Equation Quotes - page 4
I have no hang-ups in life. I don't care about groups and camps. I have been brought up with certain values and ethics. I have never been egoistic about my stardom and lineage. I don't have any qualms about breaking the ice with my colleagues. I can walk up to any actor and greet him, irrespective of what kind of equation I share with him.
Abhishek Bachchan
On notable classmate was Dan Friedan. Friedan stunned me, and I think everyone else, at his Ph. D. seminar, when he showed that Einstein's equation, the basic equation of general relativity, could be interpreted in terms of one of the basic objects in QFT, the β function that governs the energy scale. I did not see what this could possibly mean, but a few years later it showed up as one of the key ideas in string theory.
Joseph Polchinski
One of the many importants ideas introduced by Minkowski into the study of convex bodies was that of gauge function. Roughly, the gauge function is the equation of a convex body. Minkowski showed that the gauge function could be defined in a purely geometric way and that it must have certain properties analogous to those possessed by the distance of a point from the origin. He also showed that conversely given any function possessing these properties, there exists a convex body with the given function as its gauge function.
Carl Ludwig Siegel
As for negative numbers... most mathematicians of the sixteenth and seventeenth centuries did not accept them... In the fifteenth century Nicolas Chuquet and, in the sixteenth, Stifel both spoke of negative numbers as absurd numbers. ...Descartes accepted them, in part. ...he had shown that, given an equation, one can obtain another whose roots are larger than the original one by any given quantity. Thus an equation with negative roots could be transformed into one with positive roots. Since we can turn false roots into real roots, Descartes was willing to accept negative numbers. Pascal regarded the subtraction of 4 from zero as utter nonsense.
Morris Kline
One of the first algebraists to accept negative numbers was... placed negative numbers on a par with positive numbers and gave both roots of a quadratic equation, even when both were negative. Both Girard and Harriot used the minus sign for the operation of subtraction and for negative numbers.
Morris Kline
When an equation...clearly leads to two negative or imaginary roots, [Diophantus] retraces his steps and shows by how by altering the equation, he can get a new one that has rational roots. ...Diophantus is a pure algebraist; and since algebra in his time did not recognize irrational, negative, and complex numbers, he rejected equations with such solutions.
Morris Kline
Ideas and techniques known in quantum electrodynamics have been applied to the Bardeen-Cooper-Schrieffer theory of superconductivity. In an approximation which corresponds to a generalization of the Hartree-Fock fields, one can write down an integral equation defining the self-energy of an electron in an electron gas with phonon and Coulomb interaction. The form of the equation implies the existence of a particular solution which does not follow from perturbation theory, and which leads to the energy gap equation and the quasi-particle picture analogous to Bogolyubov's.
Yoichiro Nambu
The historical associations of the word algebra almost substantiate the sordid character of the subject. The word comes from the title of a book written by... Al Khowarizmi. In this title, al-jebr w' almuqabala, the word al-jebr meant transposing a quantity from one side of an equation to another and muqabala meant simplification of the resulting expressions. Figuratively, al-jebr meant restoring the balance of an equation... When the Moors reached Spain... algebrista... came to mean a bonesetter... and signs reading Algebrista y Sangrador (bonesetter and bloodletter) were found over Spanish barber shops. Thus it might be said that there is a good historical basis for the fact that the word algebra stirs up disagreeable thoughts.
Morris Kline
There are one or two things, which you can directly do in very critical times. But otherwise, this indirect influence that you can exercise on the affairs of the State is the most important role he can play. And, he can play it successfully only if he is, his ideas and his nature of functioning are seen by the public in tune with their standards. The President has to be a citizen and there must be some equation between the people and the President, and if some advice or something is to be given to the executive, it would be received with grace, it would be sometimes accepted, if it is known that the public opinion is on the side of the kind of advice the President is giving. Otherwise, he cannot exercise much influence.
K. R. Narayanan
As a transportation hub, agriculture leader, and home to more than half a million small businesses, Missouri is positioned to be at the cutting edge of growth and innovation in this country. But, we need the right policies to get us there and pro-growth tax cuts and regulatory reform are a critical part of that equation. I couldn't agree more with the president's call to get this done, and I look forward to working with him and my colleagues in Congress to provide much-needed tax relief for Missouri families and small businesses.
Roy Blunt
A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this 'variance equation' completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or non-stationary statistics.
The variance equation is closely related to the Hamiltonian (canonical) differential equations of the calculus of variations. Analytic solutions are available in some cases. The significance of the variance equation is illustrated by examples which duplicate, simplify, or extend earlier results in this field.
The duality principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results. In several examples, the estimation problem and its dual are discussed side-by-side.
Properties of the variance equation are of great interest in the theory of adaptive systems. Some aspects of this are considered briefly.
Rudolf E. Kálmán
