An observation on spaces with a zeroset diagonal

summary:We say that a space $X$ has the discrete countable chain condition (DCCC for short) if every discrete family of nonempty open subsets of $X$ is countable. A space $X$ has a zeroset diagonal if there is a continuous mapping $f\colon X^2 \rightarrow [0,1]$ with $\Delta _X=f^{-1}(0)$, where $\Delta _X=\{(x,x)\colon x\in X\}$. In this paper, we prove that every first countable DCCC space with a zeroset diagonal has cardinality at most $\mathfrak c$

Matrix of Polynomials Model based Polynomial Dictionary Learning Method for Acoustic Impulse Response Modeling

We study the problem of dictionary learning for signals that can be represented as polynomials or polynomial matrices, such as convolutive signals with time delays or acoustic impulse responses. Recently, we developed a method for polynomial dictionary learning based on the fact that a polynomial matrix can be expressed as a polynomial with matrix coefficients, where the coefficient of the polynomial at each time lag is a scalar matrix. However, a polynomial matrix can be also equally represented as a matrix with polynomial elements. In this paper, we develop an alternative method for learning a polynomial dictionary and a sparse representation method for polynomial signal reconstruction based on this model. The proposed methods can be used directly to operate on the polynomial matrix without having to access its coefficients matrices. We demonstrate the performance of the proposed method for acoustic impulse response modeling.Comment: 5 pages, 2 figure

Study on the Value Evaluation of Intellectual Property Pledge Financing

As an intangible asset, intellectual property can not only improve the asset value of the company, but also obtain financing through pledge. Especially for some small and medium-sized technology-based companies in China, intellectual property financing has become one of their important ways. However, at present, there are still some problems in the value evaluation of intellectual property pledge financing, such as the uncertainty of intellectual property rights, the lack of a unified evaluation system, the lack of relevant laws and regulations, etc., which have caused certain difficulties to the value evaluation of intellectual property rights. At present, the income method is mainly used in the value evaluation of intellectual property pledge financing in China. Taking Hangzhou Xiye Technology Co., Ltd. as an example, this paper studies the applicability of this value evaluation method, points out relevant problems, and puts forward relevant suggestions, so as to improve the value evaluation level of intellectual property pledge financing in China

Study on the Value Evaluation of Intellectual Property Pledge Financing

As an intangible asset, intellectual property can not only improve the asset value of the company, but also obtain financing through pledge. Especially for some small and medium-sized technology-based companies in China, intellectual property financing has become one of their important ways. However, at present, there are still some problems in the value evaluation of intellectual property pledge financing, such as the uncertainty of intellectual property rights, the lack of a unified evaluation system, the lack of relevant laws and regulations, etc., which have caused certain difficulties to the value evaluation of intellectual property rights. At present, the income method is mainly used in the value evaluation of intellectual property pledge financing in China. Taking Hangzhou Xiye Technology Co., Ltd. as an example, this paper studies the applicability of this value evaluation method, points out relevant problems, and puts forward relevant suggestions, so as to improve the value evaluation level of intellectual property pledge financing in China