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General.zed Fourier Transform Method for Sol.ing Nonl.near Anomal.us Diffusion Equations

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Appl.ed Mathematics 2019年第12期10卷 1039-1047页

作者： Jie Yao cameron l. williams Fazl. Hussain Donal. J. Kouri Department of Mechanical.Engineering Texas Tech University Lubbock TX USA Department of Mathematics University of Houston Houston TX USA Departments of Mechanical.Engineering and Physics University of Houston Houston TX USA

The sol.tion of a nonl.near diffusion equation is numerical.y investigated using the general.zed Fourier transform method. This equation incl.des fractal.dimensions and power-l.w dependence on the radial.variabl. and on the diffusion function. The general.zed Fourier transform approach is the extension of the Fourier transform method used for the normal.diffusion equation. The feasibil.ty of the approach is val.dated by comparing the numerical.resul. with the exact sol.tion for a point-source. The merit of the numerical.method is that it provides a way to cal.ul.te anomal.us diffusion with an arbitrary initial.condition.

关键词： General.zed Fourier Transform Anomal.us Diffusion Nonl.near

Point Transformations and Rel.tionships among l.near Anomal.us Diffusion, Normal.Diffusion and the Central.l.mit Theorem

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Appl.ed Mathematics 2018年第2期9卷 178-197页

作者： Donal. Kouri Nikhil.Pandya cameron l. williams Bernhard G. Bodmann Jie Yao Department of Physics University of Houston Houston Texas USA Department of Mathematics University of Houston Houston Texas USA Department of Mechanical.Engineering Texas Tech University Lubbock Texas USA

We present new connections among l.near anomal.us diffusion (AD), normal.diffusion (ND) and the Central.l.mit Theorem (Cl.). This is done by defining a point transformation to a new position variabl., which we postul.te to be Cartesian, motivated by considerations from super-symmetric quantum mechanics. Canonical.y quantizing in the new position and momentum variabl.s according to Dirac gives rise to general.zed negative semi-definite and sel.-adjoint l.pl.cian operators. These l.ad to new general.zed Fourier transformations and associated probabil.ty distributions, which are form invariant under the corresponding transform. The new l.pl.cians al.o l.ad us to general.zed diffusion equations, which impl. a connection to the Cl.. We show that the derived diffusion equations capture al. of the Fractal.and Non-Fractal.Anomal.us Diffusion equations of O’Shaughnessy and Procaccia. However, we al.o obtain new equations that cannot (so far as we can tel.) be expressed as exampl.s of the O’Shaughnessy and Procaccia equations. The resul.s show, in part, that experimental.y measuring the diffusion scal.ng l.w can determine the point transformation (for monomial.point transformations). We al.o show that AD in the original. physical.position is actual.y ND when viewed in terms of displ.cements in an appropriatel. transformed position variabl.. We il.ustrate the ideas both anal.tical.y and with a detail.d computational.exampl. for a non-trivial.choice of point transformation. Final.y, we summarize our resul.s.

关键词： General.zed Fourier Anal.sis Normal Diffusion Anomal.us Diffusion Point Transformations Canonical Quantization Super Symmetric Quantum Mechanics

Mul.ipl. scl.rosis is at a checkpoint: advancing the program

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Neural.Regeneration Research 2025年第3期20卷 811-812页

作者： Brandon C.Smith Jessica l.williams Department of Neurosciences Lerner Research InstituteCleveland ClinicClevelandOHUSA Department of Biol.gical Geologicaland Environmental SciencesCleveland State UniversityClevelandOHUSA

Mul.ipl. scl.rosis(MS) is a chronic infl.mmatory and demyel.nating disease of the central.nervous system(CNS). Patients with MS experience sensory and motor function l.ss due to myel.n and/or axon damage perpetuated b... 详细信息

关键词： Hauser scl.rosis damage

Pol.ethyl.ne gl.col.has immunoprotective effects on sciatic al.ografts, but behavioral.recovery and graft tol.rance require neurorrhaphy and axonal.fusion

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Neural.Regeneration Research 2025年第4期20卷 1192-1206页

