* Pillai's conjecture

# REDIRECT Catalan's conjecture # Pillai's conjecture

In 2012, Beena Pillai's laboratory has demonstrated that nucleosome sliding is one of the possible mechanism for large scale tissue specific expression of genes.

There is also another style i. e., the blending of Saakotai Rangu Iyengar's and Kumbakonam Azhaganambi Pillai's taught to hundreds of disciples by the legendary Late Sri Kumbakonam Narayanaswamy Iyer and late Sri Kumbakonam Rajappa Iyer.

It was here that Tiruvavaduthurai Rajaratnam Pillai's tapes and audio CDs were produced.

Raman Pillai's leading disciples include Madavoor Vasudevan Nair and Mankompu Sivasankara Pillai, besides late masters like Harippad Ramakrishna Pillai and Chennithala Chellappan Pillai.

After defeating Pillai, Marthanda Varma destroyed Kazhakoottam Pillai's palace.

Brinda absorbed both the sublime and intricate Dhanammal style and Naina Pillai's fast paced masculine music and blended them seamlessly into her singing.

While not all may agree with Vaiyapuri Pillai's textual criticism and dating, several question the Tiruvalluvar era on the issue of its date.

In the 18th century, the newly crowned prince Marthanda Varma ( 1706 – 1758 ), who was in his twenties, defeated the Thampi sons of Rajah Rama Varma and the Ettuveetil Pillamar ( Pillai's of the Eight Noble Nair Houses ).

For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1. 2 × 10 < sup > 12 </ sup > ( over a trillion ).

A conjecture developed by Cumrun Vafa, Amer Iqbal, and Andrew Neitzke in 2001, called " mysterious duality ", concerns a set of mathematical similarities between objects and laws describing M-theory on k-dimensional tori ( i. e. type II superstring theory on T < sup > k − 1 </ sup > for k > 0 ) on one side, and geometry of del Pezzo surfaces ( for example, the cubic surfaces ) on the other side.

The Ricci flow ( named after Gregorio Ricci-Curbastro ) was introduced by Richard Hamilton in 1981 in order to gain insight into the geometrization conjecture of William Thurston, which concerns the topological classification of three-dimensional smooth manifolds.

In number theory, the second Hardy – Littlewood conjecture concerns the number of primes in intervals.

* The Hadwiger conjecture in combinatorial geometry concerns the minimum number of smaller copies of a convex body needed to cover the body, or equivalently the minimum number of light sources needed to illuminate the surface of the body ; for instance, in three dimensions, it is known that any convex body can be illuminated by 16 light sources, but Hadwiger's conjecture implies that only eight light sources are always sufficient.

Much of Pogorzelski's research concerns the Goldbach conjecture, the still-unsolved problem of whether every even number can be represented as a sum of two prime numbers.

Such equations do not have a general theory ; particular cases such as Catalan's conjecture have been tackled.

In these papers he sketched a proof of the Poincaré conjecture and a more general conjecture, Thurston's geometrization conjecture, completing the Ricci flow program outlined earlier by Richard Hamilton.

Some analyses using the semiclassical approach to incorporating quantum effects into general relativity indicate that a feedback loop of virtual particles would circulate through the wormhole with ever-increasing intensity, destroying it before any information could be passed through it, in keeping with the chronology protection conjecture.

The Novikov self-consistency principle, also known as the Novikov self-consistency conjecture, is a principle developed by Russian physicist Igor Dmitriyevich Novikov in the mid-1980s to solve the problem of paradoxes in time travel, which is theoretically permitted in certain solutions of general relativity ( solutions containing what are known as closed timelike curves ).

In 1849 de Polignac made the more general conjecture that for every natural number k, there are infinitely many prime pairs p and p ′ such that p ′ − p

The cartographic depictions of the southern continent in the 16th and early 17th centuries, as might be expected for a concept based on such abundant conjecture and minimal data, varied wildly from map to map ; in general, the continent shrank as potential locations were reinterpreted.

The general conjecture would follow from the ABC conjecture.

Actually, the correctness of the Bieberbach conjecture was only the most important consequence of de Branges's proof, which covers a more general problem, the Milin conjecture.

Modern computer calculations have shown this conjecture to be true for integers up to at least 4 × 10 < sup > 14 </ sup >, but still no general proof has been found.

Another higher-dimensional generalization of Faltings ' theorem is the Bombieri – Lang conjecture that if X is a pseudo-canonical variety ( i. e., variety of general type ) over a number field k, then X ( k ) is not Zariski dense in X.

In particular, the Hodge conjecture holds for sufficiently general abelian varieties, for products of elliptic curves, and for simple abelian varieties.

One of the influential examples, both for the history of the more general L-functions and as a still-open research problem, is the conjecture developed by Bryan Birch and Peter Swinnerton-Dyer in the early part of the 1960s.

A special case of the conjectures, which are open in the general case, was involved in the proof of the Mordell conjecture by Gerd Faltings.

By an analysis of how minimal surfaces behave in space-time, Yau and Richard Schoen proved the long-standing conjecture that the total mass in general relativity is positive.

* 1982, Fields Medal, for " his contributions to partial differential equations, to the Calabi conjecture in algebraic geometry, to the positive mass conjecture of general relativity theory, and to real and complex Monge – Ampère equations ".

The Hadwiger conjecture has been proven only for k ≤ 6, but remains unproven in the general case.

This is probably false in general as it is inconsistent with the more likely first Hardy – Littlewood conjecture on prime k-tuples, but the first violation is likely to occur for very large values of x.

In general its properties, such as functional equation, are still conjectural – the Taniyama – Shimura conjecture ( which was proven in 2001 ) was just a special case, so that's hardly surprising.

There are more general statements ; this one is most clearly motivated by the Mordell conjecture, where such a curve C should intersect J ( K ) only in finitely many points.

Many questions around prime numbers remain open, such as Goldbach's conjecture, which asserts that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, which says that there are infinitely many pairs of primes whose difference is 2.

For example the difference between a counterexample to a lemma ( a so-called ' local counterexample ') and a counterexample to the specific conjecture under attack ( a ' global counterexample ' to the Euler characteristic, in this case ) are discussed.

Some modern costumers conjecture that the French farthingale and the " great farthingale " refer to one and the same garment, the difference in shape and construction being due to changes in fashion from the 1580s to the 1590s.

Gilbreath's conjecture is a hypothesis, or a conjecture, in number theory regarding the sequences generated by applying the forward difference operator to consecutive prime numbers and leaving the results unsigned, and then repeating this process on consecutive terms in the resulting sequence, and so forth.

Various tests of the different versions ' strengths show little difference ; conjecture about either knot's vulnerability to some failure remain pretty much only that – conjectures.

There must, however, be some difference between Achmet's work, in the form in which we have it, and that of Ibn Sirin, as the writer of the former ( or the translator ) appears from internal evidence to have been certainly a Christian, ( c. 2, 150, & c .) It exists only in Greek, or rather ( if the above conjecture as to its author be correct ) it has only been published in that language.