islam, J.N. (1985): Rotating Fields in General Relativity, Cambridge University Press, Cambridge, England. ISBN 978-0-521-11311-3]. (Digital print version published in 2009).
4. Islam, J.N. (1992, 2nd edition 2001): An Introduction to Mathematical Cosmology, Cambridge University Press, Cambridge, England. ISBN 0-521-49973-9.

Scholarly Articles
1. Islam, J.N.: Modified Mandelstam Representation for Heavy Particles. J. Math. Phys. 3, 1098-1106 (1962). http://dx.doi.org/10.1063/1.1703852
2. Islam, J.N.: Acnodes and Cusps and the Mandelstam Representation. J. Math. Phys. 4, 872-878 (1963). http://dx.doi.org/10.1063/1.1704012
3. Islam, J.N., Kim, Y.S.: Analytic Property of Three-Body Unitarity Integral. Phys. Rev. 138, B1222–B1229 (1965). http://link.aps.org/doi/10.1103/PhysRev.138.B1222
4. Islam, J.N.: Leading Landau Curves of a Class of Feynman Diagrams. J. Math. Phys. 7, 652-660 (1966). http://dx.doi.org/10.1063/1.1704978
5. Islam, J.N.: Green Function Formulation of the Dirac Field in Curved Space. Proc. R. Soc. Lond. A 294, 437-448 (1966). http://dx.doi.org/10.1098/rspa.1966.0217
6. Islam, J.N.: Field Equations in the Neighbourhood of a Particle in a Conformal Theory of Gravitation. Proc. R. Soc. Lond. A 306, 487-501 (1968). http://dx.doi.org/10.1098/rspa.1968.0163
7. Islam, J.N.: Field Equations in the Neighbourhood of a Particle in a Conformal Theory of Gravitation. II. Proc. R. Soc. Lond. A 313, 71-82 (1969). http://dx.doi.org/10.1098/rspa.1969.0180
8. Islam, J.N.: Some general relativistic inequalities for a star in hydrostatic equilibrium. Mon. Not. R. Astron. Soc. 145, 21-29 (1969)]. http://adsabs.harvard.edu/abs/1969MNRAS.145...21I
9. Islam, J.N.: Some general relativistic inequalities for a star in hydrostatic equilibrium-II. Mon. Not. R. Astron. Soc. 147, 377-386 (1970). http://adsabs.harvard.edu/abs/1970MNRAS.147..377I
10. Islam, J.N.: A class of approximate exterior rotating solutions of Einstein's equations. Math. Proc. Camb. Phil. Soc. 79, 161-166 (1976). http://dx.doi.org/10.1017/S0305004100052178
11. Islam, J.N.: Possible Ultimate Fate of the Universe. Quart. J. R. Astron. Soc. 18, 3-8 (1977). http://adsabs.harvard.edu/abs/1977QJRAS..18....3I
12. Islam, J.N.: On the static field in general relativity. Math. Proc. Camb. Phil. Soc. 81, 485-496 (1977). http://dx.doi.org/10.1017/S0305004100053548
13. Islam, J.N.: On the static field in general relativity: II. Math. Proc. Camb. Phil. Soc. 83, 299-306 (1978). http://dx.doi.org/10.1017/S0305004100054566
14. Islam, J.N.: On the stationary axisymmetric Einstein-Maxwell equations. Gen. Relativ. Gravit. 9, 687-690 (1978). http://link.springer.com/article/10.1007%2FBF00760140
15. Islam, J.N.: A Class of Exact Interior Solutions of the Einstein-Maxwell Equations. Proc. R. Soc. Lond. A 353, 523-531 (1977). http://dx.doi.org/10.1098/rspa.1977.0048
16. Islam, J.N.: The Ultimate Fate of the Universe. Sky & Telescope 57, 13-18 (1979).
17. Islam, J.N.: The long-term future of the universe. Vistas in Astronomy 23, 265–277 (1979). http://dx.doi.org/10.1016/0083-6656(79)90014-X
18. Islam, J.N.: Recently Found Solution of Einstein's Equations. Phys. Rev. Lett. 43, 601-602 (1979) http://dx.doi.org/10.1103/PhysRevLett.43.601
19. Islam, J.N.: The Far Future of the Universe. Endeavour, 8, 32-34 (1984). http://dx.doi.org/10.1016/0160-9327(84)90127-3
