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The summation of all prime numbers

A proof is given that the summation of all prime numbers can be assigned the value of 13/12, as well as values that can be assigned to the summation of all multiples and all odd multiples.

Fernando Franco Félix

Oscillation Lab

The purpose of this lab was to illustrate the validity of the law of conservation of energy along with the determination of the spring constant of a given spring. For the first part the spring constantk was to be found from a given spring. Through the suspension of various known metal masses on a vertically suspended spring, the spring constant was determined. Two methods were used: the algebraic rearrangement of Hooke's Law and a slope analysis of a linear regression on a Force (N) against Stretch Length (m) scatter plot. The spring constant k was determined to be 26.438 ± 1.063. For the second part of the lab, the aim was to validate the law of conservation of energy through the oscillation of a vertically suspended spring. Data was collected using a Vernier Motion Detector 2 machine and the various energies (kinetic energy, gravitational potential energy and spring potential energy) were collected and summed up. The sum of these energies yielded a fairly constant energy total (2.287 J ± 0.025 J) which supports the authenticity of the law of conservation of energy. While there were some uncertainties due to the lab setup, human error and equipment error it did not affect the validity of the methods during experimentation. Overall, the spring constant k of a given spring was determined and the law of conservation of energy was validated through the calculation of total energy during a suspended mass' oscillation.

Nikhil Patil

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Alleluuka

On the quantum differentiation of smooth real-valued functions

Calculating the value of Ck ∈ {1, ∞} class of smoothness real-valued function's derivative in point of R+ in radius of convergence of its Taylor polynomial (or series), applying an analog of Newton's binomial theorem and q-difference operator. (P,q)-power difference introduced in section 5. Additionally, by means of Newton's interpolation formula, the discrete analog of Taylor series, interpolation using q-difference and p,q-power difference is shown.

Kolosov Petro

Exploring the use of Big Data techniques for simulating Algorithmic Trading Strategies

In the world of information technology where huge amount of useful information is available and easily accessible, we investigate an approach to utilize this information in Algorithmic Trading. Algorithmic trading involves implementation of a strategy using computer programs to automatically buy and sell financial instruments to generate profit at a speed and frequency that is impossible for a human trader. High Frequency Trading (HFT) is one type of algorithmic trading characterized by high turnover and high order-to-trade ratios. There are different strategies that can be applied to HFT. We propose a framework to utilize information available in the form of news articles, which can be used in stock trading at high frequency. We use semantic values of news articles for different stocks to generate buy/sell signals at a high frequency. We demonstrate the performance of our framework by simulating stock trade based on generated buy/sell signals for a small period of time.

Jiten Thakkar

Sommarmatte

Just some summer math courses.

Alexander Nielsen