基于Kronecker型替换的黑盒多项式稀疏插值

本文基于新的Kronecker型替换,给出两个由黑盒表示的稀疏多项式的新确定性插值算法.令f∈R[x1,……,xn]是一个稀疏黑盒多项式,其次数上界为D.当R是C或者是有限域时,相对于已有算法,新算法具有更好的计算复杂度或者关于D的复杂度更低.特别地,对于一般黑盒模型,D是复杂度中的主要因素,而在所有的确定性算法中,本文的第二个算法的复杂度关于D是最低的.     

Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

Essential domains and two conjectures in dimension theory

This note investigates two long-standing conjectures on the Krull dimension of integer-valued polynomial rings and of polynomial rings in the context of (locally) essential domains.

     

Unraveling the mystery of efficacy in Chinese medicine formula: New approaches and technologies for research on pharmacodynamic substances

Traditional Chinese medicine (TCM) is the key to unlock treasures of Chinese civilization. TCM and its compound play a beneficial role in medical activities to cure diseases, especially in major public health events such as novel coronavirus epidemics across the globe. The chemical composition in Chinese medicine formula is complex and diverse, but their effective substances resemble “mystery boxes”. Revealing their active ingredients and their mechanisms of action has become focal point and difficulty of research for herbalists. Although the existing research methods are numerous and constantly updated iteratively, there is remain a lack of prospective reviews. Hence, this paper provides a comprehensive account of existing new approaches and technologies based on previous studies with an in vitro to in vivo perspective. In addition, the bottlenecks of studies on Chinese medicine formula effective substances are also revealed. Especially, we look ahead to new perspectives, technologies and applications for its future development. This work reviews based on new perspectives to open horizons for the future research. Consequently, herbal compounding pharmaceutical substances study should carry on the essence of TCM while pursuing innovations in the field.     

Rewiring cellular metabolism for heterologous biosynthesis of Taxol

Abstract

Taxol is one of the anticancer drugs synthesized naturally in the evergreen Taxus brevifolia forest tree belonging to the yew family (Taxaceae) growing on the Pacific. There are reportedly evidence for treating ovarian, breast and lung cancers through this drug given its unique structural and functional features. Extraction of this drug from yew trees bark is one of the most common ways of producing this drug, but 3000 trees are needed to obtain a kilogram of Taxol. Hence, further attention has recently been attracted to the metabolic engineering strategies, including, engineering cellular metabolism of microorganisms and their optimization. Accordingly, the present paper article was aimed to review recent advances in elevating the production and commercialization of Taxol through metabolic engineering techniques.     

Isolation and Characterization of Badge Hydrolysis Products

Heating a suspension of Bisphenol A diglycidyl ether (BADGE) in 20 : 80 tetrahydrofuran/water at 70°C and subsequent passage of the resulting solution through C18 columns allowed isolation and purification to > 97% of each of the two hydrolysis products 2-[4-(2,3-dihydroxypropoxy) phenyl]-2-[4-(2,3-epoxypropoxy)phenyl]propane (1HP) and 2,2-bis[4-(2,3-dihydroxypropoxy)phenyl] propane (2HP), which were characterized by UV, IR, ₁H and _I3C NMR spectroscopy and mass spectrometry.     

Construction of sliced (nearly) orthogonal Latin hypercube designs

Sliced Latin hypercube designs are very useful for running a computer model in batches, ensembles of multiple computer models, computer experiments with qualitative and quantitative factors, cross-validation and data pooling. However, the presence of highly correlated columns makes the data analysis intractable. In this paper, a construction method for sliced (nearly) orthogonal Latin hypercube designs is developed. The resulting designs have flexible sizes and most are new. With the orthogonality or near orthogonality being guaranteed, the space-filling property of the resulting designs is also improved. Examples are provided for illustrating the proposed method.     

A problem of determining a special spatial part of 3D memory kernel in an integro‐differential hyperbolic equation

The inverse problem of determining 2D spatial part of integral member kernel in integro‐differential wave equation is considered. It is supposed that the unknown function is a trigonometric polynomial with respect to the spatial variable y with coefficients continuous with respect to the variable x. Herein, the direct problem is represented by the initial‐boundary value problem for the half‐space x>0 with the zero initial Cauchy data and Neumann boundary condition as Dirac delta function concentrated on the boundary of the domain . Local existence and uniqueness theorem for the solution to the inverse problem is obtained.