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The Invertibility of Rational Univariate Representations

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Journal of Systems Science & Complexity 2022年第6期35卷 2430-2451页

作者： xiao shuijing zeng guangxing department of mathematics Nanchang UniversityNanchang 330031China

In this paper,the so-called invertibility is introduced for rational univariate representations,and a characterization of the invertibility is *** is shown that the rational univariate representations,obtained by both Rouillier’s approach and Wu’s method,are ***,the ideal created by a given rational univariate representation is *** results on invertible rational univariate representations and created ideals are *** on these results,a new approach is presented for decomposing the radical of a zero-dimensional polynomial ideal into an intersection of maximal ideals.

关键词： Invertibility polynomial ideal rational univariate representation(RUR) Wu’s method zero-dimensional

Decomposing the Radicals of Polynomial Ideals by Rational Univariate Representations

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Journal of Systems Science & Complexity 2023年第6期36卷 2703-2724页

作者： xiao shuijing zeng guangxing department of mathematics Nanchang UniversityNanchang330031China

In this paper,the notion of rational univariate representations with variables is ***,the ideals,created by given rational univariate representations with variables,are *** merit of these created ideals is that some of their algebraic properties can be easily *** the aid of the theory of valuations,some related results are *** on these results,a new approach is presented for decomposing the radical of a polynomial ideal into an intersection of prime ideals.

关键词： Polynomial ideal rational univariate representation(RUR) valuation ring Wu's method

SEMI-ALGEBRAICALLY CONNECTED COMPONENTS OF MINIMUM POINTS OF A POLYNOMIAL FUNCTION

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Journal of Systems Science & Complexity 2013年第6期26卷 1028-1046页

作者： xiao shuijing zeng guangxing department of mathematics Nanchang University

In a recent article, the authors provided an effective algorithm for both computing the global infimum of f and deciding whether or not the infimum of f is attained, where f is a multivariate polynomial over the field R of real numbers. As a complement, the authors investigate the semi- algebraically connected components of minimum points of a polynomial function in this paper. For a given multivariate polynomial f over R, it is shown that the above-mentioned algorithm can find at least one point in each semi-algebraically connected component of minimum points of f whenever f has its global minimum.

关键词： Global minimum minimum point polynomial optimization rational univariate represen-tation (RUR) semi-algebraically connected component strictly critical point.

Equality-constrained minimization of polynomial functions

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Science china mathematics 2015年第10期58卷 2181-2204页

作者： xiao shuijing zeng guangxing department of mathematics Nanchang University

This paper investigates the equality-constrained minimization of polynomial functions. Let R be the field of real numbers, and R[x1,..., xn] the ring of polynomials over R in variables x1,..., xn. For an f ∈ R[x1,..., xn] and a finite subset H of R[x1,..., xn], denote by V(f : H) the set {f( ˉα) | ˉα∈ Rn, and h( ˉα) =0, ? h ∈ H}. We provide an effective algorithm for computing a finite set U of non-zero univariate polynomials such that the infimum inf V(f : H) of V(f : H) is a root of some polynomial in U whenever inf V(f : H) = ±∞.The strategies of this paper are decomposing a finite set of polynomials into triangular chains of polynomials and computing the so-called revised resultants. With the aid of the computer algebraic system Maple, our algorithm has been made into a general program to treat the equality-constrained minimization of polynomials with rational coefficients.

关键词： polynomial function equality constraints equality-constrained minimization constrained infimum Wu’s algorithm triangular decompo

Determination of the limits for multivariate rational functions

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Science china mathematics 2014年第2期57卷 397-416页

作者： xiao shuijing zeng guangxing department of mathematics Nanchang University

The purpose of this paper is to solve the problem of determining the limits of multivariate rational *** is essential to decide whether or not limxˉ→0f g=0 for two non-zero polynomials f,g∈R[x1,...,xn]with f(0,...,0)=g(0,...,0)=*** two such polynomials f and g,we establish two necessary and sufcient conditions for the rational functionf g to have its limit 0 at the *** on these theoretic results,we present an algorithm for deciding whether or not lim(x1,...,xn)→(0,...,0)f g=0,where f,g∈R[x1,...,xn]are two non-zero *** design of our algorithm involves two existing algorithms:one for computing the rational univariate representations of a complete chain of polynomials,another for catching strictly critical points in a real algebraic *** two algorithms are based on the well-known Wu’s *** the aid of the computer algebraic system Maple,our algorithm has been made into a general *** the final section of this paper,several examples are given to illustrate the efectiveness of our algorithm.

关键词： rational function limit infinitesimal element strictly critical point rational univariate represen-tation (RUR) Wu's method transfer principle

常规正电子放射性核素的核纯度检测质控方法探究

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中国医疗设备 2024年第6期39卷 43-48页

作者：廖光星李宁杨鸿宇杨志肖国有何正中广西医科大学附属肿瘤医院核医学科(广西临床重点建设专科) 广西南宁530021

目的探讨半衰期测定法在医用正电子(^(18)F、^(11)C、^(13)N)核素纯度测定和分析中的方法。方法通过回旋加速器加速质子分别轰击重氧水、氮氧混合气及乙醇(20 mmol/L)靶水,分别产生^(18)F、^(11)C、^(13)N正电子核素样品水溶液。^(18)F... 详细信息

