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Three- and Four-Dimensional Generalized Pythagorean Numbers

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Advances in Pure Mathematics 2024年第1期14卷 1-15页

作者： Alfred w.nsche Institute of Physics Humboldt University Berlin Germany

The Pythagorean triples (a, b | c) of planar geometry w.ich satisfy the equation a2+b2=c2 w.th integers (a, b, c) are generalized to 3D-Pythagorean quadruples (a, b, c | d) of spatial geometry w.ich satisfy the equation a2+b2+c2=d2 w.th integers (a, b, c, d). Rules for a parametrization of the numbers (a, b, c, d) are derived and a list of all possible nonequivalent cases w.thout common divisors up to d2 is established. The 3D-Pythagorean quadruples are then generalized to 4D-Pythagorean quintuples (a, b, c, d | e) w.ich satisfy the equation a2+b2+c2+d2=e2 and a parametrization is derived. Relations to the 4-square identity are discussed w.ich leads also to the N-dimensional case. The initial 3D- and 4D-Pythagorean numbers are explicitly calculated up to d2, respectively, e2.

关键词： Number Theory Pythagorean Triples Tesseract 4-Square Identity Diophantine Equation

Convergence Phenomenon w.th Fourier Series of tg(x2)and Alike

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Advances in Pure Mathematics 2024年第7期14卷 556-595页

作者： Alfred w.nsche Institut fr Physik Humboldt-Universitt Berlin Berlin Germany

The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated w.th respect to their convergence. These functions are Generalized functions and the convergence is w.ak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show.that the approximations of the Fourier series possess oscillations around the function w.ich they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in pow.rs cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected w.th the Poisson theorem show.ng non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .

关键词： Gibbs Phenomenon Generalized Functions w.ak Convergence Chebyshev Polynomials of First and Second Kind Even and Odd Generating Functions for Chebyshev Polynomials Polylogarithms Completeness Relations

Spatiotemporal dynamics in butterfly hybrid zones

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Insect Science 2024年第2期31卷 328-353页

作者： Ananda R.Pereira Martins Natalie B.w.rren w.Ow.n McMillan Row.n D.H.Barrett Redpath Museum McGill University859 Sherbrooke Street WestMontrealQuebecCanada Smithsonian Tropical ResearchInstitute GamboaPanama CityPanama

Evaluating w.ether hybrid zones are stable or mobile can provide novelinsights for evolution and conservation biology. Butterflies exhibit high sensitivity to envi-ronmental changes and represent an important model system for the study of hybrid zoneorigins and maintenance. Here, w. review.the literature exploring butterfly hybrid zones,w.th a special focus on their spatiotemporal dynamics and the potential mechanisms thatcould lead to their movement or stability. w. then compare different lines of evidenceused to investigate hybrid zone dynamics and discuss the strengths and w.aknesses ofeach approach. Our goal w.th this review.is to reveal general conditions associated w.ththe stability or mobility of butterfly hybrid zones by synthesizing evidence obtained us-ing different types of data sampled across multiple regions and spatial scales. Finally, w.discuss spatiotemporal dynamics in the context of a speciation/divergence continuum, therelevance of hybrid zones for conservation biology, and recommend key topics for futureinvestigation.

关键词： butterflies human impacts hybrid zones movement spatiotemporaldynamics stability

栖息地条件对白杨与枫树林群落中高山天南星的丰富度和选定个体特征的影响

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Journal of Plant Ecology 2024年第1期17卷 33-49页

作者： Tomasz w.jcik Kinga Kostrakiew.cz-Gierałt Department of Nature Conservation and Landscape Ecology Institute of Agricultural SciencesLand Management and Environmental ProtectionUniversity of Rzeszow35-601 RzeszowPoland Department of Tourism Geography and Ecology Institute of TourismFaculty of Tourism and RecreationUniversity of Physical Education in Krakow31-571 KrakowPoland

