인공고관절의 세라믹 볼 헤드의 기계적 안정성 평가를 위한 3 차원 유한요소 해석

第12次 아시아ㆍ太平洋 矯政局長會議 參加記

A hilbert space problem book

Functional equations in several variables

We present a survey of some selected recent developments (results and methods) in the theory of Ulam's type stability In particular we provide some information on hyperstability and the fixed point methods

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On Some Recent Developments in Ulam's Type Stability

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Nonlinear Lie-type derivations of von Neumann algebras and related topics

Let $m,n\ge 2$ be positive integers, $M_m$ the set of $m\times m$ complex matrices and $M_n$ the set of $n\times n$ complex matrices. Regard $M_{mn}$ as the tensor space $M_m\otimes M_n$. Suppose $|\cdot|$ is the Ky Fan $k$-norm with $1 \le k \le mn$, or the Schatten $p$-norm with $1 \le p \le \infty$ ($p\ne 2$) on $M_{mn}$. It is shown that a linear map $\phi: M_{mn} \rightarrow M_{mn}$ satisfying $$|A\otimes B| = |\phi(A\otimes B)|$$ for all $A \in M_m$ and $B \in M_n$ if and only if there are unitary $U, V \in M_{mn}$ such that $\phi$ has the form $A\otimes B \mapsto U(\varphi_1(A) \otimes \varphi_2(B))V$, where $\varphi_i(X)$ is either the identity map $X \mapsto X$ or the transposition map $X \mapsto X^t$. The results are extended to tensor space $M_{n_1} \otimes ... \otimes M_{n_m}$ of higher level. The connection of the problem to quantum information science is mentioned.

Linear preservers and quantum information science

Remarks on the stability of Lie homomorphisms

In this article, a brief survey of recent results on linear preserver problems and quantum information science is given. In addition, characterization is obtained for linear operators φ on mn × mn Hermitian matrices such that φ(A ⊗ B) and A ⊗ B have the same spectrum for any m × m Hermitian A and n × n Hermitian B. Such a map has the form A ⊗ B ↦ U(ϕ1(A) ⊗ ϕ2(B))U* for mn × mn Hermitian matrices in tensor form A ⊗ B, where U is a unitary matrix, and for j ∈ {1, 2}, ϕ j is the identity map X ↦ X or the transposition map X ↦ X t . The structure of linear maps leaving invariant the spectral radius of matrices in tensor form A ⊗ B is also obtained. The results are connected to bipartite (quantum) systems and are extended to multipartite systems.

We characterize the additive singularity preserving almost surjective maps on Mn(F), the algebra of all n × n matrices over a field F with char F = 0. We also describe additive invertibility preserving surjective maps on Mn(F) and give examples showing that all the assumptions in these two theorems are indispensable.

Ajda Fošner

Papers

Nonlinear Lie-type derivations of von Neumann algebras and related topics

Linear preservers and quantum information science

Remarks on the stability of Lie homomorphisms

Linear preservers and quantum information science

Additive Maps on Matrix Algebras Preserving Invertibility or Singularity