How stop google from giving too much link juice to particular URLs?

We have a product website with separate pages for product details, product images, product videos, product reviews.

We want to design a card for our products which we can use everywhere i.e. on internal website ads, cross-sell etc. Below is a sample card.

There is a problem that we see here – this will create too many linkages to our product review, images and videos page. The most important page for us is the product details page and we want to give maximum link juice to that page.

How can we fix this link juice distribution problem and indicate to google that product details is the most important link out of all these links?

We are apprehensive of doing no-crawl/no-follow as we are not sure if it would solve this issue.

Morphism of Lie groups $\theta:G\rightarrow H$ giving an equivalence of categories $BG\rightarrow BH$?

Given a morphism of Lie groups $$\theta:G\rightarrow H$$  and a principal $$G$$ bundle $$\pi:P\rightarrow M$$ there are (at least) two ways to assign a principal $$H$$ bundle.

1. See that the morphism of Lie groups $$\theta:G\rightarrow H$$ gives an action of $$G$$ on $$H$$ by $$g.h=\theta(g).h$$. Given an action of $$G$$ on manifold (Lie group in this case) $$H$$ there is an associated fibre bundle $$P\times_G H\rightarrow M$$ with fibre $$H$$. This gives a principal $$H$$ bundle.
2. For principal bundle $$\pi:P\rightarrow M$$, we can find an open cover $$\{U_\alpha\}$$ of $$M$$ and  (transition) maps $$g_\alpha g_\beta:U_{\alpha\beta}\rightarrow G$$ satifsying the cocycle condition $$g_{\alpha\beta}g_{\beta\gamma}=g_{\alpha\gamma}$$ on $$U_\alpha\cap U_\beta\cap U_\gamma$$. Then the compositions $$\tau_{\alpha\beta}=\theta\circ g_{\alpha\beta}:U_{\alpha\beta}\rightarrow G\rightarrow H$$ also satifies the cocycle condition $$\tau_{\alpha\beta}\tau_{\beta\gamma}=\tau_{\alpha\gamma}$$ on $$U_\alpha\cap U_\beta\cap U_\gamma$$. One can then produce a principal $$H$$ bundle over $$M$$ given this open cover $$\{U_\alpha\}$$ of $$M$$ and smooth maps $$\tau_{\alpha\beta}:U_\alpha\cap U_\beta\rightarrow H$$ satisfying the cocycle condition. This gives a principal $$H$$ bundle.

It is a good exercise (that I have not tried) to check that principal $$H$$ bundles obtained from above two methods are (naturally) isomorphic.

Given a Lie group $$G$$, let $$BG$$ denote the category of principal $$G$$ bundles. Objects are principal $$G$$ bundles and morphisms are $$G$$-equivariant morphisms.

Given a morphism of Lie groups $$\theta:G\rightarrow H$$, above construction gives a functor (at the level of objects) $$B\theta:BG\rightarrow BH$$. It is not difficult to see that, a $$G$$-equivarint map induce a $$H$$-equivariant map. This gives a functor.

I am trying to understand what can we say about $$\theta:G\rightarrow H$$ if we know that $$B\theta:BG\rightarrow BH$$ is an equivalence of categories? Does it have to be a diffeomorphism? Any comments are welcome.

Server Hunter – Giving away $1,000 worth of VPSs To celebrate the launch of ServerHunter.com, we partnered with three hosting providers to give away three annual subscriptions to 3 powerful KVM VPSs worth over$ 1,000 USD.

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Good luck!

XRDP: connection problem, giving up (ubuntu 18.04 server)

Here’s the exact message it’s giving me: enter image description here

Ive tried opening up an ssh connection on port 3350, also tried just about every “solution” online for this. I did get connected with ultravnc earlier, but its so laggy and hard to use that I decided I needed something better.

I really like using RDP, but if you know something else I can use fullscreen with no lag let me know.

MORPH TARGET INFLUENCES continuously keeps giving me UNDEFINED when animating object in three.js

So I exported this simple 2d animation (circle that morphs into a triangle) as a gltf file into my three.js project. But when i run it, I get this error: “Uncaught TypeError: Cannot set property ‘0’ of undefined at render“. This error come this line of code: “mesh.morphTargetInfluences[ 0 ] = Math.sin(delta) * 20.0;

By looking at my code, i made sure my scene is my mesh. I also log the mesh geometry to see that is not undefined. I get no errors when i set my Morph Targets to TRUE either. But When i do console(console.log(mesh.morphTargetInfluences) i do get UNDEFINED which i don’t know why since all the mesh geometry is there.

