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Physical Sciences and Mathematics Commons™

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2011

Series

Western Kentucky University

Mathematics

Articles 1 - 16 of 16

Full-Text Articles in Physical Sciences and Mathematics

Cagan Type Rational Expectations Model On Time Scales With Their Applications To Economics, Funda Ekiz Nov 2011

Cagan Type Rational Expectations Model On Time Scales With Their Applications To Economics, Funda Ekiz

Masters Theses & Specialist Projects

Rational expectations provide people or economic agents making future decision with available information and past experiences. The first approach to the idea of rational expectations was given approximately fifty years ago by John F. Muth. Many models in economics have been studied using the rational expectations idea. The most familiar one among them is the rational expectations version of the Cagans hyperination model where the expectation for tomorrow is formed using all the information available today. This model was reinterpreted by Thomas J. Sargent and Neil Wallace in 1973. After that time, many solution techniques were suggested to solve the …

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Operation Comics: Making Math Fun, Bruce Kessler Sep 2011

Operation Comics: Making Math Fun, Bruce Kessler

Mathematics Faculty Publications

This talk gives a background on the Operation Comics series, which integrates mathematics into a comic book storyline, as an example of how creativity is not exclusive to the traditional arts, like music and dance, but is a vital part of math, science, and engineering.

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Higher Derivatives Of The Hurwitz Zeta Function, Jason Musser Aug 2011

Higher Derivatives Of The Hurwitz Zeta Function, Jason Musser

Masters Theses & Specialist Projects

The Riemann zeta function ζ(s) is one of the most fundamental functions in number theory. Euler demonstrated that ζ(s) is closely connected to the prime numbers and Riemann gave proofs of the basic analytic properties of the zeta function. Values of the zeta function and its derivatives have been studied by several mathematicians. Apostol in particular gave a computable formula for the values of the derivatives of ζ(s) at s = 0. The Hurwitz zeta function ζ(s,q) is a generalization of ζ(s). We modify Apostolʼs methods to find values of the derivatives of ζ(s,q) with respect to s at s …

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Operation Comics: The Story Continues, Bruce Kessler, Tressa Tullis Jul 2011

Operation Comics: The Story Continues, Bruce Kessler, Tressa Tullis

Mathematics Faculty Publications

This talk was given, with Tressa Tullis as the main presenter and Bruce Kessler as a minor co-presenter, at the 2011 Bridges Conference in Coimbre, Portugal, on the current developments on our Operation Comics project with Cumberland Trace Elementary.

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Operation Comics: The Story Continues, Bruce Kessler, Janet Tassell, Tressa Tullis Jul 2011

Operation Comics: The Story Continues, Bruce Kessler, Janet Tassell, Tressa Tullis

Mathematics Faculty Publications

During the 2008-2009 academic year, the author K. wrote three issues of Operation Comics, a comic book with embedded mathematics content appropriate for 4th through 6th grade students. Several printed comics were placed in Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky, US. The author Ta. was enlisted to measure the impact of the comics on the attitudes and motivation of the students using the comics. A preliminary report was given by K. at the 2009 Bridges Banff Conference, and the written report appeared in the proceedings. Since then, data has been collected on the …

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Implementation Of An Inexpensive 3d Scanner, Robert Michael Sivley May 2011

Implementation Of An Inexpensive 3d Scanner, Robert Michael Sivley

Mahurin Honors College Capstone Experience/Thesis Projects

The purpose of this project was to make 3D scanning technology accessible to the general public at an affordable price. To accomplish this, a scanner was designed that utilized structured-light projection. Coupled with triangulation, this provided an inexpensive, image-based modeling technique. Software was developed to analyze the required images and generate a 3D model. Users can edit analysis parameters during runtime to better optimize results for specific images. The 3D models generated are stored according to the .obj standard and can be opened in any commercial 3D modeling software. Results were positive, but several issues exist with the chosen scanning …

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Deterministic And Stochastic Bellman's Optimality Principles On Isolated Time Domains And Their Applications In Finance, Nezihe Turhan May 2011

Deterministic And Stochastic Bellman's Optimality Principles On Isolated Time Domains And Their Applications In Finance, Nezihe Turhan

Masters Theses & Specialist Projects

The concept of dynamic programming was originally used in late 1949, mostly during the 1950s, by Richard Bellman to describe decision making problems. By 1952, he refined this to the modern meaning, referring specifically to nesting smaller decision problems inside larger decisions. Also, the Bellman equation, one of the basic concepts in dynamic programming, is named after him. Dynamic programming has become an important argument which was used in various fields; such as, economics, finance, bioinformatics, aerospace, information theory, etc. Since Richard Bellman's invention of dynamic programming, economists and mathematicians have formulated and solved a huge variety of sequential decision …

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Development Of Fractional Trigonometry And An Application Of Fractional Calculus To Pharmacokinetic Model, Amera Almusharrf May 2011

Development Of Fractional Trigonometry And An Application Of Fractional Calculus To Pharmacokinetic Model, Amera Almusharrf

Masters Theses & Specialist Projects

No abstract provided.

