By characterizing the bijections preserving orthogonality of idempotents in both directions on the infinite dimensional complete indefinite inner product spaces, we obtain the concrete form of surjective maps completely preserving indefinite Jordan 1-†-zero product between †-standard operator algebras. Our results show that such maps are nonzero constant multiple of isomorphisms or conjugate isomorphisms.

In this paper, the author discusses the iterated function system of generalized finite type conditions. First, the author constructs an iterated function system of generalized finite type condition, which satisfies the case where an invariant set is a basic set if and only if it is a subset of (0, 1). Second, the author proves that, with respect to the nested index sequence \{{\mathrm{\Lambda }}_k{\}}_k\ge \text{0}, any iterated function system in {\mathbb{R}}^dcannot satisfy the generalized finite type condition when the exponents of contractive ratios are not commensurable. Finally, the author constructs a family of self-similar sets which satisfy the generalized finite type condition and computes the Hausdorff dimensions of them.

In this paper, we mainly discuss the convergence rate of the limit distribution of a class of normal stationary triangular arrays, and point out that the convergence rate of this triangular array is not faster than that of the extremes of random variables in the i.i.d. case.

With the help of large deviation of Brownian motion in the Hölder norm, local Strassen’s law of the iterated logarithm for increments of a Brownian motion in the Hölder norm is investigated. This paper promotes the corresponding results by Gantert and Wei.

In this paper, we introduce the τ_[n]-mutations of a class of Koszul algebra and prove that for the Koszul algebra with the global dimension ≤ n, if its Koszul dual is an admissible (n-1)-translation algebra, then the quiver of endomorphism algebra of n-APR tilting module can be realized by τ_[n]-mutation.