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1

Schonfelder, J. L. "Varying length strings in Fortran." ACM SIGPLAN Fortran Forum 11, no. 2 (June 1992): 24–32. http://dx.doi.org/10.1145/140947.140949.

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2

Kappert, Chuck. "Closed Tube with Varying Length." Physics Teacher 44, no. 9 (December 2006): 566. http://dx.doi.org/10.1119/1.2396765.

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3

Bogatyrjov, V. A., M. M. Bubnov, S. L. Semenov, and A. A. Sysoliatin. "Length-varying computer-controlled fibre drawing." Measurement Science and Technology 5, no. 11 (November 1, 1994): 1370–74. http://dx.doi.org/10.1088/0957-0233/5/11/009.

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4

Atar, Rami, Isaac Keslassy, and Gal Mendelson. "Subdiffusive Load Balancing in Time-Varying Queueing Systems." Operations Research 67, no. 6 (November 2019): 1678–98. http://dx.doi.org/10.1287/opre.2019.1851.

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The degree to which delays or queue lengths equalize under load-balancing algorithms gives a good indication of their performance. Some of the most well-known results in this context are concerned with the asymptotic behavior of the delay or queue length at the diffusion scale under a critical load condition, where arrival and service rates do not vary with time. For example, under the join-the-shortest-queue policy, the queue length deviation process, defined as the difference between the greatest and smallest queue length as it varies over time, is at a smaller scale (subdiffusive) than that of queue lengths (diffusive).
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5

Jeon, Yoontae, and Thomas McCurdy. "Time-Varying Window Length for Correlation Forecasts." Econometrics 5, no. 4 (December 11, 2017): 54. http://dx.doi.org/10.3390/econometrics5040054.

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6

Kanayama, Tadashi, and Tadashi Kotera. "Vibration of String with Time-Varying Length." Transactions of the Japan Society of Mechanical Engineers Series C 59, no. 564 (1993): 2415–20. http://dx.doi.org/10.1299/kikaic.59.2415.

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7

Kuliev, A., V. Kumar, R. Schwindt, D. Selvanathan, A. M. Dabiran, P. Chow, and I. Adesida. "0.15 μm gate-length AlGaN/GaN HEMTs with varying gate recess length." Solid-State Electronics 47, no. 1 (January 2003): 117–22. http://dx.doi.org/10.1016/s0038-1101(02)00258-7.

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8

Mayolo, Patrick, Kristin L. Kress, Paul Kang, and David E. Jaffe. "Hammertoe Correction with Wire Fixation of Varying Length." Foot & Ankle Orthopaedics 7, no. 1 (January 2022): 2473011421S0035. http://dx.doi.org/10.1177/2473011421s00357.

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Category: Midfoot/Forefoot; Lesser Toes Introduction/Purpose: Hammertoe deformities are commonly encountered and frequently require surgical intervention for pain relief and shoewear accommodation. Various techniques exist for surgical management, but proximal interphalangeal (PIP) joint fusion with Kirschner (K) -wire fixation remains an inexpensive, popular treatment. The decision to place a K wire that spans the metatarsophalangeal (MTP) joint versus only fixating the digit through the proximal phalanx is entirely dependent on provider preference and situational context. This study was performed to evaluate the effect of length of wire fixation on clinical outcomes after hammertoe reconstruction. Methods: A retrospective review of all hammertoe reconstructions by a single fellowship trained foot and ankle surgeon from 2017-2021 was performed. Hammertoe reconstructions involved PIP arthrodesis with double wire fixation and other supplemental balancing procedures as indicated. Pins were routinely removed at between 5-6 weeks and protected heel weightbearing was generally advised. Wire length was chosen at the discretion of the surgeon intraoperatively. Patients were excluded if no radiographic follow-up was available after pin removal. Patient outcomes were evaluated with radiographs and clinic notes to assess pin length, pin complications/breakage, return to the OR, MTP congruency, and PIP union rate. A logistic regression was performed to determine the odds ratio for digit congruency and non-union status. Results: 88 toes (45 patients) underwent hammertoe reconstruction with K wire fixation. Of these toes, 47 had wires that spanned the MTP and 41 that did not. There were 65 congruent MTP joints and 23 incongruent joints. 16 of the incongruent joints were pinned across the MTP while 31 in the congruent group were pinned. One toe in the MTP group required return to the OR for removal of a broken wire, compared to zero in the phalanx group (p=1.0). No pins broke in the phalanx group, compared to 3 in the MTP group (p=0.25). One toe in the proximal phalanx group had their pins pull out early but no return to the OR was needed. There were 26 (63.4%) PIP radiographic nonunions, compared to 21 (44.7%) in the MTP group (p=0.12). Conclusion: Wire failure was a rare occurrence in either group. Breakage only occurred in the MTP group, but only required one surgical intervention for removal. Pinning the MTP may allow for improved deformity correction and increased stability of the hammertoe reconstruction. Pin breakage can occur, but it may be of little clinical significance. The increased stability and control of MTP correction may be worth the potential risk of pin breakage. Pin breakage may be avoided potentially by using thicker wires, earlier removal, and protected weightbearing.
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9

