共查询到20条相似文献,搜索用时 984 毫秒
1.
B. Simon 《Functional Analysis and Its Applications》2007,41(2):143-153
We show that the parameters a n , b n of a Jacobi matrix have a complete asymptotic expansion , where 1 < |µj| < R for j ? K(R) and all R, if and only if the Jost function, u, written in terms of z (where E = z + z ?1) is an entire meromorphic function. We relate the poles of u to the µj’s.
相似文献
$a_n^2 - 1 = \sum\limits_{k = 1}^{K(R)} {p_k (n)\mu _k^{ - 2n} + O(R^{ - 2n} ),} b_n = \sum\limits_{k = 1}^{K(R)} {p_k (n)\mu _k^{ - 2n + 1} + O(R^{ - 2n} )} $
2.
Zhanmin Zhu 《Czechoslovak Mathematical Journal》2018,68(2):455-474
Let R be a ring. A subclass T of left R-modules is called a weak torsion class if it is closed under homomorphic images and extensions. Let T be a weak torsion class of left R-modules and n a positive integer. Then a left R-module M is called T-finitely generated if there exists a finitely generated submodule N such that M/N ∈ T; a left R-module A is called (T,n)-presented if there exists an exact sequence of left R-modules such that F0,..., Fn?1 are finitely generated free and Kn?1 is T-finitely generated; a left R-module M is called (T,n)-injective, if Ext n R (A,M) = 0 for each (T, n+1)-presented left R-module A; a right R-module M is called (T,n)-flat, if Tor R n (M,A) = 0 for each (T, n+1)-presented left R-module A. A ring R is called (T,n)-coherent, if every (T, n+1)-presented module is (n + 1)-presented. Some characterizations and properties of these modules and rings are given.
相似文献
$$0 \to {K_{n - 1}} \to {F_{n - 1}} \to \cdots \to {F_1} \to {F_0} \to M \to 0$$
3.
Let a be a regular element of a ring R. If either K:=r R (a) has the exchange property or every power of a is regular, then we prove that for every positive integer n there exist decompositionswhere \(Y_{n} \subseteq a^{n}R\) and E n ?R/a R. As applications we get easier proofs of the results that a strongly π-regular ring has stable range one and also that a strongly π-regular element whose every power is regular is unit-regular.
相似文献
$$R_{R} = K \oplus X_{n} \oplus Y_{n} = E_{n} \oplus X_{n} \oplus aY_{n}, $$
4.
Khachatur A. Khachatryan Emilya A. Khachatryan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2007,42(3):161-175
The paper looks for the solutions of integro-differential equations of the form in the class of functions which are absolutely continuous and of slow growth on ?. It is assumed that A and B are nonnegative parameters, 0 ≤ g ∈ L 1 (?), 0 ≤ k ∈ L 1 (?), ∫? k(x) dx = 1 and 0 ≤ λ(x) ≤ 1 is a measurable function in ?. The equation is solved by a special factorization of the corresponding integro-differential operator in combination with appropriately modified standard methods of the theory of convolution type integral equations.
相似文献
$ - \frac{{d\varphi }}{{dx}} + A\varphi (x) = g(x) + B\int_\mathbb{R} {k(x - t)\lambda (t)\varphi (t)dt, x \in \mathbb{R}} $
5.
The system where v = C*x is an output, u = S*y is a control, A(·) ∈ R n × n , B(·) ∈ R n × (n–p), C ∈ R n × (n–p), and D ∈ R n × (n–p), is considered. The elements αij(·) and βij(·) of the matrices A(·) and B(·) are arbitrary functionals satisfying the conditions It is assumed that A(·) ∈ Z 1 ∪ Z 3 and A*(·) ∈ Z 1 ∪ Z 3, where Z 1 is the class of matrices in which the first p elements of the kth superdiagonal are sign-definite and the elements above them are sufficiently small. The class Z 3 differs from Z t1 in that the elements between this superdiagonal and the (k + 1)th row are sufficiently small. If k > p, then the elements of the p × p square in the upper left corner of the matrix are sufficiently small as well. By using special quadratic Lyapunov functions, a matrix D for which y(t)–x(t) → 0 exponentially as t → ∞ is first found, and then a matrix S for which the vectors x(t) and y(t) have the same property is constructed.
相似文献
$$\frac{{dx}}{{dt}} = A\left( \cdot \right)x + B\left( \cdot \right)u,{\kern 1pt} \frac{{dy}}{{dt}} = A\left( \cdot \right)y + B\left( \cdot \right)u + D\left( {C*y - v} \right)$$
$$\mathop {\sup }\limits_{\left( \cdot \right)} |{\alpha _{ij}}\left( \cdot \right)| < \infty \left( {i,j \in 1,n} \right),\mathop {\sup }\limits_{\left( \cdot \right)} |{\beta _{ij}}\left( \cdot \right)| < \infty \left( {i \in 1,n,j \in 1,n - p} \right).$$
6.
