共查询到20条相似文献,搜索用时 31 毫秒
1.
R. Ger 《Aequationes Mathematicae》2000,60(3):268-282
Summary. Quite recently C. Alsina, P. Cruells and M. S. Tomás [2], motivated by F. Suzuki's property of isosceles trapezoids, have proposed the following orthogonality relation in a real normed linear space (X, ||·||) (X, \Vert \cdot \Vert) : two vectors x,y ? X x,y \in X are T-orthogonal whenever¶||z-x ||2 + ||z-y ||2 = ||z ||2 + ||z-(x+y) ||2 \Vert z-x \Vert^2 + \Vert z-y \Vert^2 = \Vert z \Vert^2 + \Vert z-(x+y) \Vert^2 ¶for every z ? X z \in X . A natural question arises whether an analogue of T-orthogonality may be defined in any real linear space (without a norm structure). Our proposal reads as follows. Given a functional j \varphi on a real linear space X we say that two vectors x,y ? X x,y \in X are j \varphi -orthogonal (and write x^jy x\perp_{\varphi}y ) provided that Dx,yj = 0 \Delta_{x,y}\varphi = 0 (Dh1,h2 \Delta_{h_1,h_2} stands here and in the sequel for the superposition Dh1 °Dh2 \Delta_{h_1} \circ \Delta_{h_2} of the usual difference operators).¶We are looking for necessary and/or sufficient conditions upon the functional j \varphi to generate a j \varphi -orthogonality such that the pair X,^j X,\perp_{\varphi} forms an orthogonality space in the sense of J. Rätz (cf. [6]). Two new characterizations of inner product spaces as well as a generalization of some results obtained in [2] are presented. 相似文献
2.
It is proved that all wild z-automorphisms including the well-known Nagata automorphism (all wild z-coordinates including the Nagata coordinates, respectively) of the polynomial algebra F[x, y, z] over an arbitrary field F cannot be lifted to a z-automorphism (z-coordinate, respectively) of the free associative algebra Fáx,y,z?{F\langle x,y,z\rangle}. The proof is based on the following two new results, which have their own interests: degree estimate of Q*FFáx1,?,xn?{{Q*_FF\langle x_1,\ldots,x_n\rangle}} and tameness of the automorphism group AutQ(Q*FFáx,y?){{{\rm Aut}_Q(Q*_FF\langle x,y\rangle)}}. The structure of the group of all z-automorphisms of the free associative algebra Fáx,y,z?{F\langle x,y,z\rangle} over an arbitrary field F is also determined. 相似文献
3.
Václav Tryhuk 《Czechoslovak Mathematical Journal》2000,50(3):499-508
The paper describes the general form of an ordinary differential equation of the second order which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form
f( t,uy,wy + uuz ) = f( x,y,z )u2 u+ g( t,x,u,u,w )uz + h( t,x,u,u,w )y + 2uwzf\left( {t,\upsilon y,wy + u\upsilon z} \right) = f\left( {x,y,z} \right)u^2 \upsilon + g\left( {t,x,u,\upsilon ,w} \right)\upsilon z + h\left( {t,x,u,\upsilon ,w} \right)y + 2uwz 相似文献
4.
We establish necessary and sufficient conditions under which a sequence x
0 = y
0 , x
n+1 = Ax
n
+ y
n+1 , n ≥ 0, is bounded for each bounded sequence
{ yn :n \geqslant 0 } ì { x ? èn = 1¥ D( An ) |supn \geqslant 0 || An x || < ¥ }\left\{ {y_n :n \geqslant 0} \right\} \subset \left\{ {\left. {x \in \bigcup\nolimits_{n = 1}^\infty {D\left( {A^n } \right)} } \right|\sup _{n \geqslant 0} \left\| {A^n x} \right\| < \infty } \right\}, where A is a closed operator in a complex Banach space with domain of definition D(A) . 相似文献
5.
J. B. Lasserre 《TOP》2012,20(1):119-129
We consider the semi-infinite optimization problem:
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