Geometry of the canonical Van Vleck transformation part II: Further developments and numerical treatment

J?rgensen Flemming

摘要

Abstract > Kvaal's geometric approach from Part I is developed, now with inclusion of a modified version of his efficient method for numerical determination of representing matrices and with an extension to block‐diagonalization. In Part I methods of polar decomposition (PD) and singular value decomposition (SVD) are applied to the simple operator type="mathematics"> S ( type="mathematics"> = PP <sub>0</sub> ?+? QQ <sub>0</sub> ). Now, we build on results for the PD/SVD of an arbitrary operator type="mathematics"> b . Intimate connections to L?wdin's two orthonormalization methods are found, recurring in most results concerning geometry of the canonical VVT—including the numerical analysis. Theorems of the Carlson‐Keller type are discussed in terms of the Frobenius' norm and inner product for operators. With minimum considered as one stationary value among several, the result unites the theorems of uniqueness by Klein and by J?rgensen. We review Brandow's recognition of L?wdin's methods in des Cloizeaux’ pioneering work. The canonical gave the first example of Kvaal's principal vectors. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><abstract type =“main”xml：lang =“en”> <标题类型=“main”>抽象</ title> > kvaal从第二部分开始的kvaal的几何方法，现在包含一个修改的版本的高效用于表示矩阵的数值确定的方法和扩展到块对角化。在第一部分中，极性分解</ i>（pd）和奇异值分解</ i>（svd）被应用于简单的运算符类型=“数学”> s < / i> </ span>（ type =“数学”> = pp </ i> <sub> 0 </ sub>？+？ qq </ i> <sub> 0 </ sub> </ span>）。现在，我们建立了任意运算符类型=“数学”> b </ i> </ span>的结果。对L？WDIN的两个正常化方法的密切相关，在大多数关于规范VVT的几何形状的大多数结果中重复 - 包括数值分析。 Carlson-Keller类型的定理在Frobenius的规范和运营商内部产品方面讨论。最小值被认为是几个静止值，结果将Klein和J？Rgensen的唯一性定理统一。我们审查Brandow在Des Cloizeaux的开创性工作中得到了L？WDIN的方法。规范给出了KVAAL的主要向量的第一个例子。 </ p> </ abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-21753/'>《International Journal of Quantum Chemistry》</a> <b style="margin: 0 2px;">|</b><span>2018年第21期</span><b style="margin: 0 2px;">|</b><span>共21页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=J?rgensen Flemming&option=202" target="_blank" rel="nofollow">J?rgensen Flemming;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>Physics departmentN?stved Gymnasium og HFNyg?rdsvej 43. Denmark 4700;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/1186.html" title="物理化学（理论化学）、化学物理学">物理化学（理论化学）、化学物理学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=canonical Van Vleck transformation&option=203" rel="nofollow">canonical Van Vleck transformation;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=effective Hamiltonian&option=203" rel="nofollow">effective Hamiltonian;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=geometrical interpretation&option=203" rel="nofollow">geometrical interpretation;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=polar‐ and special‐ value decomposition&option=203" rel="nofollow">polar‐ and special‐ value decomposition;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=theorem of uniqueness&option=203" rel="nofollow">theorem of uniqueness;</a> </p> <div class="translation"> 机译：规范范vleck转型;有效的汉密尔顿人;几何解释;极性和特殊值分解;唯一性定理; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704019755703.html">Geometry of the canonical Van Vleck transformation part II: Further developments and numerical treatment</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=J?rgensen Flemming&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">J?rgensen Flemming </a> <a href="/journal-foreign-21753/" target="_blank" rel="nofollow" class="tuijian_authcolor">International Journal of Quantum Chemistry .</a> <span>2018</span><span>,第21期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：典卡van vleck变换部分的几何形状第二部分：进一步的发展和数值治疗</span> </p> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704019947259.html">Phase Transformations and Microstructural Development in the U-10 WtPct Mo Alloy with Varying Zr Contents After Heat Treatments Relevant to the Monolithic Fuel Plate Fabrication Process</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Mehta Abhishek&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Mehta Abhishek,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Eriksson Nicholas&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Eriksson Nicholas,</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Newell Ryan&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">Newell Ryan,</a> <a href="/journal-foreign-24842/" target="_blank" rel="nofollow" class="tuijian_authcolor">Metallurgical and Materials Transactions, A. 