本研究于2020至2021年在西喀尔巴阡山脉的山麓地区进行,研究了高山天南星(Arum alpinum)的物种数量和选定特征的空间-时间变异。调查分别在4个永久样地中进行(Patch Ⅰ、Ⅱ、Ⅲ、Ⅳ)。Patch Ⅰ和Patch Ⅲ位于以低矮植被为主的枫树-鹅耳... 详细信息

本研究于2020至2021年在西喀尔巴阡山脉的山麓地区进行,研究了高山天南星(Arum alpinum)的物种数量和选定特征的空间-时间变异。调查分别在4个永久样地中进行(Patch Ⅰ、Ⅱ、Ⅲ、Ⅳ)。Patch Ⅰ和Patch Ⅲ位于以低矮植被为主的枫树-鹅耳枥林(Tilio cordatae-Carpinetum betuli)林地中,而Patch Ⅱ和Patch Ⅳ位于以阔叶物种为主的白杨(Populetum albae)河滩林中。调查结果表明,高山天南星最丰富种群出现在Patch Ⅰ,但Patch Ⅱ和Patch Ⅳ中也存在大量的营养体和繁殖个体。个体性状的时间变异性在Patch Ⅳ最低,其次是Patch Ⅰ和Patch Ⅱ,在Patch Ⅲ最高。所有种群中均发现叶柄长度与叶片尺寸以及有性茎长度与果序特征之间的关系显著呈正相关,这一发现证实了先前的研究。这些研究结果表明,高山天南星与特定的森林群落没有密切关联。充足的遮荫和湿润富养分的土壤对该物种有利,而干燥的土壤和过多的日照可能会限制其个体的开花与结果。

关键词：高山天南星(Arum alpinum) 枫树-鹅耳枥林河滩林开花茎果序叶片山地物种

Effect of Eu^(3+),Bi^(3+),and Li^(+) doping on luminescent property of GdNbO_(4)

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Journal of Rare Earths 2024年第1期42卷 66-75,I0003页

作者： S.w.w. Y.S.Lee Department of Physics and Integrative Institute of Basic Sciences Soongsil UniversitySeoul06978Republic of Korea

w. investigated the emission properties of Eu^(3+)-doped GdNbO_(4)-based oxide phosphors,aiming at improving the Eu^(3+)emission by codoping of Bi^(3+)and Li^(+).Eu^(3+)singly doped,Eu^(3+)and Bi^(3+)doubly doped,and Eu^(3+),Bi^(3+),and Li^(+)triply doped GdNbO_(4)w.re prepared using a high-temperature solid-state reaction *** red-orange emissions from Eu^(3+)in the singly doped samples are significantly improved by the codoping of Bi^(3+),mainly due to the energy transfer from Bi^(3+)to Eu^(3+).The additional codoping of Li^(+)is found to increase the Eu^(3+)emission *** improvement might be attributed to the increase in the photoluminescent quantum yield originating from larger grain sizes and better crystallinity.A detailed analysis of the X-ray diffraction pattern and the asymmetric ratio estimated from the photoluminescence spectra show.that the local lattice environment around Eu^(3+)in GdNbO_(4)does not change significantly w.th the codoping of Bi^(3+)and Li^(+).Our results indicate that Li^(+)doping is a promising w.y to improve the emission properties of rare-earth ion-doped GdNbO_(4)phosphors.

关键词： Eu^(3+) GdNbO_(4) Codoping of Li^(+) Photoluminescence Sensitizer Rare earths

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海涅的伤口

上海文化 2024年第1期 80-85页

作者：特奥多尔·w.阿多诺赵勇(译) 赵天舒(校) 不详

任何人如果想在海涅逝世百年之际为纪念他认真做点事情而不仅仅是发表一个正式演讲,都将不得不谈论一个伤口;谈论海涅以及他与德国传统的关系中让我们感到痛苦的东西,谈论尤其是在“二战”之后的德国被压抑的东西。海涅的名字是一个刺激... 详细信息