<html> <head>     <title>threejs - models</title>     <style>         body{             margin: 0;             overflow: hidden;         }     </style> </head> <body> <canvas id="myCanvas"></canvas>  <script src="js/three.js"></script> <script src="js/GLTFLoader.js"></script>  <script>  var renderer,     scene,     camera,     myCanvas = document.getElementById('myCanvas'); var mesh;   //RENDERER renderer = new THREE.WebGLRenderer({   canvas: myCanvas,    antialias: true }); renderer.setClearColor(0xffffff); renderer.setPixelRatio(window.devicePixelRatio); renderer.setSize(window.innerWidth, window.innerHeight);  //CAMERA camera = new THREE.PerspectiveCamera(35, window.innerWidth / window.innerHeight, 0.1, 1000 );  //SCENE scene = new THREE.Scene();  //LIGHTS var light = new THREE.AmbientLight(0xffffff, 0.5); scene.add(light);  var light2 = new THREE.PointLight(0xffffff, 0.5); scene.add(light2);  var loader = new THREE.GLTFLoader();  loader.load('morphObj.gltf', function ( gltf ) {          gltf.scene.traverse( function ( node ) {              if ( node.isMesh ) {                 mesh = node;                 mesh.material.morphTargets = true;               console.log(mesh.geometry);         }          } );          //mesh.material.morphTargets = true;         console.log(mesh.morphTargetInfluences);          //console.log(mesh.material.morphTargets);      //mesh.material = new THREE.MeshLambertMaterial();     scene.add( mesh );     mesh.position.z = -10; });    //RENDER LOOP render();  var delta = 0; var prevTime = Date.now();  function render() {      delta += 0.1;      if ( mesh !== undefined ) {         console.log("mesh is not undefined!");           mesh.rotation.y += 0.01;          //animation mesh          mesh.morphTargetInfluences[ 0 ] = Math.sin(delta) * 20.0;     }      renderer.render(scene, camera);      requestAnimationFrame(render); }      </script>> </body> </html> 

I’m very new to three.js so fusure I’m forgetting something in my program, but i don’t know what that is. I will really appreciate your help guys

Countifs and Sumproduct is giving Different results

I am using excel 2010. So, I used Countifs instead of sumproduct and to my surprise the results are different and the sumproduct results are accurate. So Would like to take your help in understanding what did I do with countifs for not getting the accurate results.

The Data and the results are provided in the below links with the formulas. Could you please help me in understanding where I am doing it wrong.

Regards, Kiran

Connection on a principal bundle $P(M,G)$ giving a functor on $\mathcal{P}_1(M)$

Question : Let $$P(M,G)$$ be a principal $$G$$ bundle. How does connection on $$P(M,G)$$ defines a functor $$\text{Hol}: \mathcal{P}_1(M)\rightarrow BG$$ (here $$BG$$ is the Lie groupoid whose morphism set is $$G$$ whose object set is $$\{*\}$$).

I have seen in some places that, giving a connection on $$P(M,G)$$ is giving a map $$P_1(M)\rightarrow G$$.

Here $$P_1(M)$$ are special collection of special types of paths. This is the morphism set of what is called the path groupoid of $$M$$, usually denoted by $$\mathcal{P}_1(M)$$ whose objects are elements of $$M$$.

Once this is done, seeing the Lie group $$G$$ as a Lie groupoid $$BG$$ (I know this is a bad notation but let me use this for this time) whose set of objects is singleton and set of morphisms is $$G$$. This would then give a functor $$\mathcal{P}_1(M)\rightarrow BG$$. They say giving a connection means giving a functor $$\mathcal{P}_1(M)\rightarrow BG$$ with some good conditions.

Then, to make sense of $$2$$-connections, they just have to consider $$\mathcal{P}_2(M)\rightarrow \text{some category}$$.

This is the set up.

I do not understand (I could not search it better) how giving a connection on $$P(M,G)$$ gives a map $$\text{Hol}:P_1(M)\rightarrow G$$. For each path $$\gamma$$ in $$M$$ they are associating an element of $$G$$ and calling it to be the holonomy of that path $$\gamma$$. They say it is given by integrating forms on paths.

All I know is, a connection on $$P(M,G)$$ is a $$\mathfrak{g}$$ valued $$1$$-form on $$P$$ with some extra conditions.

