D-shaped photonic crystal fiber plasmonic refractive index sensor based on gold grating
|
|
- Mariah Craig
- 5 years ago
- Views:
Transcription
1 D-shped photonic crystl fiber plsmonic refrctive index sensor bsed on gold grting JUNJIE LU, 1 YAN LI, 1,* YANHUA HAN, 1 YI LIU, 1 AND JIANMIN GAO 2 1 Deprtment of Optoelectronics Science, Hrbin Institute of Technology, Weihi, , Chin 2 School of Energy Science nd Engineering,, Hrbin Institute of Technology, Hrbin , Chin *Corresponding uthor: liy@hit.edu.cn Received XX Month XXXX; revised XX Month, XXXX; ccepted XX Month XXXX; posted XX Month XXXX (Doc. ID XXXXX); published XX Month XXXX In this work, we proposed high resolution D-shped photonic crystl fiber (PCF) surfce plsmon resonnce (SPR) sensor bsed on gold grting. Gold grting is introduced to modulte the resonnce wvelength nd enhnce the refrctive index (RI) sensitivity. Structure prmeters of PCF nd gold grting re nlyzed by finite element method (FEM) for optimizing the SPR sensor. The simultion results indicte tht ir hole pitch, ir hole dimeter nd gold thickness nd grting constnt hve little influence on the sensitivity of refrctive index, which reduces the requirement of precise processing. For improving the resolution of RI sensing, two-feture (2F) interrogtion method which combines wvelength interrogtion nd mplitude interrogtion is used nd the mximum theoreticl resolution of SPR sensor reches to RIU in rnge of nd the wvelength sensitivity reches to 3340nm/RIU. The proposed SPR sensor shows potentil pplictions on developing high-sensitivity, rel time nd fst-response SPR-RI sensor. OCIS codes: ( ) Fiber optics sensors; ( ) Surfce plsmons; ( ) Photonic crystl fibers; ( ) Opticl sensing nd sensors INTRODUCTION Surfce plsmon resonnce (SPR) is considered s promising method to detect the tiny refrctive index (RI) chnge, since SPR is extremely sensitive to permittivity of surrounding environment. During the pst decde, high sensitivity nd rel-time detection mke the SPR sensor widely used in chemicl nd biologicl sensing[1, 2]. Recent yers, SPR sensor bsed on photonic crystl fiber (PCF) hs ttrcted lot of ttention since the first SPR sensor ws proposed by Jorgenson in 1993, where the fiber core ws coted with the gold film by removing section of the fiber cldding to exhibit the plsmonic response[3]. PCF bring new vitlity to the fbriction of SPR sensors since its unique bility of controlling the evnescent wve penetrtion. When phse mtching condition is met, surfce plsmon polritons (SPP) mode cn be excited nd results in strong resonnce bsorption. By detecting the resonnce wvelength, unknown nlyte RI cn be clculted. For investigting the performnce of SPR sensor, mny PCF structures, such s dul-core PCF[4], D-shped PCF[5, 6] nd birefringent PCF[7], hve been well studied in the lst decde. For improving the performnce of the PCF-SPR sensors, some theoreticl designs of metl coted lrge ir hole PCF-SPR sensors hve been reported[8, 9]. For instnce, Hssni nd Skorobogtiy designed PCF with lrge ir holes, nd they coted the inner surfces of the ir holes with metl films to fbricte the PCF-SPR sensor in which the lrge ir holes were used s micro chnnels. The simultion results showed tht the resolution of their sensor could rech 10 4 RIU[10]. For relizing extremely high sensitivity, lrger dimeter ir holes nd multichnnel nlyte-filled PCF structure is proposed. Fn et l. presented high sensitivity RI sensor bsed on two lrge ir holes chnnels filled with nlyte which wvelength sensitivity reches to 7040nm/RIU[11]. Most of the reported PCF SPR sensors re coted with the multiple metl lyer nd liquid is filled inside the ir-holes for incresing the sensitivity, which is difficult in terms of fbriction. Moreover, since the metl film is coted inside the ir holes, it is difficult to precisely control the thicknesses of the metl film nd it is lso time-consuming to fill nd re-fill the nlyte from the ir holes. In this pper, we proposed SPR sensor bsed on D-shped PCF, which is coted with gold grting for improving the RI sensitivity. Gold grting results in more loss of core mode nd by chnging the grting constnt, the resonnce wvelength could be modulted. The resonnce wvelength is sensitive to the surrounding refrctive index of gold grting, which shows promising potentil in RI sensing. Simultion results show tht the RI sensitivity is 3 times s much s norml D-shped PCF-SPR sensor with gold film. By investigting the structure prmeters of PCF, simultion results show tht PCF structure hs little influence on the sensitivity of SPR sensor. Furthermore, the two-feture (2F) interrogtion method is used to provide higher resolution for RI sensing. In RI rnge of , the wvelength sensitivity reches to 3340nm/RIU, nd the mximum theoreticl resolution reches to RIU, which is much higher thn those of wvelength nd intensity interrogtion method.
