{"id":4158,"date":"2023-03-18T11:34:07","date_gmt":"2023-03-18T10:34:07","guid":{"rendered":"http:\/\/mosaic-modeling.de\/?page_id=4158"},"modified":"2023-08-22T09:53:32","modified_gmt":"2023-08-22T08:53:32","slug":"model-connector","status":"publish","type":"page","link":"https:\/\/mosaic-modeling.de\/?page_id=4158","title":{"rendered":"Model: Connector"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">On this page<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4158\/#Purpose\" >Purpose<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4158\/#Concept-of-different-naming-policies-with-and-without-connectors\" >Concept of different naming policies with and without connectors<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4158\/#Naming-policies\" >Naming policies<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4158\/#Combination-of-connectors-and-naming-policies\" >Combination of connectors and naming policies<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4158\/#Case-A-naming-policy-%E2%80%9Cintegrate%E2%80%9D-connectors\" >Case A: naming policy &#8220;integrate&#8221; + connectors<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4158\/#Case-B-naming-policy-%E2%80%9Cintegrate%E2%80%9D-without-connectors\" >Case B: naming policy &#8220;integrate&#8221; without connectors<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4158\/#Case-C-naming-policy-%E2%80%9Cencapsulate%E2%80%9D-connectors\" >Case C: naming policy &#8220;encapsulate&#8221; + connectors<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4158\/#Case-D-naming-policy-%E2%80%9Cencapsulate%E2%80%9D-without-connectors\" >Case D: naming policy &#8220;encapsulate&#8221; without connectors<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mosaic-modeling.de\/?page_id=4158\/#Explanation-of-the-editor\" >Explanation of the editor<\/a><\/li><\/ul><\/nav><\/div>\n\n<p class=\"has-vivid-cyan-blue-color has-text-color\"><strong>Optional element<\/strong><\/p>\n\n\n<p>In this section, the use of connectors in combination with two different naming policies is explained.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Purpose\"><\/span>Purpose<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Connectors are modeling objects that translate between two di\u000bfferent namespaces, usually caused by the use of different notations. To make an equation system or equation using notation \u2018A\u2019 usable in an equation system using another notation (\u2018B\u2019), you need to specify a connector that provides all pertinent variables with a synonym complying to notation \u2018B\u2019.<\/p>\n<p>It is also possible to use a connector to rename certain variables whose meaning changes when added to another equation system, e.g. if a variable\u2019s superscript switches from \u201cout\u201d to \u201cin\u201d.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Concept-of-different-naming-policies-with-and-without-connectors\"><\/span>Concept of different naming policies with and without connectors<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Should the brief introduction regarding the purpose of connectors be too confusing at this point, the following paragraphs will hopefully reduce this confusion. We start with the description of the two naming policies, which are available in MOSAICmodeling. Then, we show how equations (or equation systems) can change under these naming policies in combination with or without connectors.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Naming-policies\"><\/span>Naming policies<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>We differ between two naming policies, which will be explained below.<\/p>\n<ol>\n<li>Naming policy &#8220;integrate&#8221;<\/li>\n<li>Naming policy &#8220;encapsulate&#8221;<\/li>\n<\/ol>\n<p>The basic rules of the naming policy &#8220;integrate&#8221; are:<\/p>\n<ul>\n<li>If an equation or equation system (sub element) is added to a super equation system (super element), the sub element\u2019s variables will get the namespace of the super element;<\/li>\n<li>If a sub element is connected to a super element, and both elements use different notations, then <em>all<\/em> variable names of the sub element have to be translated (by a connector) into the super notation;<\/li>\n<li>Attention: In any time the meaning of each variable has to be uniquely defined by the notation of its namespace. If different notations are used in sub and super element, each variable has to be translated. Otherwise the meaning of some variables coming from the sub element would be undefined in the notation (and therefore in the namespace) of the super element;<\/li>\n<li>Result: After parsing, all variables have a\u00a0<em>top level naming<\/em>\u00a0according to the super notation in the top level namespace.<\/li>\n<\/ul>\n<p>The basic rules of the naming policy &#8220;encapsulate&#8221; are:<\/p>\n<ul>\n<li>If an equation or equation system (sub element) is added to a super equation system (super element), the sub element\u2019s variables will get their own namespace;<\/li>\n<li>If a sub element is added to a super element by using a connector, only the variable names of the sub element that are translated by the connector will get the super element\u2019s namespace;<\/li>\n<li>When considering the sub element, only the variables translated by a connector have a <em>top level naming<\/em> according to the super notation.