20. Islam, J.N.: On Rotating Charged Dust in General Relativity. Proc. R. Soc. Lond. A 362, 329-340 (1978). http://dx.doi.org/10.1098/rspa.1978.0136
21. Islam, J.N.: On Rotating Charged Dust in General Relativity. II. Proc. R. Soc. Lond. A 367, 71-280 (1979). http://dx.doi.org/10.1098/rspa.1979.0087
22. Islam, J.N.: On Rotating Charged Dust in General Relativity. III. Proc. R. Soc. Lond. A 372, 111-115 (1980). http://dx.doi.org/10.1098/rspa.1980.0104
23. Islam, J.N.: On rotating charged dust in general relativity. IV. Proc. R. Soc. Lond. A 385, 189-205 (1983). http://dx.doi.org/10.1098/rspa.1983.0010
24. Islam, J.N.: On Rotating Charged Dust in General Relativity. V. Proc. R. Soc. Lond. A 389, 291-298 (1983). http://dx.doi.org/10.1098/rspa.1983.0110
25. Islam, J.N., Schutz, B.F.: Motion of primordial black holes in the early universe and their likely distribution today. Gen. Relativ. Gravit. 12, 881-893 (1980). http://link.springer.com/article/10.1007%2FBF00757357
26. Islam, J.N.: The cosmological constant and classical tests of general relativity. Phys. Lett. A 97, 239–241 (1983). http://dx.doi.org/10.1016/0375-9601(83)90756-9
27. Boachie, L. A., Islam, J.N.: On a certain solution of the Einstein-Maxwell equations. Phys. Lett. A 93, 321–322 (1983). http://dx.doi.org/10.1016/0375-9601(83)90107-X
28. Islam, J.N.: Closed form for Van Stockum interior solution of Einstein's equations. Phys. Lett. A 94, 421–423 (1983). http://dx.doi.org/10.1016/0375-9601(83)90843-5
29. Islam, J.N., Bergh, N. V. d., Wils, P.: General solutions for axisymmetric differentially rotating charged dust with vanishing Lorentz force. Class. Quant. Grav. 1, 705-714 (1984).
30. Islam, J.N.: On Yang-Mills Theory in the Temporal Gauge. Proc. R. Soc. Lond. A 421, 279-301 (1989). http://dx.doi.org/10.1098/rspa.1989.0012
31. Islam, J.N.: Schrödinger Functional Equation for Yang-Mills Theory. Prog. Theor. Phys. 89, 161-185 (1993) http://ptp.oxfordjournals.org/content/89/1/161.abstract, http://ptp.ipap.jp/link?PTP/89/161/
32. Islam, J.N.: The Schrödinger equation in quantum field theory. Found. Phys. 24, 593-630 (1994). http://link.springer.com/article/10.1007%2FBF02054667
33. Azad, A.K., Islam, J.N.: Cosmological constant in the Bianchi type-I-modified Brans-Dicke cosmology. Pramana J. Phys. 60, 21-27 (2003). http://link.springer.com/article/10.1007%2FBF02705065
34. Islam, M.A., Islam, J.N.: Anharmonic solution of Schrödinger time-independent equation. Pramana J. Phys. 77, 243-261 (2011). http://link.springer.com/article/10.1007/s12043-011-0101-8
35. Firoz, K.A., Moon, Y.-J., Park, S.-H., Kudela, K., Islam, J.N., Dorman, L. I.: On the Possible Mechanisms of Two Ground-level Enhancement Events. ApJ 743, 190 (18pp) (2011). http://dx.doi.org/10.1088/0004-637X/743/2/190
36. Panna, N., Islam, J.N.: Construction of an Exact Solution of Time-Dependent Ginzburg-Landau Equations by Standard Integral for Front Propagation in Superconductors. Science Journal Of Mathematics and Statistics, Article ID sjms-101, 4 Pages, (2012). http://www.sjpub.org/sjms/abstract/sjms-101
37. Panna, N., Islam, J.N.: Construction of an exact solution of time-dependent Ginzburg-Landau equations and determination of the superconducting-normal interface propagation speed in superconductors. Interaction of Lasers with Atoms, Molecules and Clusters University of Hyderabad, Hyderabad 9-12 January 2012. (Forthcoming)

