Teaching Student Researchers How toTeaching Student Researchers How toWrite Award Winning Abstracts!Write Award Winning Abstracts!

Adapted from UNM STEM Education Outreach Adapted from UNM STEM Education Outreach Programs Teacher Professional Development Programs Teacher Professional Development Workshops materials & thWorkshops materials & the Abstract Writing e Abstract Writing Process presentation created by John Cole Process presentation created by John Cole (Intel ISEF Display & Safety Chairperson) & (Intel ISEF Display & Safety Chairperson) &

available on the SSP website under the available on the SSP website under the Resources for Students, Teachers & Affiliated Resources for Students, Teachers & Affiliated

Fair Personnel section at:Fair Personnel section at:http://www.societyforscience.org/isef/document

An abstract is a brief, written explanation of An abstract is a brief, written explanation of the research project consisting of a succinct the research project consisting of a succinct description of the project’s purpose, the description of the project’s purpose, the procedures followed, the data collected, and procedures followed, the data collected, and the conclusions reached.the conclusions reached.

An abstract is NOT a reiteration of the entire An abstract is NOT a reiteration of the entire research plan!!research plan!!

An abstract is a self-contained statement that An abstract is a self-contained statement that must make sense all by itself.must make sense all by itself.

Uses complete but concise Uses complete but concise sentences & is in the 3sentences & is in the 3rdrd person. person.

Uses present tense for the Uses present tense for the existing body of facts.existing body of facts.

Uses past tense for the Uses past tense for the completed research.completed research.

Defines specialized terminology Defines specialized terminology and abbreviations.and abbreviations.

Is 50 to 250 words long.Is 50 to 250 words long.Is typed neatly, single spaced.Is typed neatly, single spaced.

Intel ISEF rules require each Finalist to write an abstract Intel ISEF rules require each Finalist to write an abstract of no more than 250 words to be displayed with the of no more than 250 words to be displayed with the project. project.

An abstract gives the essence of the project in a brief An abstract gives the essence of the project in a brief but complete form to judges and the public viewing the but complete form to judges and the public viewing the Finalist’s project.Finalist’s project.

Once approved, SRC provides the Finalist with two Once approved, SRC provides the Finalist with two embossed copies of the abstract, one to display embossed copies of the abstract, one to display vertically at the project and the other to make copies to vertically at the project and the other to make copies to handout to judges and the public on visitors’ day.handout to judges and the public on visitors’ day.

The abstract must focus on the current year's research The abstract must focus on the current year's research and give only minimal reference to previous work. and give only minimal reference to previous work.

Details and discussions should not be included in the Details and discussions should not be included in the abstract, but may be put in the longer, written research abstract, but may be put in the longer, written research paper (if required), or given on the project exhibit board. paper (if required), or given on the project exhibit board.

Finalists at the Intel ISEF are required to use the on-line Finalists at the Intel ISEF are required to use the on-line system for submitting their abstract. Regional and local system for submitting their abstract. Regional and local fairs use the fairs use the Official Abstract Form (not necessary for most (not necessary for most local fairs). local fairs).

In addition, abstracts must not include acknowledgments In addition, abstracts must not include acknowledgments (such as referencing mentor or university laboratory). (such as referencing mentor or university laboratory).

Provides SRC a quick study of your project as it is Provides SRC a quick study of your project as it is an overview of the purpose, means, and result of an overview of the purpose, means, and result of research. research.

Helps judges (both special and category) discern Helps judges (both special and category) discern quickly whether the project qualifies for specific quickly whether the project qualifies for specific awards and whether the research is significant in awards and whether the research is significant in its specific area.its specific area.

Informs visitors to ISEF (students, teachers, and Informs visitors to ISEF (students, teachers, and the public at large) of the nature of the research.the public at large) of the nature of the research.