任何人如果想在海涅逝世百年之际为纪念他认真做点事情而不仅仅是发表一个正式演讲,都将不得不谈论一个伤口;谈论海涅以及他与德国传统的关系中让我们感到痛苦的东西,谈论尤其是在“二战”之后的德国被压抑的东西。海涅的名字是一个刺激物,只有不对它涂脂抹粉而设法解决这个问题的人才有希望提供帮助。国家社会党人并不是诽谤海涅的始作俑者。事实上,当他们将如今著名的“作者不详”字样(Dichter unbekannt)置于其诗歌《罗蕾莱》(“Die Loreley”)之下时,他们差不多是在向他致敬,从而出人意料地将那些暗中闪烁的诗句批准为民歌,它们让人想起失传已久的奥芬巴赫歌剧中巴黎莱茵河畔的仙女。

关键词：海涅刺激物奥芬巴赫莱茵河诽谤德国伤口出人意料

Glia-to-neuron reprogramming to the rescue?

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Neural Regeneration Research 2025年第5期20卷 1395-1396页

作者： Jack w.Hickmott Cindi M.Morshead Department of Surgery University of TorontoTorontoONCanada Donnelly Centre for Cellular and Biomolecular Research TorontoONCanada Institute of Biomedical Engineering University of TorontoTorontoONCanada The KITE Research Institute Toronto Rehabilitation InstituteUniversity Health NetworkTorontoONCanada

Over the last tw. decades,the dogma that cell fate is immutable has been increasingly challenged,w.th important implications for regenerative *** brea kth rough discovery that induced pluripotent stem cells could be generated from adult mouse fibroblasts is pow.rful proof that cell fate can be *** exciting extension of the discovery of cell fate impermanence is the direct cellular reprogram ming hypothesis-that terminally differentiated cells can be reprogrammed into other adult cell fates w.thout first passing through a stem cell state.

关键词： programming passing proof

被勒索的和解——评卢卡奇《反对被误解的现实主义》

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外国美学

外国美学 2024年第1期 1-28页

作者：特奥多尔·w.阿多诺赵勇赵天舒北京师范大学文学院清华大学人文学院中文系

1956年10月“匈牙利事件”爆发之后,“西方马克思主义”鼻祖卢卡奇的左翼立场虽有所调整,但是他对马克思主义认识论和反映论的看法并无太大变化。1958年6月,他在联邦德国出版《反对被误解的现实主义》（w.der den Miβverstandenden Rea...

