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Full-Text Articles in Physical Sciences and Mathematics

Strategies Community College Mexican American Adult College Algebra Students Use When Graphing Function Transformations, Roxana Pamela Jimenez Dec 2023

Strategies Community College Mexican American Adult College Algebra Students Use When Graphing Function Transformations, Roxana Pamela Jimenez

Theses and Dissertations

This qualitative case study pursued to describe the different strategies Mexican American adult students in a local community college used to graph function transformations. Participants in the study were purposefully selected using a criterion sampling to ensure participants were atypical, above average students between the ages 18-22, and had a final course average of 89.5-100 in College Algebra. Three research questions were examined 1) In what ways do Mexican American adult college students graph a function transformation? 2) Which strategies do students implement when graphing a function transformation? Qualitative research methods using think aloud semi-structured interviews were used in this …


Prevalence Of Caffeine Dependency And Daytime Fatigue Amongst Undergraduate Students, Benjamin P. Brown, Josie Nicholson, Willa Stauffer, Elise M. Crause, Katie Young Jan 2022

Prevalence Of Caffeine Dependency And Daytime Fatigue Amongst Undergraduate Students, Benjamin P. Brown, Josie Nicholson, Willa Stauffer, Elise M. Crause, Katie Young

Belmont University Research Symposium (BURS)

Caffeine is considered a legal drug with a main function of acting as a stimulant. The recommended daily dose of caffeine is up to 400 mg, however, most college students consume on average 800 mg per day (Mcllavian et al., 2013). Amongst American college students, caffeine is considered one of five most commonly consumed drugs, being compared with alcohol, marijuana, opioids, and sedatives (American Addictions Center, 2019). Within this population, there is a lack of knowledge regarding the adverse effects of caffeine and its potential impact of alertness versus sleepiness. Existing literature on this topic has shown that caffeine can …


Law Library Blog (January 2022): Legal Beagle's Blog Archive, Roger Williams University School Of Law Jan 2022

Law Library Blog (January 2022): Legal Beagle's Blog Archive, Roger Williams University School Of Law

Law Library Newsletters/Blog

No abstract provided.


Modified Hermite Operational Matrix Method For Nonlinear Lane-Emden Problem, Bushra Esaa Kashem Jul 2020

Modified Hermite Operational Matrix Method For Nonlinear Lane-Emden Problem, Bushra Esaa Kashem

Al-Qadisiyah Journal of Pure Science

Nonlinear Lane –Emden equations are significant in astrophysics and mathematical physics. The aim of this paper is submitted a new approximate method for finding solution to nonlinear Lane-Emden type equations appearing in astrophysics based on modified Hermite integration operational matrix. The suggest technique is based on taking the truncated modified Hermite series of the solution function in the nonlinear Lane-Emden equation and then changed into a matrix equation with the given conditions. Nonlinear system of algebraic equation using collection points is obtained. The present method is applied on some relevant physical problems as nonlinear Lane-Emden type equations.


Analyzing The Linearity Of Some Operators, Faton Kabashi, Azir Jusufi, Hizer Leka Oct 2019

Analyzing The Linearity Of Some Operators, Faton Kabashi, Azir Jusufi, Hizer Leka

UBT International Conference

Linear operators occupy an important place in functional analysis and linear algebra, which are among the most important and substantive disciplines of mathematics, whose methods and results have created an indispensable apparatus for the development of numerical mathematics, theory of approximations, equations differential and especially mathematical physics and applied mathematics. Also, linear operators are a central object of study in vector space theory.

A linear operator is a function which satisfies the conditions of additivity and homogeneity. Not every function is linear operators. We will try to explore some functions which are also linear operators.


Function, Meaning, And Message Of The Natural Environtment In The Story Of Keong Mas, Adinda Bunga Utami, Nanny Sri Lestari Jul 2019

Function, Meaning, And Message Of The Natural Environtment In The Story Of Keong Mas, Adinda Bunga Utami, Nanny Sri Lestari

International Review of Humanities Studies

This research discusses the meaning and function of the natural environment in one folk tale that is well known in the Javanese community. This folktale is known in all circles of society, despite having social differences. An interesting problem in this folklore is the placement of functions and environmental meanings as the main elements of stories or tales. The focus of this research is to raise the function and meaning of the natural environment contained in one story of Keong Mas. This study aims to explain carefully the function and meaning of the natural environment which is the background of …