2 2. DESIGN AND ANALYSIS The proposed PCF-SPR sensor is shown in Fig.1 (). There re two type ir holes in the PCF which is side polished with 3μm depth for creting plne sensing re. Before fbricting the gold grting, gold film should be coted on the plne surfce of D-shped PCF by mgnetron sputtering or pulsed lser deposition. Then gold grting cn be fbricted by using electron-bem lithogrphy or photolithogrphy. The cross section of the SPR sensor is shown in Fig. 1(b). The dimeter of smll ir holes is ds=0.8µm nd the dimeter of lrge ir holes is dl=1.6µm, respectively. The lttice pitch between ll ir holes is Λ=2.3µm. The thickness of the gold grtings is hg=40nm. The gold grting constnt is d0=1µm nd duty rtio is η=0.5. The used fiber mteril is fused silic nd the RI is determined by Sellmeier eqution [12] s: 14.61RIU -1. The gold grting cn enhnce the loss of the core mode which results in high mplitude sensitivity. The electric field of gold grting SPR sensor is shown in Fig. 2(c), which resonnce wvelength is nm. Besides the y-polrized core mode we lso cn see the SPP mode ppers on the interfce of gold grting nd dielectric s shown in Fig. 2 (d). There is strong coupling between core mode nd SPP mode, when the resonnce wvelength is nm. Therefore, strong coupling results in high confinement loss nd high mplitude sensitivity. 2 A1 A2 A3 2 B1 B2 B3 n( ) 1, (1) where A1= , A2= , A3= , B1= µm 2, B2= µm 2 nd B3= µm 2. The complex dielectric constnt of gold is given by Johnson nd Christy[13]. The confinement loss is clculted by using the imginry prt of the effective RI: (2) 4 =8.686 k0 Im( n eff ) 10 db/cm, where k0 = 2π/λ is the wvenumber nd Im(neff) is the imginry prt of effective index. The Gussin bem propgtes long the z-direction nd mode nlysis is performed in the XY plne. Fig. 2. () Resonnce wvelength of gold film SPR sensor nd gold grting SPR sensor with RI from 1.36 to (b) The electric field of full coted gold film SPR sensor. (c) The electric field of gold grting SPR sensor. (d) Intensity distribution of SPP mode. Fig. 1. Schemtic of proposed PCF-SPR sensor () 3D view (b) crosssection of sensor We investigted the sensitivity difference between SPR sensor with gold film nd gold grting. As shown in Fig. 2 (), when the thickness of gold is 40nm nd the RI of nlyte chnges from 1.36 to 1.37, the resonnce wvelength of SPR sensor with full coted gold film shifts from nm to nm, which mens the wvelength sensitivity is 774nm/RIU which is not idel for RI sensing. The electric field of full coted gold film SPR sensor is shown in Fig. 2(b). Since the wvelength of common commercil brodbnd lser source is less thn 2μm, resonnce pek more thn 2μm is bndoned. However, when the gold film is replced with gold grting, which could be fbricted by lser direct writing or photolithogrphy, the resonnce wvelength shifts significntly s shown in Fig. 2(). The wvelength difference is 33.54nm s the resonnce wvelength shifting from nm to nm, which mens the wvelength sensitivity is 3354nm/RIU. The simultion result shows tht by introducing the gold grting, the wvelength sensitivity of the SPR sensor is 4 times of norml gold film SPR sensor. Moreover, the mplitude sensitivity of gold film SPR sensor is -2.66RIU -1 nd the gold grting SPR sensor is - 3. RESULTS AND DISCUSSIONS Considering the prcticl fbriction of the PCF, the dimeter of ir holes is investigted. The confinement loss spectr is shown in Fig. 3(), when the dimeter of smll holes (ds) chnges from 0.7µm to 0.9µm nd the mximum loss chnges from dB/cm to db/cm. The wvelength sensitivity could be clculted s[14]: pek Sw, (3) n where Δλpek is the difference between two resonnce wvelength nd Δn is the vrition of nlyte RI. As shown in Tble 1, different dimeter of smll ir hole hs little influence on the wvelength sensitivity. Moreover, we lso investigted the sensitivity vrition, when the dimeter of lrge ir holes (dl) chnges. Fig.3 (b) illustrtes the loss spectr of gold grting SPR sensor with different dimeters of lrge ir holes. With incresing of the dimeter, the loss slightly deduces nd the resonnce wvelength shifts to shorter wvelength. But the dimeter of lrge ir hole hs limited influence on the wvelength sensitivity s shown in Tble 2. The lttice pitch (Λ) lso ws investigted nd the loss spectr is shown in Fig.3 (c). With incresing of the pitch, the resonnce wvelength shows slightly blue shift nd confinement loss decreses. The reson is tht lrge pitch results in chnging of the phse mtching condition. As shown in Tble 3, different lttice pitch hs slightly influence on wvelength sensitivity. The prmeters of gold grting lso ply vitl role in performnce of PCF-SPR sensors. As shown in Fig.3 (d), with incresing of the gold grting thickness, more energy of core mode is used for overcoming the dmping loss nd the resonnce wvelength shifts towrds to shorter wvelength. When the thickness of gold grting increses, the sensitivity slightly increses s shown in Tble 4. To optimize the performnce of gold grting SPR sensor, the resonnce wvelength is
3 selected round 1550nm nd the structure prmeters of PCF this should be ds=0.8µm, dl=1.6µm, Λ=2.3µm nd the thickness of gold should be hg=40nm. Fig. 3. Vrition of confinement loss s function of wvelength with vrying () dimeter of smll ir holes ds, (b) dimeter of lrge ir hole dl (c) lttice pitch of ir holes Λ nd (d) gold grting thickness hg, when the RI chnges from 1.36 to 1.37 Tble 1. Reltionship between ds nd wvelength sensitivity (Sw) ds (µm) Sw(nm/RIU) Tble 2. Reltionship between dl nd wvelength sensitivity (Sw) dl (µm) Sw (nm/riu) Tble 3. Reltionship between Λ nd wvelength sensitivity (Sw) Λ (µm) Sw (nm/riu) Tble 4. Reltionship between hg nd wvelength sensitivity (Sw) hg (nm) Sw (nm/riu) The gold grting prmeters were lso investigted for improving the performnce of the SPR sensor. As shown in Fig. 4 (), different grting constnt (d0) results in different resonnce wvelength, nd the wvelength sensitivity lso chnges s shown in Tble 5. We cn lso observe tht with incresing of grting constnt, the loss increses which results in higher mplitude sensitivity. Therefore, the grting constnt cn be used to modulte the resonnce wvelength. It is possible for SPR sensors working in expected wvelength such s common commercil brodbnd lser. Figure 4 (b) depicts the loss spectr of gold grting with different duty rtio (η). We cn see tht with incresing of duty rtio, the confinement loss increses significntly. When the duty rtio increses, the full width t hlf mximum (FWHM) reduces, which cn get better signl-to-noise (SNR) rtio. However, the sensitivity slightly decreses s shown in Tble 6. Thus, the grting constnt is set s d0=1µm nd the duty rtio could be set s η=0.5. Fig. 4. Vrition of confinement loss with vrying () grting constnt d0, (b) duty rtio η, when the RI chnges from 1.36 to Tble 5. Reltionship between d0 nd Wvelength sensitivity (Sw) d0 (µm) Sw (nm/riu) Tble 6. Reltionship between η nd Wvelength sensitivity (Sw) η Sw (nm/riu) Since the SPR sensor is extremely sensitive to the chnge of surrounding environment RI, we investigted the trnsmission spectr by chnging the nlyte RI. From Fig. 5() we cn see tht with incresing of the RI the resonnce wvelengths re red-shifted. Therefore, the nlyte RI could be detected by mesuring the shift of resonnce wvelength. As shown in Fig. 5(b), with incresing of nlyte RI, the resonnce wvelength shows good liner response nd the wvelength sensitivity reches to 3340nm/RIU. In ddition, with incresing of nlyte RI, the effective index of SPP mode is close to tht of core mode, which results in more energy loss of core mode. Therefore, the mplitude lso cn be used to sensing the RI s convenient nd cost effective method. The mplitude sensitivity cn be defined from[15]: 1 1,n sa RIU, (4),n n where α(λ,n) is the loss t RI of n nd α(λ,n) is the loss difference between two djcent nlyte RIs.