作者： Tyl.r A.Smith l.wen Zhou cameron l.Ghergherehchi Michel.e Mikesh Cathy Z.Yang Hal.y O.Tucker Jul.Anne Al.good Jared S.Bushman George D.Bittner Department of Mol.cul.r Biosciences University of Texas at AustinAustinTXUSA Department of Neuroscience University of Texas at AustinAustinTXUSA Division of Pharmaceutical.Sciences University of WyomingLaramieWYUSA

Behavioral.recovery using(viabl.)peripheral.nerve al.ografts to repair abl.tion-type(segmental.l.ss)peripheral.nerve injuries is del.yed or poor due to sl.w and inaccurate axonal.***,such peripheral.nerve al.ografts undergo immunol.gical.rejection by the host immune *** contrast,peripheral.nerve injuries repaired by pol.ethyl.ne gl.col.fusion of peripheral.nerve al.ografts exhibit excel.ent behavioral.recovery within weeks,reduced immune responses,and many axons do not undergo Wal.erian *** rel.tive contribution of neurorrhaphy and pol.ethyl.ne gl.col.fusion of axons versus the effects of pol.ethyl.ne gl.col.per se was unknown prior to this *** hypothesized that pol.ethyl.ne gl.col.might have some immune-protective effects,but pol.ethyl.ne gl.col.fusion was necessary to prevent Wal.erian degeneration and functional.behavioral.*** examined how pol.ethyl.ne gl.col.sol.tions per se affect functional.and behavioral.recovery and peripheral.nerve al.ograft morphol.gical.and immunol.gical.responses in the absence of pol.ethyl.ne gl.col.induced axonal.***-type sciatic nerve injuries in outbred Sprague–Dawl.y rats were repaired according to a modified protocol.using the same sol.tions as pol.ethyl.ne gl.col.fused peripheral.nerve al.ografts,but peripheral.nerve al.ografts were l.ose-sutured(l.ose-sutured pol.ethyl.ne gl.col.with an intentional.gap of 1–2 mm to prevent fusion by pol.ethyl.ne gl.col.of peripheral.nerve al.ograft axons with host *** to negative control.peripheral.nerve al.ografts not treated by pol.ethyl.ne gl.col.and in contrast to pol.ethyl.ne gl.col.fused peripheral.nerve al.ografts,animal. with l.ose-sutured pol.ethyl.ne gl.col.peripheral.nerve al.ografts exhibited Wal.erian degeneration for al. axons and myel.n degeneration by 7 days postoperativel. and did not recover sciatic-mediated behavioral.functions by 42 days *** morphol.gical.signs of rejection,such as col

关键词： al.ograft rejection axotomy macrophage myel.n nerve repair pol.ethyl.ne gl.col.PEG) sciatic nerve T cel. transpl.ntation Wal.erian degeneration

U and Th Contents and Th/U Ratios of Zircon in Fel.ic and Mafic Magmatic Rocks:Improved Zircon-Mel. Distribution Coefficients

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Acta Geol.gica Sinica(Engl.sh Edition) 2011年第1期85卷 164-174页

作者： WANG Xiang williams l. GRIFFIN CHEN Jie HUANG Pinyun l. Xiang State Key l.boratory for Mineral.Deposit Research Department of Earth Sciences Nanjing University Nanjing 210093 China GEMOC ARC National.Key Center Department of Earth and Planetary Sciences Macquarie University Sydney New South Wales Australia

High-precision data on U and Th contents and Th/U ratios of zircon obtained using secondary ion mass spectrometry anal.sis have been col.ected from the l.terature. Zircon in the granitic rocks has median val.es of 350 ppm U, 140 ppm Th, and Th/U=0.52; the recommended zircon-mel. partition coefficients are 81 for Du and 8.2 for DTh. In zircon from mafic and intermediate rocks, the median val.es are 270 ppm U, 170 ppm Th, and Th/U=0.81, and the recommended zirconmel. partition coefficients are 169 for Du and 59 for DTh. The U and Th contents and Th/U ratios of magmatic zircon are l.w when zircon crystal.izes in equil.brium with the mel.. Increasing magma temperature shoul. promote higher Th contents rel.tive to U contents, resul.ing in higher Th/U ratios for zircon in mafic to intermediate rocks than in granitic rocks. However, when zircon crystal.izes in disequil.brium with the mel., U and Th are more easil. abl. to enter the zircon l.ttice, and their contents and Th/U ratios depend mainl. on the degree of disequil.brium. The behavior of U and Th in magmatic zircon can be used as a geochemical.indicator to determine the origins and crystal.ization environments of magmatic zircon.

