THE FOUR AGES

Steve Hammer

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THE FOUR AGES

机译：四个时代

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In 1847 Charles-Valentin Alkan, Frederic Chopin's good friend and neighbour, published a massive piano sonata subtitled 'Les Quatre Ages'. The piece offers an impression of a man at 20 (impetuous, mercurial), 30 (inventive, fertile, questing), 40 (a much calmer paterfamilias), and 50 (melancholic, already (!) near death). The result is a beautiful tapestry with a unique tempo scheme: each age is slower than the last, the fourth being very slow and sombre indeed. (1)

机译：1847年，弗雷德里克·肖邦（Frederic Chopin）的好朋友和邻居查尔斯·瓦伦丁·阿尔坎（Charles-Valentin Alkan）发表了大型钢琴奏鸣曲，标题为“莱斯Quatre时代”。这件作品给人的印象是一个男人20岁（奔放，轻浮），30岁（富有创造力，肥沃，追求），40岁（一个平静得多的家长）和50岁（忧郁症，已经（！）接近死亡）。结果是精美的挂毯具有独特的拍速方案：每个年龄都比上一个年龄慢，第四个年龄非常慢且确实阴郁。（1）

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《Mesemb Study Group Bulletin 》 |2015年第3期| 共2页
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机译：为<直列式ID = “IEq1”> <替代>纠缠熵 T T ˉ < TEX-数学ID = “IEq1_TeX”> 的DocumentClass [12磅] {最小} usepackage {amsmath} usepackage {wasysym} usepackage {amsfonts} usepackage {amssymb} usepackage {amsbsy} usepackage {mathrsfs} usepackage { upgreek} setlength { oddsidemargin} { - 69pt} {开始文档} $$ mathrm【T} {划线 mathrm【T}} $$ {端文档} <直列图形的xlink：HREF = “MediaObjects / 13130__14822_IEq1.gif”/> ，<直列式ID = “IEq2”> <替代> Ĵ T ˉ 的DocumentClass [12磅] {最小} {usepackage amsmath} {usepackage wasysym} {usepackage amsfonts} {usepackage amssymb} {usepackage amsbsy} {usepackage mathrsfs} {usepackage upgreek} setlength { oddsidemargin} { - 69pt} {开始文档} $$ mathrm {Ĵ} 上划线{ mathrm【T}} $$ {端文档} <直列图形的xlink：HREF = “MediaObjects / 13130__14822_IEq2.gif”/> ，<直列式ID = “IEq3”> <替代> T < MML：MI mathvariant = “正常”>Ĵ ˉ 的DocumentClass [12磅] {最小} usepackage {amsmath} usepackage {wasysym} usepackage {amsfonts} usepackage {amssymb} usepackage {amsbsy} usepackage {mathrsfs} usepackage {upgreek} setlength { oddsidemargin} { - 69pt} {开始文档} $$ mathrm【T} {划线 mathrm {Ĵ}} $$ {端文档} <直列图形的xlink：HREF = “MediaObjects / 13130__14822_IEq3.gif”/> 变形全息CFT
2. Thermodynamics of T T ˉ documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ mathrm{T}overline{mathrm{T}} $$end{document} , J T ˉ documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ mathrm{J}overline{mathrm{T}} $$end{document} , T J ˉ documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ mathrm{T}overline{mathrm{J}} $$end{document} deformed conformal field theories [J] . Soumangsu Chakraborty, Akikazu Hashimoto The journal of high energy physics . 2020 ,第7期

机译：<内联公式ID =“IEQ1”> <替代品> T t ˉ DocumentClass [12pt] {minimal} usepackage {ammath} usepackage {isysym} usepackage {amsfonts} usepackage {amssys} usepackage {mathrsfs} usepackage {mathrsfs} usepackage {supbeek } setLength { oddsidemargin} { - 69pt} begin {document} $$ mathrm {t} overline { mathrm {t}} $$ end {document} <内联图xlink ：href =“13130_2020_13473_ARTICLICLE_IEQ1.gif”/> ， Ĵ T ˉ< / mml：mo> DocumentClass [12pt] {minimal} usepackage {ammath} usepackage {keysym} usepackage {amsfonts} usepackage {amssymb} usepackage {amsbsy} usepackage {mathrsfs} usepackage {supmeek} setLength { oddsideDemargin} {-69pt} begin {document} $$$$ mathrm {j} overline { $$ end {document} ，<内联公式id =“IEQ3”> <替代方案> T J ˉ 的DocumentClass [12磅] {最小} usepackage {amsmath} usepackage {wasysym} usepackage {amsfonts} usepackage {amssymb} usepackage {amsbsy} usepackage {mathrsfs} usepackage {upgreek} setlength { oddsidemargin} {-69pt} begin {document} $$ mathrm {t} overline { mathrm {t}} $$ end {document} 变形的保形磁场领域IES.
3. A path integral realization of joint J T ˉ documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ Joverline{T} $$end{document} , T J ˉ documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ Toverline{J} $$end{document} and T T ˉ documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ Toverline{T} $$end{document} flows [J] . Jeremías Aguilera-Damia, Victor I. Giraldo-Rivera, Edward A. Mazenc, The journal of high energy physics . 2020 ,第7期

机译：关节 <替代方案> j t ˉ documentClass [12pt] {minimal} usepackage {ammath} usepackage {keysym} usepackage {amsfonts} usepackage {amssymb} usepackage {amsbsy} usepackage {mathrsfs} usepackage {supmeek} setLength { oddsidemargin } { - 69pt} begin {document} $$ j overline {t} $$ end {document} ，<内联公式id =“IEQ2”> <替代方案> t j ˉ DocumentClass [12pt] {minimal} usepackage {ammath} usepackage {isysym} usepackage {amsfonts} usepackage {amssymb} usepackage {amsbsy} usepackage {mathrsf s} usepackage {supmeez} setLength { oddsidemargin} { - 69pt} begin {document} $$ t overline {j} $$ end {document} 和 t T ˉ < / mml：math> documentClass [12pt] {minimal} usepackage {ammath} usepackage {isysym} usepackage {amsfonts} usepackage {amssymb} usepackage {amsbsy} usepackage {mathrsfs} usepackage {supmeek} setLength { oddsidemargin} { - 69pt} begin {document} $$ t overline {t} $$ end {document} 流
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THE FOUR AGES

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