共查询到20条相似文献,搜索用时 15 毫秒
1.
Dinh Van Huynh 《Journal of Pure and Applied Algebra》2008,212(1):9-13
Let R be a prime ring and e∈R be an idempotent. We show that eRR is nonsingular, CS and if and only if is nonsingular, CS and . 相似文献
2.
Michael Bartl 《Journal of Mathematical Analysis and Applications》2007,328(1):730-742
Let n?2, Sn−1 be the unit sphere in Rn. For 0?α<1, m∈N0, 1<p?2, and Ω∈L∞(Rn)×Hr(Sn−1) with (where Hr is the Hardy space if r?1 and Hr=Lr if 1<r<∞), we study the singular integral operator, for r?1, defined by
3.
Jaeyoung Byeon 《Journal of Differential Equations》2008,244(10):2473-2497
Let Ω be a bounded domain in Rn, n?3, with the boundary ∂Ω∈C3. We consider the following singularly perturbed nonlinear elliptic problem on Ω
4.
We consider the elliptic equation -Δu+u=0 in a bounded, smooth domain Ω in R2 subject to the nonlinear Neumann boundary condition . Here ?>0 is a small parameter. We prove that any family of solutions u? for which ?∫∂Ωeu is bounded, develops up to subsequences a finite number m of peaks ξi∈∂Ω, in the sense that as ?→0. Reciprocally, we establish that at least two such families indeed exist for any given m?1. 相似文献
5.
Marcus Wagner 《Journal of Mathematical Analysis and Applications》2009,355(2):606-619
Assume that K⊂Rnm is a convex body with o∈int(K) and is a function with f|K∈C0(K,R) and f|(Rnm?K)≡+∞. We show that its lower semicontinuous quasiconvex envelope
6.
Let X1,X2,…,Xq be a system of real smooth vector fields satisfying Hörmander's rank condition in a bounded domain Ω of Rn. Let be a symmetric, uniformly positive definite matrix of real functions defined in a domain U⊂R×Ω. For operators of kind
7.
Brett A. Tangedal 《Journal of Number Theory》2007,124(2):291-313
Let F be a real quadratic field and m an integral ideal of F. Two Stark units, εm,1 and εm,2, are conjectured to exist corresponding to the two different embeddings of F into R. We define new ray class invariants and associated to each class C+ of the narrow ray class group modulo m and dependent separately on the two different embeddings of F into R. These invariants are defined as a product of special values of the double sine function in a compact and canonical form using a continued fraction approach due to Zagier and Hayes. We prove that both Stark units εm,1 and εm,2, assuming they exist, can be expressed simultaneously and symmetrically in terms of and , thus giving a canonical expression for every existent Stark unit over F as a product of double sine function values. We prove that Stark units do exist as predicted in certain special cases. 相似文献
8.
Yuan Zhou 《Journal of Mathematical Analysis and Applications》2011,382(2):577-593
The author establishes some geometric criteria for a Haj?asz-Sobolev -extension (resp. -imbedding) domain of Rn with n?2, s∈(0,1] and p∈[n/s,∞] (resp. p∈(n/s,∞]). In particular, the author proves that a bounded finitely connected planar domain Ω is a weak α-cigar domain with α∈(0,1) if and only if for some/all s∈[α,1) and p=(2−α)/(s−α), where denotes the restriction of the Triebel-Lizorkin space on Ω. 相似文献
9.
Let H be a separable Hilbert space with an orthonormal basis {en/n∈N}, T be a bounded tridiagonal operator on H and Tn be its truncation on span ({e1, e2, … , en}). We study the operator equation Tx = y through its finite dimensional truncations Tnxn = yn. It is shown that if and are bounded, then T is invertible and the solution of Tx = y can be obtained as a limit in the norm topology of the solutions of its finite dimensional truncations. This leads to uniform boundedness of the sequence . We also give sufficient conditions for the boundedness of and in terms of the entries of the matrix of T. 相似文献
10.
Daniel Simson 《Journal of Pure and Applied Algebra》2011,215(1):13-34
Integral quadratic forms q:Zn→Z, with n≥1, and the sets Rq(d)={v∈Zn;q(v)=d}, with d∈Z, of their integral roots are studied by means of mesh translation quivers defined by Z-bilinear morsifications bA:Zn×Zn→Z of q, with Z-regular matrices A∈Mn(Z). Mesh geometries of roots of positive definite quadratic forms q:Zn→Z are studied in connection with root mesh quivers of forms associated to Dynkin diagrams An,Dn,E6,E7,E8 and the Auslander-Reiten quivers of the derived category Db(R) of path algebras R=KQ of Dynkin quivers Q. We introduce the concepts of a Z-morsification bA of a quadratic form q, a weighted ΦA-mesh of vectors in Zn, and a weighted ΦA-mesh orbit translation quiver Γ(Rq,ΦA) of vectors in Zn, where Rq?Rq(1) and ΦA:Zn→Zn is the Coxeter isomorphism defined by A. The existence of mesh geometries on Rq is discussed. It is shown that, under some assumptions on the morsification bA:Zn×Zn→Z, the set admit a ΦA-orbit mesh quiver , where ΦA:Zn→Zn is the Coxeter isomorphism defined by A. Moreover, splits into three infinite connected components , , and , where are isomorphic to a translation quiver Z⋅Δ, with Δ an extended Dynkin quiver, and has the shape of a sand-glass tube. 相似文献
11.