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HechtMichel CondetFrancoise</a> <span> <a href="/journal-cn-8168/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 现代铸铁 </a> </span> <span> . 2004</span><span>,第5期</span> </span> </div> </li> <li> <div> <b>6. </b><a class="enjiyixqcontent" href="/academic-conference-cn_meeting-23612_thesis/02022925033.html">考虑冷气组分扩散的气冷涡轮流场的数值模拟第二部分数值模拟结果分析</a> <b>[C]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=王强&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 王强</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=颜培刚&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,颜培刚</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=王松涛&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,王松涛</a> <span> <a href="/conference-cn-23612/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 2006中国工程热物理学会热机气动力学学术会议 </a> <span> <span> . 2006</span> </span> </div> </li> <li> <div> <b>7. </b><a class="enjiyixqcontent" href="/academic-degree-domestic_mphd_thesis/020316233875.html">早期食管癌内镜下治疗远期疗效及术后食管狭窄危险因素的研究；第一部分内镜下分片黏膜切除术治疗早期食管癌及癌前病变的远期疗效分析；第二部分早期食管癌及癌前病变内镜黏膜下剥离术后食管顽固性狭窄危险因素探究及预测模型的构建</a> <b>[A] </b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=史磊&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 史磊</a> <span> . 2020</span> </span> </div> </li> </ul> <ul style="display: none;"> <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/patent-detail/06120101507535.html">数值核反应堆多几何形状全堆芯子通道并行任务划分方法</a> <b>[P]</b> . <span> 中国专利： CN110532093A </span> <span> . 2019-12-03</span> </div> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/patent-detail/06120111154370.html">在包括回弹补偿的片状金属成型操作的数值模拟中设计工具组的几何形状的系统和方法</a> <b>[P]</b> . <span> 中国专利： CN108694267A </span> <span> . 2018-10-23</span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130425480487.html">In vitro method for diagnosing hepatocellular carcinoma (hcc) in an individual, or for assessing an individual's predisposition to the development of hcc, or for assessing the progression of said disease in an individual, or for determining the stage or severity of said disease. disease in an individual, in vitro method for identifying and evaluating the effectiveness of hcc treatments, use of a gene nucleotide sequence, use of a gene selected from adh, aop2, smp30, nslt, asao, sap genes , pgm, p4h, apoa1, caiii, addhm, oat, oct and combinations thereof, and / or a selected protein from adh proteins, aop2, smp30, nslt, asao, sap, pgm, p4h, apoa1, caiii, addhm, oat, oct and combinations thereof, Method for selection, screening, identification, development and evaluation of the efficacy of compounds in the treatment of hcc, In vitro method to identify a stage prior to the development of hepatocellular carcinoma (hcc) in an ind iv, use of a gene selected from the adh, aop2, smp30, nslt, a</a> <b>[P]</b> . <span> 外国专利：  BRPI0617560A2 </span> <span> . 2011-07-26</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：用于诊断个体中肝细胞癌（hcc），或评估个体对hcc发生的易感性，或评估个体中所述疾病的进展，或用于确定所述疾病的阶段或严重性的体外方法。一种用于鉴定和评估hcc治疗有效性的体外方法，基因核苷酸序列的使用，选自adh，aop2，smp30，nslt，asao，sap基因，pgm，p4h，apoa1， caiii，addhm，燕麦，oct及其组合，和/或选自adh蛋白质，aop2，smp30，nslt，asao，sap，pgm，p4h，apoa1，caiii，addhm，燕麦，oct和其组合的蛋白质选择，筛选，鉴定，开发和评估化合物在治疗hcc中的功效，使用体外方法鉴定ind iv中肝细胞癌（hcc）发生之前的阶段，使用选自adh的基因，aop2，smp30，nslt，a </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130417737277.html">Processing methods of digital audio signal include receiving a set of actual numerical transformation factors, implementing the first longitude transformation, applying the second P-length transformation Q library, and extracting sequences from the numerical signal samples. Really?</a> <b>[P]</b> . <span> 外国专利：  CL2013002762A1 </span> <span> . 2014-03-07</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：数字音频信号的处理方法包括：接收一组实际的数字变换因子;实现第一经度变换;应用第二P长度变换Q库;以及从数字信号样本中提取序列。真？ </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130416523931.html">Spatially transformed film for e.g. partition building, has printing or coating pattern formed corresponding to geometry of transformation, where geometry of transformation and pattern are formed such that radiation is less transmitted</a> <b>[P]</b> . <span> 外国专利：  DE102012015735A1 </span> <span> . 2014-02-13</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：空间转换的胶片，例如隔断建筑，具有与变换几何形状相对应的印刷或涂层图案，其中形成的变换几何形状和图案使得辐射较少透射 </span> 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