Treasure of poets

No image

Sorry, this entry is only available in Russian. For the sake of viewer convenience, the content is shown below in the alternative language. You may click the link to switch the active language. Капля за каплей, день за днём В веках течёт забытый зов, И греет души он огнём Людей – Земли нашей жильцов. В…

Modular powermap

Sorry, this entry is only available in Russian. For the sake of viewer convenience, the content is shown below in the alternative language. You may click the link to switch the active language. ВНИМАНИЕ!! Данная статья находится на стадии разработки, поэтому в ней возможны погрешности. Позже будет добавлена спецификация классов приведённой в статье структуры данных….

Periodicity of modular exponentiation

Properties of modulo operation: : . Lemma “About finiteness of modular-power sequence” Suppose a given certain module , , and a certain integral number , and suppose a defined series of elements , where , , , . Then for the given sequence the condition of repeat is satisfied: , , : . by contradiction:…

The universal segment tree

2019.02.07 First of all, I want to thank lecturers Alexander Antonenko (asantonenko@gmail.com), Arthur Maximov and Igor Mazurok. I guess, if not their advices and lectures, and also excellent exposition of educational material, the universal segment tree I’ve made would either have less comfortable usage, or simply not exist. Note: in order this article to have…

Theorem “About amount of XOR-sums over the given sequence of bits”

Supporting materials: Note: this article uses supporting theorems, such as “Common commutative law” and “About amount of subsets in the given set”. Since I’m yet unable to find their analogues on English-language resources, I’ll cite their statements in this section. Theorem “The common commutative law”: suppose given non-empty set , – associative and commutative binary…

Theorem “About amount of scramblers of given length”

Statement: Suppose a given amount of bits of scrambler . Then there exist scramblers of the length . Proof: Key of the scrambler – certain sequence of bits of the length . After reviewing key as vector of set , it’s possible to make conclusion, that in total there exist keys of the length ….