<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Combination-of-connectors-and-naming-policies\"><\/span>Combination of connectors and naming policies<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>We now demonstrate the concept of different naming policies with and without connectors for the equations and connectors below:<\/p>\n<p><strong>Equations:<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-8eca3a19fd384d277bd14976c300cf96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#97;&#32;&#61;&#32;&#92;&#98;&#101;&#116;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"67\" style=\"vertical-align: -4px;\"\/>\u00a0 (equation 1, namespace: e1)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-c0af13f572dd3dd7bfa3e62eec32b154_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#97;&#32;&#61;&#32;&#92;&#98;&#101;&#116;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" style=\"vertical-align: -4px;\"\/> \u00a0 (equation 2, namespace: e2)<\/p>\n<p><strong>Connectors:<\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-63e59dcaf80ada174f7c036bde6148e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#97;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#98;&#44;&#32;&#120;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#122;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"99\" style=\"vertical-align: -4px;\"\/>\u00a0 (connector 1, may be applied on equation 1)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-e8537b596aaff4f12d29663294665ecc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#97;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#99;&#44;&#32;&#121;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#97;&#114;&#114;&#111;&#119;&#32;&#122;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"98\" style=\"vertical-align: -4px;\"\/>\u00a0 (connector 2, may be applied on equation 2)<\/p>\n<figure id=\"attachment_1893\" aria-describedby=\"caption-attachment-1893\" style=\"width: 402px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/03\/Integrate-Encapsulate-Diagram.png\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1893 size-full\" src=\"http:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/03\/Integrate-Encapsulate-Diagram.png\" alt=\"\" width=\"402\" height=\"296\" srcset=\"https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/03\/Integrate-Encapsulate-Diagram.png 402w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/03\/Integrate-Encapsulate-Diagram-300x221.png 300w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/03\/Integrate-Encapsulate-Diagram-100x74.png 100w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2015\/03\/Integrate-Encapsulate-Diagram-150x110.png 150w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/a><figcaption id=\"caption-attachment-1893\" class=\"wp-caption-text\">Figure 1: Combination of connectors and naming policies<\/figcaption><\/figure>\n<h4><span class=\"ez-toc-section\" id=\"Case-A-naming-policy-%E2%80%9Cintegrate%E2%80%9D-connectors\"><\/span>Case A: naming policy &#8220;integrate&#8221; + connectors<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>In this case, the resulting equation system is:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-b3a1ab4f8b44815751ca12462b1f70e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#101;&#48;&#46;&#98;&#32;&#61;&#32;&#101;&#48;&#46;&#92;&#98;&#101;&#116;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#101;&#48;&#46;&#122;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"130\" style=\"vertical-align: -4px;\"\/>\u00a0 (equation 1, namespace: e0)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-4ee873a89053f04ca0ecfcd181baf2ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#101;&#48;&#46;&#99;&#32;&#61;&#32;&#101;&#48;&#46;&#92;&#98;&#101;&#116;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#101;&#48;&#46;&#122;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"130\" style=\"vertical-align: -4px;\"\/>\u00a0 (equation 2, namespace: e0)<\/p>\n<p>As you can see, the policy &#8220;integrate&#8221; caused all variables to have the same namespace. The connectors renamed the variables <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-0e55b0b3943237ccfc96979505679274_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-7e5fbfa0bbbd9f3051cd156a0f1b5e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"\/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-38461fc041e953482219abf5d4cce1cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"\/>. Please note that the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-7e5fbfa0bbbd9f3051cd156a0f1b5e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"\/> of the first equation and the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-38461fc041e953482219abf5d4cce1cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"\/> of the second equation became the same variable <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ec5583fa081a1e03212c151e3c222412_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/> in the final equation system. The final system contains four distinguishable variables (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ad69adf868bc701e561aa555db995f1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-0f39b655b53423e80558c68b8c2ae1c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#116;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"11\" style=\"vertical-align: -4px;\"\/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ec5583fa081a1e03212c151e3c222412_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/>).<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Case-B-naming-policy-%E2%80%9Cintegrate%E2%80%9D-without-connectors\"><\/span>Case B: naming policy &#8220;integrate&#8221; without connectors<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Without connector, we have<strong><br \/><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-c4454efe8343afb2818f4bd12bb72986_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#101;&#48;&#46;&#97;&#32;&#61;&#32;&#101;&#48;&#46;&#92;&#98;&#101;&#116;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#101;&#48;&#46;&#120;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"133\" style=\"vertical-align: -4px;\"\/>\u00a0 (equation 1, namespace: e0)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-48a3e51645b32130bf510eeb730272c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#101;&#48;&#46;&#97;&#32;&#61;&#32;&#101;&#48;&#46;&#92;&#98;&#101;&#116;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#101;&#48;&#46;&#121;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"132\" style=\"vertical-align: -4px;\"\/>\u00a0 (equation 2, namespace: e0)<\/p>\n<p>Again, the policy &#8220;integrate&#8221; caused all variables to have the same namespace.The final equation system contains four distinguishable variables (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-0e55b0b3943237ccfc96979505679274_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-0f39b655b53423e80558c68b8c2ae1c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#116;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"11\" style=\"vertical-align: -4px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-7e5fbfa0bbbd9f3051cd156a0f1b5e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"\/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-38461fc041e953482219abf5d4cce1cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"\/>).