다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since then, a tremendous amount of work has appeared. Much of it has to do with the construction of stellar models with different equations of state applying in different zones. Other parts deal with the effects of varying chemical composition, with pulsation and tidal and rotational distortion of stars, and with the precise relations between the interior and the atmosphere of a star. The striking feature of all this work is that so much can be done without assuming any particular mechanism of stellar energy-generation. Only such very comprehensive assumptions are made about the distribution and behaviour of the energy sources that we may expect future knowledge of their mechanism to lead mainly to more detailed results within the framework of the existing general theory. An Introduction to the Study of Stellar Structure By S. Chandrasekhar. (Astrophysical Monographs sponsored by The Astrophysical Journal.) Pp. ix+509. (Chicago: University of Chicago Press; London: Cambridge University Press, 1939.) 50s. net.

An Introduction to the Study of Stellar Structure

Formally we have arrived at the middle of the book. So you may need a pause for recovering, a pause which we want to fill up by some fixed point theorems supplementing those which you already met or which you will meet in later chapters. The first group of results centres around Banach’s fixed point theorem. The latter is certainly a nice result since it contains only one simple condition on the map F, since it is so easy to prove and since it nevertheless allows a variety of applications. Therefore it is not astonishing that many mathematicians have been attracted by the question to which extent the conditions on F and the space Ω can be changed so that one still gets the existence of a unique or of at least one fixed point. The number of results produced this way is still finite, but of a statistical magnitude, suggesting at a first glance that only a random sample can be covered by a chapter or even a book of the present size. Fortunately (or unfortunately?) most of the modifications have not found applications up to now, so that there is no reason to write a cookery book about conditions but to write at least a short outline of some ideas indicating that this field can be as interesting as other chapters. A systematic account of more recent ideas and examples in fixed point theory should however be written by one of the true experts. Strange as it is, such a book does not seem to exist though so many people are puzzling out so many results.

Fixed Point Theory

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Infinite Abelian Groups

Abstract The Berezin transform Ã of an operator A, acting on the reproducing kernel Hilbert space ℋ = ℋ (Ω) over some (non-empty) set Ω, is defined by Ã(λ) = 〉Aǩ λ, ǩ λ〈 (λ ∈ Ω), where k⌢λ=kλ‖ kλ ‖ ${\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\frown$}}\\over k} _\\lambda } = {{{k_\\lambda }} \\over {\\left\\| {{k_\\lambda }} \\right\\|}}$ is the normalized reproducing kernel of ℋ. The Berezin number of an operator A is defined by ber(A)=supλ∈Ω| A˜(λ) |=supλ∈Ω| 〈 Ak⌢λ,k⌢λ 〉 | ${\\bf{ber}}{\\rm{(}}A) = \\mathop {\\sup }\\limits_{\\lambda \\in \\Omega } \\left| {\\tilde A(\\lambda )} \\right| = \\mathop {\\sup }\\limits_{\\lambda \\in \\Omega } \\left| {\\left\\langle {A{{\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\frown$}}\\over k} }_\\lambda },{{\\mathord{\\buildrel{\\lower3pt\\hbox{$\\scriptscriptstyle\\frown$}}\\over k} }_\\lambda }} \\right\\rangle } \\right|$ . In this paper, we prove some Berezin number inequalities. Among other inequalities, it is shown that if A, B, X are bounded linear operators on a Hilbert space ℋ, then ber(AX±XA)⩽ber12(A*A+AA*)ber12(X*X+XX*) $${\\bf{ber}}(AX \\pm XA) \\leqslant {\\bf{be}}{{\\bf{r}}^{{1 \\over 2}}}\\left( {A*A + AA*} \\right){\\bf{be}}{{\\bf{r}}^{{1 \\over 2}}}\\left( {X*X + XX*} \\right)$$ and ber2(A*XB)⩽‖ X ‖2ber(A*A)ber(B*B). $${\\bf{be}}{{\\bf{r}}^2}({A^*}XB) \\leqslant {\\left\\| X \\right\\|^2}{\\bf{ber}}({A^*}A){\\bf{ber}}({B^*}B).$$ We also prove the multiplicative inequality ber(AB)⩽ber(A)ber(B) $${\\bf{ber}}(AB){\\bf{ber}}(A){\\bf{ber}}(B)$$

/pdf/berezin-number-inequalities-for-operators-4w81fsjsi4.pdf

Berezin number inequalities for operators

Let be positive definite matrices. We present several reverse Heinz-type inequalities, in particularwhere is an arbitrary matrix, is Hilbert–Schmidt norm and . We also establish a Heinz-type inequality involving Hadamard product of the formin which and is a unitarily invariant norm.

Reverses and variations of Heinz inequality

We present some reverse Young-type inequalities for the Hilbert-Schmidt norm as well as any unitarily invariant norm. Furthermore, we give some inequalities dealing with operator means. More precisely, we show that if $A, B\in {\mathfrak B}(\mathcal {H})$ are positive operators and $r\geq 0$, $A\nabla _{-r}B+2r(A\nabla B-A\sharp B)\leq A\sharp _{-r}B$. We also prove that equality holds if and only if $A=B$. In addition, we establish several reverse Young-type inequalities involving trace, determinant and singular values. In particular, we show that if $A$ and $B$ are positive definite matrices and $r\geq 0$, then $\label {reverse_trace} \mbox {tr\,}((1+r)A-rB)\leq \mbox {tr}|A^{1+r}B^{-r} |-r( \sqrt {\mbox {tr\,} A} - \sqrt {\mbox {tr} B})^{2}$.

/pdf/reverse-young-type-inequalities-for-matrices-and-operators-4pesal0j5l.pdf

Reverse Young-type inequalities for matrices and operators

In this article, we establish some upper bounds for numerical radius inequalities, including those of 2×2 operator matrices and their off-diagonal parts. Among other inequalities, it is shown that if T=[0XY0], then ωr(T)≤2r−2‖f2r(|X|)+g2r(|Y∗|)‖12‖f2r(|Y|)+g2r(|X∗|)‖12 and ωr(T)≤2r−2‖f2r(|X|)+f2r(|Y∗|)‖12‖g2r(|Y|)+g2r(|X∗|)‖12, where X,Y are bounded linear operators on a Hilbert space H, r≥1, and f, g are nonnegative continuous functions on [0,∞) satisfying the relation f(t)g(t)=t (t∈[0,∞)). Moreover, we present some inequalities involving the generalized Euclidean operator radius of operators T1,…,Tn.

Upper bounds for numerical radius inequalities involving off-diagonal operator matrices

/pdf/some-generalizations-of-numerical-radius-on-off-diagonal-58zqzhsqpp.pdf

Mojtaba Bakherad

Papers

Berezin number inequalities for operators

Reverses and variations of Heinz inequality

Reverse Young-type inequalities for matrices and operators

Upper bounds for numerical radius inequalities involving off-diagonal operator matrices

Some generalizations of numerical radius on off-diagonal part of 2 × 2 operator matrices