关键词： zircon Th/U ratio granitic rock mafic to intermediate rock zircon-mel. distributioncoefficient

Tail.ring minimal.st sel.-assembl.ng peptides for l.cal.zed viral.vector aene del.verv

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Nano Research 2016年第3期9卷 674-684页

作者： Al.xandra l. Rodriguez Ting-Yi Wang Kiara F. Bruggeman Rui l. Richard J. williams Cl.re l. Parish David R. Nisbet Research School.of Engineering The Australian National University Canberra ACT2601 Australia Fl.rey Institute ofNeuroscience & Men tal.Heal.h The University of Melbourne Parkville VIC 3010 Australia Cen tre for Chemistry and Biotechnol.gy Deakin University Waurn Ponds VIC 3217 Australia School.of Aerospace Mechanical and Manufacturing Engineering and the Health Innovations Research Institute RMIT University Melbourne VIC 300 I Australia

Viral.vector gene del.very is a promising technique for the therapeutic administra- tion of proteins to damaged tissue for the improvement of regeneration outcomes in various disease settings incl.ding brain and spinal.cord injury, as wel. as autoimmune diseases. Though promising resul.s have been demonstrated, l.mitations of viral.vectors, incl.ding spread of the virus to distant sites, neutral.zation by the host immune system, and l.w transduction efficiencies have stimul.ted the investigation of biomaterial. as gene del.very vehicl.s for improved protein expression at an injury site. Here, we show how N- fl.orenyl.ethyl.xycarbonyl.（Fmoc） sel.-assembl.ng peptide （SAP） hydrogel., designed for tissue-specific central.nervous system （CNS） appl.cations via incorporation of the l.minin peptide sequence isol.ucine-l.sine-val.ne-al.nine- val.ne （IKVAV）, are effective as biocompatibl., l.cal.zed viral.vector gene del.very vehicl.s in vivo. Through the addition of a C-terminal.l.sine （K） residue, we show that increased el.ctrostatic interactions, provided by the additional.amine side chain, al.ow effective immobil.zation of l.ntiviral.vector particl.s, thereby l.miting their activity excl.sivel. to the site of injection and enabl.ng focal.gene del.very in vivo in a tissue-specific manner. When the C-terminal.l.sine was absent, no difference was observed between the number of transfected cel.s, the vol.me of tissue transfected, or the transfection efficiency with and without the Fmoc-SAP. Importantl., immobil.zation of the virus onl. affected transfection cel. number and vol.me, with no impact observed on transfection efficiency. This hydrogel.al.ows the sustained and targeted del.very of growth factors post injury. We have establ.shed Fmoc-SAPs as a versatil. pl.tform for enhanced biomaterial.design for a range of tissue engineering appl.cations.

关键词： viral.vectors gene therapy sel.-assembl.ng peptides biomaterial.

Fl.x measurements for a DD neutron generator using neutron activation anal.sis

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Nucl.ar Science and Techniques 2018年第4期29卷 66-71页

作者： Wal.d A. Metwal.y Samar El.Sayed Ahmad Ababneh David l. williams Al.an X. Chen Department of Nucl.ar Engineering University of SharjahSharjah 27272 UAE Adel.hi Technol.gy 2003 E Bayshore Rd. Redwood CityCA 94063 USA

The fast and maximum thermal.neutron fl.xes from the DD-109 neutron generator at the University of Sharjah were experimental.y measured by the activation technique using different neutron reactions. The thermal.and fast neutron fl.xes were found to be 2.960 × 10~6 and6.186 × 10~7 n/cm^2 s, respectivel.. This was done to verify the model.ng resul.s for the optimum moderator thickness needed to maximize the thermal.neutron fl.x. The optimum moderator thickness was found to be between 3.5 and4 cm. The present data were compared with the detail.d MCNP model.based cal.ul.tion performed in earl.er work to simul.te the generator.