<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Case-C-naming-policy-%E2%80%9Cencapsulate%E2%80%9D-connectors\"><\/span>Case C: naming policy &#8220;encapsulate&#8221; + connectors<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>With the naming policy &#8220;encapsulate&#8221;, new name spaces are created:<strong><br \/><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-681cd651a6b4f38075cfbfc603804bfc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#101;&#48;&#46;&#98;&#32;&#61;&#32;&#101;&#48;&#101;&#49;&#46;&#92;&#98;&#101;&#116;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#101;&#48;&#46;&#122;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"147\" style=\"vertical-align: -4px;\"\/>\u00a0 (equation 1, no unified namespace)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-7365b7f47b5078c2e083d8ff17176df5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#101;&#48;&#46;&#99;&#32;&#61;&#32;&#101;&#48;&#101;&#50;&#46;&#92;&#98;&#101;&#116;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#101;&#48;&#46;&#122;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"147\" style=\"vertical-align: -4px;\"\/>\u00a0 (equation 2, no unified namespace)<\/p>\n<p>The connectors renamed the variables <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-0e55b0b3943237ccfc96979505679274_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-7e5fbfa0bbbd9f3051cd156a0f1b5e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"\/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-38461fc041e953482219abf5d4cce1cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"\/> to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ad69adf868bc701e561aa555db995f1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ec5583fa081a1e03212c151e3c222412_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/>, respectively, so that they are now part of the top level namespace (e0). On the other hand, the unconnected variable, i.e., <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-0f39b655b53423e80558c68b8c2ae1c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#116;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"11\" style=\"vertical-align: -4px;\"\/> got lower level namespaces (e0e1, e0e2) as it existed in the notations of both equation 1 and equation 2. The final equation system contains five distinguishable variables (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ad69adf868bc701e561aa555db995f1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-b61b2e53c1c2309e47047da190ca3b56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#101;&#48;&#101;&#49;&#46;&#92;&#98;&#101;&#116;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"50\" style=\"vertical-align: -4px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-18b98ed9aa25455cd92a68ba4ec4110a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#101;&#48;&#101;&#50;&#46;&#92;&#98;&#101;&#116;&#97;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"54\" style=\"vertical-align: -4px;\"\/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-ec5583fa081a1e03212c151e3c222412_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#122;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"\/>).<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Case-D-naming-policy-%E2%80%9Cencapsulate%E2%80%9D-without-connectors\"><\/span>Case D: naming policy &#8220;encapsulate&#8221; without connectors<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Finally, using &#8220;encapsulate without connectors results in<strong><br \/><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-1997615b5ff7bf72e6cab704d49209bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#101;&#49;&#46;&#97;&#32;&#61;&#32;&#101;&#49;&#46;&#92;&#98;&#101;&#116;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#101;&#49;&#46;&#120;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"133\" style=\"vertical-align: -4px;\"\/>\u00a0 (equation 1, namespace: e1)<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-4f6ffc5afa19cc13c100145fd8e4f306_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#32;&#101;&#50;&#46;&#97;&#32;&#61;&#32;&#101;&#50;&#46;&#92;&#98;&#101;&#116;&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#101;&#50;&#46;&#121;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"132\" style=\"vertical-align: -4px;\"\/>\u00a0 (equation 2, namespace: e2)<\/p>\n<p>Now, both equations retain their individual namespaces e1 and e2. Each variable got the namespace of its original equation. The final equation system contains six distinguishable variables (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-7968a41909380215f16726d8d116faf3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#101;&#49;&#46;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-56a5d08c1849490c078f632e5184a106_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#101;&#49;&#46;&#92;&#98;&#101;&#116;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"33\" style=\"vertical-align: -4px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-51fb72efa7288f57700a504f6a52b8e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#101;&#49;&#46;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"32\" style=\"vertical-align: 0px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-828d07e110345a265c7b11332c00a6e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#101;&#50;&#46;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-1f2436741302bf9e0f21bf999cf988fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#101;&#50;&#46;&#92;&#98;&#101;&#116;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"33\" style=\"vertical-align: -4px;\"\/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/mosaic-modeling.de\/wp-content\/ql-cache\/quicklatex.com-5f2e83c96260aa844e2de1adbde4abcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#101;&#50;&#46;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"31\" style=\"vertical-align: -4px;\"\/>).