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

We generalize several inequalities involving powers of the numerical radius for off-diagonal part of $2\times2$ operator matrices of the form $T=\left[\begin{array}{cc} 0&B, C&0 \end{array}\right]$, where $B, C$ are two operators. In particular, if $T=\left[\begin{array}{cc} 0&B, C&0 \end{array}\right]$, then we get \begin{align*} {1\over 2^{{3\over2}(r-1)}}\max\{ \| \mu \|, \| \eta \| \} \leq w^{r}(T)\leq \frac{1}{2^{r+1}} \max\{ \| \mu \|, \| \eta \| \}, \end{align*} where $r\geq 2$ and $ \mu=|(C-B^{*})+i(C+B^{*})|^{r}+|(B^{*}-C)+i(C+B^{*})|^{r}$, $ \eta=|(B-C^{*})+i(B+C^{*})|^{r}+|(C^{*}-B)+i(B+C^{*})|^{r}$.

Some generalizations of numerical radius on off-diagonal part of $2\times 2$ operator matrices

The Callebaut inequality says thatwhere are positive invertible operators, and and are an operator mean and its dual in the sense of Kabo and Ando, respectively. In this paper we employ the Mond–Pecaric method as well as some operator techniques to establish a complementary inequality to the above one under mild conditions. We also present some refinements of a Callebaut-type inequality involving the weighted geometric mean and Hadamard products of Hilbert space operators.

Complementary and refined inequalities of callebaut inequality for operators

In this paper, we show some refinements of generalized numerical radius inequalities involving the Young and Heinz inequalities. In particular, we present 
\begin{align*} w_{p}^{p}(A_{1}^{*}T_{1}B_{1},...,A_{n}^{*}T_{n}B_{n})\leq\frac{n^{1-\frac{1}{r}}}{2^{\frac{1}{r}}}\Big\|\sum_{i=1}^{n}[B_{i}^{*} f^{2}(|T_{i}|)B_{i}]^{rp}+[A_{i}^{*}g^{2}(|T_{i}^{*}|)A_{i}]^{rp}\Big\|^{\frac{1}{r}} -\inf_{\|x\|=1}\eta(x), \end{align*} where $T_{i}, A_{i}, B_{i} \in {\mathbb B}({\mathscr H})\,\,(1\leq i\leq n)$, $f$ and $g$ are nonnegative continuous functions on $[0, \infty)$ satisfying $f(t)g(t)=t$ for all $t\in [0, \infty)$, $p, r\geq 1$, $N\in {\mathbb N}$ and \begin{align*} \eta(x)= \frac{1}{2}\sum_{i=1}^{n}\sum_{j=1}^{N} \Big(\sqrt[2^{j}]{ \langle (A_{i}^{*}g^{2}(|T_{i}^{*}|)A_{i})^{p}x, x\rangle^{2^{j-1}-k_{j}} \langle (B_{i}^{*} f^{2}(|T_{i}|)B_{i})^{p}x, x\rangle^{k_j}}\quad-\sqrt[2^{j}]{ \langle (B_{i}^{*}f^{2}(|T_{i}|)B_{i})^{p}x, x\rangle^{k_{j}+1} \langle (A_{i}^{*} g^{2}(|T_{i}^{*}|)A_{i})^{p}x, x\rangle^{2^{j-1}-k_{j}-1}}\Big)^{2}. 
\end{align*}

Further refinements of generalized numerical radius inequalities for Hilbert space operators

We give an estimation for the eigenvalues of matrix power functions. In particular, it has been shown that $$\lambda({(A+B)^p})\leq\lambda({2^{p-1}}({A^p}+{B^p}-\gamma I))\;(P \geq2)$$
 for all positive semi-definite matrices A, B, where γ is a positive constant. This provides a sharper bound for the known estimation for eigenvalues.

A New Estimation for Eigenvalues of Matrix Power Functions

Motivated by some recently established operator Jensen-type inequalities related to a usual convexity, in the present paper we derive several more accurate operator Jensen-type inequalities for certain subclasses of convex functions. More precisely, we obtain interpolating series of Jensen-type inequalities for log-convex and non-negative superquadratic functions. In particular, we obtain the corresponding refinements of the Jensen-Mercer operator inequality for such classes of functions.

Mojtaba Bakherad

Papers

Some generalizations of numerical radius on off-diagonal part of $2\times 2$ operator matrices

Complementary and refined inequalities of callebaut inequality for operators

Further refinements of generalized numerical radius inequalities for Hilbert space operators

A New Estimation for Eigenvalues of Matrix Power Functions

Interpolating operator Jensen-type inequalities for log-convex and superquadratic functions