M. Hickel 《Journal of Pure and Applied Algebra》2010,214(5):634-645
Let (A,mA,k) be a local noetherian ring and I an mA-primary ideal. The asymptotic Samuel function (with respect to I) : A?R∪{+∞} is defined by , ∀x∈A. Similarly, one defines, for another ideal J, as the minimum of as x varies in J. Of special interest is the rational number . We study the behavior of the asymptotic Samuel function (with respect to I) when passing to hyperplane sections of A as one does for the theory of mixed multiplicities. 相似文献
12.
Reinhard Farwig Hermann Sohr 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1459-1465
There are only very few results on the existence of unique local in time strong solutions of the Navier-Stokes equations for completely general domains Ω⊆R3, although domains with edges and corners, bounded or unbounded, are very important in applications. The reason is that the Lq-theory for the Stokes operator A is available in general only in the Hilbert space setting, i.e., with q=2. Our main result for a general domain Ω is optimal in a certain sense: Consider an initial value and a zero external force. Then the condition is sufficient and necessary for the existence of a unique local strong solution u∈L8(0,T;L4(Ω)) in some interval [0,T), 0<T≤∞, with u(0)=u0, satisfying Serrin’s condition . Note that Fujita-Kato’s sufficient condition u0∈D(A1/4) is strictly stronger and therefore not optimal. 相似文献
13.
Nicu?or Costea 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):4271-4278
We study the problem in Ω, u=0 on ∂Ω, where Ω is a bounded domain in RN, is a continuous function and λ and ε are two positive constants. We prove that for any ε>0 each λ∈(0,λ1) is an eigenvalue of the above problem, where λ1 is the principal eigenvalue of the Laplace operator on Ω. Moreover, for each eigenvalue λ∈(0,λ1) it corresponds a unique eigenfunction. The proofs will be based on the Banach fixed point theorem combined with adequate variational techniques. 相似文献
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15.
Tomasz Piasecki 《Journal of Differential Equations》2010,248(8):2171-2198
We investigate a steady flow of a viscous compressible fluid with inflow boundary condition on the density and inhomogeneous slip boundary conditions on the velocity in a cylindrical domain Ω=Ω0×(0,L)∈R3. We show existence of a solution , p>3, where v is the velocity of the fluid and ρ is the density, that is a small perturbation of a constant flow (, ). We also show that this solution is unique in a class of small perturbations of . The term u⋅∇w in the continuity equation makes it impossible to show the existence applying directly a fixed point method. Thus in order to show existence of the solution we construct a sequence (vn,ρn) that is bounded in and satisfies the Cauchy condition in a larger space L∞(0,L;L2(Ω0)) what enables us to deduce that the weak limit of a subsequence of (vn,ρn) is in fact a strong solution to our problem. 相似文献
16.
Zhi-Wei Sun 《Journal of Number Theory》2007,124(1):57-61
By some extremely simple arguments, we point out the following:
- (i)
- If n is the least positive kth power non-residue modulo a positive integer m, then the greatest number of consecutive kth power residues mod m is smaller than m/n.
- (ii)
- Let OK be the ring of algebraic integers in a quadratic field with d∈{−1,−2,−3,−7,−11}. Then, for any irreducible π∈OK and positive integer k not relatively prime to , there exists a kth power non-residue ω∈OK modulo π such that .
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19.
Robert B. Ellis 《Discrete Mathematics》2008,308(19):4446-4459
A binary code with covering radius R is a subset C of the hypercube Qn={0,1}n such that every x∈Qn is within Hamming distance R of some codeword c∈C, where R is as small as possible. For a fixed coordinate i∈[n], define to be the set of codewords with a b in the ith position. Then C is normal if there exists an i∈[n] such that for any v∈Qn, the sum of the Hamming distances from v to and is at most 2R+1. We newly define what it means for an asymmetric covering code to be normal, and consider the worst-case asymptotic densities ν*(R) and of constant radius R symmetric and asymmetric normal covering codes, respectively. Using a probabilistic deletion method, and analysis adapted from previous work by Krivelevich, Sudakov, and Vu, we show that and , giving evidence that minimum size constant radius covering codes could still be normal. 相似文献
20.
Hernán Castro 《Journal of Differential Equations》2009,246(8):2991-3037
We consider the elliptic equation −Δu+u=0 in a bounded, smooth domain Ω in R2, subject to the nonlinear Neumann boundary condition . Here p>1 is a large parameter. We prove that given any integer m?1 there exist at least two families of solutions up developing exactly m peaks ξi∈∂Ω, in the sense that , as p→∞. 相似文献