Alava, M. J., and R. K. Ritala. "Fracture of Fibrous Networks with Varying Fibre Length." Physica Scripta T33 (January 1, 1990): 155–58. http://dx.doi.org/10.1088/0031-8949/1990/t33/028.

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10

HASHIMOTO, Yoshio. "Free Vibration of String with Time-Varying Length." Transactions of the Japan Society of Mechanical Engineers Series C 57, no. 539 (1991): 2167–69. http://dx.doi.org/10.1299/kikaic.57.2167.

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11

Katkovnik, Vladimir, and LJubiša Stanković. "Periodogram with varying and data-driven window length." Signal Processing 67, no. 3 (June 1998): 345–58. http://dx.doi.org/10.1016/s0165-1684(98)00049-8.

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12

Belyakov, Anton O., Alexander P. Seyranian, and Angelo Luongo. "Dynamics of the pendulum with periodically varying length." Physica D: Nonlinear Phenomena 238, no. 16 (August 2009): 1589–97. http://dx.doi.org/10.1016/j.physd.2009.04.015.

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13

Budkowska, B. B., and C. Szymczak. "Effect of varying length of pile undergoing torsion." Computers & Structures 52, no. 5 (September 1994): 931–38. http://dx.doi.org/10.1016/0045-7949(94)90078-7.

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14

KOTERA, Tadashi. "Vibration of Cantilever Beam with Time-Varying Length." Transactions of the Japan Society of Mechanical Engineers Series C 64, no. 623 (1998): 2470–75. http://dx.doi.org/10.1299/kikaic.64.2470.

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15

Wang, Jiahui, Jing Liu, and Guang Pan. "A Nonlinear Vibration Control of a String Using the Method Based on Its Time-Varying Length." Machines 10, no. 11 (October 26, 2022): 981. http://dx.doi.org/10.3390/machines10110981.

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Strings are common components in various mechanical engineering applications, such as transmission lines, infusion pipes, stay cables in bridges, and wire rope of elevators. The string vibrations can affect the stability and accuracy of systems. In this paper, a time-varying string length method is studied for string vibration suppression. A dynamic model of a string with the time-varying length is formulated. The dimensionless variables are introduced into the nonlinear dynamic model to realize the separation of time and space variables. The finite difference method is used to solve the differential equations of time functions. The vibration characteristics of time-varying length string are analyzed, such as the free vibrations, forced vibrations and damping effect. The influences of the length time-varying frequency and length time-varying range on the suppression performances are discussed. The results show that the time-varying string length method can effectively disperse the resonance peak energy and suppress multimodal resonance at the same time. The suppression performance is better for the time-varying length string with a higher time-varying frequency and a higher time-varying range.
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16

Takeda, K., R. Kadota, and S. Yagi. "Time-varying myocardial elastance of canine left ventricle." American Journal of Physiology-Heart and Circulatory Physiology 261, no. 5 (November 1, 1991): H1554—H1562. http://dx.doi.org/10.1152/ajpheart.1991.261.5.h1554.

