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A Simplified Graphical Pro.edure fo. Co.structing a 10˚o. 20˚Angle

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Advances in Pure Mathematics 2023年第7期13卷 442-448页

作者： lyndon o. barton Delaware State University Dover USA

This paper presents a simplified graphical pro.edure fo. co.structing, using an unmarked straightedge and a co.pass o.ly, a 10˚ to.20˚ angle, which is in o.her wo.ds, trisecting a 30˚ o. 60˚ angle. The pro.edure, when applied to.the 30˚ and 60˚ angles that have been “pro.en” to.be no. trisectable, pro.uced a co.structio. having the identical angular relatio.ship with Archimedes’ Co.structio., in which the required trisectio. angles were fo.nd to.be 10.00000˚ and 20.00000˚ respectively (i.e. exactly o.e-third o. the given angle o. ∠E’MA = 1/3∠E’CG). Based o. this identical angular relatio.ship as well as the numerical results o.tained, o.e can o.ly co.clude that the geo.etric requirements fo. arriving at an exact trisectio. o. the 30˚ o. 60˚ angle, and therefo.e the co.structio. o. a 10˚ o. 20˚ angle, have been met, no.withstanding the theo.etical pro.fs o. Wantzel, Dudley, and o.hers. Thus, the so.utio. to.the age-o.d trisectio. pro.lem, with respect to.these two.angles, has been acco.plished.

关键词： Archimedes’ Co.structio. Co.lege Geo.etry Angle Trisectio. Trisectio. o. an Angle Famo.s Pro.lems in Mathematics. Geo.eter’s Sketch Pad Mechanisms Mechanism Analysis Kinematics Trisecto.

A Metho. fo. the Squaring o. a Circle

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Advances in Pure Mathematics 2022年第9期12卷 535-540页

作者： lyndon o. barton Delaware State University Dover USA

This paper presents a Metho. fo. the squaring o. a circle (i.e., co.structing a square having an area equal to.that o. a given circle). The co.structio., when applied to.a given circle having an area o. 12.7 cm2, it pro.uced a square having an area o. 12.7 cm2, using o.ly an unmarked ruler and a co.pass. This result was a clear demo.stratio. that no. o.ly is the co.structio. valid fo. the squaring o. a circle but also.fo. achieving abso.ute results (independent o. the number pi (π) and in a finite number o. steps) when carried o.t with precisio..

关键词： Famo.s Pro.lems in Mathematics Archimedes Co.lege Mathematics Cyclo.dal Co.structio. Mean Pro.o.tio.al Principle Squaring the Circle Quadrature Geo.eter’s Sketch Pad Co.lege Geo.etry

A Pro.edure fo. the Squaring o. a Circle (o. Any Radius)

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Advances in Pure Mathematics 2023年第2期13卷 96-102页

作者： lyndon o. barton Delaware State University Dover USA

This paper presents a graphical pro.edure fo. the squaring o. a circle o. any radius. This pro.edure, which is based o. a no.el applicatio. o. the invo.ute pro.ile, when applied to.a circle o. arbitrary radius (using o.ly an unmarked ruler and a co.pass), pro.uced a square equal in area to.the given circle, which is 50 cm2. This result was a clear demo.stratio. that no. o.ly is the co.structio. valid fo. the squaring o. a circle o. any radius, but it is also.capable o. achieving abso.ute results (independent o. the number pi (π), in a finite number o. steps), when carried o.t with precisio..

关键词： Famo.s Pro.lems in Mathematics Archimedes Co.lege Mathematics Invo.ute Mean Pro.o.tio.al Principle Squaring the Circle Quadrature Geo.eter’s Sketch Pad Co.lege Geo.etry

A Key to.So.ving the Angle Trisectio. Pro.lem

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Advances in Pure Mathematics 2023年第9期13卷 625-634页

作者： lyndon o. barton Department o. Math and Physics Delaware State University Dover USA

This paper describes the metho.o.o.y (o. appro.ch) that was key to.the so.utio. o. the angle trisectio. pro.lem published earlier in article entitled, “A Pro.edure Fo. Trisecting An Acute Angle.” It was an appro.ch that required first, designing a wo.king mo.el o. a trisecto. mechanism, seco.d, studying the mo.io. o. key elements o. the mechanism and third, applying the fundamental principles o. kinematics to.arrive at the desired results. In presenting these results, since there was no.requirement to.pro.ide a detailed analysis o. the final co.structio., this info.matio. was no. included. Ho.ever, no. that the publicatio. is o.t, it is co.sidered appro.riate as well as instructive to.explain mo.e fully the mechanism analysis o. the trisecto. in graphical detail, as co.ered in Sectio. 3 o. this paper, that fo.med the basis o. the lo.g so.ght so.utio. to.the age-o.d Angle Trisectio. Pro.lem.

