水平共形映射和调和Morphism

本文建立了Riemann流形之间水平共形映射之能量密度的基本公式．作为应用，得到了水平共形映射是水平相似映射的充要条件；分类了欧氏空间的开子集之间所有具有全测地纤维的水平共形映射；最后导出了由调和morphism的度量形变产生的水平共形映射力调和motphism的等价条件．因而改进和推广了Baird－Eells，Gudmundsson以及Baird的相应结果．

到欧氏空间的调和Morphisms的分类

本文使用了流形几何的方法，分类了从IR^m中开子集U到IR^n的水平相似的调和morphisms,作为推论，给出了Gudmundsson与Sigurdsson关于复欧氏空间的连通开子集之间的全纯调和morphisms的完全分类定理[8]的一个简单证明。

Alteration of ERβ gene Rsal polymorphism may contribute to reduced fertilization rate and embryonic developmental competence

This paper aims to determine the possible role of estrogen receptor-β （ERβ） gene Rsal polymorphism on sperm fertility and early embryonic development in humans. Three groups of Chinese men were recruited： in vitro fertilization （IVF） group, including 374 couples who underwent conventional IVF; intracytoplasmic sperm injection （ICSI） group, including 294 couples who underwent an ICSI procedure using ejaculated sperm; and azoospermic group, consisting of 197 couples who underwent ICSI using either testis or epididymis sperm. Rsal polymorphism in the ERβ gene was detected by polymerase chain reaction （PCR）-restriction fragment length polymorphism technique; fertilization and high-quality embryo rates were evaluated for each group. In each group, no significant differences were found in the overall rates of fertilization and high-quality embryos among GG, AG and AA genotypes. However, the proportion of cycles possessing a satisfactory high-quality embryo rate with the AA genotype was significantly lower than that in the wild-type GG genotype from each group. These results demonstrated that sperm possessing the ERβ RsalA genotype may have reduced fertilization ability and decreased early embryonic developmental potential, which could directly or indirectly contribute to the low fertilization rate and early embryonic developmental arrest in some cases.

Peroxisome Proliferator-activated Receptor-γ2 Pro12Ala and C-689T Polymorphisms and Haplotypes Affect the Profiles of Coronary Heart Disease in Diabetic Chinese People

Objectives Peroxisome proliferator-activated receptor-γ2（PPARγ2） variant Pro12Ala was demonstrated with risk of coronary heart disease （CHD） and type 2 diabetes mellitus （T2DM）. Another variant C-689T in the promoter was reported with lower receptor activity but lack of reports on association between C-689T and CHD or T2DM. Methods A total of 351 subjects without CHD and T2DM （controls） and 125 patients with CHD and T2DM （cases） were enrolled in our case-control study. Polymerase chain reaction-restricted fragments length polymorphism （PCR-RFLP） was used to detect Pro12Ala and C-689T polymorphisms. And effects on CHD merged with T2DM of the two polymorphisms were analyzed in individual and haplotype analyses. Results In the study, Pro12Pro, Pro12Ala and Ala12Ala genotype frequencies were 92.9%, 6.8% and 0.3% in controls; 92.8%, 7.2% and 0.0% in cases respectively whilst CC, CT and TT genotype frequencies were 93.4%, 6.3% and 0.3% in controls; 92.8%, 7.2% and 0.0% in cases respectively. Pro12Ala and C-689T polymorphisms were in strong linkage disequilibrium （D＇=0.81, P=0.000） and the observed haplotype frequency of Pro-C, Pro-T, Ala-C and Ala-T was 0.957, 0.006, 0.008 and 0.028 respectively. No significant associations were detected between the two polymorphisms and CHD merged with T2DM in either individual or haplotype analyses. In subjects with obesity [body mass index （BMI）≥25 kg/m^2], we found that both Pro12Ala and C-689T polymorphisms were associated with BMI. In haplotype analyses, we found that Pro12Ala and C-689T haplotypes had associations with systolic blood pressure in total population, with BMI, waist circle and total cholesterol（TC） in obesity subgroup and with fasting blood glucose and TC in males. Conclusions PPARγ2 Pro12Ala and C-689T polymorphisms and haplotypes affect the profiles of CHD merged with T2DM in Chinese Han people.

f-Harmonic Morphisms Between Riemannian Manifolds

f-Harmonic maps were first introduced and studied by Lichnerowicz in 1970.In this paper,the author studies a subclass of f-harmonic maps called f-harmonic morphisms which pull back local harmonic functions to local f-harmonic functions.The author proves that a map between Riemannian manifolds is an f-harmonic morphism if and only if it is a horizontally weakly conformal f-harmonic map.This generalizes the well-known characterization for harmonic morphisms.Some properties and many examples as well as some non-existence of f-harmonic morphisms are given.The author also studies the f-harmonicity of conformal immersions.