Esteban Andruchow 《Complex Analysis and Operator Theory》2016,10(6):1383-1409
An idempotent operator E in a Hilbert space \({\mathcal {H}}\) \((E^2=1)\) is written as a \(2\times 2\) matrix in terms of the orthogonal decomposition (R(E) is the range of E) as We study the sets of idempotents that one obtains when \(E_{1,2}:R(E)^\perp \rightarrow R(E)\) is a special type of operator: compact, Fredholm and injective with dense range, among others.
相似文献
$$\begin{aligned} {\mathcal {H}}=R(E)\oplus R(E)^\perp \end{aligned}$$
$$\begin{aligned} E=\left( \begin{array}{l@{\quad }l} 1_{R(E)} &{} E_{1,2} \\ 0 &{} 0 \end{array} \right) . \end{aligned}$$
7.
We establish that the reducibility exponent (Differentsial’nye Uravneniya, 2007, vol. 43, no. 2, pp. 191–202) of each linear system , with piecewise continuous bounded coefficient matrix A does not belong to the set of values of σ for which the perturbed system (1A+Q) with an arbitrary piecewise continuous perturbation Q satisfying the condition \(\overline {\lim } _{t \to + \infty } t^{ - 1} \ln \left\| {Q(t)} \right\| \leqslant - \sigma \) is reducible to the original system (1 A ) by some Lyapunov transformation.
相似文献
$$\dot x = A(t)x, x \in \mathbb{R}^n , t \geqslant 0$$
8.
Let K be the Calderón-Zygmund convolution kernel on R~d(d≥2).Christ and Journé defined the commutator associated with K and a∈L~∞(R~d)by T_af(x)=p.v.∫_(R~d)K(x-y)m_x,y~a·f(y)dy,which is an extension of the classical Calderón commutator. In this paper, we show that T_a is weighted weak type(1,1) bounded with A,1 weight for d≥2. 相似文献
9.
Let L be a Schrdinger operator of the form L =-? + V acting on L~2(R~n), n≥3, where the nonnegative potential V belongs to the reverse Hlder class B_q for some q≥n. Let BMO_L(R~n) denote the BMO space associated to the Schrdinger operator L on R~n. In this article, we show that for every f ∈ BMO_L(R~n) with compact support, then there exist g ∈ L~∞(R~n) and a finite Carleson measure μ such that f(x) = g(x) + S_(μ,P)(x) with ∥g∥∞ + |||μ|||c≤ C∥f∥BMO_L(R~n), where S_(μ,P)=∫(R_+~(n+1))Pt(x,y)dμ(y, t),and Pt(x, y) is the kernel of the Poisson semigroup {e-~(t(L)~(1/2))}t0 on L~2(R~n). Conversely, if μ is a Carleson measure, then S_(μ,P) belongs to the space BMO_L(R~n). This extends the result for the classical John-Nirenberg BMO space by Carleson(1976)(see also Garnett and Jones(1982), Uchiyama(1980) and Wilson(1988)) to the BMO setting associated to Schrdinger operators. 相似文献
10.
S. A. Modina 《Russian Mathematics (Iz VUZ)》2009,53(4):31-33
In this paper we study the three-element functional equation , subject to We assume that the coefficients G(z) and g(z) are holomorphic in R and their boundary values G +(t) and g +(t) belong to H(Γ), G(t)G(t ?1) = 1. We seek for solutions Φ(z) in the class of functions holomorphic outside of \(\bar R\) such that they vanish at infinity and their boundary values Φ?(t) also belong to H(Γ). Using the method of equivalent regularization, we reduce the problem to the 2nd kind integral Fredholm equation.
相似文献
$(V\Phi )(z) \equiv \Phi (iz) + \Phi ( - iz) + G(z)\Phi \left( {\frac{1}{z}} \right) = g(z), z \in R,$
$R: = \{ z:\left| z \right| < 1, \left| {\arg z} \right| < \frac{\pi }{4}\} .$
11.
Luis Dubarbie 《Positivity》2010,14(4):695-703
For metric spaces X and Y, normed spaces E and F, and certain subspaces A(X, E) and A(Y, F) of vector-valued continuous functions, we obtain a complete characterization of linear and bijective maps \({T:A(X,E)\rightarrow A(Y,F)}\) preserving common zeros, that is, maps satisfying the propertyfor any \({f, g \in A(X, E)}\), where \({Z(f) = \{x \in X: f(x) = 0\}}\). Moreover, we provide some examples of subspaces for which the automatic continuity of linear bijections having the property (P) is derived.
相似文献
$Z(f) \cap Z(g) \neq \emptyset \Longleftrightarrow Z(Tf) \cap Z(Tg) \neq \emptyset \quad\quad\quad{\rm (P)}$
12.
