## How to compute a system of ordinary differential equations with initial condictions over a continuous range

I have some questions about Mathematica programming and would appreciate if you could help me.

I want to solve a system of ordinary differential equations \ [Mu] ‘[t] and \ [Lambda]’ [t] and each equation contains a large number of terms so it is impractical to write them explicitly. I express these terms as two functions F1 and F2 that depend on two parameters P1 and P2 and \ [Lambda] [t] and \ [Mu] [t].

I have been able to solve this system for a couple of initial conditions \ [Lambda]  = ic1 and \ [Mu]  = ic2, but I would like to solve my system of equations for a continuum of values ​​\ [Lambda]  = {0, …., Pi / 2} and \ [Mu]  = {0, …., Infinity} and then get \ [Lambda] [t] and \ [Mu] [t] and use them to perform an integral on \ [Lambda]= \ [Lambda]  ={0, …., Pi / 2} and \ [Mu] =\ [Mu]  ={0, …., Infinity} that are precisely our initial conditions.

I integrate the product of a function G in the time t (where \ [Lambda] [t] and \ [Mu] [t] are taken into account for a certain initial condition defined by the continuous ranges of the integral) with the same function, but in t = 0 (where the initial conditions are taken into account with the continuous ranges of the integral).

The structure of the program is:

ode = {\[Mu]'[t] ==  F1[p1, p2, \[Lambda][t], \[Mu][t]], \[Lambda]'[t] ==  F2[p1, p2, \[Lambda][t], \[Mu][t]], \[Mu] == {0, ....,   Pi/2}, \[Lambda] == {0, ...., Infinity}};   Sol = NDSolve[ode, {\[Mu], \[Lambda]}, {t, 0, 1},Method -> "Some method to choose"]     \[Mu]1[t_] := Evaluate[\[Mu][t] /. Sol] // First \[Lambda]1[t_] := Evaluate[\[Lambda][t] /. Sol] // First   data = ParallelTable[{t,  NIntegrate[   G[p1, p2, \[Mu]1[      t] "for the initial condition \[Mu]=\[Mu]", \[Lambda]1[      t] "for the initial condition \[Lambda]=\[Lambda]"] G[p1,     p2, \[Mu] "=\[Mu]", \[Lambda] "=\[Lambda]"] , {\[Mu] "=\[Mu](initial condition)", 0,    Pi/2}, {\[Lambda] "=\[Lambda](initial condition)", 0,    Infinity}, Method -> {"Some method to choose"}]}, {t, 0, 1}]; 
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## How to stop continuous concurrent local DNS queries to dnsmasq

I set up a DNS server using dnsmasq, but it seems that it doesn’t work properly. The networking delay is up to hundreds of millisecs.

PING [server] ([server]) 56(84) bytes of data. 64 bytes from [server]: icmp_seq=1 ttl=50 time=583 ms 64 bytes from [server]: icmp_seq=2 ttl=50 time=583 ms 64 bytes from [server]: icmp_seq=3 ttl=50 time=583 ms 64 bytes from [server]: icmp_seq=4 ttl=50 time=583 ms 64 bytes from [server]: icmp_seq=5 ttl=50 time=583 ms 64 bytes from [server]: icmp_seq=6 ttl=50 time=583 ms 64 bytes from [server]: icmp_seq=7 ttl=50 time=583 ms 64 bytes from [server]: icmp_seq=8 ttl=50 time=583 ms 

Then soon I discovered that it’ll turn all right with using the default resolver systemd-resolved. By checking the log, I got the messages here below:

Jul 27 13:32:53 dnsmasq: query[A] ntp.ubuntu.com from 127.0.0.1 Jul 27 13:32:53 dnsmasq: forwarded ntp.ubuntu.com to 127.0.0.53 Jul 27 13:32:53 dnsmasq: query[A] ntp.ubuntu.com from 127.0.0.1 Jul 27 13:32:53 dnsmasq: forwarded ntp.ubuntu.com to 127.0.0.53 [countless records repeating these above...] Jul 27 13:32:53 dnsmasq: Maximum number of concurrent DNS queries reached (max: 150) Jul 27 13:32:54 dnsmasq: query[A] ntp.ubuntu.com from 127.0.0.1 Jul 27 13:32:54 dnsmasq: forwarded ntp.ubuntu.com to 127.0.0.53 [...] [probably the sigterm was sent here?] Jul 27 13:32:57 dnsmasq: query[A] ntp.ubuntu.com from 127.0.0.1 Jul 27 13:32:57 dnsmasq: forwarded ntp.ubuntu.com to 127.0.0.53 Jul 27 13:32:58 dnsmasq: no servers found in /run/dnsmasq/resolv.conf, will retry Jul 27 13:32:58 dnsmasq: query[A] ntp.ubuntu.com from 127.0.0.1 Jul 27 13:32:58 dnsmasq: query[A] ntp.ubuntu.com from 127.0.0.1 Jul 27 13:32:58 dnsmasq: query[A] ntp.ubuntu.com from 127.0.0.1 Jul 27 13:32:58 dnsmasq: query[A] ntp.ubuntu.com from 127.0.0.1 Jul 27 13:32:58 dnsmasq: query[A] ntp.ubuntu.com from 127.0.0.1 Jul 27 13:32:58 dnsmasq: exiting on receipt of SIGTERM 

