With the nonlinear component, Fermi expected energy in one mode to transfer gradually to other modes, and eventually, to be distributed equally among all modes.

With the addition theorems above and for a given k with 0 < k < 1 they therefore are solutions to the following nonlinear ordinary differential equations:

With regard to the mechanism of electric conduction, it is strongly believed that nonlinear excitations in the form of solitons play a role.

* " With feeling profound concern, grief, indignation, am compelled disclose Bahá ' í world recent developments Holy Land furnishing further incontestable proof relationship established old and new Covenant-breakers demonstrating increasing boldness, marked, tragic decline in character and spiritual condition grandchildren ` Abdu ' l-Bahá.

With his solid linguistic background, Sapir became the one student of Boas to develop most completely the relationship between linguistics and anthropology.

With the other two original X-Men, Cyclops and Phoenix, Bobby has a little brother-big brother / sister relationship, with the latter being much more pleasant.

With a goal of determining broad patterns of relationship, the issue was not to get every word right but to detect patterns.

With the band living in a Manchester flat, he had a relationship with a girl named Tracy who bore him a son, Paul Inder, although it would not be until the boy was six that Lemmy had any involvement with him.

In her memoir about her parents, With a Daughter's Eye, Mary Catherine Bateson implies that the relationship between Benedict and Mead was partly sexual.

With no movie theaters nearby, her first relationship with cinema was watching movies on Betamax.

With the end of the war, the priority of allied unity was replaced with a new challenge, the nature of the relationship between the two emerging superpowers.

With this, " the Lords ' decision heralded an end to a relationship that had developed throughout the sixteenth and seventeenth centuries between the State and the Company of Stationers ", ending both nascent publishers ' copyright and the existing system of censorship.

With her better nature overcome, the she-wolf devours each of her own children, then her relatives ' children in order of relationship, and finally the children of strangers.

With the usurpation of the Sicilian throne from Conradin by Manfred of Sicily in 1258, the relationship between the Papacy and the Hohenstaufen had changed again.

With his power over northern and central Italy secured, Otto I sought to clarify his relationship with the Byzantine Empire in the East.

With Nothing in Common ( 1986 ) – about a young man alienated from his parents who must re-establish a relationship with his father, played by Jackie Gleason – Hanks began to establish the credentials of not only a comic actor but of someone who could carry a serious role.

With respect to celestial X-ray sources, X-ray astrophysics tends to focus on the physical reason for X-ray brightness, whereas X-ray astronomy tends to focus on their classification, order of discovery, variability, resolvability, and their relationship with nearby sources in other constellations.

With the assistance of software applications and web based relationship oriented systems such as LinkedIn, these kinds of organizations are expected to provide its members with a way to keep track of the number of their relationships, meetings designed to boost the strength of each relationship using group dynamics, executive retreats and networking events as well as training in how to reach out to higher circles of influential people.

With his mother ’ s death in 1917, his fondest relationship ended and he fell into a “ horrible despair ”, adding to his ill health and the general gloom over the suffering endured by the people of his country during the war.

With Lady Douglas Sheffield, a young widow of the Howard family, he had a serious relationship from about 1569.

With his relationship with Uni over and Love Unlimited contract-bound with the label, White was able to switch both his production deal and the group to 20th Century Records.

With regard to the potential for exposure to chemicals in the workplace and MCS, the U. S. Occupational Safety and Health Administration ( OSHA ) has indicated MCS is highly controversial and there is insufficient scientific evidence to explain the relationship between the theorized causes of MCS and its symptoms.

With this new relationship came an attempt at cross-promotion, with attractions based on ABC shows at Disney parks and an annual soap festival at Walt Disney World.

With his relationship with Maud unraveling, Whistler suddenly proposed to and married Beatrice (" Trixie ") Godwin ( née Beatrix Birnie Philip ), a former pupil and the former wife of his architect Edward William Godwin, who had died two years earlier.

With Soviet Ambassador Dobrynin, Kissinger maintained a special relationship that completely bypassed the Department of State and Secretary Rogers.

With Odysseus sitting beside Eumaeus and Telemachus, the audience is especially aware of this relationship.

With the March pickup, dealers are optimistic that the April-June quarter will equal or top last year.

* 1990s: With the Yamada and Kojima household chain stores appearing throughout the suburban outskirts of Tokyo, the sale of consumer durables at Akihabara was greatly reduced, but the sale of computer goods increased in equal measure.

With its emphasis on notions of social contract and the collective will of the people, democracy can also be characterized as a form of political collectivism because it is defined as a form of government in which all eligible citizens have an equal say in the decisions that affect their lives.

With us of course it is the Judeo-Christian concept, but it must be a religion with all men created equal.

With the aid of Albrecht von Roon's army reorganization, the Prussian army was nearly equal in numbers to the Austrian army.

With each legion having 5, 120 legionaries usually supported by an equal number of auxiliary troops, the total force available to a legion commander during the Pax Romana probably ranged from 11, 000 downwards, with the more prestigious legions and those stationed on hostile borders or in restive provinces tending to have more auxiliaries.

With Tesla's salary of $ 18 per week, the payment would have amounted to over 53 years ' pay and the amount was equal to the initial capital of the company.

With the passage of the Statute of Westminster in 1931, the Union was considered equal in status to the other Dominions, and the United Kingdom could no longer legislate on behalf of South Africa.

With the advent of the Renaissance, the Polish language was finally accepted on an equal footing with Latin.

With his commissions, Zaharoff bought shares in Maxim ’ s company until he was able to tell Maxim that he was no longer an employee but an equal shareholder.

With its extensive underwater scenes and languid score ( as with nearly all of Luc Besson's films the soundtrack was composed by Eric Serra ), the film has been both praised as beautiful and serene, and in equal measure criticized as being too drawn out, overly reflective and introspective.

With the establishment of the democracy, the assembly became the de jure mechanism of government ; all citizens had equal privileges in the assembly.

With the necessary tribute grain shipments of 4 million shi ( one shi equal to 107 liters ) to the north each year, both processes became incredibly inefficient.

With Wilson's 1918 proclamation of the Fourteen Points, whose fifth point proclaimed: " A free, open-minded, and absolutely impartial adjustment of all colonial claims, based upon a strict observance of the principle that in determining all such questions of sovereignty the interests of the populations concerned must have equal weight with the equitable claims of the government whose title is to be determined ", some Algerian intellectuals — dubbed oulémas began to nurture the desire for independence or, at least, autonomy and self-rule.

With the support of both Opposition parties and Labour rebel MPs on 29 April 2009, a Liberal Democrat motion that all Gurkhas be offered an equal right of residence was passed, allowing Gurkhas who served before 1997 residence in the UK.

With this variation, the original special attribute of the 7 is transferred to the 9 card, so playing a 9 means that the next play needs to be equal or lower than 9.

With equal parts regret and relief, the Jane's Addiction experiment is at an end.

With a properly positioned tracheal tube, equal bilateral breath sounds will be heard upon listening to the chest with a stethoscope, and no sound upon listening to the area over the stomach.

With the actual rate equal to it, inflation is stable, neither accelerating nor decelerating.

With the exception of a few ' drinks ' for associates, the loot was split into 17 equal shares of around £ 150, 000 each ( George Hatherill claims that there were 18 shares ).

With open-end funds, the value is precisely equal to the NAV.

With a constant equal to the ambient light and a constant equal to the diffusion reflection.