目的探讨半衰期测定法在医用正电子(^(18)F、^(11)C、^(13)N)核素纯度测定和分析中的方法。方法通过回旋加速器加速质子分别轰击重氧水、氮氧混合气及乙醇(20 mmol/L)靶水,分别产生^(18)F、^(11)C、^(13)N正电子核素样品水溶液。^(18)F、^(11)C、^(13)N核素分别每间隔10、2、2 min测量样品水溶液放射性活度,放射性活度测定次数为5次。根据放射性核素衰变的线性拟合公式,计算核素半衰期T_(1/2)。通过γ能谱仪测定对应样品水溶液,鉴定样品放射性核素纯度。结果由半衰期测定法计算可得3种正电子核素的半衰期与γ能谱仪法测定得半衰期结果相近,^(18)F、^(11)C、^(13)N样品的放射性核素半衰期分别为(110.07±0.53)、(19.62±0.77)、(10.02±0.94)min。通过γ能谱仪测定对应样品的^(18)F、^(11)C、^(13)N核素纯度均为100%,其物理半衰期分别为109.77、20.39、9.97 min。结论半衰期测定法具有测定医用放射性核素纯度的可行性,值得推广应用。

关键词：正电子核素放射性核素半衰期测定法核纯度检测

计算等式约束下多项式在闭长方体上的精确最小值

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南昌大学学报（理科版） 2015年第2期39卷 106-114页

作者：肖水晶万玮曾广兴南昌大学数学系江西南昌330031

对于给定的一个实多项式函数f,多项式环R[x1,…,xn]中一个非空的有限子集H以及Rn中一个闭长方体∏n i=1[ai,bi],给出了一个有效算法,用来计算多项式函数f在集合∏n i=1[ai,bi]∩ZeroR(H)上的精确最小值,这里ZeroR为的实零点集。此外,该... 详细信息

对于给定的一个实多项式函数f,多项式环R[x1,…,xn]中一个非空的有限子集H以及Rn中一个闭长方体∏n i=1[ai,bi],给出了一个有效算法,用来计算多项式函数f在集合∏n i=1[ai,bi]∩ZeroR(H)上的精确最小值,这里ZeroR为的实零点集。此外,该算法可产生一个最小值点,该点被写成所谓的区间-有理单元表示。相应的有关算法通过Maple软件被编制成一个通用程序,可处理相关实例。

关键词：多项式函数等式约束极小化受约束的最小值最小值点吴方法三角分解强临界点修正结式

Brasenia-inspired hydrogel with sustained and sequential release of BMP and WNT activators for improved bone regeneration

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Chinese Chemical Letters 2023年第7期34卷 162-168页

作者： Xinqing Hao Xuewei Zhang Yue Hu Chunxia Ren Cangwei Liu Lu Wang Yijun Zhou Shuangshuang Wang Huanyu Luo guangxing Yan xiao Wang xiaomeng Wang Feilong Ren Ce Shi, Wenlong Song Hongchen Sun Hospital of Stomatology Jilin UniversityChangchun 130021China School of Materials Science and Engineering Hainan UniversityHaikou 570228China State Key Laboratory of Supramolecular Structure and Materials College of ChemistryJilin UniversityChangchun 130012.China School of Stomatology China Medical UniversityShenyang 110001China jilin Provincial Key Laboratory of Tooth Development and Bone Remodeling Changchun 130021China

Although bone morphogenetic protein(BMP) and WNT signaling play pivotal roles in bone development,homeostasis, and regeneration, the applications of proteins to stimulate corresponding signaling pathways showed limited outcomes in the repair and regeneration of bone defects that might be attributed to the reciprocal interventions of these pathways. In order to satisfy the combinational and sequential activation of BMP and WNT pathways, inspired by the heterogeneous hydrogel-liked structures of Brasenia, heterogeneous alginate/chitosan hydrogels were fabricated and spatially loaded with FK506 and BIO to achieve sustained and sequential release of the activators. Alkaline phosphatase staining, alizarin red staining and q RT-PCR results suggested that FK506 and BIO enhanced osteoblastic differentiation in vitro when used separately. Besides, by mixing and matching the activators and the hydrogel layers, a superior releasing mode that a combination of early FK506 release and following BIO release was identified via both in vitro and in vivo explorations for most efficient bone regeneration. These results suggested that drug-loaded heterogeneous hydrogels possess great potentials in treating bone loss defects for future clinical practice.

关键词： Bone regeneration FK506 BIO Heterogeneous hydrogels Osteogenic differentiation

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Mondo蛋白在肿瘤相关代谢中的研究进展

生命的化学 2019年第1期39卷 88-95页

作者：张俊华薛敏肖松舒易水晶曾飞中南大学湘雅三医院妇科长沙410000

转录因子Mondo蛋白家族包括MondoA和ChREBP(MondoB)两个家族成员,是葡萄糖介导的基因转录调控的关键调控因子,可直接调控糖酵解和脂肪酸生成相关基因的表达,在细胞代谢与能量平衡中发挥重要作用。细胞代谢改变是肿瘤的重要特征之一,为... 详细信息

转录因子Mondo蛋白家族包括MondoA和ChREBP(MondoB)两个家族成员,是葡萄糖介导的基因转录调控的关键调控因子,可直接调控糖酵解和脂肪酸生成相关基因的表达,在细胞代谢与能量平衡中发挥重要作用。细胞代谢改变是肿瘤的重要特征之一,为肿瘤细胞生长及恶性进展创造了有利条件。近年来,研究发现,Mondo蛋白在肿瘤细胞糖酵解、脂肪酸合成和谷氨酰胺利用等代谢通路中发挥着重要作用,而且Mondo蛋白调控肿瘤细胞的代谢,其在肿瘤细胞生长、增殖和侵袭等过程中的作用值得肿瘤研究者关注。因此,更好地认识Mondo蛋白调控肿瘤细胞代谢的机制,将为癌症的治疗提供新的方向。本文对Mondo蛋白家族成员的分子特征、表达调控、组织特异性功能及其在肿瘤代谢重编程和细胞增殖中的最新研究进行综述,为肿瘤的防治提供新思路。

关键词： MondoA ChREBP 代谢重编程肿瘤代谢调控