Begin with a Begin with a Research Project ProspectusResearch Project Prospectus to to outline the research project. A prospectus outline the research project. A prospectus helps the researcher identify the nature and helps the researcher identify the nature and scope of the investigation, research scope of the investigation, research methods, and anticipated conclusions methods, and anticipated conclusions and/or applications. and/or applications.

Here’s an example…Here’s an example…

Possible Title:Name:School:

Purpose of project / experimentIn a sentence of 25 words or fewer, explain the reason for your research project or a hypothesis you have selected to test.

Methods of researchExplain in a sentence or two how you plan to research your topic. What methods will you use? What resources will you need?

Data/ObservationsDetermine what data do you need to collect and what difficulties you may encounter as you research.

Conclusions/ApplicationsExplain in a sentence or two what results you anticipate your research will produce. What conclusions or applications do you hope to be able to explain?

1.1. Write a sentence making broad statement Write a sentence making broad statement about the topic of research.about the topic of research.

2.2. Write the next sentence or two focusing Write the next sentence or two focusing more narrowly on the particular intent of the more narrowly on the particular intent of the research.research.

3.3. Write several sentences indicating the Write several sentences indicating the problem to be solved and the hypothesis that problem to be solved and the hypothesis that was posed.was posed.

4.4. Write a very brief statement to describe Write a very brief statement to describe the methodology employed the methodology employed (This may be omitted if space or (This may be omitted if space or

time is short)time is short)..

5.5. Write several concise statements Write several concise statements indicating which variables were explored indicating which variables were explored and compared and if the data obtained and compared and if the data obtained supported the hypothesis. These supported the hypothesis. These sentences summarize the results and sentences summarize the results and discussion sections of the research paper.discussion sections of the research paper.

6.6. Write a sentence that gives the Write a sentence that gives the conclusion(s) of the research work and a conclusion(s) of the research work and a statement of the direction for future statement of the direction for future research.research.

7.7. Count the number of words for the Count the number of words for the sentences you just wrote. If you need to, sentences you just wrote. If you need to, edit your sentences to bring your abstract edit your sentences to bring your abstract within the required 50- 250 word count.within the required 50- 250 word count.

8.8. Put all previous sentences in paragraph Put all previous sentences in paragraph form.form.

9.9. Be sure to check your spelling AND Be sure to check your spelling AND grammar. Remember, you may soon grammar. Remember, you may soon have judges reading your work!!have judges reading your work!!

TitleNameSchool

Purpose of project / experiment:

An introductory statement of the reason for investigating the topic of the project.

A statement of the problem or hypothesis being studied.

Summarize procedures, emphasizing the key points or steps:

A summarization of the key points and an overview of how the investigation was conducted.

Omit details about the materials used unless it greatly influenced the procedure or had to be developed to do the investigation.

An abstract should only include procedures done by the student. Work done by a mentor (such as surgical procedures) or work done prior to student involvement must not be included.

Detail succinctly observations/data/results:

This section should provide key results that lead directly to the conclusions you have drawn.

It should not give too many details about the results nor include charts or graphs.

State conclusions/applications.

Purpose of the ExperimentPurpose of the Experiment An introductory statement of the reason for investigating the topic of the An introductory statement of the reason for investigating the topic of the

project. project. A statement of the problem or hypothesis being studied. A statement of the problem or hypothesis being studied.

Procedures UsedProcedures Used A summarization of the key points and an overview of how the A summarization of the key points and an overview of how the

investigation was conducted. investigation was conducted. An abstract does not give details about the materials used unless it greatly An abstract does not give details about the materials used unless it greatly

influenced the procedure or had to be developed to do the investigation. influenced the procedure or had to be developed to do the investigation. An abstract should only include procedures done by the student. Work An abstract should only include procedures done by the student. Work

done by a mentor (such as surgical procedures) or work done prior to done by a mentor (such as surgical procedures) or work done prior to student involvement must not be included. student involvement must not be included.

