Riemannian geometry – connection between Yamabe invariant and Yamabe equation

I'm trying to understand Lee and Parker's solution to the Yamabe problem. It seems to me that the constant $ lambda $ what appears in the Yamabe equation $$ square varphi = lambda varphi ^ {p-1} $$ and the Yamabe invariant $ lambda = inf_ varphi Q_g ( varphi) $ Where $ Q_g $ is the functional $$ Q_ {g} ( varphi) = frac { int_ {M} left (a | nabla varphi | ^ {2} + S varphi ^ {2} right) d V_ {g}} { | varphi | _ {p} ^ {2}} = frac {E ( varphi)} { | varphi | _ {p} ^ {2}} $$ are indeed the same, that is, if $ varphi $ is an absolute minimum for the function $ Q_g $ then $ varphi $ is a solution to the Yamabe equation with $ lambda $ as the coefficient of $ varphi ^ {p-1} $, It seems to me that Aubin has explicitly demonstrated this in his book "Some Nonlinear Problems in Riemannian Geometry."

An explicit calculation of the Euler-Lagrange equation for $ Q_g $ (This is shown on page 39 of this paper by Lee and Parker and can easily be done explicitly.) This shows that the Euler equation is
$$
a Delta varphi + S varphi | varphi | _ {p} ^ {- p} E ( varphi) varphi ^ {p-1} = 0
$$

that is the Yamabe equation with
$$
lambda = frac {E ( varphi)} { | varphi | _ {p} ^ {p}}.
$$

For the Yamabe invariant to be the same constant that occurs in the Yamabe equation, the exponent on the denominator should be 2 and not $ p $,
So I'm a bit confused: Is the Yamabe invariant the same constant in the Yamabe equation in the presence of a solution? $ varphi $? If so, where do I go wrong?

SSL Certificate – httpd and curl: Configure the https connection for a client verification p12 file

I am providing a httpd. I need to configure ssl to validate the client based on its client certificate.

I have one for that p12 Private key, client certificate, and chain CA certificate files:

CA chain Certificates:

➜ ~ openssl pkcs12 -in fitxers.p12 -cacerts -nokeys
Bag Attributes
    ...
-----BEGIN CERTIFICATE-----
$$$$$$$...
-----END CERTIFICATE-----
Bag Attributes
    ...
-----BEGIN CERTIFICATE-----
$$$$$$$...
-----END CERTIFICATE-----

Client Certificate:

➜ ~ openssl pkcs12 -in fitxers.p12 -clcerts -nokeys
Bag Attributes
    ...
-----BEGIN CERTIFICATE-----
$$$$$$$...
-----END CERTIFICATE-----

Private client key:

➜ ~ openssl pkcs12 -in fitxers.p12 -nocerts
Bag Attributes
    ...
-----BEGIN PRIVATE KEY-----
$$$$$$$...
-----END PRIVATE KEY-----

To share this p12 File in separate certificate and key files:

➜ ~ openssl pkcs12 -in container.p12 -nocerts -out client.key.pem
➜ ~ openssl pkcs12 -in fitxers.p12 -clcerts -nokeys -out client.crt
➜ ~ openssl pkcs12 -in fitxers.p12 -cacerts -nokeys -out cacerts.crt

From now on, I configured my httpd as follows:

SSLEngine On
SSLCACertificateFile /usr/local/apache2/conf/cacerts.crt
...

I try to connect to Curl:

curl --cert client.crt --key client.key.pem https://localhost:8080/token -v
*   Trying 127.0.0.1...
* TCP_NODELAY set
* Connected to localhost (127.0.0.1) port 8080 (#0)
* ALPN, offering h2
* ALPN, offering http/1.1
Enter PEM pass phrase:
* successfully set certificate verify locations:
*   CAfile: /etc/ssl/certs/ca-certificates.crt
  CApath: /etc/ssl/certs
* TLSv1.3 (OUT), TLS handshake, Client hello (1):
* TLSv1.3 (IN), TLS handshake, Server hello (2):
* TLSv1.3 (IN), TLS Unknown, Certificate Status (22):
* TLSv1.3 (IN), TLS handshake, Unknown (8):
* TLSv1.3 (IN), TLS Unknown, Certificate Status (22):
* TLSv1.3 (IN), TLS handshake, Certificate (11):
* TLSv1.3 (OUT), TLS alert, Server hello (2):
* SSL certificate problem: unable to get local issuer certificate
* Closing connection 0
curl: (60) SSL certificate problem: unable to get local issuer certificate
More details here: https://curl.haxx.se/docs/sslcerts.html

