Most patents litigated are found invalid without deciding patent infringement claims, the basis for a court's jurisdiction. Invalidating a patent without deciding the infringement claim frees large corporate infringers from liability for patent infringement of the invalidated patent.

Until the statement of the small scale uncertainty principle by Heisenberg in 1927, modern physics held to the idea of a classical determinism, and the rejection of such determinism became a cause for dissent between Einstein (as a believer in a classical determinism) and Bohr and the other supporters of the quantum revolution. On the scale of atoms and elementary particles the effect of the uncertainty principle is very important. Because of the uncertainties existing at this level, a pic...

This page explains the connection between Newton's laws, of gravitation and motion, and redshift observations, as interpreted by the Doppler, Einstein's, and Thermodynamic theories. It adopts the Thermodynamic universe theory and discards the Doppler and Einstein theories. Unlike Doppler and Einstein redshifts, Thermodynamic universe redshifts increase linearly with distance and fully explain Hubble's experimental law. Thermodynamic theory tells us that what we see when we gaze out at the ...

While extended zeta functions support investigations of Riemann's hypothesis and estimates for the Prime Number Theorem, some zeta functions offer better prospects for providing easy proofs, or disproofs. In 1859, Riemann had the idea to define Euler's function ε(x)=∑m^x for all complex numbers s=x+iy by analytic extension. This extension is important in number theory and plays a central role in the distribution of prime numbers. There are a number of ways of extending Euler's zeta functio...

Comparing observation and the Big Bang theory, observation tells us that the early universe, over a period of about 3.3 bly, consisted of radiation which later evolved into the galactic system we observe today. The Big Bang theory tells us that the early universe began about 15 bly ago as an initial expansion from nothing forming subatomic particles which lasted for a short time, fewer than 0.4 bly and later evolved into the present system.Based on Hubble's linear law v=Hr, space ex...

. Einstein's theory of special relativity did two things. First, it adopted the Lorentz transformation (LT) which preserves the velocity of light and Maxwell's equations in all systems and, second, it required that all the laws of physics should be examined as to their transformation properties under the LT. Those laws which do not keep their form invariant are to be generalized so as to obey an "equivalence postulate" which requires that all physical laws must be phrased in an identical m...

Einstein's theory, in its so called weak gravity field linearized version, approximately reduces to Newton's theory. Conflicting linearizations depend on their authors and, are heavily mathematical, involve non-physical geometrical concepts, and rely on Newtonian type tests and results. For example, Einstein's theory does not inform us how, absent force, his warped geometry might actuate Newton's gyroscope. Basically, Einstein tells us that one can ignore Newton's predictions based on Newt...

It has already been shown that all zeros are in the critical strip and that they are symmetric about the critical line. I make several assumptions and show that all zeros are on the critical line and that Riemann's functional equation presents a problem. The assumptions are, first, that Riemann's zeta function is single valued at each point of the critical strip (it is not), second, Riemann's functional equation necessarily and sufficiently sets zeroes in the critical strip (it does not) a...

It is well known that finding large prime numbers is difficult.i We have no algorithm to find primes although we have algorithms to narrow the search. The two main tools we have are theory and empirical data both supported by computers. But, with increased number size of numbers computation becomes prohibitive in time and resources. For small prime numbers, it is easy as we have exhaustively tested all less than 20 digit numbers through some fast probable prime tests and found no false res...

In this short book Fermat's Last Theorem is easily proven and Beals Conjecture is easily Disprovenusing Pythagora's Theorem

Solutions of the Navier–Stokes equations often include turbulence, which remains one of the greatest unsolved problems in physics, despite its immense importance in science and engineering. The Clay Mathematics Institute in May 2000 made this problem one of its seven Millennium Prize problems in mathematics. It offered a US $1,000,000 prize to the first person who provides a solution for a specific statement of the problem.

General Relativity is the theory of gravity that incorporates special relativity and the weak equivalence principle which states that accelerating frames of reference and gravitational fields are indistinguishable. It is a metric theory, sometimes also called a geometric theory. Metric theories describe physical phenomena in terms of differential geometry.This stands in contrast to Isaac Newton's Law of Universal Gravitation, which described gravity in terms of a vector field. The equivale...