Suppose I have a path $$\gamma$$ on $$M$$, how do I associate an element of $$G$$? Is it $$\int_{\gamma}\omega$$? How to make sense of this? It is not clear how I should see this as $$\omega$$ is a form on $$P$$ and $$\gamma$$ is a path on $$M$$.

To make sense of this, there are two possible ways I can think of.

• I have to pull back the path $$\gamma$$ which is on $$M$$ to a path on $$P$$. So that both the differential form and path are in same space.
• I have to push forward $$\omega$$ to a (collection of) form(s) on $$M$$. So that both the differential form and path are in same space.

Given a path $$\gamma:[0,1]\rightarrow M$$ with $$\gamma(0)=x$$, fix a point $$u\in \pi^{-1}(x)$$. Then, connection gives a unique path $$\widetilde{\gamma}$$ in $$P$$ whose starting point is $$u$$ such that projection of $$\widetilde{\gamma}$$ along $$\pi$$ is $$\gamma$$. The problem here is that we have to fix a point $$u$$. Only then we can get a curve. It can happen that for any two points on $$\pi^{-1}(x)$$ may give same result but I am not sure if that is true. I mean, let $$\widetilde{\gamma}_u,\widetilde{\gamma}_v$$ be lifts of $$\gamma$$ fixing $$u\in \pi^{-1}(x)$$ and $$v\in \pi^{-1}(x)$$ respectively. Does it then happen that $$\int_{\widetilde{\gamma}_u}\omega=\int_{\widetilde{\gamma}_v}\omega$$?

Even if this is the case, what does it mean to say integrating a $$\mathfrak{g}$$ valued $$1$$-form on a path? How is it defined? I guess it should give an element $$A$$ of $$\mathfrak{g}$$ (just like integrating a $$\mathbb{R}$$ valued $$1$$-form along a path gives an element of $$\mathbb{R}$$). Do we then see image of $$A$$ under $$\text{exp}:\mathfrak{g}\rightarrow G$$ to get an element of $$G$$? We can declare this to be $$\int_{\gamma}\omega$$.

Is this how we associate an element of $$G$$ to a path $$\gamma$$ in $$M$$??

Otherwise, given $$\omega$$ on $$P$$, using trivialization, we can get an open cover $$\{U_i\}$$ of $$M$$ and get forms $$\mathfrak{g}$$ valued $$1$$-forms $$\omega_i$$ on $$U_i$$ with some compatibility on intersections.

We can consider $$\gamma_i:[0,1]\bigcap \gamma^{-1}(U_i)\rightarrow U_i$$. These $$\gamma_i$$ are paths on $$U_i$$ and $$\omega_i$$ are $$1$$-forms on $$U_i$$. So, $$\int_{U_i}\gamma_i$$ makes sense. This gives a collection of elements $$\{A_i\}$$ of $$\mathfrak{g}$$ and may be all these comes from a single element $$A\in \mathfrak{g}$$ and seeing its image under $$\text{exp}:\mathfrak{g}\rightarrow G$$ gives an element in $$G$$. We can then declare it to be $$\int_{\gamma}\omega$$.

Is this how we associate an element of $$G$$ to a path $$\gamma$$ in $$M$$??

