Browsing Research by Department "MATH / Applied Mathematics"
Now showing items 120 of 73

AN ACCELERATING CODETTE FLOW IN NEK5000: APPLICATIONS IN OCEANOGRAPHY AND MAGNETOHYDRODYNAMICS
(201705)Nek5000 is a highly scalable spectral element code used in a broad array of problems in computational fluid dynamics. In this thesis, we focus on applying the code to a model problem of an accelerating Couette flow, or ... 
ADAPTIVE COVERING CODES IN THE QARY HYPERCUBE
(201112)We investigate a generalized version of the Pathological Liar Game of Ellis and Yan. In our version, there are nonnegative integer parameters M; n; e; a; q with 0 < a < q. The player (Carole) is equipped with M messages, ... 
ADAPTIVE QUADRATURE WITH A GENERAL ERROR CRITERION
(201805)Numerical algorithms are required when the solutions to mathematical problems cannot be expressed analytically. Adaptive algorithms expend the right amount of computational e↵ort to meet the error tolerance–easy problems ... 
ADAPTIVE QUASIMONTE CARLO CUBATURE
(201612)In some definite integral problems the analytical solution is either unknown or hard to compute. As an alternative, one can approximate the solution with numerical methods that estimate the value of the integral. However, ... 
AN ADAPTIVE RESCALING SCHEME FOR COMPUTING HELESHAW PROBLEMS
(201707)In this thesis, we develop efficient adaptive rescaling schemes to investigate interface instabilities associated with moving interface problems. The idea of rescaling is to map the current timespace onto a new timespace ... 
ANALYSIS OF THE APPLICATION OF THE LIAR MACHINE TO THE QARY PATHOLOGICAL LIAR GAME WITH A FOCUS ON LOWER DISCREPANCY BOUNDS
(201112)The binary pathological liar game, as described by Ellis and Yan in [Ellis and Yan, 2004], is a variation of the original liar game, as described by Berlekamp, R enyi, and Ulam in [Berlekamp, 1964], [R enyi, 1961], and ... 
ANALYSIS OF VARIATION IN MULTISTAGE MANUFACTURING PROCESS BASED ON TREE REGRESSION
(201405)In a multistage manufacturing process, variation propagates in the process when we produce products from stage to stage. Since there are limits of reducing variation through process in traditional industrial management and ... 
ANALYZING REPRODUCING KERNEL APPROXIMATION METHODS VIA A GREEN FUNCTION APPROACH
(201205)In this thesis, we use Green functions (kernels) to set up reproducing kernels such that their related reproducing kernel Hilbert spaces (native spaces) are isometrically embedded into or even are isometrically equivalent ... 
APPROXIMATION OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH NONGAUSSIAN NOISE AND APPLICATION TO A VOLATILITY MODEL
(201505)In recent decades, stochastic processes with nonGaussian noise are widely utilized in financial models. The astable Levy motion, one type of nonGaussian noise processes, provides robust data ts and events simulations ... 
A BOUNDARY INTEGRAL METHOD FOR SOLVING THE BRINKMAN'S EQUATION IN 3DIMENSIONAL FLOW
(201412)In this paper, we consider the boundary integral equation (BIE) corresponding to the Brinkmans equation. We compute the velocities of the interacting particles when the pointwise forces acting on them are known. We ... 
THE CHANGE OF KURTOSIS IN IMPORTANCE SAMPLING FOR MONTE CARLO
(201312)The Mont e Carlo (II IC) Method is commonly used to approximat e mult ivariat e integrals, which can be interpreted as means of random variab les. The IIIC method uses th e sample mean to estimate the tr ue mean. In this ... 
Comprehending the Menger Sponge
(20120131)This poster, created by undergraduate students at the Illinois Institute of Technology (IIT), details Karl Menger's 1926discovered fractal curve currently known as the Menger sponge. Menger is a former IIT faculty member. 
COMPUTATION AND ANALYSIS OF TUMOR GROWTH
(201605)The ability of tumors to metastasize is preceded by morphological instabilities such as chains or fingers that invade the host environment. Parameters that control tumor morphology may also contribute to its invasive ... 
COMPUTATIONAL COST OF SIMULATING MEAN EXIT TIME USING STOCHASTIC DIFFERENTIAL EQUATIONS
(201605)Stochastic di erential equations play an important role in modern science, including engineering, physics, computer science and nance. It has been shown that numerically solving stochastic di erential equation is a ... 
CONSTRUCTIONS IN NONADAPTIVE GROUP TESTING STEINER SYSTEMS AND LATIN SQUARES
(201405)This thesis explores and introduces new constructions for nonadaptive group testing which are particulary important for the parameter range we encounter in real life problems. After a summary of existing results, the ... 
CONTRIBUTIONS TO ALGORITHMIC MATROID PROBLEMS
(201507)In this thesis, we obtain several algorithms for problems related to matroids, a structure that generalizes the concept of linear independence in a vector space and an acyclic subgraph structure in a graph. Matroids have ... 
COORDINATEEXCHANGE ALGORITHM CONSTRUCTION OF UNIFORM SPACE FILLING DESIGN
(201405)Many scientific phenomena are now investigated by complex computer models. A computer experiment is a sequence of runs with various inputs. The uniform experimental design seeks its design points to be uniformly scattered ... 
DISJUNCTNESS PROPERTIES RESULTING FROM CONCATENATION OF GROUP TESTING MATRICES
(201505)This thesis discusses matrix properties as they relate to the idea of nonadaptive group testing. This is accomplished by first considering the history of group testing and then exploring existing results. The next chapter ... 
DYNAMIC COHERENT ACCEPTABILITY INDICES AND THEIR APPLICATIONS IN FINANCE
(201105)This thesis presents a unified framework for studying coherent acceptability indices in a dynamic setup. We study dynamic coherent acceptability indices and dynamic coherent risk measures. In particular, we establish a ... 
DYNAMIC CONIC FINANCE VIA BACKWARD STOCHASTIC DIFFERENCE EQUATIONS AND RECURSIVE CONSTRUCTION OF CONFIDENCE REGIONS
(201607)This thesis consists of two major parts, and it contributes to the fields of mathematical finance and statistics. The contribution to mathematical finance is made via developing new theoretical results in the area of ...