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A formula was derived from an active cross-bridge model for expressing the "time-varying myocardial elastance" of the left ventricular (LV) wall. To assess the validity of this model's predictions of the behavior of the intact left ventricle, eight healthy beagles were instrumented with ultrasonic crystals to measure LV diameter and a micromanometer for LV pressure measurement. During ejecting beats starting from short end-diastolic myocardial lengths, the predicted values for myocardial elastance and force closely approximated the measured values for the instantaneous external load-muscle length ratio and the external load, respectively. However, in cycles starting from long end-diastolic lengths, the predicted myocardial elastance and force values deviated from the actual values during the shortening phase of LV contraction. The differences between myocardial elastance and external load-muscle length ratio as well as those between force and external load during the shortening phase (shortening deactivation) appeared to result from an internal load in the shortening myocardium that was closely related to the product of instantaneous myocardial force and shortening velocity. Thus this model may provide reasonable approximations of myocardial elastance and force in the intact LV wall. In addition, time-varying myocardial elastance might reflect time-dependent changes in calcium activation.
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17

SAITO, Eiichi, and Seiji WATANABE. "Simple Analysis of Elevator Rope Sway with Varying Length." Proceedings of the Elevator, Escalator and Amusement Rides Conference 2021 (2021): EL1–3. http://dx.doi.org/10.1299/jsmeearc.2021.el1-3.

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18

HASHIMOTO, Yoshio. "Forced Vibration of a String with Time-Varying Length." Transactions of the Japan Society of Mechanical Engineers Series C 57, no. 541 (1991): 2785–89. http://dx.doi.org/10.1299/kikaic.57.2785.

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19

Subramaniam, Varuni, Lindsay Griffith, and Amanda J. Haes. "Varying nanoparticle pseudostationary phase plug length during capillary electrophoresis." Analyst 136, no. 17 (2011): 3469. http://dx.doi.org/10.1039/c1an15185a.

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20

Weiland, J., and I. Holod. "Drift wave transport scalings introduced by varying correlation length." Physics of Plasmas 12, no. 1 (January 2005): 012505. http://dx.doi.org/10.1063/1.1828083.

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21

Zhu, W. D., J. Ni, and J. Huang. "Active Control of Translating Media With Arbitrarily Varying Length." Journal of Vibration and Acoustics 123, no. 3 (February 1, 2001): 347–58. http://dx.doi.org/10.1115/1.1375809.

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The general control laws for pointwise controllers to dissipate vibratory energies of translating beams and strings with arbitrarily varying length are presented. Special domain and boundary control laws that can be easily implemented result as a special case. Sufficient conditions for uniform stability and uniform exponential stability of controlled systems are established via Lyapunov stability criteria. Numerical simulations demonstrate the effectiveness of the active controllers in stabilizing translating media during both extension and retraction. Optimal gains leading to the fastest rates of decay of vibratory energies of controlled systems are identified. It is shown that under the optimal control gains, translating media can be completely stabilized during extension and retraction.
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22

Wang, Jie, and Adam J. Sadowski. "Elastic imperfect tip-loaded cantilever cylinders of varying length." International Journal of Mechanical Sciences 140 (May 2018): 200–210. http://dx.doi.org/10.1016/j.ijmecsci.2018.02.027.

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23

Koslow, J. Anthony. "Managing Nonrandomly Varying Fisheries." Canadian Journal of Fisheries and Aquatic Sciences 46, no. 8 (August 1, 1989): 1302–8. http://dx.doi.org/10.1139/f89-167.