Error : Exception in thread “main” java.util.concurrent.CancellationException: Task was cancelled. at com.google.common.util.concurrent.AbstractFuture.cancellationExceptionWithCause(AbstractFuture.java:1237) at com.google.common.util.concurrent.AbstractFuture.getDoneValue(AbstractFuture.java:524) at com.google.common.util.concurrent.AbstractFuture.get(AbstractFuture.java:487) at com.google.common.util.concurrent.AbstractFuture$TrustedFuture.get(AbstractFuture.java:83) at com.google.common.util.concurrent.ForwardingFuture.get(ForwardingFuture.java:62) at com.google.api.gax.longrunning.OperationFutureImpl.get(OperationFutureImpl.java:127) Giving birth to a child in UK [migrated] I am currently in the UK on a visit visa since 13 th of October 2018 with my UK husband . He got his passport from his dad not by birth .. now i am pregnant and my due date is on 7th of September 2019. I have to go to my home country after 6 months from my first entry so i have to be in my home country by April . The thing that i want to deliver my baby in the UK to grant him the citizenship. Regarding the spouse visa , we will be capable to sumbit it after July so i am afraid we might get a reply after my delivery. So please help. elasticsearch-6.5.4 unable to start giving jvm errors on Ubuntu17.0 Good morning All, Merry Christmas and Good luck. I installed Linux Ubunto 17.0 and then I installed elasticsearch-6.5.4 followed by Java 11.0. However when I start the elastic search, it keeps giving me the errors related to jvm. Could you please help me. I was able to run elasticsearch on my old machine with Ubunto 14.0. I really appreciate your kind help because I am new to elasticsearch-6.5.4 please. Thank you. Venu@venu-INVALID:~/elasticsearch-6.5.4/bin$ java -version java version “11.0.1” 2018-10-16 LTS Java(TM) SE Runtime Environment 18.9 (build 11.0.1+13-LTS) Java HotSpot(TM) 64-Bit Server VM 18.9 (build 11.0.1+13-LTS, mixed mode)
venu@venu-INVALID:~/elasticsearch-6.5.4/bin$./elasticsearch Exception in thread “main” java.nio.file.AccessDeniedException: /home/venu/elasticsearch-6.5.4/config/jvm.options at java.base/sun.nio.fs.UnixException.translateToIOException(UnixException.java:90) at java.base/sun.nio.fs.UnixException.rethrowAsIOException(UnixException.java:111) at java.base/sun.nio.fs.UnixException.rethrowAsIOException(UnixException.java:116) at java.base/sun.nio.fs.UnixFileSystemProvider.newByteChannel(UnixFileSystemProvider.java:215) at java.base/java.nio.file.Files.newByteChannel(Files.java:370) at java.base/java.nio.file.Files.newByteChannel(Files.java:421) at java.base/java.nio.file.spi.FileSystemProvider.newInputStream(FileSystemProvider.java:420) at java.base/java.nio.file.Files.newInputStream(Files.java:155) at org.elasticsearch.tools.launchers.JvmOptionsParser.main(JvmOptionsParser.java:60) venu@venu-INVALID:~/elasticsearch-6.5.4/ venu@venu-INVALID:~/elasticsearch-6.5.4/bin$ sudo ./elasticsearch [sudo] password for venu: Java HotSpot(TM) 64-Bit Server VM warning: Option UseConcMarkSweepGC was deprecated in version 9.0 and will likely be removed in a future release. Java HotSpot(TM) 64-Bit Server VM warning: UseAVX=2 is not supported on this CPU, setting it to UseAVX=1 [2018-12-25T09:36:22,232][WARN ][o.e.b.ElasticsearchUncaughtExceptionHandler] [unknown] uncaught exception in thread [main] org.elasticsearch.bootstrap.StartupException: java.lang.RuntimeException: can not run elasticsearch as root at org.elasticsearch.bootstrap.Elasticsearch.init(Elasticsearch.java:140) ~[elasticsearch-6.5.4.jar:6.5.4] at org.elasticsearch.bootstrap.Elasticsearch.execute(Elasticsearch.java:127) ~[elasticsearch-6.5.4.jar:6.5.4] at org.elasticsearch.cli.EnvironmentAwareCommand.execute(EnvironmentAwareCommand.java:86) ~[elasticsearch-6.5.4.jar:6.5.4] at org.elasticsearch.cli.Command.mainWithoutErrorHandling(Command.java:124) ~[elasticsearch-cli-6.5.4.jar:6.5.4] at org.elasticsearch.cli.Command.main(Command.java:90) ~[elasticsearch-cli-6.5.4.jar:6.5.4] at org.elasticsearch.bootstrap.Elasticsearch.main(Elasticsearch.java:93) ~[elasticsearch-6.5.4.jar:6.5.4] at org.elasticsearch.bootstrap.Elasticsearch.main(Elasticsearch.java:86) ~[elasticsearch-6.5.4.jar:6.5.4] Caused by: java.lang.RuntimeException: can not run elasticsearch as root at org.elasticsearch.bootstrap.Bootstrap.initializeNatives(Bootstrap.java:103) ~[elasticsearch-6.5.4.jar:6.5.4] at org.elasticsearch.bootstrap.Bootstrap.setup(Bootstrap.java:170) ~[elasticsearch-6.5.4.jar:6.5.4] at org.elasticsearch.bootstrap.Bootstrap.init(Bootstrap.java:333) ~[elasticsearch-6.5.4.jar:6.5.4] at org.elasticsearch.bootstrap.Elasticsearch.init(Elasticsearch.java:136) ~[elasticsearch-6.5.4.jar:6.5.4] … 6 more venu@venu-INVALID:~/elasticsearch-6.5.4/bin\$