Observation/Data/ResultsObservation/Data/ResultsThis section should provide key results that lead directly to the This section should provide key results that lead directly to the

conclusions you have drawn. conclusions you have drawn. It should not give too many details about the results nor include It should not give too many details about the results nor include

tables or graphs. tables or graphs.

ConclusionsConclusionsConclusions from the investigation should be described briefly. Conclusions from the investigation should be described briefly. The summary paragraph should reflect on the process and The summary paragraph should reflect on the process and

possibly state some applications and extensions of the possibly state some applications and extensions of the investigation. investigation.

An abstract does not include a bibliography unless specifically An abstract does not include a bibliography unless specifically required by your local fair. The Intel ISEF requires the required by your local fair. The Intel ISEF requires the bibliography as part of the research plan to be provided on Form bibliography as part of the research plan to be provided on Form 1A.1A.

Revise and edit the abstract in the Revise and edit the abstract in the template. Once you have filled in template. Once you have filled in each section, you can easily copy and each section, you can easily copy and paste the final version into the paste the final version into the abstract form online. Such a abstract form online. Such a procedure avoids the need to retype procedure avoids the need to retype the entire abstract, thereby reducing the entire abstract, thereby reducing the chance of errors in the final the chance of errors in the final version.version.

SAMPLESAMPLEEffects of Marine Engine Exhaust Water on Algae Effects of Marine Engine Exhaust Water on Algae

Mary E. JonesMary E. JonesHometown High School, Hometown, PAHometown High School, Hometown, PA

This project in its present form is the result of bioassay This project in its present form is the result of bioassay experimentation on the effects of two-cycle marine engine exhaust experimentation on the effects of two-cycle marine engine exhaust water on certain green algae.water on certain green algae. The initial idea was to determine the The initial idea was to determine the toxicity of outboard engine lubricant. Some success with lubricants toxicity of outboard engine lubricant. Some success with lubricants eventually led to the formulation of "synthetic" exhaust water which, eventually led to the formulation of "synthetic" exhaust water which, in turn, led to the use of actual two-cycle engine exhaust water as in turn, led to the use of actual two-cycle engine exhaust water as the test substance. the test substance.

Toxicity was determined by means of the standard bottle or "batch" Toxicity was determined by means of the standard bottle or "batch" bioassay technique. Scenedesmus quadricauda and bioassay technique. Scenedesmus quadricauda and Ankistrodesmus sp. were used as the test organismsAnkistrodesmus sp. were used as the test organisms. . Toxicity was Toxicity was measured in terms of a decrease in the maximum standing crop. measured in terms of a decrease in the maximum standing crop. The effective concentration - 50% (EC 50) for Scenedesmus The effective concentration - 50% (EC 50) for Scenedesmus quadricauda was found to be 3.75% exhaust water; for quadricauda was found to be 3.75% exhaust water; for Ankistrodesmus sp. 3.1% exhaust water using the bottle techniqueAnkistrodesmus sp. 3.1% exhaust water using the bottle technique. .

Anomalies in growth curves raised the suspicion that evaporation Anomalies in growth curves raised the suspicion that evaporation was affecting the results; therefore, a flow-through system was was affecting the results; therefore, a flow-through system was improvised utilizing the characteristics of a device called a improvised utilizing the characteristics of a device called a Biomonitor.Biomonitor. Use of the Biomonitor lessened the influence of Use of the Biomonitor lessened the influence of evaporation, and the EC 50 was found to be 1.4% exhaust water evaporation, and the EC 50 was found to be 1.4% exhaust water using Ankistrodesmus sp. as the test organism. Mixed populations using Ankistrodesmus sp. as the test organism. Mixed populations of various algae gave an EC 50 of 1.28% exhaust water. of various algae gave an EC 50 of 1.28% exhaust water.