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Theoretical studies indicate that constant effort or constant escapement harvest strategies are viable long-term management policies for fisheries influenced by random environmental variability. But the marine environment and fishery recruitment do not characteristically vary randomly: their time series tend to be autocorrelated. I examined the response of a model of an age-structured fish population to these harvest strategies, if recruitment is influenced by periodic variability. Variance in fish yield and the incidence of low stock size increased with both increasing amplitude and period length of environmental forcing. Sensitivity to environmental fluctuations increased sharply at periodicities between one and several times the generation length. Low-risk fisheries, which are subject to little nonrandom recruitment variability, may be satisfactorily managed by either management strategy, although constant effort harvesting provided greater stability to industry with little risk to the fish population. Neither strategy maintained stability in high-risk fisheries with high-amplitude, low-frequency recruitment variability, but a constant escapement policy minimized risk of stock collapse.
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24

Shevchuk, Yury Vladimirovich. "Vbinary: variable length integer coding revisited." Program Systems: Theory and Applications 9, no. 4 (November 30, 2018): 239–52. http://dx.doi.org/10.25209/2079-3316-2018-9-4-239-252.

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The article introduces Vbinary, a parametrized variable-length prefix integer coding. The coding is considered by means of examples in comparison with existing codings, including Golomb/Rice and Elias codings. A naming schema is proposed that allows to specify the coding parameters concisely. Vbinary coding utilizes unusual n-ary extension technique which makes the coding versatile, usable for both bit-based and byte-based data streams. By varying parameters, Vbinary coding can be made efficient for small numbers or large numbers, tailored to specific data distribution, tuned for efficient encoding and decoding. Potential uses for the coding are network protocols, on-disk and in-memory data representation, and final stages of data compression algorithms.
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25

Sumner, Josh P., Jonathan R. Roberts, and Aimée C. Mears. "Just Noticeable Differences in the Length of Golf Irons." Proceedings 49, no. 1 (June 15, 2020): 147. http://dx.doi.org/10.3390/proceedings2020049147.

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Current custom fitting guidelines for golf clubs suggest the smallest change in club length from a standard length iron should be 6 mm (1/4”). However, no previous research suggests why this length change is used. This study aims to identify the minimum noticeable difference in the length of 7-iron clubs using just noticeable difference analysis techniques. Fifty golfers of varying ability were asked to compare a standard length 7-iron to test 7-irons of varying lengths, regarding changes in the perception of club length and body position at address. Irrespective of golfing ability, golfers could perceive a just noticeable difference of 13 mm (1/2”) from the standard length club. However, when asked if changes in body position were present, category 1 golfers noticed differences with a 6 mm change in club length and category 2 golfers noticed differences with a 13 mm change. No changes in body position were perceived by highly handicapped golfers.
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26

Wai, P. K. A., and C. R. Menyuk. "LIGHT PROPAGATION IN OPTICAL FIBERS WITH RANDOMLY VARYING BIREFRINGENCE." International Journal of Modern Physics C 05, no. 02 (April 1994): 403–5. http://dx.doi.org/10.1142/s0129183194000581.

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Polarization decorrelation in single-mode fibers with randomly varying birefringence is studied. We find that polarization decorrelation length is minimized for a given beat length if the autocorrelation length of the internal birefringence fluctuation is close to the average beat length. Implications for both soliton and linear communication systems are discussed
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27

Xin, Pengyang, Yonghui Sun, Huiyuan Kong, Yaodong Wang, Si Tan, Jingjing Guo, Tao Jiang, Wenpei Dong, and Chang-Po Chen. "A unimolecular channel formed by dual helical peptide modified pillar[5]arene: correlating transmembrane transport properties with antimicrobial activity and haemolytic toxicity." Chem. Commun. 53, no. 83 (2017): 11492–95. http://dx.doi.org/10.1039/c7cc06697j.

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28

Kelln, Brent M., Chris D. Ingersoll, and Jay Hertel. "Predicting Knee Motion During Cycling With Varying Seat Height, Pedal Arm Length, and Leg Length." Medicine & Science in Sports & Exercise 39, Supplement (May 2007): S95—S96. http://dx.doi.org/10.1249/01.mss.0000273290.21168.7d.

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29

Hoffman, B., T. Carroll, G. Lichtwark, and A. Cresswell. "The effect of varying musculotendinous length on the construction of triceps surae length-tension curves." Journal of Science and Medicine in Sport 13 (December 2010): e24-e25. http://dx.doi.org/10.1016/j.jsams.2010.10.512.

