ON FUNCTIONAL TRANSFORMATION OF THE SEMI-HYPONORMAL OPERATORS

Let H be a complex separable Hilbert space. If T=UP is a bounded operator and \(P - PU{P^ * } = D(T) \ge 0\), where we always Suppose that U is nnitary and \(P \ge 0\)，then T is called semi-hypormal. For the bounded closed set E of the real line R we set \（S(E) = \left\{ {\left. \varphi \right|{K_\varphi }({x_1},{x_2}) = \frac{{\varphi ({x_1}) - \varphi ({x_2})}}{{{x_1} - {x_2}}}{\rm{is semipositive kernel of an integral operator in }}{L^2}(E)} \right\}\）, For the closed set E of the unit circle G±, we set \[\psi '(E) = \left\{ {\left. \varphi \right|{H_\varphi }(\xi ,\eta ) = \frac{{1 - \varphi (\xi )\bar \varphi (\eta )}}{{1 - \xi \bar \eta }} is semi-positive kernel of an integral operator in {L^2}(E)} \right\}\],We haye proved Theorem 1. Let T = UP be semi-hyponormal, \(\varphi \in \psi '(\sigma (U))\)，then \(\tilde T = \varphi (U)\) is also semi-Hyponormal； Theorem 2. Let T=UP be semi-hyponormal operator, \(\psi \in S([0,\left\| T \right\|])\) and \(\psi \) be positive valued. Then \(\tilde T = U\psi (P)\) is also semi-hyponormal. Theorem 3. Let T = UP be Semi-hypormal operator and \(\psi \) be soalar-funotion on \([0,\infty )\) .If \(\tilde T = U\psi (P)\) is а]яо Semi-hypomormal, then we have \[\begin{array}{l} \sigma (\tilde T) = {l_\psi }(\sigma (T)),\\left\| {D(T)} \right\| \le \frac{1}{\pi }{\psi ^{ - 1}}(r)d\theta \end{array}\] Theorem 4. Let T=UP be semi-hypormal operator and soalar-funotion \(\psi \in S([0,\left\| T \right\|])\)，then\(\tilde T = U\psi (P)\)is semi-hypormal and (1), (2)are valid.     

A NOTE ON THE RELATIVE CANONICAL IMAGE OF A NON－HYPERELLIPTIC FIBRATION OF GENUS 4

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Simple D[X,Y; σ,a]-modules

The article classifies simple modules over a generalized Weyl algebra of degree I with basis ring D that is a commutative domain with limited minimality condition.Translated from Ukrainskii Matematecheskii Zhurnal, Vol. 44, No. 12, pp. 1628–1644, December, 1992.     

THE TRANSFORMATION OF LANDSCAPE: MODELING POLICY AND SOCIAL IMPACTS ON THE AGRICULTURAL LANDSCAPE OF LESVOS

ABSTRACT. The term landscape is more and more used as an “umbrella‘ concept, covering a series of cultural, productive and ecological processes. In order to uncover mechanisms, monitor transformations and predict changes, a complicated set of interacting factors has to be taken into account. This paper presents a model for estimating social and policy impacts on agricultural landscapes, based on the assumption that agricultural landscapes are shaped at” macro “(landscape) level by” micro “interventions at farm level. The model consists of three parts: an” ecological processes “part, which deals with processes that shape the ecological and aesthetic value of a landscape, a” population dynamics “part, which examines farmer population dynamics and a” policy impact “part, which deals with direct or indirect impacts on farming systems and farmer dynamics and refers to CAP Rural Development Measures. The model is applied for the olive and graze land agricultural landscapes of Lesvos (Greece). Results, apart from revealing landscape change patterns; help to illustrate some mechanisms behind this change and indicate that Rural Development Measures are inherent with minor but important malfunctions that cannot lead to sustainable landscape management and rural development in the area.     