The contributions of this project are twofold. First, the toxicity of two-The contributions of this project are twofold. First, the toxicity of two-cycle marine engine exhaust was found to be considerably greater cycle marine engine exhaust was found to be considerably greater than reported in the literature (1.4% vs. 4.2%). Secondly, the than reported in the literature (1.4% vs. 4.2%). Secondly, the benefits of a flow-through bioassay technique utilizing thebenefits of a flow-through bioassay technique utilizing the Biomonitor was demonstrated.Biomonitor was demonstrated.

PurposePurpose

MethodsMethods

DataData

ObservationsObservations

ConclusionsConclusions

ApplicationsApplications

Writing & Revising TipsWriting & Revising Tips

Emphasize these aspects: purpose (hypothesis), methods, scope, results, Emphasize these aspects: purpose (hypothesis), methods, scope, results, conclusions, and recommendationsconclusions, and recommendations

Focus only on the current year's research when it is a continuation project.Focus only on the current year's research when it is a continuation project. Exclude any of the mentor or supervisor’s workExclude any of the mentor or supervisor’s work Omit details and discussionsOmit details and discussions Use the past tense to describe Use the past tense to describe (However, where appropriate use active verbs rather than (However, where appropriate use active verbs rather than

passive verbs.) passive verbs.)

Use short sentences, but vary sentence structure. Use short sentences, but vary sentence structure. Use complete sentences Use complete sentences (Do not abbreviate by omitting articles or other small words in (Do not abbreviate by omitting articles or other small words in

order to save space.) order to save space.)

Avoid jargon Avoid jargon Use appropriate scientific languageUse appropriate scientific language Use concise syntaxUse concise syntax Use correct spelling, grammar, and punctuationUse correct spelling, grammar, and punctuation

Simply put, the style of an abstract should always be declarative not discursive.

Revision TechniquesRevision TechniquesAddition – adding a word, phrase, or sentenceAddition – adding a word, phrase, or sentence

OriginalOriginal: : This project is an experimentation of the effects of two-cycle This project is an experimentation of the effects of two-cycle marine engine exhaust water on certain algae. marine engine exhaust water on certain algae.

RevisedRevised: : This project is a bioassay experimentation of the effects of two-This project is a bioassay experimentation of the effects of two-cycle marine engine exhaust water on certain green algae.cycle marine engine exhaust water on certain green algae.

Deletion – deleting a word, phrase, or sentenceDeletion – deleting a word, phrase, or sentence OriginalOriginal: The researcher has developed an original code required for : The researcher has developed an original code required for

successful implementation of the environment reconstruction successful implementation of the environment reconstruction applicationapplication..

RevisedRevised: The researcher : The researcher developeddeveloped an original code required for an original code required for successful implementation of the environment reconstruction successful implementation of the environment reconstruction applicationapplication..

Revision TechniquesRevision Techniques Substitution – substituting one word, phrase, or Substitution – substituting one word, phrase, or

sentence for anothersentence for another OriginalOriginal: In the beginning, the idea was to determine the toxicity of : In the beginning, the idea was to determine the toxicity of

outboard engine lubricant.outboard engine lubricant. RevisedRevised: The : The initialinitial idea was to determine the toxicity of outboard engine idea was to determine the toxicity of outboard engine

lubricant.lubricant.

Transposition – moving words, phrases, or sentences Transposition – moving words, phrases, or sentences to another position to another position OriginalOriginal: Using optical fibers as light guides, a system was created with : Using optical fibers as light guides, a system was created with

light guided from a light source to an integrating chamber, reflected and light guided from a light source to an integrating chamber, reflected and guided back to a digital camera.guided back to a digital camera.

RevisedRevised: A system : A system using optical fibers as light guidesusing optical fibers as light guides was created with light was created with light guided from a light source to an integrating chamber, reflected, and then guided from a light source to an integrating chamber, reflected, and then guided back to a digital camera. guided back to a digital camera.

