Theorem proving

In the paper "Liouville-type theorems for a quasilinear elliptic equation of the H´enon-type", We consider the H´enon-type quasilinear elliptic equation −Δmu = |x| aup where Δmu = div(|∇u| m−2∇u), m > 1, p>m − 1 and a ≥ 0. We are concerned with the Liouville property, i.e. the nonexistence of positive solutions in the whole space RN . We prove the optimal Liouville-type theorem for dimension N

13p runordie3 27-06-2022 7 3   Download

Objectives of research: The thesis is to give and prove some uniaueness theorems of the meromorphic functions f(z) on the complex plane which has hyperorder plane less than 1 share a part of the values with its f(z + c).

27p thebadguys 08-06-2021 15 4   Download

It is the objective of this paper to prove some xed point theorems for multivalued mappings. Among other things, we extend Theorem 1.3 to nonself-mappings. Also a simple proof of Theorem 1.3 is presented. Moreover, we give an armative answer to a question of Deimling. A negative answer to a question of Downing and Kirk is included as well.

14p larachdumlanat127 20-12-2020 7 2   Download

A problem being presented by us in [4] was "Is the Theorem 1.2 true for infinite topological spaces?". In this paper, we will solve the above problem by proving that Rational Squence Topological space is a T1-space, that has πgp-regularity but also non πgp-normality.

7p tamynhan8 04-11-2020 7 2   Download

The report proposes the concept of positive boolean dependency in the database model of block form, proving equivalent theorem of three derived types, necessary and sufficient criteria of the derived type, the member problem... In addition, some properties related to this concept in the case of block r degenerated into relation are also expressed and demonstrated here.

12p dieutringuyen 07-06-2017 39 2   Download

Formal methods mathematical languages, techniques and tools, used to specify and verify systems, goal is help engineers construct more reliable systems. Introduction to Formal Methodspresents about introduction; formal specification; formalformal verificationverification; model checking; theorem proving.

29p ngkhacvu 22-05-2015 71 6   Download

Đặc tả và kiểm chứng hình thức là một pha quan trọng nhằm nâng cao độ tin cậy và chất lượng của phần mềm. Có thể chia đặc tả phần mềm ra làm hai loại: đặc tả phi hình thức là đặc tả dựa trên ngôn ngữ tự nhiên và đặc tả hình thức là đặc tả dựa trên kiến trúc toán học. Đặc tả phi hình thức không được chặt chẽ bằng đặc tả hình thức nhưng được nhiều người biết và có thể dùng để trao đổi với nhau để làm chính xác hóa các điểm chưa rõ,...

4p banhbeovodung 20-06-2013 75 6   Download

The Devil said to Daniel Webster: "Set me a task I can't carry out, and I'll give you anything in the world you ask for." Daniel Webster: "Fair enough. Prove that for n greater than 2, the equation an + bn = cn has no non-trivial solution in the integers." They agreed on a three-day period for the labor, and the Devil disappeared. At the end of three days, the Devil presented himself, haggard, jumpy, biting his lip. Daniel Webster said to him, "Well, how did you do at my task? Did you prove the theorem?' "Eh? No . . . no, I haven't...

18p muathu_102 28-01-2013 50 3   Download

We introduce the notion of cotype of a metric space, and prove that for Banach spaces it coincides with the classical notion of Rademacher cotype. This yields a concrete version of Ribe’s theorem, settling a long standing open problem in the nonlinear theory of Banach spaces. We apply our results to several problems in metric geometry. Namely, we use metric cotype in the study of uniform and coarse embeddings, settling in particular the problem of classifying when Lp coarsely or uniformly embeds into Lq . We also prove a nonlinear analog of the Maurey-Pisier theorem, and use it to...

53p dontetvui 17-01-2013 65 8   Download

We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ingredients. The first is Szemer´di’s theorem, which ase serts that any subset of the integers of positive density contains progressions of arbitrary length. The second, which is the main new ingredient of this paper, is a certain transference principle. This allows us to deduce from Szemer´di’s e theorem that any subset of a sufficiently pseudorandom set (or measure) of positive relative density contains progressions of arbitrary length. ...

68p dontetvui 17-01-2013 46 6   Download

In this article we study several homology theories of the algebra E ∞ (X) of Whitney functions over a subanalytic set X ⊂ Rn with a view towards noncommutative geometry. Using a localization method going back to Teleman we prove a Hochschild-Kostant-Rosenberg type theorem for E ∞ (X), when X is a regular subset of Rn having regularly situated diagonals. This includes the case of subanalytic X. We also compute the Hochschild cohomology of E ∞ (X) for a regular set with regularly situated diagonals and derive the cyclic and periodic cyclic theories. ...