Linear Functional Equations and Twisted Polynomials

A certain variety of non-switched polynomials provides a uni-figure representation for a wide range of linear functional equations. This is properly adapted for the calculations. We reinterpret from this point of view a number of algorithms.

Preservation of Quasi-isomorphisms of Complexes

We consider the preservation property of the homomorphism and tensor product functors for quasi-isomorphisms and equivalences of complexes. Let X and Y be two classes of R-modules with Ext〉I（X,Y） = 0 for each object X ∈ X and each object Y ∈ Y. We show that if A,B ∈ C^（R） are X-complexes and U, V ∈ Cr（R） are Y-complexes, then U V Hom（A, U） Hom（A, Y）; A B Hom（B, U） Hom（A, U）. As an application, we give a sufficient condition for the Hom evaluation morphism being invertible.

Semistable representations of quivers with automorphism

Let Q be a quiver with automorphism σ. We prove that semistable representations of Q over F_q give rise to semistable modules over the F_q-algebra A(Q, σ; q) associated with(Q, σ). As an application, we obtain a description of the semistable subcategories of A(Q, σ; q)-modules and determine the slopes of semistable A(Q, σ; q)-modules in the case that Q is a Dynkin or tame quiver.

高血压药物基因多态性分析对安徽皖南地区高血压患者个体化治疗的参考价值

目的:分析皖南地区高血压患者β受体阻滞剂、血管紧张素受体拮抗剂(ARB)、血管紧张素转换酶抑制剂(ACEI)、钙离子拮抗剂及利尿剂药物基因多态性分布频率,为高血压药物基因检测工作和个性化用药提供理论依据。方法:搜集2021年7月至2023年4月皖南医学院弋矶山医院839例高血压住院患者药物基因检测信息,分析各基因位点分布频率。结果:ACE(I/D)I/I、I/D及D/D基因型频率分别为42.1%、46.0%、11.9%;肾上腺素能受体β1(ADRB1)(1165G>C)G/G、G/C及C/C基因型频率分别为8.3%、40.0%、51.6%;血管紧张素Ⅱ受体1(AGTR1)(1166A>C)A/A、A/C及C/C基因型频率分别为90.2%、9.8%、0.0%;CYP2C9*3(1075A>C)*1/*1、*1/*3及*3/*3基因型频率分别为91.3%、8.7%、0.0%;CYP2D6*10(100C>T)*1/*1、*1/*10及*10/*10基因型频率分别为25.0%、36.6%、38.4%;CYP3A5*3(6986A>G)*1/*1、*1/*3及*3/*3基因型频率分别为7.0%、39.0%、54.0%;钠尿肽前体蛋白A(NPPA)(2238T>C)T/T、T/C及C/C基因型频率分别为97.9%、2.1%、0.0%。此外,皖南地区多个药物相关基因位点基因型分布频率与中国其他地区存在统计学差异(P<0.05)。结论:皖南地区高血压药物相关基因位点基因型分布频率具有一定偏向性,且与中国其他地区相比存在统计学差异,提示开展高血压药物基因多态性检测对皖南地区高血压药物个体化应用具有一定指导意义。

Single Nucleotide Polymorphism Identification in Polyploids： A Review, Example, and Recommendations

Understanding the relationship between genotype and phenotype is a major biological question and being able to predict phenotypes based on molecular genotypes is integral to molecular breeding. Whole- genome duplications have shaped the history of all flowering plants and present challenges to elucidating the relationship between genotype and phenotype, especially in neopolyploid species. Although single nucleotide polymorphisms （SNPs） have become popular tools for genetic mapping, discovery and appli- cation of SNPs in polyploids has been difficult. Here, we summarize common experimental approaches to SNP calling, highlighting recent polyploid successes. To examine the impact of software choice on these analyses, we called SNPs among five peanut genotypes using different alignment programs （BWA-mem and Bowtie 2） and variant callers （SAMtools, GATK, and Freebayes）. Alignments produced by Bowtie 2 and BWA-mem and analyzed in SAMtools shared 24.5% concordant SNPs, and SAMtools, GATK, and Freebayes shared 1.4% concordant SNPs. A subsequent analysis of simulated Brassica napus chromosome 1A and 1C genotypes demonstrated that, of the three software programs, SAMtools performed with the highest sensitivity and specificity on Bowtie 2 alignments. These results, however, are likely to vary among species, and we therefore propose a series of best practices for SNP calling in polyploids.