Revision TechniquesRevision TechniquesCombination – combining sentences and/or paragraphs, Combination – combining sentences and/or paragraphs,

which usually results in the use of multiple revision which usually results in the use of multiple revision techniques and a considerable shortening of the passage.techniques and a considerable shortening of the passage.

Original: Original: The project was started with an investigation of methods in The project was started with an investigation of methods in use today and possible alternatives. Two alternative methods that use today and possible alternatives. Two alternative methods that seemed to be promising were chosen — the first method is to kill seemed to be promising were chosen — the first method is to kill bacteria with pulsing high voltage, and the second is boiling with high bacteria with pulsing high voltage, and the second is boiling with high efficient heat exchangingefficient heat exchanging..

Revised: Revised: The project The project investigated investigated two alternative methods in use two alternative methods in use today: today: 1) killing1) killing bacteria with pulsing high voltage; bacteria with pulsing high voltage; 2)2) boiling boiling bacteria bacteria with awith a high efficient heat high efficient heat exchangeexchange..

USE OF REGRESSION ANALYSES TO BUILD ECOLOGICAL MODELS OF POISON USE OF REGRESSION ANALYSES TO BUILD ECOLOGICAL MODELS OF POISON DART FROGS IN THEIR NATIVE HABITATSDART FROGS IN THEIR NATIVE HABITATSGabriel Thailand JoachimGabriel Thailand JoachimCibola High School, Albuquerque, NMCibola High School, Albuquerque, NM

All over the world frogs are dying off at an alarming rate due to pollution, global warming, All over the world frogs are dying off at an alarming rate due to pollution, global warming, deforestation, Chytrid fungus, and habitat destruction. Any conservation efforts must take into account deforestation, Chytrid fungus, and habitat destruction. Any conservation efforts must take into account ecological variables important to frog survival. The purpose of the current study is to model the ecological variables important to frog survival. The purpose of the current study is to model the ecological complexity of Dendrobates pumilio, Dendrobates auratus, and other diurnal frogs in the ecological complexity of Dendrobates pumilio, Dendrobates auratus, and other diurnal frogs in the lowlands of Costa Rica for purposes of conservation. Dendrobates pumilio, D. auratus, and other lowlands of Costa Rica for purposes of conservation. Dendrobates pumilio, D. auratus, and other diurnal frogs were censused at Estacion Biologica El Zota in the summer of 2009. Biotic and abiotic diurnal frogs were censused at Estacion Biologica El Zota in the summer of 2009. Biotic and abiotic factors thought to contribute to frog presence were measured. These factors were: microclimate factors thought to contribute to frog presence were measured. These factors were: microclimate (temperature and RH) and biodiversity (prey, predators, buttresses, nursery plants, other animals, leaf (temperature and RH) and biodiversity (prey, predators, buttresses, nursery plants, other animals, leaf litter depth, tree diameter, and habitat). Results of Student t-tests showed that D. auratus and D. litter depth, tree diameter, and habitat). Results of Student t-tests showed that D. auratus and D. pumilio could be found in areas of significantly different temperature and relative humidity. Weak pumilio could be found in areas of significantly different temperature and relative humidity. Weak correlations were found between frog presence and a composite score for biodiversity. Correlations correlations were found between frog presence and a composite score for biodiversity. Correlations between biotic and abiotic factors were low; but showed important relationships within the ecosystem. between biotic and abiotic factors were low; but showed important relationships within the ecosystem. Binary logistic regression analyses were run on all frog data revealing one partial model (other diurnal Binary logistic regression analyses were run on all frog data revealing one partial model (other diurnal frogs) and one succesful model (D. pumilio). Predictors for the D. pumilio model are mean leaf litter, frogs) and one succesful model (D. pumilio). Predictors for the D. pumilio model are mean leaf litter, edge and riverine habitats,percent cover, presence of other diurnal frogs, and buttresses. The model edge and riverine habitats,percent cover, presence of other diurnal frogs, and buttresses. The model for other diurnal frogs showed that habitat and presence of other frogs were the principal predictors of for other diurnal frogs showed that habitat and presence of other frogs were the principal predictors of frog presence; but for mathmatical reasons did not get included in the model. These models can be frog presence; but for mathmatical reasons did not get included in the model. These models can be used to target sites preferred by frogs for conservation efforts. used to target sites preferred by frogs for conservation efforts.