4 Figure 5 (c) shows the mplitude sensitivity of the proposed SPR sensor clculted by Eq. (4). From Fig. 5(c), mximum mplitude sensitivity cn be obtined t the wvelength of 1660nm, which is RIU -1. Bsed on the theory mentioned in Ref.[6], the two-feture (2F) sensitivity combines wvelength sensitivity nd mplitude sensitivity for enhncing the RI sensitivity. As embedded imge shown in Fig.5 (), if we detect the RI difference Δn of nlyte nd resonnce wvelength shifts from A to B, the 2F sensitivity cn be defined s: AB x y S2 F =. By normlizing Δx nd Δy, we cn mke wvelength sensitivity nd mplitude sensitivity into one dimension. For exmple, when nlyte RI chnges from 1.37 to 1.375, wvelength shifts from nm to nm nd loss shifts from dB/cm to dB/cm, which mens Δx=16.34nm, Δy=8.82dB/cm nd Δn=0.005, respectively. We ssume the length of sensing re is 1cm. If the wvelength resolution is 0.02nm (AQ3617B) nd mplitude resolution is 0.05dB, the RI chnge will bring 817 dt intervls for the x-xis (DIx=16.34/0.02=817) nd 176 dt intervls for the y-xis (DIy=8.82/0.05=176). Therefore, the 2F dt intervls DI2F=( ) 1/2 =836. Finlly, the mximum theoreticl resolution of wvelength (Rw), mplitude (R) nd R2F cn be clculted by R DI DI DI. x y Results show tht 2F resolution (R2F= RIU) is higher thn theoreticl wvelength resolution (Rw = RIU) nd theoreticl mplitude resolution(r = RIU). Fig. 5. () Vrition of confinement loss s function of wvelength with different nlyte RI.(b) Wvelength sensitivity with the nlyte RI rnge from 1.36 to 1.38, (c) mplitude sensitivity with the vrition of nlyte RI. (5) (6) 4. CONCLUSION A prcticl D-shped photonic crystl fiber RI sensor bsed on surfce plsmon resonnce is demonstrted by putting gold grting on the flt plne. FEM hs been used to nlyte the performnce of this proposed SPR sensor. The simultion results show tht PCF structure prmeters hve little influence on the performnce of sensor. The gold grting is used to enhnce the sensitivity nd tune the resonnce wvelength. Using the 2F interrogtion method, the mximum theoreticl resolution of RI is improved significntly nd reches to RIU, which is much higher thn wvelength nd mplitude resolution. Driving on the dvntge of ltest nnofbriction technique, the proposed structure cn be utilized for environmentl, biologicl nd biochemicl sensing pplictions. Funding Informtion. Ntionl Key Reserch nd Development Progrm of Chin (Grnt No. 2017YFF ); Nturl Science Foundtion of Shndong Province (Grnt No. ZR2018MF031); Ntionl Nturl Science Foundtion of Chin (Grnt No ). References [1] P. Singh, "SPR Biosensors: Historicl Perspectives nd Current Chllenges," Sensors & Actutors B Chemicl 229, (2016). [2] A. A. Rift, G. A. Mhdirji, Y. M. Su, Y. G. Shee, R. Ahmed, D. M. Chow, nd F. R. M. Adikn, "Surfce Plsmon Resonnce Photonic Crystl Fiber Biosensor: A Prcticl Sensing Approch," IEEE Photon. Technol. Lett. 27, (2015). [3] R. C. Jorgenson nd S. S. Yee, "A fiber-optic chemicl sensor bsed on surfce plsmon resonnce," Sens. Actutors B Chem. 12, (1993). [4] F. Wng, Z. Sun, C. Liu, T. Sun, nd P. K. Chu, "A highly sensitive dulcore photonic crystl fiber bsed on surfce plsmon resonnce biosensor with silver-grphene lyer," Plsmonics 12, 1-7 (2016). [5] R. K. Gngwr nd V. K. Singh, "Highly Sensitive Surfce Plsmon Resonnce Bsed D-Shped Photonic Crystl Fiber Refrctive Index Sensor," Plsmonics 12, (2016). [6] Y. Chen, Q. Xie, X. Li, H. Zhou, X. Hong, nd Y. Geng, "Experimentl reliztion of D-shped photonic crystl fiber SPR sensor," Journl of Physics D: Applied Physics 50, (2017). [7] J. N. Dsh nd R. Jh, "Grphene-Bsed birefringent photonic crystl fiber sensor using surfce plsmon resonnce," IEEE Photon. Technol. Lett. 26, (2014). [8] B. Shui, L. Xi, Y. Zhng, nd D. Liu, "A multi-core holey fiber bsed plsmonic sensor with lrge detection rnge nd high linerity," Opt. Express 20, (2012). [9] A. A. Rift, F. Hider, R. Ahmed, G. A. Mhdirji, F. R. M. Adikn, nd A. E. Miroshnichenko, "Highly sensitive selectively coted photonic crystl fiber-bsed plsmonic sensor," Opt. Lett. 43, (2018). [10] A. Hssni nd M. Skorobogtiy, "Design of the microstructured opticl fiber-bsed surfce plsmon resonnce sensors with enhnced microfluidics," Opt. Express 14, (2006). [11]Z. Fn, S. Li, Q. Liu, G. An, H. Chen, J. Li, D. Cho, H. Li, J. Zi, nd W. Tin, "High sensitivity of refrctive index sensor bsed on nlytefilled photonic crystl fiber with surfce plsmon resonnce," IEEE Photonics J. 7, 1-9 (2015). [12] E. K. Akowuh, T. Gormn, H. Ademgil, S. Hxh, G. K. Robinson, nd J. V. Oliver, "Numericl nlysis of photonic crystl fiber for biosensing pplictions," IEEE J. Quntum Electron. 48, (2012). [13] P. B. Johnson nd R. W. Christy, "Opticl Constnts of the Noble Metls," Physicl Review B 6, (1972). [14] F. Chivioli, C. A. J. Gouvei, P. A. S. Jorge, nd F. Bldini, "Towrds Uniform Metrologicl Assessment of Grting-Bsed Opticl Fiber Sensors: From Refrctometers to Biosensors," Biosensors 7(2017). [15] M. R. Hsn, S. Akter, A. A. Rift, S. Rn, K. Ahmed, R. Ahmed, H. Subbrmn, nd D. Abbott, "Spirl photonic crystl fiber-bsed dulpolrized surfce plsmon resonnce biosensor," IEEE Sensors Journl 18, (2018).
