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(Edited) One of the most interesting findings about the game (rediscovered by Matthew Kay) is that the answers each day are not chosen randomly from the list of possible 5 letter words in the English dictionary. The very Wardle said in an interview in the New York Times that he narrowed down the list of Wordle words to about 2,500 which are most likely to be known by his partner (the first recipient of the game). That means that there are some words that have more probability to be the target word each day than others. To see that, we will plot the distributions of the rank of the past answers in the corpus of words of English. We are going to use two sources: the corpus of commonly-used words from the Google Web Trillion Word Corpus and the BNC word frequency list and put them together:
Are the double letters in the witches' speech representative of the frequency with which double letters occur in a typical English text?To find out, let's take another look at the frequency of bigrams in Peter Norvig's analysis of a huge 744-billion-word corpus of documents that were digitized at Google.The following SAS/IML statements continue the program that analyzes bigrams. The matrix M is a 26 x 26 matrix that contains the proportion of every bigram in the corpus:
The diagonal elements of the bigram matrix contain the proportions of double-letter bigrams: AA, BB, CC, and so forth. By sorting the diagonal elements, you can find the double-letter combinations that appear most frequently in the corpus. The most common double letter is L, with LL accounting for 0.6% of all bigrams. Other common double-letter bigrams are SS, EE, OO, and TT. Some double letters did not appear in the corpus: JJ, KK, QQ, VV, WW, and YY.
I find it puzzling that the bigrams AA appear as often as the bigram ZZ. I would think articles about blizzards, puzzles, jazz, and pizza would completely swamp the few articles about aardvarks. I think the resolution to this quandary is that the corpus includes proper nouns, not just dictionary words.The double-A bigram will show up every time that there is a mention of AA and AAA batteries, the American Automobile Association (AAA) and proper nouns such as Paas egg-dying kits, Alderaan, and any boy named Aaron, Isaac, Jamaal, or Rashaad.
Returning to the Three Witches' incantation in Macbeth, we note that the most common double letters in the speech are different from the most common letters in the Google corpus. This is to be expected: the frequencies in a small sample almost always deviate from the frequencies in a population or in a large sample. Nevertheless, there is some similarity. The OO bigram is the most frequent double-letter bigram in the witches' speech, and it is also fairly common (#4) among all double-letter bigrams in the Google corpus. The LL bigram also appears frequently in the incantation and in the corpus (#1). However, the BB bigram appears much more often in the incantation than would be expected by looking at the corpus because the "double double... caldron bubble" refrain is repeated four times in the short passage.
This leads to an interesting statistical question: how much variation is there in the frequencies? The Google corpus provides an estimate for frequencies "in the wild," which we can think of as being extremely close to the frequencies in the "population" of all written English text.Obviously a random passage of text of a certain length will exhibit sample variation. There is also variation due to the type of text. The distribution of words (and therefore letters) is different between scholarly writing, journalism, poetry, and Twitter messages. (U think? AFAIK, LOL!)
In a future blog post, I will discuss the variation in these frequencies. Then I think it is time to get "cracking" and apply all this frequency analysis to the problem of solving a simple substitution cipher such as you might encounter in the Cryptoquote word puzzle.
You could do that. Novak was concerned with the empirical frequencies that appear in common English usage, which is quite different from the dictionary frequencies. I should stress that the summary statistics that I use in this article are rounded to 5 decimal places. Rather than saying that KK doesn't appear in the corpus, I should have said, "the proportion of the KK bigram is extremely small." I did better in the previous article when I said, "the grey cells are bigrams that were not found in the corpus or were extremely rare."
A large crack, stretching several kilometers, made a sudden appearance recently in south-western Kenya. The tear, which continues to grow, caused part of the Nairobi-Narok highway to collapse and was accompanied by seismic activity in the area.
The East African Rift Valley stretches over 3,000km from the Gulf of Aden in the north towards Zimbabwe in the south, splitting the African plate into two unequal parts: the Somali and Nubian plates. Activity along the eastern branch of the rift valley, running along Ethiopia, Kenya and Tanzania, became evident when the large crack suddenly appeared in south-western Kenya.