Persistent Global Activation of the Persistent Global Activation of the AplysiaAplysia Serotonergic Serotonergic System After Sensitizing StimuliSystem After Sensitizing Stimuli

The marine mollusk The marine mollusk AplysiaAplysia responds to noxious stimulation with a stereotyped arousal responds to noxious stimulation with a stereotyped arousal reaction that includes escape locomotion, increased heart rate and sensitization of reaction that includes escape locomotion, increased heart rate and sensitization of defensive reflexes. Although previous studies have shown that serotonin (5-HT) is defensive reflexes. Although previous studies have shown that serotonin (5-HT) is important for most of these behavioral responses, it is still unclear how the 5-HT system important for most of these behavioral responses, it is still unclear how the 5-HT system is activated in response to noxious stimuli. To address this question, I used a specific is activated in response to noxious stimuli. To address this question, I used a specific staining of the 5-HT neurons in the living central nervous system (CNS) that allowed me staining of the 5-HT neurons in the living central nervous system (CNS) that allowed me to (1) systematically record their electrical activity following a noxious stimulus, and (2) to (1) systematically record their electrical activity following a noxious stimulus, and (2) trace their projections using the neuronal tracer Neurobiotin. I found that in response to trace their projections using the neuronal tracer Neurobiotin. I found that in response to tail-nerve shock, a procedure known to mimic a noxious tail stimulus, the vast majority tail-nerve shock, a procedure known to mimic a noxious tail stimulus, the vast majority of 5-HT neurons increased their firing rate for several minutes and became more of 5-HT neurons increased their firing rate for several minutes and became more excitable. 5-HT neurons were found to project toward various peripheral targets such as excitable. 5-HT neurons were found to project toward various peripheral targets such as the gill, heart, body wall, tail, siphon, head, and tentacles as well as to other ganglia in the gill, heart, body wall, tail, siphon, head, and tentacles as well as to other ganglia in the CNS. This study shows that the the CNS. This study shows that the AplysiaAplysia 5-HT system is globally and persistently 5-HT system is globally and persistently activated after a noxious stimulus. Such an activation might serve to synchronize the activated after a noxious stimulus. Such an activation might serve to synchronize the different aspects of the arousal reaction in different aspects of the arousal reaction in AplysiaAplysia..

PERIOD ANALYSIS OF CATACLYSMIC VARIABLE X10 PERIOD ANALYSIS OF CATACLYSMIC VARIABLE X10

AND ITS IMPLICATIONS ON THE ORIGIN OF LOW STATESAND ITS IMPLICATIONS ON THE ORIGIN OF LOW STATES

Cataclysmic variables are binary systems, each consisting of a Cataclysmic variables are binary systems, each consisting of a white dwarf (the primary) and a low mass star (the secondary). white dwarf (the primary) and a low mass star (the secondary). Usually, matter flows from the secondary onto the primary, Usually, matter flows from the secondary onto the primary, producing X-rays upon impact. However, previous observations producing X-rays upon impact. However, previous observations have indicated that certain cataclysmic variables frequently exhibit have indicated that certain cataclysmic variables frequently exhibit low states – a dramatic decrease in mass transfer (and thus X-ray low states – a dramatic decrease in mass transfer (and thus X-ray production) for an extended period of time. Low states can last up production) for an extended period of time. Low states can last up to several years, and this phenomenon is currently not well to several years, and this phenomenon is currently not well understood. This research is primarily focused on creating a understood. This research is primarily focused on creating a model to elucidate the origin of low states using data gathered model to elucidate the origin of low states using data gathered from X10, a magnetic cataclysmic variable that experienced a low from X10, a magnetic cataclysmic variable that experienced a low state in year 2005. The model proposed in this study attributes state in year 2005. The model proposed in this study attributes low states to the magnetic interactions between the secondary’s low states to the magnetic interactions between the secondary’s starspots and the primary, and its predictions on which systems starspots and the primary, and its predictions on which systems should exhibit low states and which ones should not have all been should exhibit low states and which ones should not have all been confirmed by past observations. confirmed by past observations.