Conventions, Habits, And U.S. Teachers’ Meanings For Graphs, Kevin C. Moore, Jason Silverman, Teo Paoletti, Dave Liss, Stacy Musgrave Mar 2019

Conventions, Habits, And U.S. Teachers’ Meanings For Graphs, Kevin C. Moore, Jason Silverman, Teo Paoletti, Dave Liss, Stacy Musgrave

Department of Mathematics Facuty Scholarship and Creative Works

In this paper, we use relevant literature and data to motivate a more detailed look into relationships between what we perceive to be conventions common to United States (U.S.) school mathematics and individuals’ meanings for graphs and related topics. Specifically, we draw on data from pre-service (PST) and in-service (IST) teachers to characterize such relationships. We use PSTs’ responses during clinical interviews to illustrate three themes: (a) some PSTs’ responses implied practices we perceive to be conventions of U.S. school mathematics were instead inherent aspects of PSTs’ meanings; (b) some PSTs’ responses implied they understood certain practices in U.S. school …


Professional Orientation Of Students Based On The Skills Of Mathematical Modeling, Z Siddikov Apr 2018

Professional Orientation Of Students Based On The Skills Of Mathematical Modeling, Z Siddikov

Scientific journal of the Fergana State University

Professional orientation of students based on the skills of mathematical modeling


Professional Orientation Of Students Based On The Skills Of Mathematical Modeling, Z Siddikov Apr 2018

Professional Orientation Of Students Based On The Skills Of Mathematical Modeling, Z Siddikov

Scientific journal of the Fergana State University

Professional orientation of students based on the skills of mathematical modeling


Transplanting A Bacterial Immune System: Determining The Function Of A Novel Crispr System, Riannon Smith, Melena Garrett Jan 2018

Transplanting A Bacterial Immune System: Determining The Function Of A Novel Crispr System, Riannon Smith, Melena Garrett

Research on Capitol Hill

CRISPR (Clusters of Regularly Interspaced Short Palindromic Repeats) loci and cas (CRISPR-associated) genes provide adaptive immunity (see panel below) in bacteria and have recently been repurposed for genome editing.

Systems are structurally and functionally diverse.

  • 2 classes, 6 types, 33 subtypes
  • Very few have been studied experimentally
  • None of the Type IV systems have been characterized


Effect Of Alf3-Coated Li4ti5o12 On The Performance And Function Of The Lini0.5mn1.5o4||Li4ti5o12 Full Battery-An In-Operando Neutron Powder Diffraction Study, Gemeng Liang, Anoop Somanathan Pillai Sushamakumari Amma, Vanessa K. Peterson, Kuan-Yu Ko, Chia-Ming Chang, Cheng-Zhang Lu, Chia-Erh Liu, Shih-Chieh Liao, Jin-Ming Chen, Zaiping Guo, Wei Kong Pang Jan 2018

Effect Of Alf3-Coated Li4ti5o12 On The Performance And Function Of The Lini0.5mn1.5o4||Li4ti5o12 Full Battery-An In-Operando Neutron Powder Diffraction Study, Gemeng Liang, Anoop Somanathan Pillai Sushamakumari Amma, Vanessa K. Peterson, Kuan-Yu Ko, Chia-Ming Chang, Cheng-Zhang Lu, Chia-Erh Liu, Shih-Chieh Liao, Jin-Ming Chen, Zaiping Guo, Wei Kong Pang

Australian Institute for Innovative Materials - Papers

The LiNi0.5Mn1.5O4||Li4Ti5O12(LMNO||LTO) battery possesses a relatively-high energy density and cycle performance, with further enhancement possible by application of an AlF3coating on the LTO electrode particles. We measure the performance enhancement to the LMNO||LTO battery achieved by a AlF3coating on the LTO particles through electrochemical testing and use in-operando neutron powder diffraction to study the changes to the evolution of the bulk crystal structure during battery cycling. We find that the AlF3coating along with parasitic Al doping slightly increases capacity and greatly increases rate capability of the LTO electrode, as well as significantly reducing capacity loss on cycling, facilitating a gradual …


Inverse Function: Pre-Service Teachers’ Techniques And Meanings, Teo Paoletti, Irma E. Stevens, Natalie L.F. Hobson, Kevin C. Moore, Kevin R. Laforest Jan 2018