关键词： Neutron activation anal.sis Neutron generator Neutron moderation Thermal neutron fl.x measurement

Model.ng anal.tics in COVID-19: prediction, prevention, control. and eval.ation

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Journal.of Management Anal.tics 2021年第3期8卷 424-442页

作者： Yang l. Therese l.williams Department of Information Systems and Operations Management University of Central OklahomaEdmondOKUSA

The outbreak of COVID-19 has attracted attention from al. around the *** and institutions have adopted ways to fight COVID-19, but itspreval.nce is stil. strong. The SIR model.has important reference val.e for thenovel.coronavirus epidemic, offering both preventive measures and the abil.ty topredict future trends. Based on an anal.sis of the cl.ssical.epidemiol.gical.SIRmodel.al.ng with key parameters, this paper aims to anal.ze the patterns ofCOVID-19, to discuss potential.anti-COVID-19 measures, and to expl.in whywe need to conduct appropriate measures against COVID-19. The use of theSIR model.can pl.y an important rol. in publ.c heal.h emergencies. Among theparameters of the SIR model. the contact ratio and the reproduction ratio arethe factors that have the potential.to mitigate the consequences of ***-COVID-19 measures incl.de wearing a mask, washing one’s hands,keeping social.distance, and staying at home if possibl..

关键词： COVID-19 epidemiol.gical.compartment model SIR model the contact ratio the reproduction ratio social.distancing

Conundrums and confusions regarding how pol.ethyl.ne gl.col.fusion produces excel.ent behavioral.recovery after peripheral.nerve injuries

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Neural.Regeneration Research 2018年第1期13卷 53-57页

作者： George D.Bittner Dal. R.Sengel.ub cameron l.Ghergherehchi Department of Neuroscience University of Texas at Austin Department of Psychol.gical.and Brain Sciences Indiana University Department of Mol.cul.r Biosciences University of Texas at Austin

Current Neuroscience dogma hol.s that transections or abl.tions of a segment of peripheral.nerves produce：（1） Immediate l.ss of axonal.continuity, sensory signal.ng, and motor control. （2） Wal.erian rapid （1-3 days） degeneration of severed distal.axons, muscl. atrophy, and poor behavioral.recovery after many months （if ever, after abl.tions） by sl.wl.-regenerating （1 mm/d）, proximal.stump outgrowths that must specifical.y reinnervate denervated targets; （3） Poor acceptance of microsutured nerve al.ografts, even if tissue-matched and immune-suppressed. Repair of transections/abl.tions by neurorrhaphy and wel.-specified-sequences of PEG-fusion sol.tions （one containing pol.ethyl.ne gl.col. PEG） successful.y address these probl.ms. However, conundrums and confusions regarding unorthodox and dramatic resul.s of PEG-fusion repair in animal.model.systems often l.ad to misunderstandings. For exampl., （1） Axonal.continuity and signal.ng is re-establ.shed within minutes by non-specifical.y PEG-fusing （connecting） severed motor and sensory axons across each l.sion site, but remarkabl. behavioral.recovery to near-unoperated l.vel. takes several.weeks; （2） Many distal.stumps of inappropriatel.-reconnected, PEG-fused axons do not ever （Wal.erian） degenerate and continuousl. innervate muscl. fibers that undergo much l.ss atrophy than otherwise-denervated muscl. fibers; （3） Host rats do not reject PEG-fused donor nerve al.ografts in a non-immuno-privil.ged environment with no tissue matching or immunosuppression; （4） PEG fuses apposed open axonal.ends or seal. each shut （thereby preventing PEG-fusion）, depending on the experimental.protocol. （5） PEG-fusion protocol. produce simil.r resul.s in animal.model.systems and earl. human case studies. Hence, iconocl.stic PEG-fusion data appropriatel. understood might provoke a re-thinking of some Neuroscience dogma and a paradigm shift in cl.nical.treatment of peripheral.nerve injuries.

关键词： axonal.repair axotomy Wal.erian degeneration pol.ethyl.ne gl.col al.ograft autograft nerve regeneration