On Discrete Hopf Fibrations, Grand Unification Groups, the Barnes-Wall, Leech Lattices, and Quasicrystals

A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) how a subsequent 2-1 mapping (projection) of P16 onto a 8D-hyperplane might furnish the 2160 vertices of the uniform 241 polytope in 8-dimensions, and such that one can capture the chain sequence of polytopes 241,231,221,211in D=8,7,6,5dimensions, leading, respectively, to the sequence of Coxeter groups E8,E7,E6,SO(10)which are putative GUT group candidates. An embedding of the E8⊕E8and E8⊕E8⊕E8lattice into the Barnes-Wall Λ16 and Leech Λ24 lattices, respectively, is explicitly shown. From the 16D lattice E8⊕E8one can generate two separate families of Elser-Sloane 4D quasicrystals (QC’s) with H4 (icosahedral) symmetry via the “cut-and-project” method from 8D to 4D in each separate E8 lattice. Therefore, one obtains in this fashion the Cartesian product of two Elser-Sloane QC’s Q×Qspanning an 8D space. Similarly, from the 24D lattice E8⊕E8⊕E8one can generate the Cartesian product of three Elser-Sloane 4D quasicrystals (QC’s) Q×Q×Qwith H4 symmetry and spanning a 12D space.

Understanding the Laws Underlying the Development of Chinese Civilisation

At a meeting on cultural inheritance and development held in Beijing,June 2,2023,President Xi Jinping put forward a holistic and systematic explanation of the distinctive features of Chinese civilisation-consistency,originality,unity,inclusiveness,and a peaceful nature.President Xi Jinping's profound exposition has granted us a deeper understanding of the laws underlying the development of Chinese civilisation by shedding light on its intrinsic characteristics.

Long-term trends in the abundance and breeding performance in Adélie penguins:the Argentine Ecosystem Monitoring Program

In this work,we report long-term trends in the abundance and breeding performance of Adélie penguins(Pygoscelis adeliae)nesting in three Antarctic colonies(i.e.,at Martin Point,South Orkneys Islands;Stranger Point/Cabo Funes,South Shetland Islands;and Esperanza/Hope Bay in the Antarctic Peninsula)from 1995/96 to 2022/23.Using yearly count data of breeding groups selected,we observed a decline in the number of breeding pairs and chicks in crèche at all colonies studied.However,the magnitude of change was higher at Stranger Point than that in the remaining colonies.Moreover,the index of breeding success,which was calculated as the ratio of chicks in crèche to breeding pairs,exhibited no apparent trend throughout the study period.However,it displayed greater variability at Martin Point compared to the other two colonies under investigation.Although the number of chicks in crèche of Adélie penguins showed a declining pattern,the average breeding performance was similar to that reported in gentoo penguin colonies,specifically,those undergoing a population increase(even in sympatric colonies facing similar local conditions).Consequently,it is plausible to assume a reduction of the over-winter survival as a likely cause of the declining trend observed,at least in the Stranger Point and Esperanza colonies.However,we cannot rule out local effects during the breeding season affecting the Adélie population of Martin Point.

China's Greatest Contribution to the World Lies in Safeguarding Democracy and Wellbeing for One-Fifth of Humanity

China has a population that is one-fifth of humanity. Most of its people live in rural areas. This country has been built and developed on the ruins of semi-colonialism and semi-feudalism and on a foundation of ＂poverty and blankness.＂ The founding of New China created the political condition for the advancement of people＇s democracy. Since the adoption of reform and open policies, or gaige kaifang, China has gradually found an effective way, suited for Chinese conditions,

Perturbation to Lie symmetry and another type of Hojman adiabatic invariants for Birkhoffian systems

The perturbation to Lie symmetry and another type of Hojman adiabatic invariants induced from the perturbation to Lie symmetry for Birkhoffian systems are studied. The exact invariants of Lie symmetry for the system without perturbation are given. Based on the concept of adiabatic invariant, the perturbation to Lie symmetry is discussed and another new type of Hojman adiabatic invariants that have the different form from that in [Acta Phys. Sin. 55 3833] for the perturbed system are obtained.

Russian and English View on Lies in Conflict Dialogues—— Analysis of Conflict Communication Acts in Russian and English Fiction

What is a lie？ Why do people tell lies？ What compels them to make false utterances？ How do people treat lie, deception or fudge？ Is the attitude to them the same in different cultures？ If not, what differences are there？ An answer to these and some other questions is being sought in the paper. Producing a false utterance, the sender deprives the communication partner of the right to receive full information. The article presents views of Russians and representatives of Anglo-American culture on telling lies drawing the readers＇ attention to very serious situations, such as family conflicts between spouses, aggravated with lies. The material for analysis is taken from the texts by Russian playwright Anton Chekhov and the American novel writer Irwin Shaw. The analysis is based on the study of verbal and non-verbal markers of false utterances generated by quarreling spouses. A complex method of researching the literary material combining linguistic, extra-linguistic, and paralinguistic analysis of conflict speech acts with false utterances of different kinds is applied.

