So the difference from the fixed point becomes δ ( dxdf ) x=x∗ . For the fixed
point to be stable, the absolute value of this difference should be less than that of
δ. Thus, the condition for the stability of the fixed point x∗ is given by ∣ ∣ ∣ ∣ (
Author: Mallik Asok Kumar
Category: Juvenile Nonfiction
This book is more than a mathematics textbook. It discusses various kinds of numbers and curious interconnections between them. Without getting into hardcore and difficult mathematical technicalities, the book lucidly introduces all kinds of numbers that mathematicians have created. Interesting anecdotes involving great mathematicians and their marvelous creations are included. The reader will get a glimpse of the thought process behind the invention of new mathematics. Starting from natural numbers, the book discusses integers, real numbers, imaginary and complex numbers and some special numbers like quaternions, dual numbers and p-adic numbers. Real numbers include rational, irrational and transcendental numbers. Iterations on real numbers are shown to throw up some unexpected behavior, which has given rise to the new science of "Chaos". Special numbers like e, pi, golden ratio, Euler's constant, Gauss's constant, amongst others, are discussed in great detail. The origin of imaginary numbers and the use of complex numbers constitute the next topic. It is shown why modern mathematics cannot even be imagined without imaginary numbers. Iterations on complex numbers are shown to generate a new mathematical object called 'Fractal', which is ubiquitous in nature. Finally, some very special numbers, not mentioned in the usual textbooks, and their applications, are introduced at an elementary level. The level of mathematics discussed in this book is easily accessible to young adults interested in mathematics, high school students, and adults having some interest in basic mathematics. The book concentrates more on the story than on rigorous mathematics.
The LINAC Coherent Light Source (LCLS), developed at the Stanford Linear
Accelerator Center (SLAC) in California, was the first free-electron laser
producing very short pulses of hard X-rays. The X-ray pulse bandwidth can be
Author: Dennis F. Vanderwerf
Category: Technology & Engineering
This book traces the evolution of our understanding and utilization of light from classical antiquity and the early thoughts of Pythagoras to the present time. From the earliest recorded theories and experiments to the latest applications in photonic communication and computation, the ways in which light has been put to use are numerous and astounding. Indeed, some of the latest advances in light science are in fields that until recently belonged to the realm of science fiction. The author, writing for an audience of both students and other scientifically interested readers, describes fundamental investigations of the nature of light and ongoing methods to measure its speed as well as the emergence of the wave theory of light and the complementary photon theory. The importance of light in the theory of relativity is discussed as is the development of electrically-driven light sources and lasers. The information here covers the range o f weak single-photon light sources to super-high power lasers and synchrotron light sources. Many cutting-edge topics are also introduced, including entanglement-based quantum communication through optical fibers and free space, quantum teleportation, and quantum computing. The nature and use of "squeezed light" - e.g. for gravitational wave detection - is another fascinating excursion, as is the topic of fabricated metamaterials, as used to create invisibility cloaks. Here the reader also learns about the realization of extremely slow speed and time-reversed light. The theories, experiments, and applications described in this book are, whenever possible, derived from original references. The many annotated drawings and level of detail make clear the goals, procedures, and conclusions of the original investigators. Where they are required, all specialist terms and mathematical symbols are defined and explained. The final part of the book covers light expe riments in the free space of the cosmos, and also speculates about scenarios for the cosmological origins of light and the expected fate of the photon in a dying universe.
In the course of our attempt to reconstruct the form of the story in the missing X ,
we have had occasion more than once to note the fact that the account by
Cæsarius supplies a parallel to Group B in details which are found in no other
It may seem odd to you to add in order to multiply , but the following examples
should convince you as well as illustrate the procedure that is followed . a2 x a3 =
( a X a ) ( a xa x a ) = a Xa x a X a Xa = a . If a = 2 , you can verify this statement by
Author: Germaine Beiser
Describes the universal influence of gravity and discusses theories about the nature of this force from those of Pythagoras to those of Einstein.