<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Explanation-of-the-editor\"><\/span>Explanation of the editor<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Every connector consists of three pieces of information: The sub notation, the super notation and a variable matching list. However, there are several ways to\u00a0<em>create<\/em> a connector. The standard way is to specify the sub and super notation directly and create the variable namings that need to be matched by hand. If you already have connectible elements (equations or equation systems) that you want to match, you can also load them into the connector editor. In this case, the notations and the variable namings are extracted from the loaded connected elements, which usually saves much work. The stored information, however, is still only the sub notation, the super notation and the variable matching list.<\/p>\n<figure id=\"attachment_4935\" aria-describedby=\"caption-attachment-4935\" style=\"width: 1920px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_Connector.png\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-4935\" src=\"http:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_Connector.png\" alt=\"\" width=\"1920\" height=\"1080\" srcset=\"https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_Connector.png 1920w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_Connector-300x169.png 300w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_Connector-1024x576.png 1024w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_Connector-768x432.png 768w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_Connector-1536x864.png 1536w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_Connector-1110x624.png 1110w, https:\/\/mosaic-modeling.de\/wp-content\/uploads\/2023\/08\/Editor_Connector-528x297.png 528w\" sizes=\"auto, (max-width: 1920px) 100vw, 1920px\" \/><\/a><figcaption id=\"caption-attachment-4935\" class=\"wp-caption-text\">Figure 1: The connector editor enables you to specify connectors that rename variables in your equation system, e.g., because you use equation systems of your colleagues.<\/figcaption><\/figure>\n\n\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table><thead><tr><th class=\"has-text-align-center\" data-align=\"center\">Element<\/th><th class=\"has-text-align-left\" data-align=\"left\">Explanation<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">File<\/td><td class=\"has-text-align-left\" data-align=\"left\">Filename of your connector once you have saved or loaded it<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Description<\/td><td class=\"has-text-align-left\" data-align=\"left\">A description of the current connector<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Keywords<\/td><td class=\"has-text-align-left\" data-align=\"left\">Optional keywords for your connector<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Usages<\/td><td class=\"has-text-align-left\" data-align=\"left\">Model elements, i.e., equations or functions, in which the connector is used<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Edit Matching<\/td><td class=\"has-text-align-left\" data-align=\"left\">Load the sub and the super notation. The variables of the sub notation will be replaced by the matches from the super notation. To connect variables from sub and super notation, add the respective variable with the &#8220;+Sub&#8221; and &#8220;+Super&#8221; buttons and match them. Do not forget to match the indices on the right side if the variables contains indices, e.g., for components<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">View Notations<\/td><td class=\"has-text-align-left\" data-align=\"left\">Take a look at all defined symbols in sub and super notation<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">View Connector<\/td><td class=\"has-text-align-left\" data-align=\"left\">See how exactly variables from the sub notation are translated into the super notation<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Test Connector<\/td><td class=\"has-text-align-left\" data-align=\"left\">Test your connector for an arbitry model element that uses the sub notation, e.g., an equation system<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 1: Elements of the connector editor.<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Optional element In this section, the use of connectors in combination with two different naming policies is explained. Purpose Connectors are modeling objects that translate between two di\u000bfferent namespaces, usually caused by the use of different notations. To make an equation system or equation using notation \u2018A\u2019 usable in an equation system using another notation [&hellip;]<\/p>\n","protected":false},"author":252,"featured_media":0,"parent":4140,"menu_order":6,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-4158","page","type-page","status-publish","czr-hentry"],"_links":{"self":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4158","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/users\/252"}],"replies":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4158"}],"version-history":[{"count":23,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4158\/revisions"}],"predecessor-version":[{"id":5685,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4158\/revisions\/5685"}],"up":[{"embeddable":true,"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=\/wp\/v2\/pages\/4140"}],"wp:attachment":[{"href":"https:\/\/mosaic-modeling.de\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4158"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}