In httpd server logs I get:

(Tue Sep 17 11:17:28.144219 2019) (ssl:info) (pid 8:tid 139871525332736) (client 10.0.2.4:52926) AH01964: Connection to child 68 established (server 10.0.2.47:443)
(Tue Sep 17 11:17:28.148318 2019) (ssl:debug) (pid 8:tid 139871525332736) ssl_engine_kernel.c(2375): (client 10.0.2.4:52926) AH02645: Server name not provided via TLS extension (using default/first virtual host)
(Tue Sep 17 11:17:28.155178 2019) (ssl:info) (pid 8:tid 139871525332736) (client 10.0.2.4:52926) AH02008: SSL library error 1 in handshake (server 10.0.2.47:443)
(Tue Sep 17 11:17:28.155569 2019) (ssl:info) (pid 8:tid 139871525332736) SSL Library Error: error:14094416:SSL routines:ssl3_read_bytes:sslv3 alert certificate unknown (SSL alert number 46)
(Tue Sep 17 11:17:28.155609 2019) (ssl:info) (pid 8:tid 139871525332736) (client 10.0.2.4:52926) AH01998: Connection closed to child 68 with abortive shutdown (server 10.0.2.47:443)
(Tue Sep 17 11:19:01.114529 2019) (ssl:info) (pid 8:tid 139871448463104) (client 10.255.0.2:48060) AH01964: Connection to child 69 established (server 10.0.2.47:443)
(Tue Sep 17 11:19:01.114667 2019) (ssl:debug) (pid 8:tid 139871448463104) ssl_engine_kernel.c(2354): (client 10.255.0.2:48060) AH02044: No matching SSL virtual host for servername localhost found (using default/first virtual host)
(Tue Sep 17 11:19:01.114674 2019) (ssl:debug) (pid 8:tid 139871448463104) ssl_engine_kernel.c(2354): (client 10.255.0.2:48060) AH02044: No matching SSL virtual host for servername localhost found (using default/first virtual host)
(Tue Sep 17 11:19:01.114679 2019) (core:debug) (pid 8:tid 139871448463104) protocol.c(2314): (client 10.255.0.2:48060) AH03155: select protocol from , choices=h2,http/1.1 for server 10.0.2.47
(Tue Sep 17 11:19:01.117705 2019) (ssl:info) (pid 8:tid 139871448463104) (client 10.255.0.2:48060) AH02008: SSL library error 1 in handshake (server 10.0.2.47:443)
(Tue Sep 17 11:19:01.117827 2019) (ssl:info) (pid 8:tid 139871448463104) SSL Library Error: error:14094418:SSL routines:ssl3_read_bytes:tlsv1 alert unknown ca (SSL alert number 48)
(Tue Sep 17 11:19:01.117858 2019) (ssl:info) (pid 8:tid 139871448463104) (client 10.255.0.2:48060) AH01998: Connection closed to child 69 with abortive shutdown (server 10.0.2.47:443)

I also tried with cacerts.pem With curl --cacert ./cacerts.pem --cert client.crt --key client.key.pem https://localhost:8080/token -v

Any ideas?

Networking – Virtualbox Ubuntu VM does not get IP on a wired connection, it gets on Wifi

I have a Windows XP host running Oracle VirtualBox. I have 3 Ubuntu (1604) VMs installed on them. They are all configured as a bridge network. When I use a wired LAN connection, I will never assign an IP address for the VMs connecting to the network. But if I use a WLAN (say a mobile WLAN), all IPs and things work great.

Any advice on how to solve this problem and obtain IP addresses in a wired network would be very helpful. Thank you very much

Network – The connection is made on one IP address, but not on another on the same host / network

I'm debugging a problem where some http random requests take longer than usual. (Normal are a few ms, unusually 1000 ms to a minute or more)

The host has multiple IPs and the service I work with is represented by Nginx on two of these IPs.

When I send requests to the first IP, everything works as expected and all requests are fast.
When I send requests to the second IP, a random request takes several seconds or more.

