Mathematics Commons^™

Ramanujan–Fine Integrals For Level 10, Shaun Cooper, Timothy Huber, Jeffery Opoku

School of Mathematical & Statistical Sciences Faculty Publications

We investigate the question of when an eta quotient is a derivative of a formal power series with integer coefficients and present an analysis in the case of level 10. As a consequence, we establish and classify an infinite number of integral evaluations such as

∫e−2π/10√0q∏j=1∞(1−qj)3(1−q10j)8(1−q5j)7dq=14(10−45–√−−−−−−−−√−1). We describe how the results were found and give reasons for why it is reasonable to conjecture that the list is complete for level 10.

Module 1 Exam, Karon Klipple, Cheryl Hedden

Module 1 Assessments

Directions:

- Your exam must be completed by you and you alone.

- No resources - books, websites, people - can be used, except a calculator.

- You will have to sign a statement affirming that you followed these rules.

- Once you start the exam, you must finish it.

- The exam includes 11 questions.

- It will probably take you about an hour, but Canvas will allow you up to 4 hours to complete it.

- The exam is due NO LATER THAN Thursday February 15th at 12:45pm. NO LATE EXAMS WILL BE ACCEPTED. I encourage you to …

Identities For Whitehead Products And Infinite Sums, Jeremy Brazas

Mathematics Faculty Publications

Whitehead products and natural infinite sums are prominent in the higher homotopy groups of the n-dimensional infinite earring space En" role="presentation"> and other locally complicated Peano continua. In this paper, we derive general identities for how these operations interact with each other. As an application, we consider a shrinking wedge of finite (n−1)" role="presentation">-connected CW-complexes and compute the infinite-sum closure W2n−1(X)" role="presentation"> of the set of Whitehead products [α,β]" role="presentation"> in π2n−1(X)" role="presentation"> where α,β∈πn(X)" role="presentation"> are represented in respective sub-wedges that meet only at the basepoint. In particular, we show that W2n−1(X)" role="presentation"> is canonically isomorphic to …

Biophysical Modeling And Experimental Analysis Of The Dynamics Of C. Elegans Body-Wall Muscle Cells, X. Du, J. Crodelle, Victor J. Barranca, S. Li, Y. Shi, S. Gao, D. Zhou

Mathematics & Statistics Faculty Works

This study combines experimental techniques and mathematical modeling to investigate the dynamics of C. elegans body-wall muscle cells. Specifically, by conducting voltage clamp and mutant experiments, we identify key ion channels, particularly the L-type voltage-gated calcium channel (EGL-19) and potassium channels (SHK-1, SLO-2), which are crucial for generating action potentials. We develop Hodgkin-Huxley-based models for these channels and integrate them to capture the cells’ electrical activity. To ensure the model accurately reflects cellular responses under depolarizing currents, we develop a parallel simulation-based inference method for determining the model’s free parameters. This method performs rapid parallel sampling across high-dimensional parameter spaces, …

Module 1 Check Ups, Karon Klipple, Cheryl Hedden

Module 1 Assessments

No abstract provided.

Module 1 Project I, Karon Klipple, Cheryl Hedden

Module 1 Assessments

Your instructor will give you a variety of news clippings that include percentages and a set of questions associated with each. Select one that you find the most interesting.

Activity 1.4 Cards, Karon Klipple, Cheryl Hedden

Module 1 Workbook

No abstract provided.

Activity Percentage Contexts Cards, Karon Klipple, Cheryl Hedden

Module 1 Workbook

No abstract provided.

Module 1 Student Workbook, Karon Klipple, Cheryl Hedden

Module 1 Workbook

No abstract provided.

Module 2 Exam Questions, Karon Klipple, Cheryl Hedden

Module 2 Assessments

Use only class notes and assignments and NOT computers, Internet and calculator.

Module 2 Check Ups, Karon Klipple, Cheryl Hedden

Module 2 Assessments

Table : Matching Division Expressions

Module 2 Fall 2024 Project Sample, Karon Klipple, Cheryl Hedden

Module 2 Assessments

Individual Tax Rates for New Mexico

Module 2 - Student Workbook, Karon Klipple, Cheryl Hedden

Module 2 Workbook

No abstract provided.

Module 2 - Warm Up 2c.5 Cards, Karon Klipple, Cheryl Hedden

Module 2 Workbook

No abstract provided.

Module 2 Power Point Activity 2a.3, Karon Klipple, Cheryl Hedden

Module 2 Workbook

No abstract provided.

Module 2 Part A - Multiplication Is Repeated Addition, Karon Klipple, Cheryl Hedden

Module 2 Workbook

No abstract provided.

Module 2 Activity - 2b.4 Cards, Karon Klipple, Cheryl Hedden

Module 2 Workbook

No abstract provided.

Module 2 Activity- 2b.3 Cards, Karon Klipple, Cheryl Hedden

Module 2 Workbook

No abstract provided.

From Λ-Hollow Frames To Λ-Repletions In W: Ii. Λ-Repletions In W, Richard N. Ball, Anthony W. Hager, Joanne Walters-Wayland

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this article we analyze the fine structure of the essential extensions of an object of W, the category of divisible archimedean lattice ordered groups with designated weak units. In particular, we show that an object Ghas an ordinally indexed sequence {τ^α_G}_δG of essential extensions with the following features. τ⁰_G is (isomorphic to) the identity function on G.

• For every α>0, τ^α_G is an essential extension of G into a W-object which is of the form RLfor some frame L, and which is λ-replete for some λ.

• Every such …

A Family Of Markov Chains, Schur Functions, And Exterior Powers, Philip Feinsilver, John P. Mcsorley

Journal of Stochastic Analysis

No abstract provided.