The electrostatic potential can be expressed in terms of the inter-ionic separation and a constant ( Madelung constant ) that takes account of the geometry of the crystal.

** the Madelung constant for crystal structures held by ionic bonding

The Madelung constant being calculated for the NaCl ion labeled 0 in the expanding spheres method.

The Madelung constant shall allow for the calculation of the electric potential V < sub > i </ sub > of all ions of the lattice felt by the ion at position r < sub > i </ sub >

with being the ( dimensionless ) Madelung constant of the ith ion

Madelung said of hadith: " Work with the narrative sources, both those that have been available to historians for a long time and others which have been published recently, made it plain that their wholesale rejection as late fiction is unjustified and that with without a judicious use of them, a much more reliable and accurate portrait of the period can be drawn than has been realized so far.

It is the first member of the 6d-block ; in accordance with the Madelung rule, its electronic configuration should be 7s < sup > 2 </ sup > 5f < sup > 14 </ sup > 6d < sup > 1 </ sup >.

This configuration agrees with the Madelung energy ordering rule, which predicts that 4s is filled before 3d.

A formalism has been worked out for those piezoelectric crystals, for which the polarization is of the crystal-field induced type, that allows for the calculation of piezoelectrical coefficients from electrostatic lattice constants or higher-order Madelung constants.

Around this time Erwin Madelung also developed a hydrodynamic version of Schrödinger's equation which is incorrectly considered as a basis for the density current derivation of the de Broglie – Bohm theory.

This period is known to have a large number of exceptions to the Madelung rule.

Benign symmetric lipomatosis ( Madelung disease ) is another condition involving lipomatosis.

The quantum hydrodynamic equation is an equation in Bohmian mechanics, which, it turns out, has a mathematical relationship to classical fluid dynamics ( see Madelung equations ).

Wilferd Madelung has rejected the stance of indiscriminately dismissing everything not included in " early sources " and in this approach tendentious alone is no evidence for late origin.

It is named after Erwin Madelung, a German physicist.

This graph demonstrates the non-convergence of the expanding spheres method for calculating the Madelung Constant for NaCl as compared to the expanding cubes method, which is convergent.

The latter view is favored by contemporary academic scholar Madelung.

The Madelung synthesis is a chemical reaction that produces ( substituted or unsubstituted ) indoles by the intramolecular cyclization of N-phenylamides using strong base at high temperature.

Wilferd Ferdinand Madelung ( born 26 December 1930 ) is a scholar of Islam.

Pekka Pyykkö, for example, used computer modeling to calculate the positions of elements up to Z = 172, and found that several were displaced from the Madelung energy-ordering rule.

Pekka Pyykkö, for example, used computer modeling to calculate the positions of elements up to Z = 172, and found that several were displaced from the Madelung rule.

There occur as many Madelung constants in a crystal structure as ions occupy different lattice sites.

For example, for the ionic crystal NaCl, there arise two Madelung constants – one for Na and another for Cl.

In quantum chemistry they arise as solutions to chemical kinetic systems, in which case they are derived from the Schrödinger equation by way of Madelung equations.

* Hussein ibn ' Ali by Wilferd Madelung, an article of Encyclopædia Iranica.

Madelung notes other traditions suggesting that Hasan may have been poisoned by another wife, the daughter of Suhayl ibn Amr, or perhaps by one his servants and also cites the early historians ( Baladhuri, Waqidi, etc .).

* Hasan ibn ' Ali by Wilferd Madelung, In Encyclopædia Iranica

* AL-BAQER by Wilferd Madelung, an article in Encyclopædia Iranica

* Ali al-Hadi by Wilferd Madelung an article of Encyclopædia Iranica

According to The Succession to Muhammad by Wilferd Madelung, Senior Research Fellow at the Institute for Ismaili Studies in London, Umar later described the event as a falta, a precipitate arrangement ( p. 30 ).

* Ali ibn Husayn by Wilferd Madelung, an article in Encyclopædia Iranica

However, one recent publication, The Succession to Muhammad written by Institute for Ismaili Studies in London's researcher Wilfred Madelung, ex Laudian Professor of Arabic at the University of Oxford, examines the course of events from 632, and the death of Muhammad, through the rise of the Umayyads — and rehabilitates some of the Shia narratives.

The Shi ’ a and Institute for Shia Ismaili Studies in London's Shia ' ism researcher Wilferd Madelung believe that Malik was poisoned by Muawiyah I.

This was approximately 12 years after the probable advent of great saphenous vein stripping in 1844 by Madelung.

The Shi ’ a and Wilferd Madelung believe that Malik was poisoned by Muawiyah I.

* Madelung, Wilferd and Toby Mayer ( ed.

Contemporary Western scholars of hadith include: Herbert Berg, Fred M. Donner and Wilferd Madelung.

Madelung has immersed himself in the hadith literature and has made his own selection and evaluation of tradition.

The Madelung equations, being quantum Euler equations ( fluid dynamics ), differ philosophically from the de Broglie – Bohm mechanics and are the basis of the hydrodynamic interpretation of quantum mechanics.

The positions shown in the table above correspond to the assumption that the Madelung rule will continue to hold for higher atomic numbers ; this assumption may or may not be true.

However Umar himself was characteristically guarded about his own creation, Dr. Wilferd Madelung in his book The Succession to Muhammad summarising Umar's contribution:

All period 2 elements completely obey the Madelung rule ; in period 2s, lithium and beryllium fill the 2s subshell, and boron, carbon, nitrogen, oxygen, fluorine, and neon fill the 2p subshell.

According to Wilferd Madelung, Muhammad loved them and declared them as his Ahl al-Bayt very frequently.

Madelung believed that Hasan was poisoned and that the famous early Islamic historian al-Tabari suppressed the tale out of concern for the faith of the common people.

Examples of intramolecular reactions are the Smiles rearrangement, the Dieckmann condensation and the Madelung synthesis.

* Madelung, Wilferd.

In 1935, Georg Hans Madelung, a German engineer, professor, and aircraft designer, showed that a vehicle does not need a long tapered tail at high speeds.

Madelung, Wilferd -- The Succession to Muhammad, Cambridge University Press, 1997.