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30

Roesch, Francis A. "Composite Estimators for Forest Growth Derived from Symmetric, Varying-Length Observation Intervals." Forests 10, no. 5 (May 11, 2019): 409. http://dx.doi.org/10.3390/f10050409.

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Estimates of growth or change in a forest population parameter for a specific length of time, such as cubic meters of wood per hectare per year, are often made from sample observation intervals of different lengths of time. For instance, a basic building block of growth estimators in forest inventory systems is often the annual mean of the first differences of all observations for a particular year, regardless of observation interval length. The aggregate differences between successive observations on re-measured forest sample plots can be viewed as a linear combination, while forest growth is usually assumed to be non-linear. Bias can be assumed to exist whenever a linear combination is used to estimate a specific segment of an underlying non-linear trend. The amount of bias will depend upon the relationship of the intended estimation interval relative to the set of observation intervals. Here, three specific segments, relative to each year of interest, form the bases for a standard set of three estimands. Bias-ratio-adjusted composite estimators for use with observations made on alternative sets of symmetric interval lengths are compared in a simulation against this standard set of estimands. The first estimand has a one-year basis, the second has a five-year mid-interval basis, and the third has a five-year end-of-period basis. For the first and second bases, the initial results clearly show a logical ordering of bias and mean-squared error by observation interval length relative to the target interval length. As expected, some deviance from these clear trends are shown for the end-of-period basis. In the presence of three simple distributions of symmetric measurement intervals, the bias-ratio adjustments and subsequent composite estimators are shown to usually be effective in reducing bias and mean-squared error, while being most obviously effective for the most disparate distribution of intervals and for the end-of-period basis.
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31

TAKEUCHI, Masato, Kensuke HARA, and Hiroshi YAMAURA. "Non-linear dynamic analysis of time varying length flexible body." Proceedings of the Dynamics & Design Conference 2020 (August 25, 2020): 513. http://dx.doi.org/10.1299/jsmedmc.2020.513.

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32

R. P, Zingre. "Varying Length Pendulum and Viscosity of the Liquid: A Review." International Journal for Research in Applied Science and Engineering Technology 6, no. 3 (March 31, 2018): 1444–45. http://dx.doi.org/10.22214/ijraset.2018.3224.

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33

Nguyen, Tung Lam, Hong Quang Nguyen, and Minh Duc Duong. "Payload motion control for a varying length flexible gantry crane." Automatika 62, no. 3-4 (October 2, 2021): 520–29. http://dx.doi.org/10.1080/00051144.2021.1991176.

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34

Chen, L., C. Yang, Y. Xiao, X. Yan, L. Hu, M. Eggersdorfer, D. Chen, D. A. Weitz, and F. Ye. "Millifluidics, microfluidics, and nanofluidics: manipulating fluids at varying length scales." Materials Today Nano 16 (December 2021): 100136. http://dx.doi.org/10.1016/j.mtnano.2021.100136.

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35

Pham, Phuong-Tung, Gyoung-Hahn Kim, and Keum-Shik Hong. "Vibration Control of a Timoshenko Cantilever Beam with Varying Length." International Journal of Control, Automation and Systems 20, no. 1 (January 2022): 175–83. http://dx.doi.org/10.1007/s12555-021-0490-5.

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36

Patil, Dr Amit M., Amol M. Kolhe, and Chetanraj D. Patil. "Vibration Analysis of Cracked Cantilever Beam with Varying Crack Length." Saudi Journal of Engineering and Technology 05, no. 05 (May 30, 2020): 251–57. http://dx.doi.org/10.36348/sjet.2020.v05i05.006.

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37

Park, Joo-Hoon, Ok-Byung Choi, Hwan Myung Lee, Jin-Young Lee, Sung-Jo Kim, Eun-Hee Cha, Seon-Nam Park, et al. "Thermotropic Liquid Crystalline Dimers with Varying Alkoxy Terminal Chain Length." Molecular Crystals and Liquid Crystals 599, no. 1 (August 13, 2014): 96–104. http://dx.doi.org/10.1080/15421406.2014.935970.

