id
processing priority
4
site type
3 (personal blog or private political site, e.g. Blogspot, Substack, also small blogs on own domains)
review version
11
html import
20 (imported)
first seen date
2024-10-12 08:26:23
expired found date
-
created at
2024-10-12 08:26:23
updated at
2026-01-12 15:57:29
length
21
crc
23606
tld
2211
nm parts
0
nm random digits
0
nm rare letters
0
is subdomain of id
13642151 (wordpress.com)
previous id
0
replaced with id
0
related id
-
dns primary id
0
dns alternative id
0
lifecycle status
0 (unclassified, or currently active)
deleted subdomains
0
page imported products
0
page imported random
0
page imported parking
0
count skipped due to recent timeouts on the same server IP
0
count content received but rejected due to 11-799
0
count dns errors
0
count cert errors
0
count timeouts
0
count http 429
0
count http 404
0
count http 403
0
count http 5xx
0
next operation date
-
server bits
—
server ip
-
mp import status
20
mp rejected date
-
mp saved date
-
mp size orig
199134
mp size raw text
14636
mp inner links count
11
mp inner links status
20 (imported)
title
Pengfei's Notes
description
site name
Pengfei's Notes
author
updated
2026-01-11 11:13:00
raw text
Pengfei's Notes Pengfei's Notes Solve IVPs using Laplace Transform – a problematic example Laplace transform has been used to solve Initial Value Problems. This is a topic covered in a standard differential equation course at most universities. In this post I will describe a strange situation: the solution of 2nd order ODE obtained by using Laplace transform appears to violate one of the two initial conditions. Then a short justification will be given. It turns out to be a very simple problem, just one may get caught off guard. Background . Consider a 2nd order linear constant coefficient differential equation: , , . Applying Laplace transform, we get , where the capital-case functions are the Laplace transforms of the corresponding lowercase functions: and . It follows that , or equally, . Applying the inverse transform, we obtain the solution of the IVP. Laplace Transform of the delta functions . Let be the delta function at . We know that . In part...
redirect type
0 (-)
block type
0 (no issues)
detected language
1 (English)
category id
SEC and Crypto [en] (228)
index version
2025123101
spam phrases
0
text nonlatin
0
text cyrillic
0
text characters
10772
text words
2118
text unique words
641
text lines
518
text sentences
162
text paragraphs
33
text words per sentence
13
text matched phrases
1
text matched dictionaries
2
links self subdomains
0
links other subdomains
0
links other domains
0
links spam adult
0
links spam random
0
links spam expired
0
links ext activities
0
links ext ecommerce
0
links ext finance
0
links ext crypto
0
links ext booking
0
links ext news
0
links ext leaks
0
links ext ugc
17 - s0.wp.com, wp.me, s1.wp.com, wordpress.com
links ext klim
0
links ext generic
0
dol status
0
dol updated
2026-01-11 11:13:00
rss status
32 (unknown)
rss found date
2024-10-12 08:26:24
rss size orig
143058
rss items
10
rss spam phrases
0
rss detected language
1 (English)
inbefore feed id
-
inbefore status
0 (new)
sitemap path
sitemap status
40 (completed successful import of reports.txt file to table in_pages)
sitemap review version
2
sitemap urls count
94
sitemap urls adult
0
sitemap filtered products
0
sitemap filtered videos
0
sitemap found date
2024-10-12 08:26:23
sitemap process date
2024-10-12 08:26:23
sitemap first import date
-
sitemap last import date
2025-12-26 14:34:08