Josip Plemelj ( December 11, 1873 – May 22, 1967 ) was a Slovene mathematician, whose main contributions were to the theory of analytic functions and the application of integral equations to potential theory.

Spurred on by Hilbert, Göttingen mathematicians attacked this new area of ​​ research and Plemelj was one of the first to publish original results on the question, applying the theory of integral equations to the study of harmonic functions in potential theory.

On May 1898 Plemelj presented his doctoral thesis under Escherich's tutelage entitled O linearnih homogenih diferencialnih enačbah z enolično periodičnimi koeficienti ( Über lineare homogene Differentialgleichungen mit eindeutigen periodischen Koeffizienten, About linear homogeneous differential equations with uniform periodical coefficients ).

Their proofs difficult, while Plemelj showed how to use the ring we get if we extend the rational numbers by √ 5.

In fact, Plemelj correctly proves that any monodromy group can be realised by a regular linear system which is Fuchsian at all but one of the singular points.

* 1873 – Josip Plemelj, Slovenian mathematician ( d. 1967 )

* December 11 – Josip Plemelj, Slovenian mathematician ( d. 1967 )

His mother Marija, née Mrak, found bringing up the family alone very hard, but she was able to send her son to school in Ljubljana where Plemelj studied from 1886 to 1894.

1912 Plemelj published a very simple proof for the Fermat's last theorem for exponent n = 5, which was first given almost simultaneously by Dirichlet in 1828 and Legendre in 1830.

His Doctor thesis contains the famous Sokhotski – Plemelj theorem.

Sochocki is mainly remembered for the Casorati – Sokhotski – Weierstrass theorem and for the Sokhotski – Plemelj theorem.

* Josip Plemelj solves the Riemann problem about the existence of a differential equation with a given monodromic group and uses Sokhotsky-Plemelj formulae.

Josip Plemelj published a solution in 1908.

The notation with interchanged arguments,, is often encountered ; and similarly for the integral of the second kind.

Problems in which integral equations are encountered include radiative energy transfer and the oscillation of a string, membrane, or axle.

The Gaussian integral is encountered very often in physics and numerous generalizations of the integral are encountered in quantum field theory.

Two of the most commonly specified measures are the cross-section for thermal neutron absorption, and resonance integral which considers the contribution of absorption peaks at certain neutron energies specific to a particular nuclide, usually above the thermal range, but encountered as neutron moderation slows the neutron down from an original high energy.

Second and higher order ordinary differential equations ( more generally, systems of nonlinear equations ) rarely yield closed form solutions, though implicit solutions and solutions involving nonelementary integrals are encountered.

it is probably worth mentioning that certain non-negative ratios are readily encountered, which are appropriately labelled by similarly related indices, and which do satisfy equations corresponding to 1., 2. and 3., but which nevertheless don't satisfy the Wigner – d ' Espagnat inequality.

We now have enough relations to compute the polynomials of all the links we've encountered, and can use the above equations in reverse order to work up to the cinquefoil knot itself:

During this time, he encountered differential equations that he could only solve numerically.

Then, one can prove that solutions exist at least locally, using ideas not terribly dissimilar from those encountered in studying other differential equations.

Perhaps the most common situation in which these are encountered is as the solution to Stratonovich stochastic differential equations ( SDE ).

The Imperial German Cavalry, while as colourful and traditional as any in peacetime appearance, had adopted a practice of falling back on infantry support when any substantial opposition was encountered.

In the Enterprise episode " The Communicator ", an alien species is encountered whose blood chemistry, while not explicitly stated, is sufficiently different from terrestrial organisms that it is not red and iron is toxic to it.

In Greece, he encountered an Ionian theologian, who has been identified as Athenagoras of Athens ; while in the east, he was taught by an Assyrian, sometimes identified with Tatian, and a Jew, who was possibly Theophilus of Caesarea.

* Failing in his role as fast armoured scout to report to Jellicoe the exact position of the German ships he encountered, or to keep in contact with the German fleet while he retreated to the main British Grand Fleet.

Rumiñahui fell back to Quito, and, while in pursuit of the Inca army, Benalcázar encountered another, quite sizable, conquering party led by Guatemalan Governor Pedro de Alvarado.

Cantor's theory of transfinite numbers was originally regarded as so counter-intuitive — even shocking — that it encountered resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig Wittgenstein raised philosophical objections.

While there he is said to have encountered a statue of Alexander the Great, and realized with dissatisfaction he was now at an age when Alexander had the world at his feet, while he had achieved comparatively little.

While searching for the energy of the Black Lantern simultaneously dispatching various Doomsday ' clones ' created from the original to distract Earth's heroes by sending them after the other members of the Superman family with the aid of a robotic duplicate of Lois Lane created to give him an honest opinion on his actions, Luthor encountered Brainiac in space while attempting to alter the last of the Black Lantern energy, acting upon an unspoken theory of his.

Living in cities, workers encountered material goods such as they had never seen while in the village.

These were more suitable for the mixed conditions encountered while snowboarding mainly off-piste, but having to get back to ski lifts on packed snow.

However, vertical cavers have often encountered longer stalactites while exploring.

The most frequently encountered trombones are the tenor trombone and bass trombone, while the E alto trombone became less common as tenor technique extended the upper range of that instrument, but is now enjoying a resurgence as the importance of its lighter sonority in many classical and early romantic works is appreciated.

He encountered advanced liberal religious thought while completing his studies at the University of Leiden in Holland for the ministry of the Dutch Reformed Church in Cape Town.

The value of the method lies in the fact that specific design problems, once encountered, are never seen again because they are immediately eliminated, while the parts that appear successful are tested over and over.

It may be that a " Lord Marcus Sandys, ex-Governor of Bengal " encountered it while in India under the Honourable East India Company in the 1830s, and commissioned the local apothecaries to recreate it.

In 1937, while researching folklore in Haiti, Zora Neale Hurston encountered the case of a woman who appeared in a village, and a family claimed she was Felicia Felix-Mentor, a relative who had died and been buried in 1907 at the age of 29.

* 1736: Europeans encountered rubber – the discovery was made by Charles-Marie de la Condamine while on expedition in South America.

Also, Zawinski criticizes several language and library deficiencies he encountered while programming in Java, precisely an overhead of certain classes but also a lack of features such as C-like assertions and typedefs.

According to Heyerdahl, something happened between Admiral Roggeveen's discovery of the island in 1722 and James Cook's visit in 1774 ; while Roggeveen encountered white, Indian, and Polynesian people living in relative harmony and prosperity, Cook encountered a much smaller population consisting mainly of Polynesians and living in privation.

Forster's attitude brought him into conflict with people of different nations he encountered and made him welcome nowhere, as he was too revolutionary and antinational for Germans, proud and opposing in his dealings with Englishmen, too unconcerned about Polish science for Poles, and too insignificant politically and ignored while in France.

When the binary encountered Neptune, it interacted in such a way that orbital energy was transferred from Triton to its companion ; the latter was expelled, while Triton became bound to Neptune.

The spin cast reel is an attempt to solve the problem of backlash found in bait cast designs, while reducing line twist and snare complaints sometimes encountered with traditional spinning reel designs.

Violaceous Trogons will consume wasps and wasp larvae encountered while digging nests.