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1

Coddington, Jonathan, and Nikolaj Scharff. "PROBLEMS WITH ZERO-LENGTH BRANCHES." Cladistics 10, no. 4 (December 1994): 415–23. http://dx.doi.org/10.1111/j.1096-0031.1994.tb00187.x.

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2

Wooldridge, Mark D., R. Lewis Nowlin, and Angelia H. Parham. "Evaluation of Zero-Length Vertical Curves." Transportation Research Record: Journal of the Transportation Research Board 1658, no. 1 (January 1999): 52–59. http://dx.doi.org/10.3141/1658-07.

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3

LaCoste, Lucien. "The zero‐length spring gravity meter." Leading Edge 7, no. 7 (July 1988): 20–21. http://dx.doi.org/10.1190/1.1439525.

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4

Chakraborty, Sumanta, Dawood Kothawala, and Alessandro Pesci. "Raychaudhuri equation with zero point length." Physics Letters B 797 (October 2019): 134877. http://dx.doi.org/10.1016/j.physletb.2019.134877.

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5

Fontanini, Michele, Euro Spallucci, and T. Padmanabhan. "Zero-point length from string fluctuations." Physics Letters B 633, no. 4-5 (February 2006): 627–30. http://dx.doi.org/10.1016/j.physletb.2005.12.039.

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6

Taranenko, M., M. Mtchedlidze, N. Sumbatyan, and G. Korshunova. "A Zero-Length Diazirine Photoactive Nucleoside." Nucleosides, Nucleotides and Nucleic Acids 22, no. 5-8 (October 2003): 715–17. http://dx.doi.org/10.1081/ncn-120022617.

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7

Kubertin, Silke. "Zero-sums of length kq in Zqd." Acta Arithmetica 116, no. 2 (2005): 145–52. http://dx.doi.org/10.4064/aa116-2-3.

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8

Kampeas, Joseph, Asaf Cohen, and Omer Gurewitz. "Traffic Classification Based on Zero-Length Packets." IEEE Transactions on Network and Service Management 15, no. 3 (September 2018): 1049–62. http://dx.doi.org/10.1109/tnsm.2018.2825881.

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9

Padmanabhan, T. "Duality and Zero-Point Length of Spacetime." Physical Review Letters 78, no. 10 (March 10, 1997): 1854–57. http://dx.doi.org/10.1103/physrevlett.78.1854.

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10

Stoica, O. C. "Kaluza theory with zero-length extra dimensions." International Journal of Modern Physics D 25, no. 11 (October 2016): 1640004. http://dx.doi.org/10.1142/s0218271816400046.

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A new approach to the Kaluza theory and its relation to the gauge theory is presented. Two degenerate metrics on the [Formula: see text]-dimensional total manifold are used, one corresponding to the spacetime metric and giving the fiber of the gauge bundle, and the other one to the metric of the fiber and giving the horizontal bundle of the connection. When combined, the two metrics give the Kaluza metric and its generalization to the non-Abelian case, justifying thus his choice. Considering the two metrics as fundamental rather than the Kaluza metric explains why Kaluza’s theory should not be regarded as five-dimensional (5D) vacuum gravity. This approach suggests that the only evidence of extra dimensions is given by the existence of the gauge forces, explaining thus why other kinds of evidence are not available. In addition, because the degenerate metric corresponding to the spacetime metric vanishes along the extra dimensions, the lengths in the extra dimensions is zero, preventing us to directly probe them. Therefore, this approach suggests that it is not justified to search for experimental evidence of the extra dimensions as if they are merely extra spacetime dimensions. On the other hand, the new approach uses a very general formalism, which can be applied to known and new generalizations of the Kaluza theory aiming to achieve more and make different experimental predictions.
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11

Duncan, W. L., and K. P. Möller. "A ‘zero length’ criterion for ZLC chromatography." Chemical Engineering Science 55, no. 22 (November 2000): 5415–20. http://dx.doi.org/10.1016/s0009-2509(00)00160-3.

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12

Speake, Clive C., and Christopher J. Collins. "Torsion balances with fibres of zero length." Physics Letters A 382, no. 16 (April 2018): 1069–74. http://dx.doi.org/10.1016/j.physleta.2018.02.015.

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13

Han, Dongchun, and Hanbin Zhang. "On zero-sum subsequences of prescribed length." International Journal of Number Theory 14, no. 01 (November 21, 2017): 167–91. http://dx.doi.org/10.1142/s1793042118500112.

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Let [Formula: see text] be an additive finite abelian group with exponent [Formula: see text]. For any positive integer [Formula: see text], let [Formula: see text] be the smallest positive integer [Formula: see text] such that every sequence [Formula: see text] in [Formula: see text] of length at least [Formula: see text] has a zero-sum subsequence of length [Formula: see text]. Let [Formula: see text] be the Davenport constant of [Formula: see text]. In this paper, we prove that if [Formula: see text] is a finite abelian [Formula: see text]-group with [Formula: see text] then [Formula: see text] for every [Formula: see text], which confirms a conjecture by Gao et al. recently, where [Formula: see text] is a prime.
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14

Gao, Weidong, and Ravindranathan Thangadurai. "On zero-sum sequences of prescribed length." Aequationes mathematicae 72, no. 3 (December 2006): 201–12. http://dx.doi.org/10.1007/s00010-006-2841-y.