Both IPs are on the same NIC:

2: eth0:  mtu 1500 qdisc mq      master bond0 state UP group default qlen 1000
link/ether 00:0c:29:5e:47:7d brd ff:ff:ff:ff:ff:ff
3: bond0:  mtu 1500 qdisc noqueue state UP group default 
link/ether 00:0c:29:5e:47:7d brd ff:ff:ff:ff:ff:ff
inet 192.168.10.73/24 brd 192.168.10.255 scope global bond0
   valid_lft forever preferred_lft forever
inet 192.168.10.72/32 scope global bond0
   valid_lft forever preferred_lft forever
inet 192.168.10.75/32 scope global bond0
   valid_lft forever preferred_lft forever
inet 192.168.10.76/32 scope global bond0
   valid_lft forever preferred_lft forever
inet 192.168.10.54/32 scope global bond0
   valid_lft forever preferred_lft forever

So for example:

curl -H "Host: xxx" http://192.168.10.54/test

will happen to be slow while

curl -H "Host: xxx" http://192.168.10.75/test

is always fast.

Both IPs are served by the same nginx server block:

server {
        listen 192.168.10.75:6700;
        listen 192.168.10.54:6700;

        location / {
                proxy_pass http://...;
        }
}

I checked open ports, but there are only a few hundred connections on each IP.

This is under Linux (3.16.0-8-amd64 # 1 SMP Debian 3.16.64-2 (2019-04-01) x86_64 GNU / Linux)

I have no iptable rules

I am not sure how to proceed with the debugging and I would be pleased about hints 🙂

Specific questions:

  • I could check which IP-level settings differ on the same connection
  • Which metrics can I check to give me clues to the cause

Embedded Systems – How to Connect IOT Devices to the Android App (Initial Connection)

background
I'm starting a new project and would like custom IOT sensors for an app I write. I want to keep everything as simple as possible, so that no important software or the like is executed on the IOT devices. I want them to be as simple as sending and receiving curl statements (I know that they need something, but assume that they are as stupid as possible for the design they want, so I do not make assumptions).

Question:
So I'm not sure how I'm going to make the first connection between the app and the IOT device without it being connected to the internet. I was thinking about setting up an HTTP listener in the app, where the IOT device is set to connect to "Default SSID" at startup, if a connection has not yet been established. Once this call has been made, the app can handle the rest of the connections.

I was wondering if this approach is valid and if it is possible in Android. Is there a better standard way to make connections with IOT devices for the first time?

Thank you in advance 🙂 I just do not want to end 6 months with a bad design approach.

How do I limit the connection to the port?

How do I limit the connection to the port? Web Hosting Talk

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var sidebar_align = & right; & # 39 ;;
var content_container_margin = parseInt (& # 39; 350px & # 39;);
var sidebar_width = parseInt (& # 39; 330px & # 39;);
// ->

  1. How do I limit the connection to the port?

    Hello
    Is there a way to limit the number of connections each IP address can open to port or service?
    like limit connection to port 2082 or cpanel service … etc.


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Network – No open port connection in an uncomplicated firewall (UFW) on the local LAN

My settings on a small server are like this

 $ sudo ufw status
Status: active

To                         Action      From
--                         ------      ----
22/tcp                     LIMIT       Anywhere                  
22                         ALLOW       192.168.100.0/24          
90                         ALLOW       192.168.100.0/24          
31337                      ALLOW       192.168.100.0/24          
3438                       ALLOW       192.168.100.0/24          
9000                       ALLOW       192.168.100.0/24          
9090                       ALLOW       192.168.100.0/24          
445                        ALLOW       192.168.100.0/24          
8200                       ALLOW       192.168.100.0/24          
1900                       ALLOW       192.168.100.0/24          
22/tcp (v6)                LIMIT       Anywhere (v6)          

The device I want to connect to the server uses port 3438 and has the IP 192.168.100.69. The server has the IP address 192.168.100.169. I am using a second server that is almost identical, and there are no issues connecting the device to the same settings.

I can connect to the server using a graphical user interface with Port 9000. The service on the server to which I want to connect is up and running. (It's a logitechmediaserver.) So it's just port 3438 that still seems to be blocked.