Correc tion:TiO_(2) nanoparticles in aquatic environments:impact on heavy metals distribution in sediments and overlying water

Correction to:Acta Geochimica(2022)41:968–981 https://doi.org/10.1007/s11631-022-00555-w In the original publication of the article,the affi liation of“Behzad Aghabarari”was published incorrectly.The correct affi liation should read as follows“Department of Nanotechnology and Advanced Materials,Material and Energy Research Center,Karaj,Iran”.

COMPARISON OF HOMOLOGIES AND AUTOMATIC EXTENSIONS OF INVARIANT DISTRIBUTIONS

Let G be a reductive Nash group,acting on a Nash manifold X.Let Z be a G-stable closed Nash submanifold of X and denote by U the complement of Z in X.Letχbe a character of G and denote by g the complexified Lie algebra of G.We give a sufficient condition for the natural linear map H_(k)(g,S(U)×χ)→H_k(g,S(X)×χ)between the Lie algebra homologies of Schwartz functions to be an isomorphism.For k=0,by considering the dual,we obtain the automatic extensions of g-invariant(twisted by-χ)Schwartz distributions.

Simple and Pseudo Quadratic Leibniz Superalgebras

Compactness of subspaces of a Z2-graded vector space is introduced and used to study simple Leibniz superalgebras. We introduce left and right super-invariance of bilinear forms over superalgebras. Pseudo-quadratic Leibniz superalgebras are Leibniz superalgebras endowed with a non degenerate, supersymmetric and super-invariant bilinear form. In this paper, we show that every nondegenerate, supersymmetric and super-invariant bilinear form over a Leibniz superalgebra induce a Lie superalgebra over the underlying vector space. Then by using double extension extended to Leibniz superalgebras, we study pseudo-quadratic Leibniz superalgebras and the induced Lie superalgebras. In particular, we generalize some results on Leibniz algebras to Leibniz superalgebras.

Mathematical Aspects of SU (2) and SO(3,R) Derived from Two-Mode Realization in Coordinate-Invariant Form

Some mathematical aspects of the Lie groups SU (2) and in realization by two pairs of boson annihilation and creation operators and in the parametrization by the vector parameter instead of the Euler angles and the vector parameter c of Fyodorov are developed. The one-dimensional root scheme of SU (2) is embedded in two-dimensional root schemes of some higher Lie groups, in particular, in inhomogeneous Lie groups and is represented in text and figures. The two-dimensional fundamental representation of SU (2) is calculated and from it the composition law for the product of two transformations and the most important decompositions of general transformations in special ones are derived. Then the transition from representation of SU (2) to of is made where in addition to the parametrization by vector the convenient parametrization by vector c is considered and the connections are established. The measures for invariant integration are derived for and for SU (2) . The relations between 3D-rotations of a unit sphere to fractional linear transformations of a plane by stereographic projection are discussed. All derivations and representations are tried to make in coordinate-invariant way.

Lie symmetry analysis and invariant solutions for the(3+1)-dimensional Virasoro integrable model

Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions for the(3+1)-dimensional Virasoro integrable model,including the interaction solution between a kink and a soliton,the lump-type solution and periodic solutions,have been studied analytically and graphically.

On the Construction and Classification of the Common Invariant Solutions for Some P(1,4) -Invariant Partial Differential Equations

We consider the following (1 + 3)-dimensional P(1,4)-invariant partial differential equations (PDEs): the Eikonal equation, the Euler-Lagrange-Born-Infeld equation, the homogeneous Monge-Ampère equation, the inhomogeneous Monge-Ampère equation. The purpose of this paper is to construct and classify the common invariant solutions for those equations. For this aim, we have used the results concerning construction and classification of invariant solutions for the (1 + 3)-dimensional P(1,4)-invariant Eikonal equation, since this equation is the simplest among the equations under investigation. The direct checked allowed us to conclude that the majority of invariant solutions of the (1 + 3)-dimensional Eikonal equation, obtained on the base of low-dimensional (dimL ≤ 3) nonconjugate subalgebras of the Lie algebra of the Poincaré group P(1,4), satisfy all the equations under investigation. In this paper, we present obtained common invariant solutions of the equations under study as well as the classification of those invariant solutions.