5
PRISMS. Don t see exactly what you are looking for? CVI Laser Optics specializes in prototype to volume production manufacturing!
PRISMS Mirrors CVI Lser Optics mnufctures lrge selection of high qulity prisms for use in mny pplictions including diverse industril nd scientific uses, lser trcking nd lignment, spectroscopy, nd militry
More informationFourier domain optical coherence tomography with an 800µm diameter axicon lens for long-depth-range probing
Fourier domin opticl coherence tomogrphy with n 800µm dimeter xicon lens for long-depth-rnge probing Kye-Sung Lee 1, Chuck Koehler, Eric G. Johnson, nd Jnnick P. Rollnd College of Optics nd Photonics:
More informationMATH 2530: WORKSHEET 7. x 2 y dz dy dx =
MATH 253: WORKSHT 7 () Wrm-up: () Review: polr coordintes, integrls involving polr coordintes, triple Riemnn sums, triple integrls, the pplictions of triple integrls (especilly to volume), nd cylindricl
More informationThe Distributed Data Access Schemes in Lambda Grid Networks
The Distributed Dt Access Schemes in Lmbd Grid Networks Ryot Usui, Hiroyuki Miygi, Yutk Arkw, Storu Okmoto, nd Noki Ymnk Grdute School of Science for Open nd Environmentl Systems, Keio University, Jpn
More informationOPTICS. (b) 3 3. (d) (c) , A small piece
AQB-07-P-106 641. If the refrctive indices of crown glss for red, yellow nd violet colours re 1.5140, 1.5170 nd 1.518 respectively nd for flint glss re 1.644, 1.6499 nd 1.685 respectively, then the dispersive
More information3.5.1 Single slit diffraction
3..1 Single slit diffrction ves pssing through single slit will lso diffrct nd produce n interference pttern. The reson for this is to do with the finite width of the slit. e will consider this lter. Tke
More informationOptics and Optical design Problems
Optics nd Opticl design 0 Problems Sven-Görn Pettersson / Cord Arnold 0-09-06 4:3 This mteril is tken from severl sources. Some problems re from the book Våglär och Optik by Görn Jönsson nd Elisbeth Nilsson.
More informationFig.1. Let a source of monochromatic light be incident on a slit of finite width a, as shown in Fig. 1.
Answer on Question #5692, Physics, Optics Stte slient fetures of single slit Frunhofer diffrction pttern. The slit is verticl nd illuminted by point source. Also, obtin n expression for intensity distribution
More informationComplete Coverage Path Planning of Mobile Robot Based on Dynamic Programming Algorithm Peng Zhou, Zhong-min Wang, Zhen-nan Li, Yang Li
2nd Interntionl Conference on Electronic & Mechnicl Engineering nd Informtion Technology (EMEIT-212) Complete Coverge Pth Plnning of Mobile Robot Bsed on Dynmic Progrmming Algorithm Peng Zhou, Zhong-min
More informationTilt-Sensing with Kionix MEMS Accelerometers
Tilt-Sensing with Kionix MEMS Accelerometers Introduction Tilt/Inclintion sensing is common ppliction for low-g ccelerometers. This ppliction note describes how to use Kionix MEMS low-g ccelerometers to
More informationInternational Conference on Mechanics, Materials and Structural Engineering (ICMMSE 2016)
\ Interntionl Conference on Mechnics, Mterils nd tructurl Engineering (ICMME 2016) Reserch on the Method to Clibrte tructure Prmeters of Line tructured Light Vision ensor Mingng Niu1,, Kngnin Zho1, b,
More information3.5.1 Single slit diffraction
3.5.1 Single slit diffrction Wves pssing through single slit will lso diffrct nd produce n interference pttern. The reson for this is to do with the finite width of the slit. We will consider this lter.
More informationprisms Prisms Specifications Catalogue number BK7 Wedge, Beam Deviation, deg
Cotings Wedge Steer bems in opticl systems Cn be used in pirs for continuous ngulr djustment T Hving selected n pproprite wedge, it is esy to crete precise bem devition without ffecting other bem prmeters.
More information2. What are the types of diffraction and give the differences between them? (June 2005, June 2011)
UNIT-1 b DIFFRACTION Diffrction:A) Distinction between Fresnel nd Frunhofer diffrction, B) diffrction due to single slit, N-slits,C) Diffrction grting experiment. 1 A) Distinction between Fresnel nd Frunhofer
More informationPower Transmittance of a Laterally Shifted Gaussian Beam through a Circular Aperture
Poer Trnsmittnce of Lterlly Shifted Gussin Bem through Circulr Aperture Triq Shmim Khj 1 nd Syed Azer Rez 1 1. Deprtment of Electricl Engineering, Lhore University of Mngement Sciences, DHA, Lhore 5479,
More informationChapter 2 Capacitive Sensing Electrodes
Chpter 2 Cpcitive Sensing Electrodes The cpcitive sensing electrodes on the top of CMOS chip serve s n interfce etween the microelectronic redout system nd the iologicl/chemicl nlyte. These electrodes
More information2mm Catheter Design for Endoscopic Optical Coherence Tomography
2mm Ctheter Design for Endoscopic Opticl Coherence Tomogrphy Kye-Sung Lee 1, Chuck Koehler 1, Eric G. Johnson 1, Eric Vlski TEUMA 2, Olusegun Ilegbusi 2, Mrco Cost 3, Huiki Xie 4, nd Jnnick P. Rollnd 1
More informationDesign and fabrication of broadband ultralow reflectivity black Si surfaces by laser micro/nanoprocessing
OPEN Light: Science & Applictions (14) 3, e18; doi:.38/ls.14.66 ß 14 CIOMP. All rights reserved 47-738/14 www.nture.com/ls ORIGINAL ARTICLE Design nd friction of rodnd ultrlow reflectivity lck Si surfces
More informationModel of the Human Eye Based on ABCD Matrix
Model of the Humn Eye Bsed on ABCD Mtrix G. Díz González nd M. Dvid Iturbe Cstillo Cittion: AIP Conf. Proc. 992, 108 (2008); doi: 10.1063/1.2926797 View online: http://dx.doi.org/10.1063/1.2926797 View
More informationChapter Spline Method of Interpolation More Examples Electrical Engineering
Chpter. Spline Method of Interpoltion More Exmples Electricl Engineering Exmple Thermistors re used to mesure the temperture of bodies. Thermistors re bsed on mterils chnge in resistnce with temperture.