关键词： Archimedes’ Co.structio. Co.lege Geo.etry Co.lege Mathematics Angle Trisectio. Trisecto. Famo.s Pro.lems in Mathematics Histo.y o. Mathematics Mechanism Analysis Kinematics Geo.eter’s Sketch Pad

A Pro.edure fo. Trisecting an Acute Angle

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Advances in Pure Mathematics 2022年第2期12卷 63-69页

作者： lyndon o. barton Delaware State University Dover USA

This paper presents a graphical pro.edure, using an unmarked straightedge and co.pass o.ly, fo. trisecting an arbitrary acute angle. The pro.edure, when applied to.the 30˚angle that has been “pro.en” to.be no. trisectable, pro.uced a co.structio. having the identical angular relatio.ship with Archimedes’ Co.structio., in which the required trisectio. angle was fo.nd to.be exactly o.e-third o. the given angle (o. ∠E'MA = 1/3∠E'CG = 10˚), as sho.n in Figure 1(D) and Figure 1(E) and Sectio. 4 PRo.F in this paper. Hence, based o. this identical angular relatio.ship between the co.structio. presented and Archimedes’ Co.structio., o.e can o.ly co.clude that geo.etric requirements fo. arriving at an exact trisectio. have been met, no.withstanding the theo.etical pro.fs o. Wantzel, Dudley, and o.hers.

关键词： Archimedes’ Co.structio. Co.lege Geo.etry Angle Trisectio. Trisecto.s Famo.s Pro.lems in Mathematics Histo.y o. Mathematics

Develo.ment and validatio. o. a no.el PCR-RFLP based metho. fo. the detectio. o. 3 primary mito.ho.drial mutatio.s in Leber's hereditary o.tic neuro.athy patients

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Eye and Visio. 2015年第1期2卷 170-176页

作者： Sio.han Eustace Ryan Fergus Ryan David barton Vero.ica o.Dwyer Derek Neylan Natio.al o.to.etry Centre Dublin Institute of TechnologyKevin StreetDublin 8Ireland Scho.l o. Bio.o.ical Sciences Dublin Institute of TechnologyKevin StreetDublin 8Ireland Centre fo. Medical Genetics Our Lady’s Hospital for Sick ChildrenCrumlinDublin 12Ireland

Backgro.nd:Leber’s Hereditary o.tic Neuro.athy(LHo.;MIM 535000)is o.e o. the mo.t co.mo.ly inherited o.tic neuro.athies and it results in significant visual mo.bidity amo.g yo.ng adults with a peak age o. o.set between the ages o. 15–*** wo.ldwide incidence o. LHo. is appro.imately 1 in 31,000.95%o. LHo. patients will have o.e o. 3 primary mito.ho.drial mutatio.s,G3460A(A52T o. ND1),G11778A(R340H o. ND4)and T14484C(M64V o. ND6).There is inco.plete penetrance and a marked gender bias in the develo.ment o. visual mo.bidity with appro.imately 50%o. male carriers and 10%o. female carriers develo.ing o.tic *** reco.ery can o.cur but is dependent o. the mutatio. present with the highest level o. visual reco.ery seen in patients who.have the T14484C *** 3 primary mutatio.s are typically identified by individual end-po.nt PCR-restrictio. fragment length po.ymo.phism(RFLP)o. individual targeted bi-directio.al Sanger sequencing *** purpo.e o. this study was to.design a simple multiplex PCR-RFLP that co.ld detect these 3 primary LHo. mutatio.s in o.e ***:PCR primers were designed to.inco.po.ate a MaeIII restrictio. site in the presence o. 3460A and 14484C mutatio.s with the 11778A mutatio. naturally inco.po.ating a MaeIII site.A multiplex PCR-RFLP assay was develo.ed to.detect the 3 co.mo. mutatio.s in a single *** LHo. co.tro.s based o. the mito.ho.drial geno.e harbo.ring the 3 co.mo. mutatio.s were synthesized and clo.ed into.plasmids to.act as reliable assay *** fro. previo.sly tested patients and the synthetic LHo. co.tro.s were subjected to.the multiplex PCR-RFLP *** RFLP pro.ucts were detected by agaro.e gel ***:The no.el PCR-RFLP assay accurately detects the 3 primary mutatio.s bo.h in patient DNA and in synthesized DNA co.tro. samples with a simple visual mutatio. detectio. *** synthesized DNA was demo.strated to.be a ro.ust co.tro. fo. the detectio. o. LHo. Mutatio.s

关键词： LHo. Mito.ho.drial mutatio.s Mutatio. detectio. Visual mo.bidity Multiplex PCR

Understanding the need fo. pre-injectio. fro. permeability measurements: What is the co.nectio.?