53p dontetvui 17-01-2013 47 7   Download

It is well known that not every orientation-preserving homeomorphism of the circle to itself is a conformal welding, but in this paper we prove several results which state that every homeomorphism is “almost” a welding in a precise way. The proofs are based on Koebe’s circle domain theorem. We also give a new proof of the well known fact that quasisymmetric maps are conformal weldings. 1. Introduction Let D ⊂ R2 be the open unit disk, let D∗ = S 2 \D and let T = ∂D = ∂D∗ be the unit circle. ...

45p dontetvui 17-01-2013 47 8   Download

We prove analogues for hypergraphs of Szemer´di’s regularity lemma and e the associated counting lemma for graphs. As an application, we give the first combinatorial proof of the multidimensional Szemer´di theorem of Furstenberg e and Katznelson, and the first proof that provides an explicit bound. Similar results with the same consequences have been obtained independently by Nagle, R¨dl, Schacht and Skokan. o 1.

51p noel_noel 17-01-2013 67 7   Download

The purpose of this paper is to prove that the stable homotopy category of algebraic topology is ‘rigid’ in the sense that it admits essentially only one model: Rigidity Theorem. Let C be a stable model category. If the homotopy category of C and the homotopy category of spectra are equivalent as triangulated categories, then there exists a Quillen equivalence between C and the model category of spectra. Our reference model is the category of spectra in the sense of Bousfield and Friedlander [BF, §2] with the stable model structure. The point of the rigidity theorem is that its...

28p noel_noel 17-01-2013 51 6   Download

We study the problem of conformally deforming a metric to a prescribed symmetric function of the eigenvalues of the Ricci tensor. We prove an existence theorem for a wide class of symmetric functions on manifolds with positive Ricci curvature, provided the conformal class admits an admissible metric. 1. Introduction Let (M n , g) be a smooth, closed Riemannian manifold of dimension n.

58p noel_noel 17-01-2013 52 6   Download

Let k be a local field, and Γ ≤ GLn (k) a linear group over k. We prove that Γ contains either a relatively open solvable subgroup or a relatively dense free subgroup. This result has applications in dynamics, Riemannian foliations and profinite groups. Contents 1. Introduction 2. A generalization of a lemma of Tits 3. Contracting projective transformations 4. Irreducible representations of non-Zariski connected algebraic groups 5. Proof of Theorem 1.3 in the finitely generated case 6. Dense free subgroups with infinitely many generators 7.

49p noel_noel 17-01-2013 55 7   Download

We settle an old question about the existence of certain ‘sums-of-squares’ formulas over a field F , related to the composition problem for quadratic forms. A classical theorem says that if such a formula exists over a field of characteristic 0, then certain binomial coefficients must vanish. We prove that this result also holds over fields of characteristic p

23p noel_noel 17-01-2013 49 7   Download

We prove the topological (or combinatorial) rigidity property for real polynomials with all critical points real and nondegenerate, which completes the last step in solving the density of Axiom A conjecture in real one-dimensional dynamics. Contents 1. Introduction 1.1. Statement of results 1.2. Organization of this work 1.3. General terminologies and notation 2. Density of Axiom A follows from the Rigidity Theorem 3. Derivation of the Rigidity Theorem from the Reduced Rigidity Theorem

94p noel_noel 17-01-2013 46 8   Download

Monopole Floer homology is used to prove that real projective three-space cannot be obtained from Dehn surgery on a nontrivial knot in the three-sphere. To obtain this result, we use a surgery long exact sequence for monopole Floer homology, together with a nonvanishing theorem, which shows that monopole Floer homology detects the unknot. In addition, we apply these techniques to give information about knots which admit lens space surgeries, and to exhibit families of three-manifolds which do not admit taut foliations. ...

91p noel_noel 17-01-2013 48 8   Download

We describe a Schubert induction theorem, a tool for analyzing intersections on a Grassmannian over an arbitrary base ring. The key ingredient in the proof is the Geometric Littlewood-Richardson rule of [V2]. As applications, we show that all Schubert problems for all Grassmannians are enumerative over the real numbers, and sufficiently large finite fields. We prove a generic smoothness theorem as a substitute for the Kleiman-Bertini theorem in positive characteristic.

25p noel_noel 17-01-2013 49 5   Download