HI-19

HI-19 is a system developed for identifying and distinguishing peoples' handwritings. This is the first such project.

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MSL

MSL is a dynamic-type OOP general-purpose programming language. This project is a pure-C/C++ compiler for MSL, and VM for running it. In this article it is explained how to compile it from the source code.

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TRON

A simple Python 3D graphics library based on OpenGL. Created to allow easier development of small Python 3D programs.

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AngouriMath

An open-source calculator and package for it.

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Two-bodies collision

When simulating the gravity force between two particles, we usually use the iterative method. However, it would be more efficient to find the position of each of the two bodies at every moment of time. We are given two particles with one fixed and one floating, with masses $m_1$ and $m_2$ and the only force applied to the first one is $ F = \frac{m_1 m_2}{(S - r)^2} $, where $S$ - the initial distance between the particles, $r$ - the current distance traveled by the first particle. We also know $v_1 = v_2 = 0$, $v_2 = const$. The goal is to find out the speed of the first particle at the moment of their collision.

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Motion equation for a thrown particle and the air resistance

Consider the problem when the only force applied to the particle is the gravity force. For this problem $x(t) = v_x t$ and $y(t) = v_y t - \frac{a t^2}{2}$ where $v_x = v cos(\phi)$ and $v_y = v sin(\phi)$ for $\phi$ - the angle between the horizone and the initial velocity. However, when it comes to extra force, the problem turns out to be more complicated.

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B function

The B-function seems extremely easy at first glance to solve. However, this problem remains unsolved up to today's date. The B-function is defined as $B(x)=xsin(x)$ and the main goal is to find all the roots of equation $B(x)=c$ for $c \in R$.

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Ensemble voting problem

We are given $n$ classifiers and $c$ classes. Each classifier has one voice. Each classifier will vote for $class 0$ with the probability of $p$, $p > 1/c$. For each other class it will vote with the probability of $(1 - p) / (c - 1)$. Once the classifiers have voted, we find out the most voted classes and pick one of them equally likely - the picked class called "elected." The problem is to find out the probability of $class 0$ being finally elected.

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Exponentials sum equation

Find invert function $ f(x) $ to solve $a^{x} + b^{x} = c$

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Non-trivial function equation

Find all functions $f(x)$ that satisfy $f(x) = xf(x^2) + x$

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X power X equation

How to solve $x^x = c$ for $c \in R^+$?

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