Inverse Function: Pre-Service Teachers’ Techniques And Meanings, Teo Paoletti, Irma E. Stevens, Natalie L.F. Hobson, Kevin C. Moore, Kevin R. Laforest

Department of Mathematics Facuty Scholarship and Creative Works

Researchers have argued teachers and students are not developing connected meanings for function inverse, thus calling for a closer examination of teachers’ and students’ inverse function meanings. Responding to this call, we characterize 25 pre-service teachers’ inverse function meanings as inferred from our analysis of clinical interviews. After summarizing relevant research, we describe the methodology and theoretical framework we used to interpret the pre-service teachers’ activities. We then present data highlighting the techniques the pre-service teachers used when responding to tasks that involved analytical and graphical representations of functions and inverse functions in both decontextualized and contextualized situations and discuss …


Reflectance Of Xuv Light On A Two Dimensional Conducting Rough Surface, Chelsea Thangavelu Aug 2017

Reflectance Of Xuv Light On A Two Dimensional Conducting Rough Surface, Chelsea Thangavelu

Student Works

A Fortran program is set up to solve for the reflectance of XUV light from a rough two dimensional surface, resembling experimental mirrors used to reflect XUV light. Because the roughness of the surface is on the order of magnitude of the wavelength of XUV light, our approach requires a Greene's Function instead of using traditional geometrical optics or physical optics. Our Fortran program calculates the impedance (Z) matrix which requires integration over Greene's Function at non-singular points. The Z matrix helps solve for the induced surface current J(x') at non-singular points. At singular points, the program implements a series …


Magnetic Nanostructure Application In Sers Detection Of Melatonin And Resonance Raman Characterization Of Binding Of Catechol Moieties With Antibiotic, Siqi Sun Jul 2017

Magnetic Nanostructure Application In Sers Detection Of Melatonin And Resonance Raman Characterization Of Binding Of Catechol Moieties With Antibiotic, Siqi Sun

USF Tampa Graduate Theses and Dissertations

Raman spectroscopy provides characteristic peaks of the target molecules that can be observed with appropriate laser, spectrometer and detector. These characteristic peaks can reveal ‘fingerprint’ information of a molecule even in a myriad of cases and combinations. It makes Raman spectroscopy a highly sensitive and selective analytical technique. Raman spectroscopy has a variety of chemical, environmental and biological applications. In this dissertation, modified Raman method are applied in life sciences and pharmaceutical studies.

The major challenge against development of Raman spectroscopy is how to improve the intensity of Raman signal. Surface Enhance Raman Scattering (SERS) and resonance Raman(RR) are utilized …


Plant Diversity Influences The Structure And Function Of A Restored Prairie And Its Responses To Added Disturbances, Rebecca Bevans Apr 2017

Plant Diversity Influences The Structure And Function Of A Restored Prairie And Its Responses To Added Disturbances, Rebecca Bevans

School of Natural Resources: Dissertations, Theses, and Student Research

As global warming, human conversion of natural landscapes to agricultural uses, and widespread biodiversity losses continue to alter the ecosystems we depend on, an understanding of the relationship between ecosystem structure, composition, and function is needed to maintain valuable ecosystem states and their associated functions. Research testing the limits of an ecosystem’s ability to maintain essential structure and functioning under disturbance conditions can aid in this goal.

In this study, I measured the relationship between plant diversity, community structure and functional traits, and their responses to added disturbances. I added disturbances representing those either caused or intensified by human activity …


Effects Of Surrounding Water Table On A Forested Wetland Habitat In East Coast Of Virginia, Lane Stokes Oct 2016

Effects Of Surrounding Water Table On A Forested Wetland Habitat In East Coast Of Virginia, Lane Stokes

Civil & Environmental Engineering Theses & Dissertations

Exchanges into and out of a wetland, including surface water flow, groundwater flow, and constituents in the flows, usually determine the wetland physicochemical characteristics and biodiversity. To date, of these three exchanges, groundwater flow is the least studied, particularly in the United States of America. In this thesis, field observations were conducted at a forested non-tidal wetland, located on a flat hilltop. The position of the wetland is such that groundwater outflow is the only significant exchange that could be impacted by the surrounding land use. In addition, a spatially variable steady-state model was set up to extrapolate the observations …