We obtain conditions for the existence and uniqueness of an optimal control for the linear nonstationary operator-differential equation with a quadratic performance criterion. The operators A(t) and B(t) are closed and may have nontrivial kernels. The results are applied to differential-algebraic equations and to partial differential equations that do not belong to the Cauchy-Kowalewskaya type.
相似文献
$\frac{d}{{dt}}[A(t)y(t)] + B(t)y(t) = K(t)u(t) + f(t)$
13.
Luc Guyot 《Archiv der Mathematik》2017,108(4):357-363
Let R be a unital commutative ring, and let M be an R-module that is generated by k elements but not less. Let \(\text {E}_n(R)\) be the subgroup of \(\text {GL}_n(R)\) generated by the elementary matrices. In this paper we study the action of \(\text {E}_n(R)\) by matrix multiplication on the set \(\text {Um}_n(M)\) of unimodular rows of M of length \(n \ge k\). Assuming R is moreover Noetherian and quasi-Euclidean, e.g., R is a direct product of finitely many Euclidean rings, we show that this action is transitive if \(n > k\). We also prove that \(\text {Um}_k(M) /\text {E}_k(R)\) is equipotent with the unit group of \(R/\mathfrak {a}_1\) where \(\mathfrak {a}_1\) is the first invariant factor of M. These results encompass the well-known classification of Nielsen non-equivalent generating tuples in finitely generated Abelian groups. 相似文献
14.
Let R be a noncommutative ring. Two epimorphisms from R to totally ordered division rings are called equivalent if there exists an order-preserving isomorphism ? : (D 1, ? 1) → (D 2, ? 2) satisfying ? ° α 1 = α 2. In this paper we study the real epi-spectrum of R, defined to be the set of all equivalence classes (with respect to this relation) of epimorphisms from R to ordered division rings. We show that it is a spectral space when endowed with a natural topology and prove a variant of the Artin-Lang homomorphism theorem for finitely generated tensor algebras over real closed division rings.
相似文献
$$\alpha_{i}:R\to (D_{i},\leqslant_{i}),\quad i = 1,2 $$
15.
Basudeb Dhara 《Czechoslovak Mathematical Journal》2018,68(1):95-119
Let R be a noncommutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, let F, G and H be three generalized derivations of R, I an ideal of R and f(x1,..., x n ) a multilinear polynomial over C which is not central valued on R. If for all r = (r1,..., r n ) ∈ I n , then one of the following conditions holds:
相似文献
$$F(f(r))G(f(r)) = H(f(r)^2 )$$
- (1)there exist a ∈ C and b ∈ U such that F(x) = ax, G(x) = xb and H(x) = xab for all x ∈ R
- (2)there exist a, b ∈ U such that F(x) = xa, G(x) = bx and H(x) = abx for all x ∈ R, with ab ∈ C
- (3)there exist b ∈ C and a ∈ U such that F(x) = ax, G(x) = bx and H(x) = abx for all x ∈ R
- (4)f(x1,..., x n )2 is central valued on R and one of the following conditions holds
- (a)there exist a, b, p, p’ ∈ U such that F(x) = ax, G(x) = xb and H(x) = px + xp’ for all x ∈ R, with ab = p + p’
- (b)there exist a, b, p, p’ ∈ U such that F(x) = xa, G(x) = bx and H(x) = px + xp’ for all x ∈ R, with p + p’ = ab ∈ C.
- (a)
16.
The uncertain system is considered, where the coefficients a ij (n) of the m×m matrix A n are functionals of any nature subject to the constraints
Such systems include, in particular, switched-type systems, whose matrix A can take values in a given finite set.By using a special Lyapunov function, a bound δ ≤ δ(α0,α*) ensuring the global asymptotic stability of the system is found. In particular, the system is stable if the last inequality is replaced by a i,j (n) = 0 for j < i.It is shown that pulse-width modulated systems reduce to the uncertain systems under consideration; moreover, in the case of a pulse-width modulation of the first kind, the coefficients of the matrix A are functions of x(n), and in the case of a modulation of the second kind, they are functionals. 相似文献
$x_{n + 1} = A_n x_n , n = 0,1,2, \ldots ,$
$\begin{array}{*{20}c} {\left| {a_{i,i} (n)} \right| \leqslant \alpha _ * < 1,} \\ {\left| {a_{i,j} (n)} \right| \leqslant \alpha _0 for j \geqslant i + 1,} \\ {\left| {a_{i,j} (n)} \right| \leqslant \delta for j < i.} \\ \end{array} $
17.