THE STRING TOPOLOGY BV ALGEBRA, HOCHSCHILD COHOMOLOGY THE STRING TOPOLOGY BV ALGEBRA, HOCHSCHILD COHOMOLOGY

AND THE GOLDMAN BRACKET ON SURFACESAND THE GOLDMAN BRACKET ON SURFACES

This project provides an algebraic description of the String Topology Batalin-Vilkovisky This project provides an algebraic description of the String Topology Batalin-Vilkovisky algebra for a large class of manifolds. Such a description previously existed only for algebra for a large class of manifolds. Such a description previously existed only for spheres and projective spaces.spheres and projective spaces.The homology H(LX) of the space of free loops of a closed oriented smooth manifold X The homology H(LX) of the space of free loops of a closed oriented smooth manifold X has a rich algebraic structure called string topology, discovered by Chas and Sullivan in has a rich algebraic structure called string topology, discovered by Chas and Sullivan in 1999. In particular, H(LX) is a Batalin-Vilkovisky (BV) algebra. However this structure is 1999. In particular, H(LX) is a Batalin-Vilkovisky (BV) algebra. However this structure is hard to compute in algebraic terms.hard to compute in algebraic terms.This project studies string topology in the case when the manifold X is aspherical. In this This project studies string topology in the case when the manifold X is aspherical. In this case the Hochschild cohomology Gerstenhaber algebra HH(A) of the group algebra A of case the Hochschild cohomology Gerstenhaber algebra HH(A) of the group algebra A of the fundamental group of X has a BV structure. My main result is a theorem establishing the fundamental group of X has a BV structure. My main result is a theorem establishing a natural isomorphism between the Hochschild cohomology BV algebra HH(A) and the a natural isomorphism between the Hochschild cohomology BV algebra HH(A) and the string topology BV algebra H(LX). In particular, for a closed oriented surface X of string topology BV algebra H(LX). In particular, for a closed oriented surface X of hyperbolic type this gives a complete description of the BV algebra operations on H(LX) hyperbolic type this gives a complete description of the BV algebra operations on H(LX) and HH(A) terms of the Goldman bracket of loops on X. and HH(A) terms of the Goldman bracket of loops on X. There are several conjectures connecting the string topology BV algebra with algebraic There are several conjectures connecting the string topology BV algebra with algebraic structures on the Hochschild cohomology of algebras related to the manifold X. My structures on the Hochschild cohomology of algebras related to the manifold X. My theorem is the first such hypothesis that has been proven. The proof is based on a theorem is the first such hypothesis that has been proven. The proof is based on a combination of topological and algebraic constructions allowing to compute and compare combination of topological and algebraic constructions allowing to compute and compare multiplications and BV operators on both H(LX) and HH(A).multiplications and BV operators on both H(LX) and HH(A).

How Would You Revise This?How Would You Revise This?

ORIGINALORIGINAL REVISIONREVISIONThe purpose of my The purpose of my

projectproject is to find the is to find the connection between connection between the ratio of radii of an the ratio of radii of an ellipse and ellipse and itsits mechanical advantage mechanical advantage on specified angle of on specified angle of rotation intervals.rotation intervals.

This project examined This project examined the connection the connection between the ratio of between the ratio of radii of an ellipse and radii of an ellipse and the mechanical the mechanical advantage of a specified advantage of a specified angle of rotation angle of rotation intervals. intervals.