S-Noetherian Rings of the Forms 𝒜[X] and 𝒜[[X]]

Let 𝒜 = (A _n ) _n≥0 be an ascending chain of commutative rings with identity, S ? A ₀ a multiplicative set of A ₀, and let 𝒜[X] (respectively, 𝒜[[X]]) be the ring of polynomials (respectively, power series) with coefficient of degree i in A _i for each i ∈ ?. In this paper, we give necessary and sufficient conditions for the rings 𝒜[X] and 𝒜[[X]] to be S ? Noetherian.     

ON THE NECESSARY AND SUFFICI ENT CONDITIONS OF THE CONTINUITY OF M-P INVERSES A_x~+

Some necessary and sufficient conditions of the oontinuity of A_x~+ are given in [1] In this paper, some advances on the base and the condition of the oontinuity of A_~+ for Semi-Fredholm operators A_x are presented.     

ON THE QUOTIENT RING OF COMMUTATIVE RINGS WITH ACC^{\perp}ON ANNIHILATOR IDEALS.

The author concludes that every commutative ring with ascending chain condition an annihilator ideals has a Kasch quotient ring, which generalizes the Theorem^{[1]} that every commutative noetherian ring has a Kasch quosient ring. If follows that if R is a commutative ting with acc^{\perp}，then that Q(R) is semiprimary is equivalent to that it is perfect, or to that R satisfies regular condition. Besides, that Q(R) is quasi-frobenius equals that Q(R) is FPF or PF, and that Q(R) is artinian equals that R/N, are of finite dimension, i=1,2,\ldots,n. N_{i}=J^{i}\cap R.     

扩展的Boussinesq系统Lax对的Bäcklund变换和递推求解公式的导出

本文研究2+1维的扩展经典Boussinesq系统.首先,研究了系统的Lax对,找出了一个形式十分新颖的带有一个任意函数的Backlund变换.然后,又导出了Lax对的特征函数的生成公式.最后,利用Backlund变换和Lax对特征函数生成公式相结合得出了Lax对的递推求解公式.利用此递推公式,求出了一些Lax对的解.     

ON THE RECOVERY OF A CURVE ISOMETRICALLY IMMERSED IN E~n

It is known from classical differential geometry that one can reconstruct a curve with (n - 1) prescribed curvature functions, if these functions can be differentiated a certain number of times in the usual sense and if the first (n - 2) functions are strictly positive. It is established here that this result still holds under the assumption that the curvature functions belong to some Sobolev spaces, by using the notion of derivative in the distributional sense. It is also shown that the mapping which associates with such prescribed curvature functions the reconstructed curve is of class C∞.     

ISOLATED POINTS OF THE APPROXIMATE POINT SPECTRUM OF CERTAIN LATTICE HOMOMORPHISMS ON Co (X)

Abstract

Suppose X is a locally compact Hausdorff space and C (X) the apace of all continuous complex valued functions on X which vanish at infinity. Let T be a (complex) linear lattice homomorphism on C_o (X) whose adjoint is also a lattice homomorphism. It is sham that every non-zero isolated point of the approximate point spectrum of T lies in the point spectrum of T. An example is given to show that the exclusion of zero is necessary, even when X is compact. The same techniques are then used to show that if also the spectrum of T is finite then T can be written, in a natural manner, as a direct sum of two such lattice homomorphisms; one being an n'th root of an invertible multiplication operator and the other quasi-nilpotent.     

基于广义\mbox{\boldmath $Z_{4}$}线性Calderbank-McGuire码的对偶

本文讨论了广义Z4线性Calderbank-McGuire码的对偶的迹表示及2-adic表示, 同时给出了其最小Lee权估计.     

不包含{4,8,9}-圈的平面图是3-可染的

主要围绕Steinberg提出猜想:每个不包含4-圈和5-圈的平面图都是3-可染色的,对一些平面图类展开研究,提出要解决的问题:不包含{4,8,9}-圈的平面图是3-可染的.现从四个方面:不包含{4,8,9}-圈的平面图G的一些结构性质;不包含{4,8,9}-圈的平面图G中内部非分离6-圈的性质;不包含{4,8,9}-圈的平面图G不包含内部的6-面;f0不是一个6-面来证明结论,即不包含{4,8,9}-圈的平面图是3-可染的.     