Alignment For Comprehensive Two-Dimensional Gas Chromatography (Gcxgc) With Global, Low-Order Polynomial Transformations, Davis Rempe, Stephen Reichenbach, Stephen Scott Apr 2016

Alignment For Comprehensive Two-Dimensional Gas Chromatography (Gcxgc) With Global, Low-Order Polynomial Transformations, Davis Rempe, Stephen Reichenbach, Stephen Scott

UCARE Research Products

As columns age and differ between systems, retention times for GC x GC may vary between runs. In order to properly analyze chromatograms, it is often desirable to align chromatographic features between chromatograms. This alignment can be characterized by a mapping of retention times from one chromatogram to the retention times of another chromatogram. Alignment methods can be classified as global or local, i.e., whether the geometric differences between chromatograms are characterized by a single function for the entire chromatogram or by a combination of many functions for different regions of the chromatogram. Previous work has shown that global, low-degree …


The Characterization Of A Recombinant Virophage Integrase, Martin Christopher Chacon Jan 2016

The Characterization Of A Recombinant Virophage Integrase, Martin Christopher Chacon

Open Access Theses & Dissertations

Virophages are satellite-like dsDNA viruses that parasitize giant viruses of the family Mimiviridae. Mavirus is the second virophage discovered that associates with its host virus Cafeteria roenbergensis Virus (CroV). When co-infecting their common host cell Cafeteria roenbergensis, a marine zooplankton that is widely spread throughout the oceans, mavirus will inhibit CroV's replication. In addition, mavirus was shown to share high similarities to the Maverick/Polinton eukaryotic DNA transposons. A coding sequence in mavirus genome (MV02) reveals high homology to retroviral integrases such as those found in HIVs. The putative integrase MV02 is predicted to integrate mavirus DNA into the host genome. …


Bacterial Diversity And Function Within An Epigenic Cave System And Implications For Other Limestone Cave Systems, Kathleen Merritt Brannen-Donnelly Dec 2015

Bacterial Diversity And Function Within An Epigenic Cave System And Implications For Other Limestone Cave Systems, Kathleen Merritt Brannen-Donnelly

Doctoral Dissertations

There are approximately 48,000 known cave systems in the United States of America, with caves formed in carbonate karst terrains being the most common. Epigenic systems develop from the downward flow of meteoric water through carbonate bedrock and the solutional enlargement of interconnected subsurface conduits. Despite carbonate karst aquifers being globally extensive and important drinking water sources, microbial diversity and function are poorly understood compared to other Earth environments. After several decades of research, studies have shown that microorganisms in caves affect water quality, rates of carbonate dissolution and precipitation, and ecosystem nutrition through organic matter cycling. However, limited prior …


Moments Of The Neutron G2 Structure Function At Intermediate Q2, Wolfgang Korsch, P. Solvignon, N. Liyanage, J.-P. Chen, Seonho Choi, K. Slifer, K. Aniol, T. Averett, W. Boeglin, A. Camsonne, G. D. Cates Jul 2015

Moments Of The Neutron G2 Structure Function At Intermediate Q2, Wolfgang Korsch, P. Solvignon, N. Liyanage, J.-P. Chen, Seonho Choi, K. Slifer, K. Aniol, T. Averett, W. Boeglin, A. Camsonne, G. D. Cates

Physics and Astronomy Faculty Publications

We present new experimental results for the 3He spin structure function g2 in the resonance region at Q2 values between 1.2 and 3.0(GeV/c)2. Spin dependent moments of the neutron were extracted. Our main result, the inelastic contribution to the neutron d2 matrix element, was found to be small at ⟨Q2⟩=2.4(GeV/c)2 and in agreement with the lattice QCD calculation. The Burkhardt-Cottingham sum rule for 3He and the neutron was tested with the measured data and using the Wandzura-Wilczek relation for the low x unmeasured region.


