Physical Sciences and Mathematics Commons^™

Student Selected As Finalist For Chemistry Award, Heather Lindquist

News and Events

No abstract provided.

Student Rights Advocate And Author To Speak, Teresa A. Sherman

News and Events

No abstract provided.

Model Created To Help Teachers Envision Fourth Spatial Dimension, Rachel Hatch

News and Events

No abstract provided.

Green Chemistry Using Bismuth Salts Bismuth (Iii) Iodide Catalyzed Deprotection Of Acetals And Ketals In H2o, Aaron D. Bailey '07

Honors Projects

Since the Pollution Prevention Act was passed in 1990, synthetic organic chemists have focused on the use of environmentally friendly reagents. Often, many synthetic labs use metal catalysts (compounds containing Hg, Ni, Pb, & Sn) that are toxic to or have detrimental effects on the environment. Unlike many heavy metal compounds, bismuth and its compounds have been found to be relatively non-toxic and environmentally friendly. Due to poor shielding of the nucleus by the f electrons bismuth compounds have been shown to be efficient Lewis acid catalysts for many reactions.

The goal of this project to utilize bismuth compounds, specifically …

Rapid Face Detection Using Independent Component Analysis, Aditya Rajgarhia '07

Honors Projects

Face detection is the task of determining the locations and sizes of human faces in arbitrary digital images, while ignoring any other objects to the greatest possible extent. A fundamental problem in computer vision, it has important applications in fields ranging from surveillance-based security to autonomous vehicle navigation. Although face detection has been studied for almost a decade, the results are not satisfactory for a variety of practical applications, and the topic continues to receive attention.

A commonly used approach for detecting faces is based on the techniques of "boosting" and "cascading", which allow for real-time face detection. However, systems …

Symbolization Of Generating Functions; An Application Of The Mullin–Rota Theory Of Binomial Enumeration, Tian-Xiao He, Peter S, Leetsch Hsu

Scholarship

We have found that there are more than a dozen classical generating functions that could be suitably symbolized to yield various symbolic sum formulas by employing the Mullin–Rota theory of binomial enumeration. Various special formulas and identities involving well-known number sequences or polynomial sequences are presented as illustrative examples. The convergence of the symbolic summations is discussed.

Fourier Transform Of Bernstein–Bézier Polynomials, Tian-Xiao He, Charles Chui, Qingtang Jiang

Scholarship

Explicit formulae, in terms of Bernstein–Bézier coefficients, of the Fourier transform of bivariate polynomials on a triangle and univariate polynomials on an interval are derived in this paper. Examples are given and discussed to illustrate the general theory. Finally, this consideration is related to the study of refinement masks of spline function vectors.

The Sheffer Group And The Riordan Group, Tian-Xiao He, Peter Shiue, Leetsch Hsu

Scholarship

We define the Sheffer group of all Sheffer-type polynomials and prove the isomorphism between the Sheffer group and the Riordan group. An equivalence of the Riordan array pair and generalized Stirling number pair is also presented. Finally, we discuss a higher dimensional extension of Riordan array pairs.

Construction Of Biorthogonal B-Spline Type Wavelet Sequences With Certain Regularities, Tian-Xiao He

Scholarship

No abstract provided.

Two Number-Theoretic Problems That Illustrate The Power And Limitations Of Randomness, Andrew Shallue

Scholarship

This thesis contains work on two problems in algorithmic number theory. The first problem is to give an algorithm that constructs a rational point on an elliptic curve over a finite field. A fast and easy randomized algorithm has existed for some time. We prove that in the case where the finite field has characteristic 2, there is a deterministic algorithm with the same asymptotic running time as the existing randomized algorithm.

Iron(Iii) P-Toluenesulfonate Catalyzed Synthesis Of Homoallyl Ethers From Acetals And Aldehydes, Ram Mohan, Matthew Spafford, Erin Anderson, Joshua Lacey, Ann Palma

Scholarship

Iron(III) p-toluenesulfonate, Fe(OTs)3.6H20, is an inexpensive, versatile and commercially available catalyst for the allylation of acetals using allyltrimethylsilane to yield homoallyl ethers in moderate to good yields. The one-pot conversion of aldehydes to homoallyl ethers using alkoxysilanes has also been accomplished using Fe(OTs)3.6H20 as a catalyst. The use of mild reaction conditions and a relatively non-corrosive catalyst make this method an attractive option for the synthesis of a range of homoallyl ethers.

Reactivity Of Ionic Liquids, Ram Mohan, Shahana Chowdhury, Janet Scott

Scholarship

Ionic liquids are becoming widely used in synthetic organic chemistry and yet relatively little attention has been paid to the intrinsic reactivity of these low temperature molten salts. Clues to the non-innocent nature of many ionic liquids are contained in the reports of altered reactivity of dissolved substrates, unexpected catalytic activity and unforeseen by-product formation. In this review, we focus on the reactivity of ionic liquids, as opposed to reactivity in ionic liquids (although discussion of the latter is often included where it aids understanding of the former).