/var/log/ufw.log looks like this:

Sep 10 08:43:22 RPi3 kernel: (59546.635454) (UFW BLOCK) IN=eth0 OUT= MAC=b8:27:eb:3d:f7:ef:00:04:20:1e:1e:98:08:00:45:00:00:2c:2d:ea:00:00:40:06:02:4$
Sep 10 08:43:33 RPi3 kernel: (59557.638106) (UFW BLOCK) IN=eth0 OUT= MAC=b8:27:eb:3d:f7:ef:00:04:20:1e:1e:98:08:00:45:00:00:28:2d:fb:00:00:40:06:02:3$
Sep 10 09:13:32 RPi3 kernel: (61356.620129) (UFW BLOCK) IN=eth0 OUT= MAC=b8:27:eb:3d:f7:ef:00:04:20:1e:1e:98:08:00:45:00:00:65:32:c5:00:00:40:06:fd:2$
Sep 10 09:13:32 RPi3 kernel: (61356.739031) (UFW BLOCK) IN=eth0 OUT= MAC=b8:27:eb:3d:f7:ef:00:04:20:1e:db:e6:08:00:45:00:00:65:b9:26:00:00:40:06:77:2$
Sep 10 09:13:53 RPi3 kernel: (61377.373901) (UFW BLOCK) IN=eth0 OUT= MAC=b8:27:eb:3d:f7:ef:80:2a:a8:df:d3:b3:08:00:45:00:00:34:61:65:40:00:32:06:dd:7$
Sep 10 09:13:54 RPi3 kernel: (61378.622169) (UFW BLOCK) IN=eth0 OUT= MAC=b8:27:eb:3d:f7:ef:80:2a:a8:df:d3:b3:08:00:45:00:00:34:61:66:40:00:32:06:dd:7$
Sep 10 09:13:55 RPi3 kernel: (61380.059084) (UFW BLOCK) IN=eth0 OUT= MAC=b8:27:eb:3d:f7:ef:80:2a:a8:df:d3:b3:08:00:45:00:00:34:43:a3:40:00:33:06:32:9$
Sep 10 09:13:57 RPi3 kernel: (61381.185812) (UFW BLOCK) IN=eth0 OUT= MAC=b8:27:eb:3d:f7:ef:80:2a:a8:df:d3:b3:08:00:45:00:00:34:61:67:40:00:32:06:dd:7$
Sep 10 09:14:10 RPi3 kernel: (61394.395071) (UFW BLOCK) IN=eth0 OUT= MAC=b8:27:eb:3d:f7:ef:80:2a:a8:df:d3:b3:08:00:45:00:00:34:43:a4:40:00:33:06:32:9$
Sep 10 09:14:12 RPi3 kernel: (61396.287604) (UFW BLOCK) IN=eth0 OUT= MAC=b8:27:eb:3d:f7:ef:80:2a:a8:df:d3:b3:08:00:45:00:00:34:61:69:40:00:32:06:dd:6$
Sep 10 09:14:38 RPi3 kernel: (61423.067216) (UFW BLOCK) IN=eth0 OUT= MAC=b8:27:eb:3d:f7:ef:80:2a:a8:df:d3:b3:08:00:45:00:00:34:43:a5:40:00:33:06:32:9$

Any ideas?

Transit – Fly from Winnipeg to Auckland with 2hrs 20 mins connecting time in Chicago. Is it enough for an international connection?

You'll be fine. As you will notice, you will be cleared in advance by the US Customs authorities in Winnipeg, and with the exception of exceptional circumstances (which I have never had to fight back and forth across the US border for more than 30 years) you will not interact with US Customs & Immigration Agents at Chicago Airport at all. In fact, your YWG ORD flight will be treated the same as any other flight coming from a US destination to ORD. You will clear the New Zealand Customs upon your arrival in Auckland and your luggage will most likely be checked into YWG at AKL (though you may wish to confirm this only for your reassurance with the Gate Agents in Winnipeg). I have to get from one gate to another in Chicago, and 2h20m is enough time to do that, even if the terminal is changed.

Note, however, that the return will be different. If you're flying through Chicago (or another US destination), you'll need to re-request your baggage, pass US Customs, and check your baggage there. Along with the time it takes to change terminals, this is a more time-consuming process.

Windows – Hyper-V: After the setup of the external switch – Host loses the Internet in the browser (but I still have a connection to it)

I have a dedicated Windows 10 server – far away from me, in the data center.

In Hyper-V, I create an external switch to connect my VMs with "white" IPs to the Internet.
I connect it to the network card with the internet (the server also has a different network card, but no connection, possibly for the local data center network, I think).

When I use this external switch, my host has lost the internet in the browser (!), But I still have a hassle-free connection via RDP (!). Somehow I see my server on the internet, but my server does not see internet.


On the previous server, I have a problem connecting to an external switch. What can this be? Maybe it's something new with & # 39; Default Switch & # 39; in Hyper-V that can not be deleted?

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