It begins by inviting you to tell a story about an agent , Jones , who chooses to
perform , and succeeds in performing , some action X . Tell the story so that it is
vividly clear that Jones is morally responsible for doing X . If you are a libertarian
With Point X , the story is launched . Movement and struggle are unavoidable . A
special quality that will help to identify Point X is the quality of success - or -
failure . If the writer has established ( a ) two conflicting forces , ( b ) the issue
Thus we are unsure of the identity of X-6, but we cannot exclude the possibility of
the New Testament source as Mary Magdalene. The story of the adulteress in
John 8 is a section that also popped up in an ancient edition of the Gospel of
S'A x B'A, 192 pp, Quality PB, 1SBN 1 -58023- 1 86- 1 $16.95 Our Dance with
God: Finding Prayer, Perspective and Meaning in the Stories of Our Lives By
Karyn D. Kedar Inspiring spiritual insight to guide you on your life journeys and
Author: David Zeller
Publisher: Jewish Lights Publishing
Category: Biography & Autobiography
Shares stories about the part each teacher played in integrating mind and heart, body and soul, psychology and religion, west and east, matter and spirit, theory and experience, and how each teaching became the stepping stone to reclaiming his own spiritual tradition. $15,000 first printing.
A darkly seductive and passionate tale of secret societies, elaborate rites and sexual experimentation, in the tradition of the captivating classic Story of O and Kubrick’s film Eyes Wide Shut.
Author: A.J. Molloy
Publisher: Harper Collins
A darkly seductive and passionate tale of secret societies, elaborate rites and sexual experimentation, in the tradition of the captivating classic Story of O and Kubrick’s film Eyes Wide Shut. Shy American student Alexandra Beckmann—‘X’ to her friends—arrives in Naples desperate for adventures beyond the sheltered life she has led. She is there to study the Camorra, an infamous Italian crime organization. But in the sun-soaked, ancient city streets, her research leads her to a man like no one else she has ever met. Irresistibly handsome, Lord Marcus Roscarrick is an Italian aristocrat with a mysterious past. Yet, underneath his refined exterior, X senses a man who is well-acquainted with danger. Soon they begin a passionate affair, and X is drawn into Roscarrick’s world—a world she never dreamed existed. But as she falls ever more deeply under Roscarrick’s spell, X must decide whether she dares to submit entirely to this shadowy realm of dark desire.
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The next chapter ( x ) contains the first blot upon the picture in the story of the
sons of Aaron - Nadab and Abihu by name — who , perhaps too much elated by
the dignity of their new office , and despising the restrictions by which it was
As the length of the incidence waves is known , by studying the angles of
reflection the distances between atoms in the crystal can be determined . That is
to say , the crystalline structure of the metal is disclosed by examining it with X -
rays and ...
The story noted that Malcolm had abandoned the Black Muslim teachings of hate
for the white man and total ... and after his break with the movement , appeared
on page fifteen under the headline , " Malcolm X : Authority on Muslims Fears ...
Bobbs Merrill , 1948 3.50 Historical novel ; early colonization in America x 614.8
Floherty . FIVE ALARM . Lippincott , 1949 2.50 The story of fire fighting x 070
Floherty . SHOOTING THE NE.S. Lippincott , 1949 2.50 Careers of cameramen x
THE STORY OF X - RAYS FROM RONTGEN TO ISOTOPES , A. R. Bleich , M.D.
This book , by a member of the American College of Radiology , gives the
scientific explanation of x - rays , their applications in medicine , industry and art ,
Sixth German Artillery , operations at Verdun , X , 2889 Ski , use of , by Germans ,
VII , 2132 Slavs in Germany , II , 406 Slavs in Russia , II , 406 Smith - Dorrien ,
General , III , 692 Smoke screen , I , 74 Smorgon , fighting around , IX , 2667
Isle of Pleasures , The Italian Story - Tellers , The It Snows XIX . 105 XV . 298 IX .
200 XI . 404 XX . 297 XVI . 201 XII . 331 VI . 297 XI . 7 IX . 250 xv . 46 VI . 83 XX .
304 II . 332 XVII . 283 V. 116 XVI . 369 IV . 241 XII . 389 Il . 135 XIX . 178 . X. 233 ...
74 x 5 . Pp . 192. 6s . Mills & B. CARMAN ( Dulce ) -The Riddle of the Ranges . A
New Zealand romance . 77 x 5. Pp . 253. ... HECHT ( Ben ) -The Collected Stories
of Ben Hecht . Prefaced by some introductory thoughts by the author . 87 x 59.
Little Big is a lonely ng with his first round of duty as a fully Indian boy . The story
of his search for a playmate ed police mount . An Easy - to - Read Photo Story is
told in simple text and charming illustrations . 12 x 11 • black & white photos ...
Category: Best books
An annually revised, annotated list of children's books selected from the titles listed in Children's books in print.