Some Properties of Morphisms in Effect Algebras

In the present paper the properties of morphisms in effect algebras are discussed. The conditions for the morphisms in effect algebras to be join-preservation and meet-preservation are given. From the categorical point of view, some properties of ideals, filters and congruence relations under morphisms are obtained.

Practical Cryptanalysis of a Public Key Cryptosystem Based on the Morphism of Polynomials Problem

Multivariate Public Key Cryptography （MPKC） has intensively and rapidly developed during the past three decades. MPKC is a promising candidate for post-quantum cryptography. However, designing it is universally regarded as a difficult task to design a secure MPKC foundation scheme, such as an encryption scheme and key exchange scheme. In this work, we investigate the security of a new public key cryptosystem that is based on the Morphism of Polynomials （MP）. The public key cryptosystem proposed by Wang et al. （Wuhan University, China） comprises a key exchange scheme and encryption scheme. Its security can be provably reduced to the hardness of solving a new difficult problem, namely, the Decisional Multivariate Diffie Hellman （DMDH） problem. This problem Js a variant of the MP problem, which is difficult to solve by random systems. We present a proposition that reduces the DMDH problem to an easy example of the MP problem. Then, we propose an efficient algorithm for the Key Recover Attack （KRA） on the schemes of the public key cryptosystem. In practice, we are able to entirely break the cryptosystem＇s claimed parameter of 96 security levels in less than 17.252 s. Furthermore, we show that finding parameters that yield a secure and practical scheme is impossible.

New Public-Key Cryptosystem Based on the Morphism of Polynomials Problem

During the last two decades, there has been intensive and fast development in Multivariate Public Key Cryptography （MPKC）, which is considered to be an important candidate for post-quantum cryptography. However, it is universally regarded as a difficult task, as in the Knapsack cryptosystems, to design a secure MPKC scheme （especially an encryption scheme） employing the existing trapdoor construction. In this paper, we propose a new key-exchange scheme and an MPKC scheme based on the Morphism of Polynomials （MP） problem. The security of the proposed schemes is provably reducible to the conjectured intractability of a new difficult problem, namely the Decisional Multivariate Diffie-Hellman （DMDH） problem derived from the MP problem. The proposed key agreement is one of several non-number-theory-based protocols, and is a candidate for use in the post-quantum era. More importantly, by slightly modifying the protocol, we offer an original approach to designing a secure MPKC scheme. Furthermore, the proposed encryption scheme achieves a good tradeoff between security and efficiency, and seems competitive with traditional MPKC schemes.

The Automorphism Group of Green Algebra of 9-Dimensional Taft Hopf Algebra

Let H3 be the 9-dimensional Taft Hopf algebra,let r(H3)be the corresponding Green ring of H3,and let Aut(R(H3))be the automorphism group of Green algebra R(H3)=R■Zr(H3)over the real number fieldR.We prove that the quotient group Aut(R(H3))/T1 is isomorphic to the direct product of the dihedral group of order 12 and the cyclic group of order 2,where T1 is the isomorphism class which contains the identity map and is isomorphic to a group G={(c,d)∈R^(2)∣∣(c,d)≠(−1/3,−1/6)}with multiplication given by(c1,d1)⋅(c2,d2)=(c1+c2+2c1c2−4d1d2+2c1d2+2d1c2,d1+d2−2c1c2−2d1d2+4c1d2+4d1c2).

Automorphism Groups of Some Finite p-Groups

The automorphism group of G is determined, where G is a nonabelian p-group given by a central extension as 1→Zpm→G→Zp×…×Zp→1 such that its derived subgroup has order p.

(n,d)-(Ext)-phantom态射与(n,d)-环

引入了(n,d)-phantom态射与(n,d)-Ext-phantom态射的概念.利用它们,给出了(n,d)-环、n-遗传环以及n-正则环的一系列新刻画.

On structure of cluster algebras of geometric type Ⅰ：In view of sub-seeds and seed homomorphisms

Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for(rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also,we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.

循环纯phantom态射

通过引入循环纯phantom态射的概念,给出循环纯phantom态射的一些等价刻画,证明每个R-模都有核为循环纯内射模的满的循环纯phantom覆盖,并讨论循环纯phantom预覆盖在环变换下的传递性.

Harmonic polynomial morphisms between Euclidean spaces

Two non-existence theorems on harmonic polynomial morphisms between Euclidean spaces have been shown.

Finite morphisms of projective and K■hler manifolds

In this paper we study finite morphisms of projective and compact K■hler manifolds, in particular,positivity properties of the associated vector bundle,deformation theory and ramified endomorphisms.