The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on rea...The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on real reflexive Banach spaces, as well as the approximation in a neighborhood of zero, of solutions of a feedback system [A,B] assumed to be non-linear, by solutions of another linear, This approximation allows us to obtain appropriate estimates of the solutions. These estimates have a significant effect on the study of the robust stability and sensitivity of such a system see <a href="#ref1">[1]</a> <a href="#ref2">[2]</a> <a href="#ref3">[3]</a>. We then consider a linear FS <img src="Edit_4629d4d0-bbb2-478d-adde-391efde3d1e0.bmp" alt="" />, and prove that, if <img src="Edit_435aae08-e821-4b4d-99d2-e2a2b47609c1.bmp" alt="" />;<img src="Edit_4fa030bc-1f97-4726-8257-ca8d00657aac.bmp" alt="" /> , with <img src="Edit_63ab4faa-ba40-45fe-8b8a-7a6caef91794.bmp" alt="" />the respective solutions of FS’s [A,B] and <img src="Edit_e78e2e6d-8934-4011-93eb-8b7eb52fa856.bmp" alt="" /> corresponding to the given (u,v) in <img src="Edit_0e18433c-8c7a-454f-8eec-6eb9fb69469a.bmp" alt="" /> . There exists,<img src="Edit_3dcd8afc-8cea-4c06-a920-e4148a5f793e.bmp" alt="" />, positive real constants such that, <img src="Edit_edb88446-3e39-4fe0-865a-114de701e78e.bmp" alt="" />. These results are the subject of theorems 3.1, <span style="font-size:10.0pt;font-family:;" "="">... </span>, 3.3. The proofs of these theorems are based on our lemmas 3.2, <span style="font-size:10.0pt;font-family:;" "="">... </span>, 3.5, devoted according to the hypotheses on A and B, to the existence of the inverse of the operator <em>I+BA</em> and <img src="Edit_2db1326b-cb5b-44cf-8d1f-df22bd6da45f.bmp" alt="" />. The results obtained and demonstrated along this document, present an extension in general Banach space of those in <a href="#ref4">[4]</a> on a Hilbert space <em>H</em> and those in <a href="#ref5">[5]</a> on a extended Hilbert space <img src="Edit_b70ce337-1812-4d4b-ae7d-a24da7e5b3cf.bmp" alt="" />.展开更多
We investigate the adjoints of linear fractional composition operators C ? acting on classical Dirichlet space D(B N ) in the unit ball B N of ? N , and characterize the normality and essential normality of C ? on D(B...We investigate the adjoints of linear fractional composition operators C ? acting on classical Dirichlet space D(B N ) in the unit ball B N of ? N , and characterize the normality and essential normality of C ? on D(B N ) and the Dirichlet space modulo constant function D 0(B N ), where ? is a linear fractional map ? of B N . In addition, we also show that for any non-elliptic linear fractional map ? of B N , the composition maps σ o ? and ? o σ are elliptic or parabolic linear fractional maps of B N .展开更多
The maximum of k numerical functions defined on , , by , ??is used here in Statistical classification. Previously, it has been used in Statistical Discrimination [1] and in Clustering [2]. We present first some theore...The maximum of k numerical functions defined on , , by , ??is used here in Statistical classification. Previously, it has been used in Statistical Discrimination [1] and in Clustering [2]. We present first some theoretical results on this function, and then its application in classification using a computer program we have developed. This approach leads to clear decisions, even in cases where the extension to several classes of Fisher’s linear discriminant function fails to be effective.展开更多
文摘The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on real reflexive Banach spaces, as well as the approximation in a neighborhood of zero, of solutions of a feedback system [A,B] assumed to be non-linear, by solutions of another linear, This approximation allows us to obtain appropriate estimates of the solutions. These estimates have a significant effect on the study of the robust stability and sensitivity of such a system see <a href="#ref1">[1]</a> <a href="#ref2">[2]</a> <a href="#ref3">[3]</a>. We then consider a linear FS <img src="Edit_4629d4d0-bbb2-478d-adde-391efde3d1e0.bmp" alt="" />, and prove that, if <img src="Edit_435aae08-e821-4b4d-99d2-e2a2b47609c1.bmp" alt="" />;<img src="Edit_4fa030bc-1f97-4726-8257-ca8d00657aac.bmp" alt="" /> , with <img src="Edit_63ab4faa-ba40-45fe-8b8a-7a6caef91794.bmp" alt="" />the respective solutions of FS’s [A,B] and <img src="Edit_e78e2e6d-8934-4011-93eb-8b7eb52fa856.bmp" alt="" /> corresponding to the given (u,v) in <img src="Edit_0e18433c-8c7a-454f-8eec-6eb9fb69469a.bmp" alt="" /> . There exists,<img src="Edit_3dcd8afc-8cea-4c06-a920-e4148a5f793e.bmp" alt="" />, positive real constants such that, <img src="Edit_edb88446-3e39-4fe0-865a-114de701e78e.bmp" alt="" />. These results are the subject of theorems 3.1, <span style="font-size:10.0pt;font-family:;" "="">... </span>, 3.3. The proofs of these theorems are based on our lemmas 3.2, <span style="font-size:10.0pt;font-family:;" "="">... </span>, 3.5, devoted according to the hypotheses on A and B, to the existence of the inverse of the operator <em>I+BA</em> and <img src="Edit_2db1326b-cb5b-44cf-8d1f-df22bd6da45f.bmp" alt="" />. The results obtained and demonstrated along this document, present an extension in general Banach space of those in <a href="#ref4">[4]</a> on a Hilbert space <em>H</em> and those in <a href="#ref5">[5]</a> on a extended Hilbert space <img src="Edit_b70ce337-1812-4d4b-ae7d-a24da7e5b3cf.bmp" alt="" />.
基金supported by National Natural Science Foundation of China (Grant Nos. 10671141, 10371091)
文摘We investigate the adjoints of linear fractional composition operators C ? acting on classical Dirichlet space D(B N ) in the unit ball B N of ? N , and characterize the normality and essential normality of C ? on D(B N ) and the Dirichlet space modulo constant function D 0(B N ), where ? is a linear fractional map ? of B N . In addition, we also show that for any non-elliptic linear fractional map ? of B N , the composition maps σ o ? and ? o σ are elliptic or parabolic linear fractional maps of B N .
文摘The maximum of k numerical functions defined on , , by , ??is used here in Statistical classification. Previously, it has been used in Statistical Discrimination [1] and in Clustering [2]. We present first some theoretical results on this function, and then its application in classification using a computer program we have developed. This approach leads to clear decisions, even in cases where the extension to several classes of Fisher’s linear discriminant function fails to be effective.