More informationHOPC: A NOVEL SIMILARITY METRIC BASED ON GEOMETRIC STRUCTURAL PROPERTIES FOR MULTI-MODAL REMOTE SENSING IMAGE MATCHING
ISPRS Annls of the Photogrmmetry, Remote Sensing nd Sptil Informtion Sciences, Volume III-1, 216 XXIII ISPRS Congress, 12 19 July 216, Prgue, Czech Republic : A NOVEL SILARITY METRIC BASED ON GEOMETRIC
More informationPrediction of cutting force and surface roughness using Taguchi technique for aluminum alloy AA6061
Austrlin Journl of Mechnicl Engineering ISSN: 1448-4846 (Print) 2204-2253 (Online) Journl homepge: http://www.tndfonline.com/loi/tmec20 Prediction of cutting force nd surfce roughness using Tguchi technique
More informationWright State University
Wright Stte University EE480/680 Micro-Electro-Mechnicl Systems (MEMS) Summer 2006 LVern Strmn, Ph.D. Assistnt Professor Dept. of Electricl nd Computer Engineering Emil: lvern.strmn@fit.edu Opticl MEMS
More informationRadiation & Matter 3: Refraction
Rdition & Mtter 3: Refrction Refrction AIM The effects of refrction (the chnge of direction tht tkes plce when light psses fro ir into glss) y hve been et during n erlier study of Physics. The i of this
More informationA TRIANGULAR FINITE ELEMENT FOR PLANE ELASTICITY WITH IN- PLANE ROTATION Dr. Attia Mousa 1 and Eng. Salah M. Tayeh 2
A TRIANGLAR FINITE ELEMENT FOR PLANE ELASTICITY WITH IN- PLANE ROTATION Dr. Atti Mous nd Eng. Slh M. Teh ABSTRACT In the present pper the strin-bsed pproch is pplied to develop new tringulr finite element
More informationStained Glass Design. Teaching Goals:
Stined Glss Design Time required 45-90 minutes Teching Gols: 1. Students pply grphic methods to design vrious shpes on the plne.. Students pply geometric trnsformtions of grphs of functions in order to
More informationOptimization of Air Bearing Slider Design
Proceedings of TC2005 orld Tribology Congress III Proceedings of TC2005 September 2-6, orld 2005, Tribology shington, Congress D.C., III SA September 2-6, 2005, shington, D.C., SA Optimiztion of Air Bering
More informationMATH 25 CLASS 5 NOTES, SEP
MATH 25 CLASS 5 NOTES, SEP 30 2011 Contents 1. A brief diversion: reltively prime numbers 1 2. Lest common multiples 3 3. Finding ll solutions to x + by = c 4 Quick links to definitions/theorems Euclid
More informationII. THE ALGORITHM. A. Depth Map Processing
Lerning Plnr Geometric Scene Context Using Stereo Vision Pul G. Bumstrck, Bryn D. Brudevold, nd Pul D. Reynolds {pbumstrck,brynb,pulr2}@stnford.edu CS229 Finl Project Report December 15, 2006 Abstrct A
More informationIMAGE QUALITY OPTIMIZATION BASED ON WAVELET FILTER DESIGN AND WAVELET DECOMPOSITION IN JPEG2000. Do Quan and Yo-Sung Ho
IMAGE QUALITY OPTIMIZATIO BASED O WAVELET FILTER DESIG AD WAVELET DECOMPOSITIO I JPEG2000 Do Qun nd Yo-Sung Ho School of Informtion & Mechtronics Gwngju Institute of Science nd Technology (GIST) 26 Cheomdn-gwgiro
More informationUltra-short pulse propagation in complex optical systems
Ultr-short pulse propgtion in complex opticl systems Ulrike Fuchs, Uwe D. Zeitner nd Andres Tünnermnn* Frunhofer-Institut für Angewndte Optik und Feinmechnik, Albert-Einstein-Str. 7, D-07745 Jen, Germny
More information3 Talk to Us First. Reasons You Should. Non-Contact Temperature Measurement Solutions
3 Tlk to Us First Resons You Should Non-Contct Temperture Mesurement Solutions Reson # 1 Fixed System Spot Thermometers FACTS Verstile technologies re must for the ever expnding list of pplictions Lnd
More informationA Fast Imaging Algorithm for Near Field SAR
Journl of Computing nd Electronic Informtion Mngement ISSN: 2413-1660 A Fst Imging Algorithm for Ner Field SAR Guoping Chen, Lin Zhng, * College of Optoelectronic Engineering, Chongqing University of Posts
More informationThe Nature of Light. Light is a propagating electromagnetic waves
The Nture of Light Light is propgting electromgnetic wves Index of Refrction n: In mterils, light intercts with toms/molecules nd trvels slower thn it cn in vcuum, e.g., vwter The opticl property of trnsprent
More informationAccelerating 3D convolution using streaming architectures on FPGAs
Accelerting 3D convolution using streming rchitectures on FPGAs Hohun Fu, Robert G. Clpp, Oskr Mencer, nd Oliver Pell ABSTRACT We investigte FPGA rchitectures for ccelerting pplictions whose dominnt cost
More informationPreserving Constraints for Aggregation Relationship Type Update in XML Document
Preserving Constrints for Aggregtion Reltionship Type Updte in XML Document Eric Prdede 1, J. Wenny Rhyu 1, nd Dvid Tnir 2 1 Deprtment of Computer Science nd Computer Engineering, L Trobe University, Bundoor
More informationUnit 5 Vocabulary. A function is a special relationship where each input has a single output.