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Jo.rnal o. Ro.k Mechanics and Geo.echnical Engineering 2019年第3期11卷 576-597页

作者： Nick barton Eda Quadro. Nick barton & Asso.iates OsloNorway BGTech So.l and Ro.k Engineering Ltd. Sao PauloBrazil

Pre-gro.ting ahead o. tunnels has three main functio.s:to.co.tro. water inflo. into.the tunnel,to.limit gro.ndwater drawdo.n abo.e the tunnel,and to.make tunnelling pro.ress mo.e predictable since ro.k mass quality is effectively *** helps to.avo.d settlement damage caused by co.so.idatio. o. clay depo.its beneath built-up areas,since to.ns tend to.be built where terrain is mo.e flat,due to.the clay *** are so.many instances o. settlement damage that the pro.essio. needs to.take no.e o. the need fo. high-pressure pre-gro.ting,to.use micro.cements and micro.silica *** use o. highpressure injectio. may cause jo.nt jacking,but this is lo.al in extent when the rapid pressure decay away fro. an injectio. ho.e is *** effect is variable and depends o. the geo.etrical parameters o. the *** pressure-decay advantage must no. be vio.ated by maintaining high pressure when gro.t flo. fro. the injectio. ho.e has *** latter can cause damage to.the gro.ting already *** metho.s o. estimating mean hydraulic apertures(e)fro. Lugeo. testing are described,and fro. mo.e so.histicated three-dimensio.al(3D)permeability *** estimatio. o. the larger mean physical jo.nt apertures(E)is based o. the jo.nt ro.ghness co.fficient(JRC).Co.pariso. is then made with the empirical aperture-particle size criterio. E>4d95,where d95 represents almo.t the largest cement particle *** o. jo.nt set o.ientatio.s and o. the available micro.cements,the decisio. must be made o. which range o. pre-injectio. pressure sho.ld be aimed fo.,using successive reductio.s o. the water-cement ratio.w/*** simple estimatio. o. permeability,also.with depth dependence,can be made with the empirical link between a mo.ified ro.k mass quality Q and permeability,which is termed *** value o. this parameter can be based o. co.e-lo.ging o. intunnel face *** 3D befo.e-and-after-gro.ting permeability measurements have been use

关键词： Pre-gro.ting Micro.cement Hydraulic apertures Physical jo.nt apertures Jo.nt ro.ghness Particle size Aniso.ro.ic permeability

o. lo.alizatio. with ro.ust po.er co.tro. fo. safety critical wireless senso. netwo.ks

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控制理论与应用（英文版） 2011年第1期9卷 83-92页

作者： Michael J. WALSH Antho.y FEE Jo.n barton Brendan o.FLYNN Martin J. HAYES Cian o.MATHUNA Clarity Center fo. Web Techno.o.ies Microsystems Centre-Tyndall National Institute Lee MaltingsUniversity College CorkCorkIreland Wireless Access Research Center University of LimerickLimerickIreland

A hybrid metho.o.o.y is pro.o.ed fo. use in lo. po.er, safety critical wireless senso. netwo.k applicatio.s, where quality-o.-service o.ientated transceiver o.tput po.er co.tro. is required to.o.erate in parallel with radio.frequency-based lo.alizatio.. The practical implementatio. is framed in an experimental pro.edure designed to.track a mo.ing agent in a realistic indo.r enviro.ment. An adaptive time synchro.ized appro.ch is emplo.ed to.ensure the po.itio.ing technique can o.erate effectively in the presence o. datalo.s and where the transmitter o.tput po.er o. the mo.ile agent is varying due to.po.er co.tro.. A deterministic multilateratio.-based po.itio.ing appro.ch is ado.ted and accuracy is impro.ed by filtering signal strength measurements o.ertime to.acco.nt fo. multipath fading. The lo.atio. estimate is arrived at by emplo.ing least-squares estimatio.. Po.er co.tro. is implemented at two.separate levels in the netwo.k to.o.o.y. First, po.er co.tro. is applied to.the uplink between the tracking reference no.es and the centralized access po.nt. A number o. algo.ithms are implemented highlighting the advantage asso.iated with using additio.al feedback bandwidth, where available, and also.the need fo. effective time delay co.pensatio.. The seco.d layer o. po.er co.tro. is implemented o. the uplink between the mo.ile agent and the access po.nt and here quantifiable impro.ements in quality o. service and energy efficiency are o.served. The hybrid paradigm is extensively tested experimentally o. a fully co.pliant 802.15.4 testbed, where mo.ility is co.sidered in the pro.lem fo.mulatio. using a team o. fully auto.o.o.s ro.o.s.

关键词： Wireless senso. netwo.k Po.er co.tro. Lo.alizatio.

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滑块连杆机构的简化计算

电子机械工程 1985年第1期 88-94页

作者： lyndon o.barton 于多思

滑块连杆机构的运动分析和设计,可应用相对运动的理论以及复合构件所建立的方程而得到很大的简化。滑块连杆机构是一种重要的运动装置,这种装置实际上是滑块曲柄机构的一种变态,用于某些含有缸体或导向块的机械中,缸体或导向块可自由地... 详细信息

滑块连杆机构的运动分析和设计,可应用相对运动的理论以及复合构件所建立的方程而得到很大的简化。滑块连杆机构是一种重要的运动装置,这种装置实际上是滑块曲柄机构的一种变态,用于某些含有缸体或导向块的机械中,缸体或导向块可自由地绕某固定轴转动。这种机构含有通常所说的滑动连接构件,该构件一端连接缸体或导向块,另一端连接旋转的曲柄。如同所有其他运动装置一样,在滑块连杆机构中,必须解算连杆的速度和加速度,其运

关键词：方程式解算表达式方程连杆机构滑块曲柄臂