Raftul cu initiativa Book Archive


A Boundary Value Problem for equations whose order by Zainulabidova Z.M.

By Zainulabidova Z.M.

Translated from Differentsial'nye Uravneniya, Vol. forty, No. 10, 2004.

Show description

Read Online or Download A Boundary Value Problem for equations whose order degenerates along the perpendicular lines of change of type PDF

Best mathematics books


For seven years, Paul Lockhart’s A Mathematician’s Lament loved a samizdat-style recognition within the arithmetic underground, ahead of call for triggered its 2009 ebook to even wider applause and debate. An impassioned critique of K–12 arithmetic schooling, it defined how we shortchange scholars through introducing them to math the opposite direction.

Control of Coupled Partial Differential Equations

This quantity comprises chosen contributions originating from the ‘Conference on optimum regulate of Coupled structures of Partial Differential Equations’, held on the ‘Mathematisches Forschungsinstitut Oberwolfach’ in April 2005. With their articles, best scientists hide a extensive variety of subject matters corresponding to controllability, feedback-control, optimality platforms, model-reduction concepts, research and optimum keep watch over of circulation difficulties, and fluid-structure interactions, in addition to difficulties of form and topology optimization.

Basic Hypergeometric Series, Second Edition (Encyclopedia of Mathematics and its Applications)

This up-to-date variation will proceed to satisfy the desires for an authoritative entire research of the speedily transforming into box of uncomplicated hypergeometric sequence, or q-series. It comprises deductive proofs, workouts, and precious appendices. 3 new chapters were extra to this variation masking q-series in and extra variables: linear- and bilinear-generating features for uncomplicated orthogonal polynomials; and summation and transformation formulation for elliptic hypergeometric sequence.

Extra info for A Boundary Value Problem for equations whose order degenerates along the perpendicular lines of change of type

Sample text

Let p ∈ Z be a prime, let k > 0 be an integer, and let τ be a nonzero prime ideal of E such that p ∈ τ k ⊂ E(p) ⊂ E, and such that E(p)/τ k is a field. 5. Let [E(p)/τ k : Z/pZ] = e ≥ 1 and [E/τ : E(p)/τ k ] = f ≥ 1. Then [E/τ : Z/pZ] = ef ≥ 1, and Z/pZ-dim(τ/τ k ) = ef (k − 1) ≥ 0. 7. 6) occurs in the following natural way. Let p be a rational prime, let p ∈ τ ⊂ E be a prime ideal, and let k ≥ 1 an integer such that p ∈ τ k . Then E/τ is a field and E/τ k is a finite Z/pZ-algebra with Jacobson radical τ/τ k .

8, (u(E) + τ )/τ = 1. Since p > 2, u(E/τ ) = 1, so some element of u(E/τ ) does not lift to an element of u(E). This completes the proof. 10. Let E be an rtffr Dedekind domain with finite unit group. There are at most finitely many prime ideals τ ⊂ E and finitely many integers k > 0 such that τ k ∩ Z is a prime ideal in Z, and such that each unit of E/τ k lifts to a unit of E. Proof: Let card(u(E)) = m be finite. The set P = {primes p ∈ Z there are integers s > 0 and t ≥ 0 such that pst (ps − 1) ≤ m} is finite.

2 Analytic methods We link the power cancellation property to the sequence of rational primes. 1 as follows. Let k be an algebraic number field with E its ring of algebraic integers and with class number h(k). Let G be an rtffr abelian group with class number h(G). 14. 1. Let k be an algebraic number field, let [k : Q] = f , and let h(k) denote the class number of k. Let E be the ring of algebraic integers in k. Then E is a ring whose additive group (E, +) is a free abelian group of finite rank f .

Download PDF sample

Rated 4.89 of 5 – based on 24 votes