Although most of the time rifting is unnoticeable to us, the formation of new faults, fissures and cracks or renewed movement along old faults as the Nubian and Somali plates continue moving apart can result in earthquakes.
The complicated driving force at the stress corrosion cracking (SCC) tip of the safe-end dissimilar metal-welded joints (DMWJs) in the pressurized water reactor (PWR) is mainly caused by the heterogeneous material mechanical properties. In this research, to accurately evaluate the crack driving force at the SCC in DMWJs, the stress-strain condition, stress triaxiality, and J-integral of the crack tip at different positions are analyzed based on the heterogeneous material properties model. The results indicate that the larger driving force will be provided for the I-type crack when the crack is in the SA508 zone and the interface between the 316L region and base metal. In addition, the heterogeneous material properties inhibit the J-integral of the crack in the 316L region, which has a promoting effect when the crack is in the SA508 zone and weld metal. It provides a new idea for analyzing driving force at the crack tip and safety evaluation of DMWJs in PWRs.
In this study, to further study the driving force and mechanical field around the tip of SCC of DMWJs in PWRs, the stress-strain state, stress triaxiality, and J-integral at the crack tip at different positions were analyzed based on the elastic-plastic fracture mechanics approach.
In this research, the stress-strain condition, stress triaxiality, and J-integral of the SCC tip at different positions of the Alloy 52M DMWJ are analyzed based on the heterogeneous material model. The main acquired results are summarized as follows:(1)When the stress intensity factor KI is constant, the heterogeneous mechanical properties of the Alloy 52M DMWJ do not cause the uneven distribution of the stress state at the crack tip of the noninterface crack. But the stress curve of the interface crack is showing asymmetrical distribution along the crack tip.(2)By combining the stress-strain condition of the Alloy 52M DMWJ at different SCC tips positions, the larger tensile stress would be provided for the I-type crack when the crack is in the SA508 zone and the interface between the 316L region and base metal.(3)When the stress intensity factor KI is constant, the J-integral at the tip of SCC in the Alloy 52M DMWJ decreases from the 316L region to the SA508 zone. The heterogeneous mechanical properties have inhibition on the J-integral of the crack in the 316L region. On the other hand, it has a promoting effect when the crack is in the SA508 zone and weld metal.
The Crack Pot is a community-created cosmetic item for the Soldier. It is an upturned flower pot with a vertical crack above the Soldier's left eye and a team-colored flower sprouting out the top that wobbles with the player's movements.
ABSTRACT: Recent years have seen the rise of musical corpus studies, primarily detailing harmonic tendencies of tonal music. This article extends this scholarship by addressing a new genre (rap music) and a new parameter of focus (rhythm). More specifically, I use corpus methods to investigate the relation between metric ambivalence in the instrumental parts of a rap track (i.e., the beat) and an emcee's rap delivery (i.e., the flow). Unlike virtually every other rap track, the instrumental tracks of Outkast's "Mainstream" (1996) simultaneously afford hearing both a four-beat and a three-beat metric cycle. Because three-beat durations between rhymes, phrase endings, and reiterated rhythmic patterns are rare in rap music, an abundance of them within a verse of "Mainstream" suggests that an emcee highlights the three-beat cycle, especially if that emcee is not prone to such durations more generally. Through the construction of three corpora, one representative of the genre as a whole, and two that are artist specific, I show how the emcee T-Mo Goodie's expressive practice highlights the rare three-beat affordances of the track.
The metric structure of Outkast's "Mainstream," from their second album, ATLiens, differs from the vast majority of other rap tracks and provides an opportunity to examine the relationship between a particular flow and a particular beat. As I will describe below, "Mainstream" proffers two metric structures to an emcee, the typical duple meter (i.e., 4/4) as well as a triple meter (i.e., 3/4). In this article, I will argue that different emcees on the track attend to different aspects of the metric structure; I will support this argument through the construction of a corpus of rap flows representative of the genre as a whole and two separate corpora of individual emcees' flows. The corpus analysis will highlight unusual features of one of the verses of the track, features that cannot be explained by conventional modes of emceeing nor by the style of the artist of the verse. Instead, I will assert that at least some aspects of one of the verses have been tailored to the particularities of the beat of "Mainstream." 2b1af7f3a8