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“Drawing” Upon Your Students’ Creativity: Teaching (Your Subject Here) With Comic Books, Bruce Kessler Apr 2011

“Drawing” Upon Your Students’ Creativity: Teaching (Your Subject Here) With Comic Books, Bruce Kessler

Mathematics Faculty Publications

During Spring 2009, Dr. Kessler created and published a comic book series that embedded math content into the story for 4th-6th grade students. The comics were well received in the classrooms at Cumberland Trace Elementary. Dr. Kessler contends that this approach to teaching and learning can be used in any content area, and is useful for engaging students who might not be as interested otherwise. This session will explore ways of utilizing the skills of your students to construct learning comics in your classes, regardless of the funds, technology, and artistic experience at your disposal. The session will include a …

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Wavelet-Based Analysis Of Neutron-Induced Photon Spectral Data, Bruce Kessler, Alexander Barzilov, Phillip Womble Apr 2011

Wavelet-Based Analysis Of Neutron-Induced Photon Spectral Data, Bruce Kessler, Alexander Barzilov, Phillip Womble

Mathematics Faculty Publications

Neutron-based methods of non-destructive inter- rogation of objects for the purpose of their characterization are well-established techniques, employed in the field of bulk material analysis, contraband detection, unexploded ordnance, etc. The characteristic gamma rays produced in nuclear reactions initiated by neutrons in the volume of the irradiated object (inelastic neutron scattering, thermal neutron capture, and activation) are used for the elemental identification. In many real-world applications, an automated spectral analysis is needed, and many algorithms are used for that purpose. The Applied Physics Institute at Western Kentucky University has recently started to employ a mathematical spectrum analysis technique based on …

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A “Peak” At The Algorithm Behind “Peaklet Analysis” Software, Bruce Kessler Mar 2011

A “Peak” At The Algorithm Behind “Peaklet Analysis” Software, Bruce Kessler

Mathematics Faculty Publications

In response to a problem posed by faculty at the Applied Physics Institute at Western Kentucky University, the speaker has developed an algorithm for providing an automated analysis of spectrum data for the purpose of determining the elemental composition of the item generating the data. A full, non-provisional patent application has been filed on the idea, and a full marketing campaign has started to license software implementing the algorithm. This presentation will give a brief explanation of the mathematics in use in the algorithm, and will give some examples of the software in action.

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A Primer On Chaos And Fractals, Bruce Kessler Mar 2011

A Primer On Chaos And Fractals, Bruce Kessler

Mathematics Faculty Publications

This is a prelude to a performance of the play "Arcadia" exclusively for the science and math majors of Lipscomb University. One of the main characters of the story is a mathematical genius, and has realized the power and limitations of iterations in generating mathematical models and structures, although she is living in the early 1800's. This talk gives an introduction to the ideas of chaos theory, fractals, and randomness.

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King, John (Sc 594), Manuscripts & Folklife Archives Feb 2011

King, John (Sc 594), Manuscripts & Folklife Archives

MSS Finding Aids

Finding aid and full-text (click on "Additional Files" below) for Manuscripts Small Collection 594. Ciphering book of John King including mathematical exercises, numeration of money, simple and compound reduction, weights and measures, and word problems.

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Bowles, John (Sc 593), Manuscripts & Folklife Archives Feb 2011

Bowles, John (Sc 593), Manuscripts & Folklife Archives

MSS Finding Aids

Finding aid and full-text (click on "Additional Files" below) for Manuscripts Small Collection 593. Ciphering book kept by John Bowles of Granville County, North Carolina. Bowles used "Pike's Arithmetic" in making his ciphering book.

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Curd, Spencer, 1788-1832 (Sc 966), Manuscripts & Folklife Archives Feb 2011

Curd, Spencer, 1788-1832 (Sc 966), Manuscripts & Folklife Archives

MSS Finding Aids

Finding aid and full text (click on "Additional Files" below) for Manuscripts Small Collection 966. Ciphering book (94 p.), focusing chiefly on surveying and navigating rules for solving problems as well as giving specific problems, of Spencer Curd, Logan County, Kentucky, with accompanying genealogical data.

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Operation Comics: The Story Continues, Bruce Kessler, Janet Tassell, Tressa Tullis Jan 2011

Operation Comics: The Story Continues, Bruce Kessler, Janet Tassell, Tressa Tullis

Mathematics Faculty Publications

During the 2008-2009 academic year, the author K. wrote three issues of Operation Comics, a comic book with embedded mathematics content appropriate for 4th through 6th grade students. Several printed comics were placed in Cumberland Trace Elementary in the Warren County School System in Bowling Green, Kentucky, US. The author Ta. was enlisted to measure the impact of the comics on the attitudes and motivation of the students using the comics. A preliminary report was given by K. at the 2009 Bridges Banff Conference, and the written report appeared in the proceedings. Since then, data has been collected on the …

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