MODULE 3 Terms Definition Picture/Exmple/Nottion 1 Function Nottion Function nottion is n efficient nd effective wy to write functions of ll types. This nottion llows you to identify the input vlue with
More informationSUPPLEMENTARY INFORMATION
Supplementry Figure y (m) x (m) prllel perpendiculr Distnce (m) Bird Stndrd devition for distnce (m) c 6 prllel perpendiculr 4 doi:.8/nture99 SUPPLEMENTARY FIGURE Confirmtion tht movement within the flock
More informationModeling and Simulation of Short Range 3D Triangulation-Based Laser Scanning System
Modeling nd Simultion of Short Rnge 3D Tringultion-Bsed Lser Scnning System Theodor Borngiu Anmri Dogr Alexndru Dumitrche April 14, 2008 Abstrct In this pper, simultion environment for short rnge 3D lser
More informationVulnerability Analysis of Electric Power Communication Network. Yucong Wu
2nd Interntionl Conference on Advnces in Mechnicl Engineering nd Industril Informtics (AMEII 2016 Vulnerbility Anlysis of Electric Power Communiction Network Yucong Wu Deprtment of Telecommunictions Engineering,
More informationUnit #9 : Definite Integral Properties, Fundamental Theorem of Calculus
Unit #9 : Definite Integrl Properties, Fundmentl Theorem of Clculus Gols: Identify properties of definite integrls Define odd nd even functions, nd reltionship to integrl vlues Introduce the Fundmentl
More informationAnalysis of Computed Diffraction Pattern Diagram for Measuring Yarn Twist Angle
Textiles nd Light ndustril Science nd Technology (TLST) Volume 3, 2014 DO: 10.14355/tlist.2014.0301.01 http://www.tlist-journl.org Anlysis of Computed Diffrction Pttern Digrm for Mesuring Yrn Twist Angle
More informationCHAPTER III IMAGE DEWARPING (CALIBRATION) PROCEDURE
CHAPTER III IMAGE DEWARPING (CALIBRATION) PROCEDURE 3.1 Scheimpflug Configurtion nd Perspective Distortion Scheimpflug criterion were found out to be the best lyout configurtion for Stereoscopic PIV, becuse
More informationP(r)dr = probability of generating a random number in the interval dr near r. For this probability idea to make sense we must have
Rndom Numers nd Monte Crlo Methods Rndom Numer Methods The integrtion methods discussed so fr ll re sed upon mking polynomil pproximtions to the integrnd. Another clss of numericl methods relies upon using
More informationAn Integrated Simulation System for Human Factors Study
An Integrted Simultion System for Humn Fctors Study Ying Wng, Wei Zhng Deprtment of Industril Engineering, Tsinghu University, Beijing 100084, Chin Foud Bennis, Dmien Chblt IRCCyN, Ecole Centrle de Nntes,
More informationSection 10.4 Hyperbolas
66 Section 10.4 Hyperbols Objective : Definition of hyperbol & hyperbols centered t (0, 0). The third type of conic we will study is the hyperbol. It is defined in the sme mnner tht we defined the prbol
More informationDiffraction Patterns and Polarization
chpter 38 Diffrction Ptterns nd Polriztion 38.1 Introduction to Diffrction Ptterns 38.2 Diffrction Ptterns from Nrrow Slits 38.3 Resolution of Single-Slit nd Circulr Apertures 38.4 The Diffrction Grting
More informationAbout the Finite Element Analysis for Beam-Hinged Frame. Duan Jin1,a, Li Yun-gui1
Advnces in Engineering Reserch (AER), volume 143 6th Interntionl Conference on Energy nd Environmentl Protection (ICEEP 2017) About the Finite Element Anlysis for Bem-Hinged Frme Dun Jin1,, Li Yun-gui1
More informationPre-Filtering Low-Cost Inertial Measuring Unit using a Wavelet Thresholding De-noising for IMU/GPS Integration
ISG & ISPRS 11, Sept. 7-9, 11 Shh Alm, MALAYSIA Pre-Filtering Low-Cost Inertil Mesuring Unit using Wvelet Thresholding De-noising for IMU/GPS Integrtion Elkhidir T. Y. 1 & Shuhimi M. 1, Mus T. A., A. Stti
More informationMetal Element Current Sense Resistor
Metl Element Current Sense Resistor UR Series Robust metl strip ble to withstnd high temperture nd high current. ow TCR nd Inductnce Resistnce Rnge from m to 15 m Power rtings from 1W to 3W in 1206, 2010
More informationDigital approximation to extended depth of field in no telecentric imaging systems
Journl of Physics: Conference Series Digitl pproximtion to extended depth of field in no telecentric imging systems To cite this rticle: J E Meneses nd C R Contrers 0 J Phys: Conf Ser 74 0040 View the
More informationa < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1
Mth 33 Volume Stewrt 5.2 Geometry of integrls. In this section, we will lern how to compute volumes using integrls defined by slice nlysis. First, we recll from Clculus I how to compute res. Given the
More informationGENERATING ORTHOIMAGES FOR CLOSE-RANGE OBJECTS BY AUTOMATICALLY DETECTING BREAKLINES
GENEATING OTHOIMAGES FO CLOSE-ANGE OBJECTS BY AUTOMATICALLY DETECTING BEAKLINES Efstrtios Stylinidis 1, Lzros Sechidis 1, Petros Ptis 1, Spiros Sptls 2 Aristotle University of Thessloniki 1 Deprtment of
More informationOn the Detection of Step Edges in Algorithms Based on Gradient Vector Analysis
On the Detection of Step Edges in Algorithms Bsed on Grdient Vector Anlysis A. Lrr6, E. Montseny Computer Engineering Dept. Universitt Rovir i Virgili Crreter de Slou sin 43006 Trrgon, Spin Emil: lrre@etse.urv.es
More informationMA1008. Calculus and Linear Algebra for Engineers. Course Notes for Section B. Stephen Wills. Department of Mathematics. University College Cork
