field of partial differential equations, Harnack's principle or Harnack's theorem is a corollary of Harnack's inequality which deals with the convergence...

theory. Harnack's inequality applied to harmonic functions. He also worked on the real algebraic geometry of plane curves, proving Harnack's curve theorem...

Arvid Falk Harnack (1913–1991), German anti-Nazi resistance fighter, film and stage director, brother of Arvid Harnack Harnack's principle This page lists...

or principle is a theorem with wide applicability (e.g. the law of large numbers, law of cosines, Kolmogorov's zero–one law, Harnack's principle, the...

Loeb, Peter; Walsh, Bertram (1965). "The equivalence of Harnack's principle and Harnack's inequality in the axiomatic system of Brelot". Annales de...

convergence. Non-probabilistic proofs were available earlier. The boundary Harnack principle is proved using Brownian motion (see also). Non-probabilistic proofs...

he meant Fish-Harnack's tactful approach to the Nazis' increasing incursion into the university in 1931 and 1932. By the time Fish-Harnack arrived in Giessen...

a bounded domain Ω. Then for every non-negative harmonic function u, Harnack's inequality sup V u ≤ C inf V u {\displaystyle \sup _{V}u\leq C\inf _{V}u}...

constant functions. In addition to these basic inequalities, one has Harnack's inequality, which states that positive harmonic functions on bounded domains...

Mathematics Institutions University of Zagreb Thesis Special classes of Excessive Functions Satisfying Harnack's Principle  (1990) Doctoral advisor Murali Rao...

members to find suitable lawyers. Falk Harnack's cousin, Klaus Bonhoeffer, was asked to represent the Harnacks but had refused. In the end, only four...

Li and Shing-Tung Yau discovered a new method for applying the maximum principle to control the solutions of the heat equation. Their results take the...

manner of life and his age, acknowledges one principle, but says that the prophecies are from an opposing principle, being led to this view by the responses...

Moser, Jürgen On Harnack's theorem for elliptic differential equations. Comm. Pure Appl. Math. 14 (1961), 577–591. Moser, Jürgen. A Harnack inequality for...

Their proof makes use of the maximum principle techniques which they had previously used to prove differential Harnack estimates.[CY75] Later they made use...

Ash Wednesday Supper, 1584), De la causa, principio et uno (On Cause, Principle and Unity, 1584), De l'infinito, universo et mondi (On the Infinite, Universe...

were used to account for historians' biases. Troeltsch's claim in the principle concludes that absolutes within history cannot exist. Troeltsch surmised...

accommodate Russian concerns that such a resolution would undermine the principle of state sovereignty. Russia, which holds a veto in the Security Council...

notes to the passages just cited, in Lightfoot's and in Gebhardt and Harnack's editions will be found references to other early writers who have used...

two principles but as from one single principle". It holds that the Father, as the "principle without principle", is the first origin of the Spirit, but...

man to 'living beings', forms the strongest argument for Harnack's hypothesis.": 697  "Harnack ... argued that Basil and all the Cappadocians interpreted...

and a Refutation of the Argument of Latomus, in which he expounded the principle of justification to Jacobus Latomus, an orthodox theologian from Louvain...

essence or divine nature-which alone is the principle of all things, besides which no other principle can be found. This reality neither begets nor...

church, often called the formal principle of the Reformation, and the doctrine of justification, the material principle of Lutheran theology. Lutheranism...

assuming f(x) is zero for some unit vector x and f(y) < 0 if |y| < 1. By Harnack's inequality applied to −f − f ( r x ) ≥ − 1 − r ( 1 + r ) n − 1 f ( 0 )...

narrator as narrative", p. 8 (2007). Society of Biblical Literature. "The principle essay in this regard is P. Vielhauer, 'On the "Paulinism" of Acts', in...

be included among those mysterious expressions discussed by Adolf von Harnack, "which belong to no known speech, and by their singular collocation of...

followers of Ritschl include Wilhelm Herrmann, Julius Kaftan and Adolf von Harnack. Catholic forms of theological liberalism have existed since the 19th century...

were to be removed from their posts. Regarding this as an affront to the principle of baptism, Martin Niemöller founded the Pfarrernotbund (Pastors' Emergency...

including the standard works of the Latter Day Saints movement and Divine Principle in the Unification Church. In antiquity, two schools of exegesis developed...