Λλ Correlation Function In Au+Au Collisions At √SNn=200  Gev, J. Kevin Adkins, Renee Fatemi, Suvarna Ramachandran, L. Adamczyk, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev, J. Alford, C. D. Anson, A. Aparin, D. Arkhipkin, E. C. Aschenauer Jan 2015

Λλ Correlation Function In Au+Au Collisions At √SNn=200  Gev, J. Kevin Adkins, Renee Fatemi, Suvarna Ramachandran, L. Adamczyk, G. Agakishiev, M. M. Aggarwal, Z. Ahammed, I. Alekseev, J. Alford, C. D. Anson, A. Aparin, D. Arkhipkin, E. C. Aschenauer

Physics and Astronomy Faculty Publications

We present ΛΛ correlation measurements in heavy-ion collisions for Au+Au collisions at √SNN=200  GeV using the STAR experiment at the Relativistic Heavy-Ion Collider. The Lednický-Lyuboshitz analytical model has been used to fit the data to obtain a source size, a scattering length and an effective range. Implications of the measurement of the ΛΛ correlation function and interaction parameters for dihyperon searches are discussed.


Cctv Surveillance: The Differing Aims And Functions Of Cctv Within The Corporate Stratum, Johan Malmenbratt, David J. Brooks Jan 2015

Cctv Surveillance: The Differing Aims And Functions Of Cctv Within The Corporate Stratum, Johan Malmenbratt, David J. Brooks

Australian Security and Intelligence Conference

Closed Circuit Television (CCTV) systems are found in a variety of environments and used for a multitude of purposes, leading to differing views of CCTV within an organisation. In accordance to management theory, organisations contain a stratum of work where each level requires specific skills set. In accordance with this work stratum, the study’s methodology used semi-structured interviews with different levels of security personnel in a Casino complex to extract and undertake a thematic analysis. The study extracted 10 CCTV surveillance features across two themes, being its aims and functions. CCTV features included creating a safe environment, protection, legal compliance …


The Impacts Of Water Availability On Macroinvertebrate, Ector Matias Martell Jan 2015

The Impacts Of Water Availability On Macroinvertebrate, Ector Matias Martell

Open Access Theses & Dissertations

In many regions around the world climate is changing and biotic communities are changing with it. In areas like the southwestern U.S., drought is one of the major sources of disturbance. Although droughts are an integral part of the natural hydrological cycles, they can have devastating effects on freshwater ecosystems when disrupted by extended periods of drought, resulting in changes to the structure and function of biotic communities. In this study, we surveyed four streams in the Sacramento Mountains of New Mexico from 2010 to 2014: Agua Chiquita, Rio Peñasco, Wills Creek, and the Sacramento River; These years encompassed an …


Functions On Adjacent Vertex Degrees Of Trees With Given Degree Sequence, Hua Wang Nov 2014

Functions On Adjacent Vertex Degrees Of Trees With Given Degree Sequence, Hua Wang

Department of Mathematical Sciences Faculty Publications

In this note we consider a discrete symmetric function f(x, y) where f(x; a) + f(y, b) ≥ f(y, a) + f(x, b) for any x ≥ y and a ≥ b, associated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the corresponding graph invariant, defined as Σ uv∈E(T) f(deg(u), deg(v)), are characterized by the “greedy tree” and “alternating greedy tree”. This is achieved through simple generalizations of previously used ideas on similar questions. As special cases, the already known extremal structures of the Randić index follow as corollaries. The extremal structures for …


Linked-Cluster Expansion For The Green's Function Of The Infinite-U Hubbard Model, Ehsan Khatami, Edward Perepelitsky, Marcos Rigol, Sriram B. Shastry Jun 2014

Linked-Cluster Expansion For The Green's Function Of The Infinite-U Hubbard Model, Ehsan Khatami, Edward Perepelitsky, Marcos Rigol, Sriram B. Shastry

Faculty Publications

We implement a highly efficient strong-coupling expansion for the Green's function of the Hubbard model. In the limit of extreme correlations, where the onsite interaction is infinite, the evaluation of diagrams simplifies dramatically enabling us to carry out the expansion to the eighth order in powers of the hopping amplitude. We compute the finite-temperature Green's function analytically in the momentum and Matsubara frequency space as a function of the electron density. Employing Padé approximations, we study the equation of state, Kelvin thermopower, momentum distribution function, quasiparticle fraction, and quasiparticle lifetime of the system at temperatures lower than, or of the …


Linked-Cluster Expansion For The Green's Function Of The Infinite-U Hubbard Model, Ehsan Khatami, Edward Perepelitsky, Marcos Rigol, Sriram B. Shastry Jan 2014