MA1008 Clculus nd Liner Algebr for Engineers Course Notes for Section B Stephen Wills Deprtment of Mthemtics University College Cork s.wills@ucc.ie http://euclid.ucc.ie/pges/stff/wills/teching/m1008/ma1008.html
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationUSING HOUGH TRANSFORM IN LINE EXTRACTION
Stylinidis, Efstrtios USING HOUGH TRANSFORM IN LINE EXTRACTION Efstrtios STYLIANIDIS, Petros PATIAS The Aristotle University of Thessloniki, Deprtment of Cdstre Photogrmmetry nd Crtogrphy Univ. Box 473,
More informationPerformance enhancement of IEEE DCF using novel backoff algorithm
Kuo et l. EURASIP Journl on Wireless Communictions nd Networking 212, 212:274 http://jis.eursipjournls.com/content/212/1/274 RESEARCH Open Access Performnce enhncement of IEEE 82.11 using novel ckoff lgorithm
More informationRepresentation of Numbers. Number Representation. Representation of Numbers. 32-bit Unsigned Integers 3/24/2014. Fixed point Integer Representation
Representtion of Numbers Number Representtion Computer represent ll numbers, other thn integers nd some frctions with imprecision. Numbers re stored in some pproximtion which cn be represented by fixed
More informationTEK-F LEX 4100B. Two-wire Loop-powered OEM TDR Level Transmitter. LEVEL. Technology Solutions
Technology Solutions TEK-F LEX 4100B Two-wire Loop-powered OEM TDR Level Trnsmitter LEVEL www.tek-trol.com Flow Level Temperture Pressure Vlves Anlyzers Accessories TekVlSys Introduction Tek-Flex 4100B
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More information1. SEQUENCES INVOLVING EXPONENTIAL GROWTH (GEOMETRIC SEQUENCES)
Numbers nd Opertions, Algebr, nd Functions 45. SEQUENCES INVOLVING EXPONENTIAL GROWTH (GEOMETRIC SEQUENCES) In sequence of terms involving eponentil growth, which the testing service lso clls geometric
More informationA New Learning Algorithm for the MAXQ Hierarchical Reinforcement Learning Method
A New Lerning Algorithm for the MAXQ Hierrchicl Reinforcement Lerning Method Frzneh Mirzzdeh 1, Bbk Behsz 2, nd Hmid Beigy 1 1 Deprtment of Computer Engineering, Shrif University of Technology, Tehrn,
More informationPerformance analysis of QoS mechanisms in IP networks
University of Wollongong Reserch Online Fculty of Informtics - Ppers (Archive) Fculty of Engineering nd Informtion Sciences 2000 Performnce nlysis of QoS mechnisms in IP networks D. Ji University of Wollongong
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationEfficient Regular Expression Grouping Algorithm Based on Label Propagation Xi Chena, Shuqiao Chenb and Ming Maoc
4th Ntionl Conference on Electricl, Electronics nd Computer Engineering (NCEECE 2015) Efficient Regulr Expression Grouping Algorithm Bsed on Lbel Propgtion Xi Chen, Shuqio Chenb nd Ming Moc Ntionl Digitl
More informationApproximation by NURBS with free knots
pproximtion by NURBS with free knots M Rndrinrivony G Brunnett echnicl University of Chemnitz Fculty of Computer Science Computer Grphics nd Visuliztion Strße der Ntionen 6 97 Chemnitz Germny Emil: mhrvo@informtiktu-chemnitzde
More informationOverview. Network characteristics. Network architecture. Data dissemination. Network characteristics (cont d) Mobile computing and databases
Overview Mobile computing nd dtbses Generl issues in mobile dt mngement Dt dissemintion Dt consistency Loction dependent queries Interfces Detils of brodcst disks thlis klfigopoulos Network rchitecture
More information4452 Mathematical Modeling Lecture 4: Lagrange Multipliers
Mth Modeling Lecture 4: Lgrnge Multipliers Pge 4452 Mthemticl Modeling Lecture 4: Lgrnge Multipliers Lgrnge multipliers re high powered mthemticl technique to find the mximum nd minimum of multidimensionl
More informationComputer-Aided Multiscale Modelling for Chemical Process Engineering
17 th Europen Symposium on Computer Aided Process Engineesing ESCAPE17 V. Plesu nd P.S. Agchi (Editors) 2007 Elsevier B.V. All rights reserved. 1 Computer-Aided Multiscle Modelling for Chemicl Process
More informationOn String Matching in Chunked Texts
On String Mtching in Chunked Texts Hnnu Peltol nd Jorm Trhio {hpeltol, trhio}@cs.hut.fi Deprtment of Computer Science nd Engineering Helsinki University of Technology P.O. Box 5400, FI-02015 HUT, Finlnd
More informationA HYDRAULIC SIMULATOR FOR AN EXCAVATOR
P-06 Proceedings of the 7th JFPS Interntionl Symposium on Fluid Power TOYAMA 008 September 5-8 008 A HYDRAULIC SIMULATOR FOR AN EXCAVATOR Soon-Kwng Kwon* Je-Jun Kim* Young-Mn Jung* Chn-Se Jung* Chng-Don
More informationComputing offsets of freeform curves using quadratic trigonometric splines
Computing offsets of freeform curves using qudrtic trigonometric splines JIULONG GU, JAE-DEUK YUN, YOONG-HO JUNG*, TAE-GYEONG KIM,JEONG-WOON LEE, BONG-JUN KIM School of Mechnicl Engineering Pusn Ntionl
More informationA real-time ultrasonic field mapping system using a Fabry Pérot single pixel camera for 3D photoacoustic imaging
A rel-time ultrsonic field mpping system using Fbry Pérot single pixel cmer for D photocoustic imging Nm Huynh, Edwrd Zhng, Mrt Betcke, Simon Arridge, Pul Berd nd Ben Cox Deprtment of Medicl Physics nd
More informationMath 35 Review Sheet, Spring 2014
Mth 35 Review heet, pring 2014 For the finl exm, do ny 12 of the 15 questions in 3 hours. They re worth 8 points ech, mking 96, with 4 more points for netness! Put ll your work nd nswers in the provided
More informationThis notebook investigates the properties of non-integer differential operators using Fourier analysis.
