A5103102580- Geometric and Algebraic Topology
- Homotopy and Cohomology in Algebraic Topology
- Dark Matter and Cosmic Phenomena
- Astrophysics and Cosmic Phenomena
- Particle physics theoretical and experimental studies
- Algebraic structures and combinatorial models
- Mathematical Dynamics and Fractals
- semigroups and automata theory
- Teaching and Learning Programming
- Geometry and complex manifolds
- High-Energy Particle Collisions Research
- Pelvic floor disorders treatments
- Ovarian cancer diagnosis and treatment
- Advanced Topology and Set Theory
- Colorectal Cancer Surgical Treatments
- Topological and Geometric Data Analysis
- Statistics Education and Methodologies
- Advanced Topics in Algebra
- Stoma care and complications
- Finite Group Theory Research
- Uterine Myomas and Treatments
- Radiation Therapy and Dosimetry
- Digital and Cyber Forensics
- Neutrino Physics Research
- Structural Behavior of Reinforced Concrete
University of Puget Sound
2019-2024
The Ohio State University
1991-2024
University of Chicago
1997-2005
Fermi National Accelerator Laboratory
1997-2002
Princeton University
2002
Nelson Engineering (United States)
1998
Women's Cancer Center of Nevada
1994
Lindsey Wilson College
1987
We study the spectrum and average mass composition of cosmic rays with primary energies between 10^{17} eV 10^{18} using a hybrid detector consisting High Resolution Fly's Eye (HiRes) prototype MIA muon array. Measurements have been made change in depth shower maximum as function energy. A complete Monte Carlo simulation response comparisons simulations leads to conclusion that ray intensity is changing f rom heavier lighter this energy range. The consistent earlier measurements supports...
Diffuse ultrahigh energy gamma-radiation can arise from a variety of astrophysical sources, including the interaction extremely high cosmic rays with 3K microwave background radiation or collapse topological defects created in early Universe. We describe sensitive search for diffuse gamma-rays at energies using CASA-MIA experiment. An isotropic flux is not detected, and we place stringent upper limits on fraction gamma-ray component relative to (less than one part 10,000) 570 TeV 55,000 TeV....
Abstract An efficient method for simulating instruction sets is described. The allows compiled set simulation using the macro expansion capabilities found in many languages. Additionally, we show how semantics of C case statement branching to be incorporated an manner. compared with conventional interpreted techniques and shown offer considerable performance benefits.
We have carried out a high statistics $(2\ifmmode\times\else\texttimes\fi{}{10}^{9}$ events) search for ultrahigh energy \ensuremath{\gamma}-ray emission from the x-ray binary sources Cygnus X-3 and Hercules X-1. Using data taken with CASA-MIA detector over five year period (1990--1995), we find no evidence steady either source. The derived 90 % C.L. upper limit to integral flux of $\ensuremath{\gamma}$ rays is...
We present a free student-facing tool for creating 3D plots and smartphone-based virtual reality (VR) visualizations STEM courses. Visualizations are created through an in-browser interface using simple plotting commands. Then QR codes generated, which can be interpreted with smartphone app, requiring only inexpensive Google Cardboard compatible viewer. Example uses math, physics, chemistry, other fields presented, including project-based assignment calculus courses at The Ohio State...
Singular maps of surfaces into a hyperbolic 3-manifold are utilized to find upper bounds on meridian length, <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script l"> <mml:semantics> <mml:mi>ℓ</mml:mi> <mml:annotation encoding="application/x-tex">\ell</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-curve length and maximal cusp volume for the manifold. This allows proof fact that there exist knots with arbitrarily...
By a result of Manolescu [14] there are topological closed n-manifolds that cannot be triangulated for each n 5. We show here 6 we can choose such manifolds to aspherical.
We discuss a decade of initiatives to improve the teaching and learning calculus at The Ohio State University. Calculus OSU is taught in lecture/recitation format with large lectures tightly coordinated, so all innovations had occur within that framework. show how many smaller projects built upon one another create larger transformation, these were each situated culture department. Projects discussed include conversion an open-source textbook, development online hybrid version course,...
A combination of Bestvina–Brady Morse theory and an acyclic reflection group trick produces a torsion-free finitely presented $\mathbb{Q}$-Poincaré duality which is not the fundamental aspherical closed ANR $\mathbb{Q}$-homology manifold. The construction suggests asking groups act freely on $\mathbb{Q}$-acyclic spaces (i.e., are $\operatorname{FH} (\mathbb{Q})$). For example, orbifold $\Gamma$ good satisfies duality, we show (\mathbb{Q})$ if Euler characteristics certain fixed sets vanish.
Abstract The elastic displacements caused by a point load imposed on the surface of layered, spherical, and self‐gravitating Earth can be expressed in terms infinite series Legendre polynomials or their derivatives, multiplied constants, called Love numbers, that depend summation index degree. Truncating these causes oscillatory errors computed displacement field, particularly near field load, but Farrell (1972, https://doi.org/10.1029/RG010i003p00761 ) circumvented this problem using Kummer...
An interactive open-source calculus textbook is compared to a popular commercial textbook. Structured as non-inferiority study, use of the does not harm student outcomes, and there evidence that better than in promoting post-course enjoyment mathematics confidence mathematical ability. The viewed be more readable well. Given textbooks are affordable, aligned with values academia, may result similar committees tasked deciding which adopt should consider this
For an odd prime $p$ , we consider free actions of $(\mathbb {Z}_{/{p}})^2$ on $S^{2n-1}\times S^{2n-1}$ given by linear $\mathbb {R}^{4n}$ . Simple examples include a lens space cross space, but $k$ -invariant calculations show that other quotients exist. Using the tools Postnikov towers and surgery theory, are classified up to homotopy -invariants homeomorphism Pontrjagin classes. We will present these results demonstrate how calculate classes from rotation numbers.
We discuss the impact of coronavirus pandemic on mathematics instruction at a large, public university with focus first-year calculus courses. At this university, many courses are taught in large lectures accompanying recitations. Due to previous educational initiatives, we were positioned leverage transformation required by sudden switch online and hybrid teaching. made substantial valuable changes, especially around assessment. also recent innovations provide additional pathways support...
Electronic $K$ x rays emitted by muonic Ar atoms in the gas phase were observed using a superconducting transition-edge-sensor microcalorimeter. The high-precision energy spectra provided clear signature of presence accompanied few electrons, which have never been before. One-, two-, and three-electron bound, i.e., H-like, He-like, Li-like, identified from electronic hyper-satellite rays. These are after charge transfer process collisions with surrounding atoms. With aid theoretical...
We determine the homotopy type of quotients S n × by free actions Z /p where 2p > + 3. Much like actions, they can be classified via first p-localized k-invariant, but there are restrictions on possibilities, and these sufficient to every possibility in = 3 case.We use this complete classification , for p 3, reducing problem simultaneous pairs binary quadratic forms.Although not which k-invariants realizable general, sometimes used rule out groups that contain as a normal Abelian subgroup.
Let $T(\Z_m \times \Z_n)$ denote the maximal number of points that can be placed on an $m n$ discrete torus with "no three in a line," meaning no coset cyclic subgroup $\Z_m \Z_n$. By proving upper bounds and providing explicit constructions, for distinct primes $p$ $q$, we show $T(\Z_p \Z_{p^2}) = 2p$ \Z_{pq}) p+1$. Via Gr\"obner bases, compute $2 \leq m 7$ n 19$.