社会变迁中心理与行为的稳定性: 以谦虚效应为例

面对百年未有之大变局及生活质量生活方式的剧烈变迁,人们的心理行为乃至文化会如何变异?作者假设尽管社会变迁会影响和改变人类的某些心理和行为,但有些心理行为,因其受深层文化影响,会十分稳定,不受社会变迁的影响。近30年的有关谦虚效应的跨文化研究为这一假设提供了佐证。谦虚是中国传统文化深层结构中的集体主义的产物,这种跨文化差异本质上来源于东西方文化中个人主义与集体主义的差异。总结谦虚效应的30年系列研究结果表明尽管中国的经济社会发生了前所未有的发展,这个跨文化效应基本不变,说明源于深层文化的心理和行为存在高度的稳定性。

Educational Innovation in Lying Flat Phenomenon-A Case Study of the Balinese Teaching Experience

Lying flat(Tang Ping)is a prevalent way of life in contemporary countries throughout the world.It is an avoidance behavior chosen by individuals in response to limited social resources and ongoing harsh social competition.Previous studies have demonstrated that the phenomena of“lying flat”has a major negative effect on student learning.In order to investigate the impact of educational innovation on the phenomenon of“lying flat”,we will observe students’learning behaviors under the traditional education model and innovative teaching methods in our Bali teaching practice to determine the causes of“lying flat”and the means to improve educational innovation.The study found that“lying flat”is caused not just by students’discontent with their level difference,but also by the conflict between external resources and internal pressure.In addition,educational reforms on three levels,including further stratified education,strengthening teacher education and promoting effective communication between students and teachers,and employing online resources to promote students’interest in learning,can ameliorate the phenomenon of pupils“lying flat”.This study contends that educational innovation can have a positive effect on the phenomena of“lying flat”.

多尺度特征融合的点云配准算法研究

现有点云配准算法提取的特征不够丰富,导致配准精度很难进一步提升。针对该问题,本文提出一种基于深度学习的多尺度特征融合点云配准算法。首先,利用EdgeConv提取多个不同尺度的特征,该特征能够保持局部几何结构特性;接着,引入非线性极化注意力对其输出特征进行筛选,从而提高特征信息的有效性;然后,将以上多尺度特征进行融合并再次利用EdgeConv提取其特征,从而提高特征的表达能力;在刚体姿态估计阶段,采用线性李代数处理旋转变换以充分挖掘点云中的变换信息;最后,根据配准过程中提取点云特征的变化,动态调整损失函数各组成部分的权重,获得更准确的模型预测结果。在ModelNet40数据集上进行实验,本文算法在训练集和测试集样本种类相同时的旋转误差为1.8267,位移误差为0.0010;在训练集和测试集的样本种类不相同时(泛化实验)的旋转误差为2.9794,位移误差为0.0010。实验结果表明,本文算法的配准精度相比当前主流算法均有提高且泛化性能较好。

Lie-Yamaguti代数的相对微分算子

本文研究Lie-Yamaguti代数的相对微分算子.首先给出Lie-Yamaguti代数上相对微分算子的概念并给出等价刻画.随后,引入Lie-Yamaguti代数上相对微分算子的上同调.最后,讨论Lie-Yamaguti代数上相对微分算子的无穷小形变.

具有高阶导子Lie-Yamaguti代数的上同调

研究具有高阶导子的Lie-Yamaguti代数,称之为LieYHDer对。首先给出LieYHDer对的上同调,然后研究了LieYHDer对的中心扩张,根据上同调考虑LieYHDer的形变。

一种世界坐标系下的GNSS/SINS松组合导航矩阵李群滤波算法

针对在地心地固(ECEF)坐标系下基于右不变误差的卡尔曼滤波在GNSS/SINS组合导航中,因位置矢量数值较大导致系统线性误差运动学矩阵和观测矩阵不稳定进而降低滤波器性能的问题,提出一种世界坐标系下的GNSS/SINS松组合导航矩阵李群滤波算法。首先在世界坐标系中构建导航状态和考虑地球自转的运动学方程。然后在世界坐标系下定义矩阵李群上的右不变误差,该误差在右群作用下保持不变,并重新推导和设计基于该误差的矩阵李群滤波算法,根据GNSS观测构建世界坐标系下的观测矩阵。实验结果表明,在低精度惯导场景中相对于ECEF坐标系下的传统扩展卡尔曼滤波,所提算法的北向、东向、地向位置误差均方根分别减小了82.6%、61.8%和10.6%,具有一定的实用价值。

带权罗-巴李超三系

给出带权罗-巴李超三系的表示和上同调。作为应用,引入和研究带权罗-巴李超三系的形式形变。

陈述、意合与列锦——《天净沙·秋思》新解

《天净沙·秋思》被誉为“秋思之祖”“直空今古”。“枯藤老树昏鸦”等名词句,功能上,半显半隐,静中生动,属诗意的动态陈述;句法上,运用意合组句,实虚相生,景语其后,更含所托,通过隐喻,发出了“得志不易”的永恒之叹;修辞上,凭借骈偶这种特殊的语法手段,铺排名词,列锦生辉。