So.. How to resolve this problem which makes me crazy, plz 🙁

The content from dnsmasq.conf is here:

strict-order resolv-file=/etc/resolv.conf.dnsmasq listen-address=0.0.0.0 server=/aliyuncs.com/100.100.2.136 server=/aliyuncs.com/100.100.2.138 server=/*.cn/100.100.2.136 server=/*.cn/100.100.2.138  bogus-nxdomain=100.100.2.136 bogus-nxdomain=100.100.2.138  log-queries log-facility=/var/log/dnsmasq/dnsmasq.log log-async=50  #EOF 

And resolv.conf.dnsmasq:

nameserver 100.100.2.136 nameserver 100.100.2.138 nameserver 208.67.222.123 nameserver 208.67.220.123 nameserver 8.8.8.8 nameserver 8.8.4.4 nameserver 1.2.4.8 nameserver 210.2.4.8 nameserver 208.67.222.222 nameserver 208.67.220.220 

resolv.conf:

# Dynamic resolv.conf(5) file for glibc resolver(3) generated by resolvconf(8) #     DO NOT EDIT THIS FILE BY HAND -- YOUR CHANGES WILL BE OVERWRITTEN # 127.0.0.53 is the systemd-resolved stub resolver. # run "systemd-resolve --status" to see details about the actual nameservers.  nameserver 127.0.0.53 options timeout:2 attempts:3 rotate single-request-reopen 
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## How to identify a continuous shape and break it into minimum number of rectangles?

The input in this case is going to be coordinates in 2D of the vertices of the shape. There will be no curves, but the shape can have holes. The algorithm or program needs to identify the continuous shape and break it into rectangles. The number of rectangles so created has to be optimized too.

I did read about spatial segmentation, but I am confused how to implement it. Any suggestions or help will be greatly appreciated.

Thanks!

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## Continuous Crawls Search

Hope everyone is doing well, does search Continuous Crawls pick up metadatas? and also which one is preferred? is it similar do incremental or has some down side? Regards

## When do you have enough automatic testing to be confident in your continuous integration pipeline?

Continuous integration with testing is useful for making sure that you have “shippable” code checked in all the time.

However, it is really difficult to keep up a comprehensive suite of tests and often, it feels like the build is going to be buggy anyways.

How much tests should you have to feel confident in your CI pipeline testing? Do you use some sort of metric to decide when there is enough tests?

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## Is the injectivity radius (semi) continuous on a non-complete Riemannian manifolds?

Let $$\mathcal{M}$$ be a Riemannian manifold, and let $$\mathrm{inj} \colon \cal M \to (0, \infty]$$ be its injectivity radius function.

It is known that if $$\cal M$$ is connected and complete, then $$\mathrm{inj}$$ is a continuous function: see for example [Lee, Introduction to Riemannian Manifolds, 2018, Prop. 10.37].

What is known in the case where $$\cal M$$ is not complete? Is $$\mathrm{inj}$$ also continuous? If not, is there a known counter-example? Would $$\mathrm{inj}$$ still be semi-continuous?

This question is similar to the question “The continuity of Injectivity radius”, but the discussion there focuses on compact or complete manifolds.

## Structure Preserving Continuous Hash Function

This question was originally posted on super user, but redirected here based on some suggestions.

I am completely new with computer science, and not only recently did I run into the notion of hashing. Currently, I use md5sum` for indexing reason, but am curious if hash functions can do more things. After educating myself on the surface by reading the wikipedia page on hash functions, I wondered if continuous hash functions can be made true. Luckily, it is called locality sensitive hashing, and I can find open algorithms online.

What makes me more curious, and is something that I have not found, is can I further ask the continuous hash functions to preserve structure? More specifically, the problem I have in mind is to index all of the files I have. Not only do I hope the indexing to be continuous (so the hash won’t change too much while I minor-edit a file), I also want it to preserve structure (so for example if I concatenate two files, the hash of the third file should be a reasonable function in the hash of the first two).

Please let me know if I should provide more specific information. Again, I am completely new to this field, so I might have missed something obvious.

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## Honour 4x mobile problem- continuous reboot

I have a Huawei honor 4x android mobile when I switch on the mobile it is continuously getting rebooted without booting booting I could see the logo of honor and it just getting rebooted battery is fine but am unable to recover the phone from this state , i don’t need any data just want to reset completely or bring back to normal state any idea or suggestions would be really helpful

Thanks

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## Characterization of continuous weakly closed 1-forms

Recall that a differential $$k$$-form $$\alpha$$ on a smooth manifold $$M$$ is called weakly closed if

$$\int_M \alpha \wedge d\beta = 0,$$

for all smooth forms $$\beta$$ of degree $$n-k-1$$, where $$n = \dim M$$. My question is:

If $$\alpha$$ is a weakly closed continuous 1-form on a closed manifold $$M$$, can we conclude that $$\alpha$$ is the sum of a smooth closed 1-form and $$d\phi$$, where $$\phi$$ is a $$C^1$$ function on $$M$$?

This appears to follow from the properties of the de Rham regularization operator(s) and associated homotopy operator(s) on forms; see, for instance, Theorem 12.5 in V. Gol’dshtein and M. Troyanov, Sobolev inequalities for differential forms and $$L_{q,p}$$-cohomology, Journal of Geometric Analysis, vol. 6, no. 4, 2006.

Any thoughts on this would be appreciated.