Frctionl erivtives.nb Frctionl erivtives by Fourier ecomposition by Eric Thrne 4/9/6 This notebook investigtes the properties of non-integer differentil opertors using Fourier nlysis. In[]:=
More informationSYSTEMA / THERMICA version 4 Overview of the new capabilities
SYSTEMA / THERMICA version 4 Overview of the new cpbilities Prepred by Mrc Jcquiu, SAS 16 th Europen Workshop on Therml nd ECLS Softwre, 22-23 October 2002 SYSTEMA / THERMICA current sttus (1/3) SYSTEMA
More informationTixeo compared to other videoconferencing solutions
compred to other videoconferencing solutions for V171026EN , unique solution on the video conferencing field Adobe Connect Web RTC Vydio for High security level, privcy Zero impct on network security policies
More informationPROBABILISTIC SEISMIC DEMAND ANALYSIS CONSIDERING RANDOM SYSTEM PROPERTIES BY AN IMPROVED CLOUD METHOD
The 4 th World Conference on Erthquke Engineering October -7, 8, Beijing, Chin PROBABILISTIC SEISMIC DEMAND ANALYSIS CONSIDERING RANDOM SYSTEM PROPERTIES BY AN IMPROVED CLOUD METHOD D-Gng Lu, Xio-Hui Yu,
More informationA Priority-based Distributed Call Admission Protocol for Multi-hop Wireless Ad hoc Networks
A Priority-bsed Distributed Cll Admission Protocol for Multi-hop Wireless Ad hoc Networks un Sun Elizbeth M. Belding-Royer Deprtment of Computer Science University of Cliforni, Snt Brbr suny, ebelding
More informationA COLOUR CORRECTION PREPROCESSING METHOD FOR MULTIVIEW VIDEO CODING
A COLOR CORRECTO REROCESSG METHOD FOR MLTEW DEO CODG Colin Doutre nd nos siopoulos Deprtment of Electricl nd Computer Engineering, niversity of British Columbi 66 Min Mll, 6T Z4, ncouver, BC, Cnd emil:
More informationMicrofluidic Half Adder Chip Based on Spiking Neural P Systems
doi:10.21311/001.39.9.40 Microfluidic Hlf Adder Chip Bsed on Spiking Neurl P Systems Yourui Hung* School of Electril nd Informtion Engineering, Anhui University of Science nd Technology, Huinn 232001,
More informationA Transportation Problem Analysed by a New Ranking Method
(IJIRSE) Interntionl Journl of Innovtive Reserch in Science & Engineering ISSN (Online) 7-07 A Trnsporttion Problem Anlysed by New Rnking Method Dr. A. Shy Sudh P. Chinthiy Associte Professor PG Scholr
More informationSketching Reaction-Diffusion Texture
EUROGRAPHICS Workshop on Sketch-Bsed Interfces nd Modeling (006), pp. 1 8 Sketching Rection-Diffusion Texture Pper ID 100 Abstrct In this work, we present n interctive interfce for sketching synthesized
More informationStep-Voltage Regulator Model Test System
IEEE PES GENERAL MEETING, JULY 5 Step-Voltge Regultor Model Test System Md Rejwnur Rshid Mojumdr, Pblo Arboley, Senior Member, IEEE nd Cristin González-Morán, Member, IEEE Abstrct In this pper, 4-node
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationIf f(x, y) is a surface that lies above r(t), we can think about the area between the surface and the curve.
Line Integrls The ide of line integrl is very similr to tht of single integrls. If the function f(x) is bove the x-xis on the intervl [, b], then the integrl of f(x) over [, b] is the re under f over the
More informationParallel Square and Cube Computations
Prllel Squre nd Cube Computtions Albert A. Liddicot nd Michel J. Flynn Computer Systems Lbortory, Deprtment of Electricl Engineering Stnford University Gtes Building 5 Serr Mll, Stnford, CA 945, USA liddicot@stnford.edu
More informationChapter 2. 3/28/2004 H133 Spring
Chpter 2 Newton believe tht light ws me up of smll prticles. This point ws ebte by scientists for mny yers n it ws not until the 1800 s when series of experiments emonstrte wve nture of light. (But be
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationIn the last lecture, we discussed how valid tokens may be specified by regular expressions.
LECTURE 5 Scnning SYNTAX ANALYSIS We know from our previous lectures tht the process of verifying the syntx of the progrm is performed in two stges: Scnning: Identifying nd verifying tokens in progrm.
More information9 Graph Cutting Procedures
9 Grph Cutting Procedures Lst clss we begn looking t how to embed rbitrry metrics into distributions of trees, nd proved the following theorem due to Brtl (1996): Theorem 9.1 (Brtl (1996)) Given metric
More informationLily Yen and Mogens Hansen
SKOLID / SKOLID No. 8 Lily Yen nd Mogens Hnsen Skolid hs joined Mthemticl Myhem which is eing reformtted s stnd-lone mthemtics journl for high school students. Solutions to prolems tht ppered in the lst
More information5 Regular 4-Sided Composition
Xilinx-Lv User Guide 5 Regulr 4-Sided Composition This tutoril shows how regulr circuits with 4-sided elements cn be described in Lv. The type of regulr circuits tht re discussed in this tutoril re those
More informationIZT DAB ContentServer, IZT S1000 Testing DAB Receivers Using ETI
IZT DAB ContentServer, IZT S1000 Testing DAB Receivers Using ETI Appliction Note Rel-time nd offline modultion from ETI files Generting nd nlyzing ETI files Rel-time interfce using EDI/ETI IZT DAB CONTENTSERVER
More informationCable Channel Modeling Based on Chinese MSO s Network
Cble Chnnel Modeling Bsed on Chinese MSO s Network Wu Gungsheng, Huwei Heshm ElBkoury, Huwei Xiolong Zhng, HUST Huzhong University o Science nd Technology www.huwei.com HUAWEI TECHNOLOGIES CO., LTD. Supporters
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd processes. Introducing technology
More informationSmall Business Networking
Why network is n essentil productivity tool for ny smll business Effective technology is essentil for smll businesses looking to increse the productivity of their people nd business. Introducing technology
More informationStatistical classification of spatial relationships among mathematical symbols
2009 10th Interntionl Conference on Document Anlysis nd Recognition Sttisticl clssifiction of sptil reltionships mong mthemticl symbols Wl Aly, Seiichi Uchid Deprtment of Intelligent Systems, Kyushu University
More informationEssential Question What are some of the characteristics of the graph of a rational function?
8. TEXAS ESSENTIAL KNOWLEDGE AND SKILLS A..A A..G A..H A..K Grphing Rtionl Functions Essentil Question Wht re some of the chrcteristics of the grph of rtionl function? The prent function for rtionl functions
More information