Browse real student projects, abstracts, and awards.
ISEF · 2019
Mathematics
This paper shows a thorough examination of fully homomorphic encryption schemes and their performance in programs. We do an analysis of one specific, widely-used scheme – the Gentry-Sahai-Wa…
ISEF · 2019
Mathematics Third Award
This project is motivated by studying Chebyshev polynomials such as cos?(mx) is a polynomial of cos?(x). It is interesting to know if there are other non-constant continuous functions f havi…
ISEF · 2019
Mathematics
Traditionally introduced in terms of advanced topological constructions, many link invariants may also be defined in much simpler terms given their values on a few initial links and a recurs…
ISEF · 2019
Mathematics
Purpose: The problem of finding the shortest path between the two given points is a classical problem in geometry. These paths are called geodesic lines. The existence of non-self-intersecti…
ISEF · 2019
Mathematics
A wonderful fact called Thurston's geometrization conjecture states that there are essentially only eight three-dimensional geometries. One of them is Nil geometry, which is a Lie group call…
ISEF · 2019
Mathematics
There is the theory of doodles and twins in combinatorial topology, which is similar to link and braid theory. A doodle on a surface is a union of several closed curves that are intersecting…
ISEF · 2019
Mathematics
Traditional economic theory relies on assumptions of homogeneous agents reaching equilibrium under ideal conditions; there has been a push away from classical economics toward more real worl…
ISEF · 2019
Mathematics
In this study, we consider a discrete dynamic system starting with n arbitrary points on a circle. In one transition, each point moves simultaneously from its current state counterclockwise…
ISEF · 2019
Mathematics Fourth Award
Given a Vector Bundle (Coherent Sheaf) with Integrable Connection on a variety in positive characteristic, its p-curvature measures the amount of horizontal sections of the bundle and its va…
ISEF · 2019
Mathematics
*Introduction Mersenne Primes:- A number of the form 2^n – 1 where n is a natural number is a Mersenne number. If its value is prime then it is known as a Mersenne Prime. Mersenne primes are…
ISEF · 2019
Mathematics
Cooperative games are systems in which entities, players, can join to form subsets, known as coalitions. While players contribute varying amounts, known as marginal impacts, to different coa…
ISEF · 2019
Mathematics
There’s no doubt that in recent years the connection between different subjects is really cruical. For this exact reason I intend to proof mathematical theories with the help of syllogisms.…
ISEF · 2019
Mathematics
In low-dimensional topology, one of the most beautiful and complex topics is braid theory. There are deep connections between braids, knots, mappings on surfaces, and even algebraic geometry…
ISEF · 2019
Mathematics Third Award
Dimensionality reduction techniques are becoming widely used in academia, business, and machine learning to reduce the time required to process a higher dimensional dataset. In this context,…
ISEF · 2019
Mathematics Third Award
Given S, a set of n points contained in the unit square Q = [0, 1]^2, let f(S) denote the area of the largest axes-parallel rectangle that does not contain any of the points of S in its inte…
ISEF · 2019
Mathematics
In this paper, we present the best possible parameters \alpha_i, \beta_i\ (i=1,2,3) and \alpha_4,\beta_4\in(1/2,1) such that the double inequalities \begin{align*} \alpha_1Q(a,b)+(1-\alpha_1…
ISEF · 2019
Mathematics
Low-rank matrix completion has attracted significant attention because this technique can be applied to solve many inference problems. Recently, Tang et al. (2018) proposed a quantum-inspire…
ISEF · 2019
Mathematics Fourth Award
The Planetary Transfer Calculator (PTC) is a tool to calculate and visualise transfers between planets, moons, and stars. The coding system uses a complex combination of mathematical algorit…
ISEF · 2019
Mathematics
Stock price change in the short term is highly unpredictable and often does not relate to underlying economic or company performance. Stock technical analysis indicators are commonly used to…
ISEF · 2019
Mathematics
Inadequate hospitalization projections increase the cost of health care and reflect the ineffectiveness of the healthcare services in the primary care setting (Mkanta, 2016). Studies have co…
ISEF · 2019
Mathematics
In modern cryptosystems, even if the adversaries can access the communication medium and initially have the same knowledge as the communicators, sent messages are still safe, since they are…
ISEF · 2019
Mathematics
Purpose: There is always a pressing need for secure cryptography. Most problems used in cryptography act on finite abelian groups, which are groups with finite elements with all pairs of ele…
ISEF · 2019
Mathematics
Presented research belongs to number theory and is a part of a more ambitious project to test Chebyshev’s bias numerically for prime numbers up to 1.84*10^19. Chebyshev’s bias, known from 18…
ISEF · 2019
Mathematics
The Toda lattice is a Hamiltonian system which attempts to model a one-dimensional solid. The system was originally introduced by Japanese physicist Morikazu Toda in 1967, and is still relev…
ISEF · 2019
Mathematics Fourth Award
Creating a crease in a ring-shaped circular piece of paper results in a saddle-shaped structure which when cut creates a frustum with inner and outer edges in contact with a surface. The pur…
ISEF · 2019
Mathematics
Time-distance maps have scales expressed in time units rather than in distance units such that distances between points are proportional to the time-distances. Time-distance maps provide a v…
ISEF · 2019
Mathematics
Moment of inertia is a quantity measuring of the resistance of a body to the angular acceleration. The quantity can be commonly calculated using integral calculus of which could be very comp…
ISEF · 2018
Mathematics
In recent years, with the rising popularity of soccer games in China, fans violence has also increased dramatically. Overexcited soccer fans have physical confrontations with opposition supp…
ISEF · 2018
Mathematics First Award
This paper presents the solution to the open problem of the fine classification of second minimal odd periodic orbits of continuous endomorphisms on the real line. It is rigorously proven th…
ISEF · 2018
Mathematics
The exploration of Egyptian Fractions is part of the field of pure mathematics, Number Theory. First used by the Egyptians to express fractions with 2 in the numerator or 10 in the denominat…