Linked-Cluster Expansion For The Green's Function Of The Infinite-U Hubbard Model, Ehsan Khatami, Edward Perepelitsky, Marcos Rigol, Sriram B. Shastry

Ehsan Khatami

We implement a highly efficient strong-coupling expansion for the Green's function of the Hubbard model. In the limit of extreme correlations, where the onsite interaction is infinite, the evaluation of diagrams simplifies dramatically enabling us to carry out the expansion to the eighth order in powers of the hopping amplitude. We compute the finite-temperature Green's function analytically in the momentum and Matsubara frequency space as a function of the electron density. Employing Padé approximations, we study the equation of state, Kelvin thermopower, momentum distribution function, quasiparticle fraction, and quasiparticle lifetime of the system at temperatures lower than, or of the …


Compilation And Comparison Of Electron Penetration Ranges As A Function Of Effective Number Of Valence Electrons, Teancum Quist Apr 2013

Compilation And Comparison Of Electron Penetration Ranges As A Function Of Effective Number Of Valence Electrons, Teancum Quist

Senior Theses and Projects

The continuous-slow-down approximation (CSDA) is used to create a simple composite analytical formula to estimate the range or maximum penetration depth of bombarding electrons into traditional materials including conductors, semiconductors, and insulators. This formula generates an approximation to the range using a single fitting parameter, Nv, described as the effective number of valence electrons. This applicability of the formulation extends to electrons with energies from 10MeV. These calculations are of great value for studies of high electron bombardment, such as electron spectroscopy or the vacuum of space. A list comprised of 187 materials has been collected that greatly …


Electron Penetration Ranges As A Function Of Effective Number Of Valence Electrons, Teancum Quist, Blake Moore, Greg Wilson, Jr Dennison Apr 2013

Electron Penetration Ranges As A Function Of Effective Number Of Valence Electrons, Teancum Quist, Blake Moore, Greg Wilson, Jr Dennison

Posters

The Continuous-Slow-Down Approximation (CSDA) is used to create a simple composite analytical formula to estimate the range or maximum penetration depth of incident electrons into diverse materials including conductors, semiconductors, and insulators. This formula generates an approximation to the range using a single fitting parameter, Nv, described as the effective number of valence electrons. This range of the formulation extends to electrons with energies from <10 eV to >10MeV, with 20% accuracy. A list comprised of 222 materials has been collected that greatly extends the applicability of this model. Several key material constants were compiled for each material, including the atomic …


Sensor Response Of Polypyrrole Trilayer Benders As A Function Of Geometry, Stephen John, Gursel Alici, Geoffrey M. Spinks, John D. W. Madden, Gordon G. Wallace Mar 2013

Sensor Response Of Polypyrrole Trilayer Benders As A Function Of Geometry, Stephen John, Gursel Alici, Geoffrey M. Spinks, John D. W. Madden, Gordon G. Wallace

Gordon Wallace

Trilayer polypyrrole benders are capable of generating voltages and currents when applied with an external force or displacement, demonstrating potential as mechanical sensors. Previous work has identified the effects of dopant and electrolyte on the sensor output, and a 'deformation induced ion flux' model was proposed. The current work aims to identify the change in sensor response with input amplitude and bender geometry as a function of frequency. The current and charge output from the trilayer benders were found to increase proportionally with input displacement and bender strain for multiple input frequencies, indicating linearity. Sensitivities of the current and charge …


Sensor Response Of Polypyrrole Trilayer Benders As A Function Of Geometry, Stephen John, Gursel Alici, Geoffrey M. Spinks, John D. W. Madden, Gordon G. Wallace Feb 2013

Sensor Response Of Polypyrrole Trilayer Benders As A Function Of Geometry, Stephen John, Gursel Alici, Geoffrey M. Spinks, John D. W. Madden, Gordon G. Wallace

Gursel Alici

Trilayer polypyrrole benders are capable of generating voltages and currents when applied with an external force or displacement, demonstrating potential as mechanical sensors. Previous work has identified the effects of dopant and electrolyte on the sensor output, and a 'deformation induced ion flux' model was proposed. The current work aims to identify the change in sensor response with input amplitude and bender geometry as a function of frequency. The current and charge output from the trilayer benders were found to increase proportionally with input displacement and bender strain for multiple input frequencies, indicating linearity. Sensitivities of the current and charge …