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38

HASHIMOTO, Yoshio. "On the Energy of a String with Time-varying Length." Transactions of the Japan Society of Mechanical Engineers Series C 70, no. 693 (2004): 1258–62. http://dx.doi.org/10.1299/kikaic.70.1258.

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39

Yang, Tianzhi, Bo Fang, Song Li, and Wenhu Huang. "Explicit analytical solution of a pendulum with periodically varying length." European Journal of Physics 31, no. 5 (July 21, 2010): 1089–96. http://dx.doi.org/10.1088/0143-0807/31/5/011.

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40

Usman, Muahammad, and Ali Raza. "Development of adjustable stiffness actuator by varying lever arm length." Journal of the Chinese Institute of Engineers 40, no. 8 (October 19, 2017): 651–58. http://dx.doi.org/10.1080/02533839.2017.1385423.

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41

Franke-Trieger, Annett, Claude Jolly, Alexander Darbinjan, Thomas Zahnert, and Dirk Mürbe. "Insertion Depth Angles of Cochlear Implant Arrays With Varying Length." Otology & Neurotology 35, no. 1 (January 2014): 58–63. http://dx.doi.org/10.1097/mao.0000000000000211.

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42

DIMRI, VIJAY P., and KIRTI SRIVASTAVA. "THE OPTIMUM GATE LENGTH FOR THE TIME-VARYING DECONVOLUTION OPERATOR1." Geophysical Prospecting 38, no. 4 (May 1990): 405–10. http://dx.doi.org/10.1111/j.1365-2478.1990.tb01853.x.

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43

Kwon, Ki Yong, Arthur Weber, and Wen Li. "Varying-Length Polymer Microneedle Arrays Fabricated by Droplet Backside Exposure." Journal of Microelectromechanical Systems 23, no. 6 (December 2014): 1272–80. http://dx.doi.org/10.1109/jmems.2014.2352412.

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44

Zahraie, Banafsheh, Reza Kerachian, and Bahram Malekmohammadi. "Reservoir operation optimization using adaptive varying chromosome length genetic algorithm." Water International 33, no. 3 (August 22, 2008): 380–91. http://dx.doi.org/10.1080/02508060802272804.

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45

Zhang, Feipeng, Xuerong Chen, and Yong Zhou. "Proportional hazards model with varying coefficients for length-biased data." Lifetime Data Analysis 20, no. 1 (May 7, 2013): 132–57. http://dx.doi.org/10.1007/s10985-013-9257-5.

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46

Durvasula, S. "On vibration of eccentrically stiffened plates with varying stiffener length." Journal of Sound and Vibration 99, no. 4 (April 1985): 568–71. http://dx.doi.org/10.1016/0022-460x(85)90542-5.

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47

Bao, Ji-hu, Peng Zhang, and Chang-ming Zhu. "Dynamic Analysis of Flexible Hoisting Rope with Time-Varying Length*." International Applied Mechanics 51, no. 6 (November 2015): 710–20. http://dx.doi.org/10.1007/s10778-015-0729-z.

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48

Bao, Ji-hu, Peng Zhang, Chang-Ming Zhu, and Wei Sun. "Transverse vibration of flexible hoisting rope with time-varying length." Journal of Mechanical Science and Technology 28, no. 2 (February 2014): 457–66. http://dx.doi.org/10.1007/s12206-013-1110-y.

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49

Lee, Eric D., Daniel Maynes, Julie Crockett, and Brian D. Iverson. "Thermal atomization on superhydrophobic surfaces of varying temperature jump length." International Journal of Heat and Mass Transfer 216 (December 2023): 124587. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2023.124587.

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50

Kumar, V., Guang Chen, Shiping Guo, and I. Adesida. "Field-plated 0.25-/spl mu/m gate-length AlGaN/GaN HEMTs with varying field-plate length." IEEE Transactions on Electron Devices 53, no. 6 (June 2006): 1477–80. http://dx.doi.org/10.1109/ted.2006.874090.

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