算子代数∑(X,Y)的乘法连续性(Ⅰ)

算子代数∑（Ｘ，Ｙ）的乘法连续性（Ⅰ）卜庆营（哈尔滨工业大学数学系，１５０００１）李燕杰（大庆石油学院，黑龙江省安达市１５１４００）基金项目：国家自然科学基金资助课题．１９９２年４月２４日收到．本文设Ｘ，Ｙ是复数域上的两个线性空间，且（Ｘ，Ｙ）组成一...     

A CLASS OF HOMOGENEOUS LEFT INVARIANT OPERATORS ON THE NILPOTENT LIE GROUP G^{d+2}

This paper is devoted to a class of homogeneous left invariant operators L\ on the nilpotent Lie group G^{d+2} of the form $L-\lambda=-\sum\limits_{j=1}^d X_j^2-i\sum\limits_{m=1}^2 \lambda _m T_m,\lambda=\lambda_1,\lambda_2)\in C^2$ where {X_1,\cdots ,X_d,T_1, T_2} is a base of left invariant vector fields on G^{d+2}. With aid of harmonic analysis on nilpotent Lie groups and the method of increment operators, for all admissible L_\lambda, subelliptic estimate and an explicit inverse axe given and the hypoellipticity and the global solvability are obtained. Also, the structure of the set of admissible points \lambda is described exhaustively.     

ON J-SELFADJOINT EXTENSION OF THE PRODUCT OF TWO nTH-ORDER J-SYMMETRIC ORDINARY DIFFERENTIAL OPERATORS ON [a,b]

The problem of J-selfadjointness of the product of two nth-order J-symmetric operators on [a,b] is studied. We give a condition to ensure that the product operator is a J-selfadjoint extension.     

ON THE INADEQUACY OF THE RELATIONAL SEMANTIC FOR THE “UNTIL” OPERATOR

Modal logics with the binary operator Until are considered. It is shown that there exists a continuum of consistent U-logics without Kripke frames, and that each U-logic whose class of order does not have the finite frame property.     

ON THE TAYLOR'S JOINT SPECTRUM OF 2n-TUPLE (L_A, R_B)

Let A= (A_1, …, A_n) and B=(B_1, …, B_n) be double commuting n-tuples of operators on Hilbert space H and let L_(A_i), and R_(B_j), decode the left and right multiplications induced by A_i and B_j, respectively. The following results are proven: Sp (L_A, R_B)=Sp(A)×Sp(B), Sp_e(L_A, R_B)=Sp_e(A)×Sp(B) ∪ Sp(A)×Sp_e(B).     

THE IMPACTS OF MARINE RESERVES ON LIMITED‐ENTRY FISHERIES

ABSTRACT. We utilize a spatial bioeconomic model to investigate the impacts of creating reserves on limited‐entry fisheries. We find that reserve creation can produce win‐win situations where aggregate biomass and the common license (lease) price increase. These situations arise in biological systems where dispersal processes are prevalent and the fishery prior to reserve creation is operating at effort levels in a neighborhood of open‐access levels. We also illustrate that using strictly biological criteria for siting reserves (e.g., setting aside the most biological productive areas) will likely induce the most vociferous objections from the fishing industry. In general, we find that the dispersal rate and the degree the patches are connected play a significant role on the net impacts on the fishing sector.     

关于一类抛物型Monge-Ampère方程解的注记

本文讨论如下抛物型Monge-Ampere方程的第一初边值问题-ut+det1/nD2u=g(x,t),(x,t)∈Q=Ω×(0,T],u=ψ(z,t),(z,t)∈apQ,其中Ω为Rn中有界凸集.证明了在更一般的结构条件下[3,7]的结果仍然成立.证明中重要的一点是在Rn×R中非柱型域上"冻结问题"的可解性.     

矩阵方程X+A^{*}X^{-q}A=Q(q\geq 1)的Hermitian正定解

本文研究矩阵方程X A~*X~(-q)A=Q(q≥1)的Hermitian正定解,给出了存在正定解的充分条件和必要条件,构造了求解的迭代方法.最后还用数值例子验证了迭代方法的可行性和有效性.