Death
Dr. Islam died on 16th March 2013 in Chittagong, Bangladesh. With his death we have lost a creative, thoughtful and active member of the relativity-and-gravitation community.

Reference
For more details one can see the following reference
1. http://en.wikipedia.org/wiki/Jamal_Nazrul_Islam (References are compiled by the present author)

15

Science Discussion Forum / Higgs boson finally discovered?

« on: July 05, 2012, 05:48:35 PM »

Most people think they know what mass is, but they understand only part of the story. For instance, an elephant is clearly bulkier and weighs more than an ant. Even in the absence of gravity, the elephant would have greater mass—it would be harder to push and set in motion. Obviously the elephant is more massive because it is made of many more atoms than the ant is, but what determines the masses of the individual atoms? What about the elementary particles that make up the atoms—what determines their masses? Indeed, why do they even have mass?

Unlike protons and neutrons, truly elementary particles—such as quarks and electrons—are not made up of smaller pieces. The explanation of how they acquire their rest masses gets to the very heart of the problem of the origin of mass. The account proposed by contemporary theoretical physics is that fundamental particle masses arise from interactions with the Higgs field. A key player in physicists’ tentative theories about mass is a new kind of field that permeates all of reality, called the Higgs field. Elementary particle masses are thought to come about from the interaction with the Higgs field. If the Higgs field exists, theory demands that it have an associated particle, the Higgs boson. In short, this Higgs particle becomes the source of all mass. Using particle accelerators (giant machines such as LHC), scientists are now hunting for the Higgs. Scientists are studying Higgs particle for not only it is important but it's existence is directly related to our existence in this universe.

The Higgs boson is named after Peter Ware Higgs (born 29th may 1929), a British theoretical physicist, who was one of six authors in the 1960s who wrote the ground-breaking papers covering what is now known as the Higgs mechanism and described the related Higgs field and boson.

On 4 July 2012, the two main experiments at the LHC (Large Hadron Collider), ATLAS (A Toroidal LHC ApparatuS) and CMS (Compact Muon Solenoid), both reported independently the confirmed existence of a previously unknown particle with a mass of about 125 GeV/c² (about 133 proton masses, on the order of 10^-25 kg), which is "consistent with the Higgs boson" and widely believed to be the Higgs boson. They acknowledged that further work would be needed to confirm that it is indeed the Higgs boson and not some other previously unknown particle (meaning that it has the theoretically predicted properties of the Higgs boson) and, if so, to determine which version of the Standard Model it best supports.

One possible signature of a Higgs boson from a simulated proton–proton collision. It decays almost immediately into two jets of hadrons and two electrons, visible as lines.

Finally found (Image: Thomas McCauley/Lucas Taylor/CERN/CMS Collaboration)

There's a 5-in-10 million chance that this is a fluke. That was enough for physicists to declare that the Higgs boson – the world's most-wanted particle – has been discovered. Rapturous applause, whistles and cheers filled the auditorium at CERN, near Geneva, Switzerland.

Almost 50 years after its existence was first predicted, the breakthrough means that the standard model of particle physics, which explains all known particles and the forces that act upon them, is now complete.

A Higgs boson with a mass of around 125 to 126 gigaelectronvolts (GeV) was seen separately by the twin CMS and ATLAS detectors at the LHC, each with a confidence level of 5 sigma, or standard deviations, the heads of the experiments announced today at CERN.

Even by particle physicists' strict standards, that's statistically significant enough to count as a particle discovery.
"I think we have it," said Rolf Heuer, director general of CERN, as he concluded a hotly-anticipated seminar.

It's elementary
The Higgs boson gives all elementary particles mass, allowing for the existence of matter. It is the fundamental unit, or quantum, of the Higgs field, an all pervading entity that all particles must pass through. Some, like the photon, slip through unhindered – they are massless. Others, though, must struggle like a fly trapped in treacle. The Higgs and its field are required by the standard model, but had never been conclusively detected before today's report.

The seminar was full of emotion and elation. An emotional Peter Higgs, who postulated the boson that is his namesake in 1964, wiped a tear from his eye as the teams finished their presentations in the Cern auditorium. "I would like to add my congratulations to everyone involved in this achievement," he added later. "It's really an incredible thing that it's happened in my lifetime." 

"This is an important result and should earn Peter Higgs the Nobel Prize," Professor Stephen Hawking told BBC News.

There was also some humour: "It is very nice of the standard model boson to be at that mass," says Gianotti. "Because of that mass we can measure it. Thanks nature."
The physicists were a little reticent to call the discovery a "Higgs boson", preferring to call it the discovery of a "new boson".

That's because they don't yet know its properties – and so can't confirm how similar it is to the Higgs of the standard model. "It's the beginning of a long journey to investigate all the properties of this particle," says Heuer.
One property that needs to be investigated is the particle's spin: the standard model says it should have a value of zero; a more exotic boson would give a value of two. Oliver Buchmueller of CMS says the LHC should be able to determine the new boson's spin by the end of 2012.

We know that the standard model is not complete – it does not contain dark matter or gravity, for a start – so a non-standard model Higgs could be very exciting.
"Everyone is not just excited about the discovery, but about the prospects this discovery offers to the field," says Heuer.

References
Paul Rincon Higgs boson-like particle discovery claimed at LHC, BBC News Science and Environment, 4 July 2012. Link: http://www.bbc.co.uk/news/world-18702455.

Gordon Kane The Mysteries of Mass, Published in The Frontiers of Physics, Scientific American Special Edition, 2005