1956年10月“匈牙利事件”爆发之后,“西方马克思主义”鼻祖卢卡奇的左翼立场虽有所调整,但是他对马克思主义认识论和反映论的看法并无太大变化。1958年6月,他在联邦德国出版《反对被误解的现实主义》（w.der den Miβverstandenden Realismus,English:Realism in Our Time）,为现实主义的创作方法辩护,对先锋文学则全盘否定,同时他也首次提出了艺术形式和技巧的客观性问题。是年年底,阿多诺在《月刊》（Der Monat,Vol.11,November 1958,pp.37ff.）发表《被勒索的和解——论格奥尔格·卢卡奇》（“Erpreβte Vers?hnung:Zu Georg Lukács:w.der den Miβverstandenden Realismus”）予以辨析和批驳,为现代主义辩护。这便是阿多诺撰写此文的由来。1934年8月,在苏联作家高尔基和党内重要官员日丹诺夫的提议下,“社会主义现实主义”这一理论命题和创作原则横空出世。该原则包含了经典马克思主义文学理论的一些成分,但重心已经转移。恩格斯认为,作者的见解在现实主义文学中越隐蔽越好,但社会主义现实主义则更强调说教方法。斯大林说,作家应当是“灵魂工程师”;日丹诺夫说,这意味着作家有责任在社会改造中起作用,他应当忠实描绘处在革命进程中的生活,包括用社会主义精神从思想上改造和教育劳动者。于是,社会主义现实主义中补充了“革命浪漫主义”的概念,日丹诺夫甚至认为,把“革命浪漫主义”和“最崇高的英雄主义与博大的视野”结合起来,是社会主义现实主义的组成部分。1卢卡奇是马克思主义反映论和现实主义文学的维护者,在他看来,现实主义作品才是唯一真正的文学作品,而拓展社会主义现实主义则成了他的题中应有之义。与此相对应,现代主义的先锋派文学艺术则被卢卡奇视为病态之作和“颓废派”。而由于这种艺术样式借助主观的经验“幻觉”形成与现实世界的关系,卢卡奇便认为它们无法正确地“反映”这个现实。为了给现代文学安上法西斯主义罪名,他甚至找到里尔克的一首歪诗,“并像一头闯进瓷器店的公牛一样在诗中横冲直撞”,想以此证明现代主义文学问题多多。作为现代主义文学艺术的捍卫者,阿多诺对卢卡奇的“歪理邪说”自然不能坐视不管,于是在此文中见招拆招,迎头痛击,就成了阿多诺的基本战术。概而言之,阿多诺批判卢卡奇的观点主要体现在:一、青年卢卡奇是值得敬佩的,但后来随着他进入苏联阵营,其奉行的马克思主义便越来越成为“钦定”的马克思主义,其言谈话语也越来越具有了文化官员的口吻。二、黑格尔的思想是卢卡奇的理论武库,但许多时候他都在误用或滥用黑格尔。博克瑙曾经说过,“他再也受不了人们用市议会精神谈论黑格尔逻辑和在黑格尔逻辑范畴内谈论市政法规了”。卢卡奇拿黑格尔说事亦可作如是观。三、卢卡奇指责为现代文学辩护的人严重高估了形式和风格,但他忘了艺术作为认识正是通过形式、风格和技术,才能有效区别于科学认识。普鲁斯特在其作品中把最精确的“现实主义”的观察与非意愿记忆的形式美学法则紧密结合在一起,便很能说明问题。四、艺术存在于现实之中,并在现实中发挥着作用,但它之所以有价值,是因为它始终站在现实的对立面。因此,艺术作品内容的真实与社会现实的真实并不相同,假如取消了这一区分,所有的作品在美学上都将失去基础。五、艺术对现实的认识不是通过照相式或“透视式”地描绘,而是通过其自主性构成来表达被现实所采取的经验形式所掩盖的东西。卢卡奇简化了艺术与科学的辩证统一,使之完全合而为一,仿佛艺术作品只是从透视角度预测了一些社会科学随后努力证实的东西。六、卢卡奇一直在对批判现实主义和社会主义现实主义进行区分并加以论证,但他并没有意识到后者是对每一种不守规矩之冲动的扼杀。同时,他对社会主义现实主义的加持也削弱了他对他所赞扬的批判现实主义的敏感。1

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Generalized time-dependent generator coordinate method for induced fission dynamics

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Frontiers of physics 2024年第4期19卷 1-12页

作者： B.Li D.Vretenar T.Nikšić J.Zhao P.w.Zhao J.Meng State Key Laboratory of Nuclear Physics and Technology School of PhysicsPeking UniversityBeijing 100871China Physics Department Faculty of ScienceUniversity of Zagreb10000 ZagrebCroatia Center for Circuits and Systems Peng Cheng LaboratoryShenzhen 518055China

The generalized time-dependent generator coordinate method(TD-GCM)is extended to include pairing *** correlated GCM nuclear w.ve function is expressed in terms of time-dependent generator states and w.ight *** particle–hole channel of the effective interaction is determined by a Hamiltonian derived from an energy density functional,w.ile pairing is treated dynamically in the standard BCS approximation w.th time-dependent pairing tensor and single-particle occupation *** the inclusion of pairing correlations,various time-dependent phenomena in open-shell nuclei can be described more *** model is applied to the description of saddle-to-scission dynamics of induced *** generalized TD-GCM charge yields and total kinetic energy distribution for the fission of 240Pu,are compared to those obtained using the standard time-dependent density functional theory(TD-DFT)approach,and w.th available data.

关键词： nuclear density functional theory generator coordinate method fission dynamics