Huaxin Lin 《Mathematische Zeitschrift》2009,263(4):903-922
Let C be a unital AH-algebra and A be a unital simple C*-algebras with tracial rank zero. It has been shown that two unital monomorphisms \({\phi, \psi: C\to A}\) are approximately unitarily equivalent if and only ifwhere T(A) is the tracial state space of A. In this paper we prove the following: Given \({\kappa\in KL(C,A)}\) with \({\kappa(K_0(C)_+\setminus\{0\})\subset K_0(A)_+\setminus\{0\}}\) and with κ([1 C ]) = [1 A ] and a continuous affine map \({\lambda: T(A)\to T_{\mathfrak f}(C)}\) which is compatible with κ, where \({T_{\mathfrak f}(C)}\) is the convex set of all faithful tracial states, there exists a unital monomorphism \({\phi: C\to A}\) such thatfor all \({c\in C_{s.a.}}\) and \({\tau\in T(A).}\) Denote by \({{\rm Mon}_{au}^e(C,A)}\) the set of approximate unitary equivalence classes of unital monomorphisms. We provide a bijective mapwhere KLT(C, A)++ is the set of compatible pairs of elements in KL(C, A)++ and continuous affine maps from T(A) to \({T_{\mathfrak f}(C).}\) Moreover, we found that there are compact metric spaces X, unital simple AF-algebras A and \({\kappa\in KL(C(X), A)}\) with \({\kappa(K_0(C(X))_+\setminus\{0\})\subset K_0(A)_+\setminus\{0\}}\) for which there is no homomorphism h: C(X) → A so that [h] = κ.
相似文献
$ [\phi]=[\psi]\quad {\rm in}\quad KL(C,A)\quad {\rm and}\quad \tau\circ \phi=\tau\circ \psi \quad{\rm for\, all}\tau\in T(A),$
$[\phi]=\kappa\quad{\rm and}\quad \tau\circ \phi(c)=\lambda(\tau)(c)$
$\Lambda: {\rm Mon}_{au}^e (C,A)\to KLT(C,A)^{++},$
18.
We consider some class of non-linear systems of the form where A(·) ∈ ? n × n , A i (·) ∈ ? n × n , b(·) ∈ ? n , whose coefficients are arbitrary uniformly bounded functionals.
$\dot x = A( \cdot )x + \sum\limits_{i = 1}^l {A_i ( \cdot )x(t - \tau _i (t)) + b( \cdot )u} ,$
A special type of the Lyapunov-Krasovskii functional is used to synthesize dynamic control described by the equation where ρ(·) ∈ ?1, m(·) ∈ ? n , which makes the system globally asymptotically stable. Also, the situation is considered where the control u enters into the system not directly but through a pulse element performing an amplitude-frequency modulation.
相似文献
$\dot u = \rho ( \cdot )u + (m( \cdot ),x),$
19.
The Automorphism Group of a Class of Nilpotent Groups with Infinite Cyclic Derived Subgroups 下载免费PDF全文
The automorphism group of a class of nilpotent groups with infinite cyclic derived subgroups is determined. Let G be the direct product of a generalized extraspecial Z-group E and a free abelian group A with rank m, where E ={(1 kα_1 kα_2 ··· kα_nα_(n+1) 0 1 0 ··· 0 α_(n+2)...............000...1 α_(2n+1)000...01|αi∈ Z, i = 1, 2,..., 2 n + 1},where k is a positive integer. Let AutG G be the normal subgroup of Aut G consisting of all elements of Aut G which act trivially on the derived subgroup G of G, and AutG/ζ G,ζ GG be the normal subgroup of Aut G consisting of all central automorphisms of G which also act trivially on the center ζ G of G. Then(i) The extension 1→ Aut_(G') G→ AutG→ Aut(G')→ 1 is split.(ii) Aut_(G') G/Aut_(G/ζ G,ζ G)G≌Sp(2 n, Z) ×(GL(m, Z)■(Z~)m).(iii) Aut_(G/ζ G,ζ GG/Inn G)≌(Z_k)~(2n)⊕(Z)~(2nm). 相似文献
20.
In recent years, it has become popular to realize Boolean functions by combinational circuits. In many cases, the further use of the scheme constructed requires its geometric realization, i.e., a certain embedding in one or another specific geometric structure. The role of such structure is often played by the unit n-dimensional cube.In this paper, we consider quasihomeomorphic embeddings of combinational circuits in hypercubes such that the nodes of the scheme go into vertices of the hypercube and bundles of arcs go into similar bundles or the so-called transition trees of the hypercube having no common internal vertices.
Let B be a finite complete basis of functional elements and R B(n) be the minimum dimension of a hypercube such that, for any function f(x 1, …, x n ) of Boolean logic, there is a certain scheme of functional elements in basis B realizing f(x 1, …, x n ) which can be quasihomeomorphically embedded in this cube. The main result of this work consists in derivation of the following estimates:
Here, c B and c′B are basis-dependent constants. 相似文献
$n - \log \log (n) - c_B \leqslant R_B (n) \leqslant n - \log \log (n) + c'_B .$