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15

Bruhn, Henning, and Arthur Ulmer. "Packing A-paths of length zero modulo four." European Journal of Combinatorics 99 (January 2022): 103422. http://dx.doi.org/10.1016/j.ejc.2021.103422.

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16

Anderson, D. D., and J. R. Juett. "Length functions in commutative rings with zero divisors." Communications in Algebra 45, no. 4 (October 7, 2016): 1584–600. http://dx.doi.org/10.1080/00927872.2016.1222400.

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17

Brandani, Stefano, and Douglas M. Ruthven. "Moments Analysis of the Zero Length Column Method." Industrial & Engineering Chemistry Research 35, no. 1 (January 1996): 315–19. http://dx.doi.org/10.1021/ie950287m.

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18

Gabizon, Ariel, and Ronen Shaltiel. "Increasing the output length of zero-error dispersers." Random Structures & Algorithms 40, no. 1 (February 8, 2011): 74–104. http://dx.doi.org/10.1002/rsa.20359.

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19

Peng, Jiangtao, Guoyou Qian, Fang Sun, and Linlin Wang. "On the structure of n-zero-sum free sequences over cyclic groups of order n." International Journal of Number Theory 10, no. 08 (October 29, 2014): 1991–2009. http://dx.doi.org/10.1142/s1793042114500663.

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Let G be a finite cyclic group of order n. The Erdős–Ginzburg–Ziv theorem states that each sequence of length 2n - 1 over G has a zero-sum subsequence of length n. A sequence without a zero-sum subsequence of length n is called n-zero-sum free. Savchev and Chen characterized all the n-zero-sum free sequences of length n + k - 1 over G, where [Formula: see text]. In the present paper, we determine all the n-zero-sum free sequences of length [Formula: see text] over G.
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20

Hwang, Yu-Jer, Joseph Granelli, and Julia Lyubovitsky. "Effects of Zero-Length and Non-Zero-Length Cross-Linking Reagents on the Optical Spectral Properties and Structures of Collagen Hydrogels." ACS Applied Materials & Interfaces 4, no. 1 (December 21, 2011): 261–67. http://dx.doi.org/10.1021/am2013147.

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21

Wani, Salman Sajad, Dylan Sutherland, Behnam Pourhassan, Mir Faizal, and Hrishikesh Patel. "Compactification, T-duality and quantum erasers." International Journal of Modern Physics A 36, no. 18 (June 12, 2021): 2150102. http://dx.doi.org/10.1142/s0217751x21501025.

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Using T-duality, we will argue that a zero point length exists in the low-energy effective field theory of string theory on compactified extra dimensions. Furthermore, if we neglect all the oscillator modes, this zero point length would modify low quantum mechanical systems. As this zero length is fixed geometrically, it is important to analyze how it modifies purely quantum mechanical effects. Thus, we will analyze its effects on quantum erasers, because they are based on quantum effects like entanglement. It will be observed that the behavior of these quantum erasers gets modified by this zero point length. As the zero point length is fixed by the radius of compactification, we argue that these results demonstrate a deeper connection between geometry and quantum effects.
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22

Peres, Yuval, Karoly Simon, and Boris Solomyak. "Fractals with Positive Length and Zero Buffon Needle Probability." American Mathematical Monthly 110, no. 4 (April 2003): 314. http://dx.doi.org/10.2307/3647880.

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23

Gao, Weidong, Siao Hong, and Jiangtao Peng. "On zero-sum subsequences of length kexp⁡(G) II." Journal of Combinatorial Theory, Series A 187 (April 2022): 105563. http://dx.doi.org/10.1016/j.jcta.2021.105563.

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24

Brandani, Stefano. "Effects of nonlinear equilibrium on zero length column experiments." Chemical Engineering Science 53, no. 15 (August 1998): 2791–98. http://dx.doi.org/10.1016/s0009-2509(98)00075-x.

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25

Savelberg, H. H. C. M., J. G. M. Kooloos, R. Huiskes, and J. M. G. Kauer. "Elastic modulus and ‘zero-force’ length in carpal ligaments." Journal of Biomechanics 24, no. 6 (January 1991): 474. http://dx.doi.org/10.1016/0021-9290(91)90109-z.

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26

Peres, Yuval, Károly Simon, and Boris Solomyak. "Fractals with Positive Length and Zero Buffon Needle Probability." American Mathematical Monthly 110, no. 4 (April 2003): 314–25. http://dx.doi.org/10.1080/00029890.2003.11919967.

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27

Mangano, Enzo, Stefano Brandani, and Douglas M Ruthven. "Analysis and Interpretation of Zero Length Column Response Curves." Chemie Ingenieur Technik 85, no. 11 (October 2, 2013): 1714–18. http://dx.doi.org/10.1002/cite.201300083.

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28

Kothawala, Dawood, and T. Padmanabhan. "Entropy density of spacetime from the zero point length." Physics Letters B 748 (September 2015): 67–69. http://dx.doi.org/10.1016/j.physletb.2015.06.066.

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29

Mintaş, Fatmagül. "The length function of a twistor spinor with zero." Annals of Global Analysis and Geometry 41, no. 4 (October 11, 2011): 493–514. http://dx.doi.org/10.1007/s10455-011-9296-7.

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30

Thomas, Robin, and Youngho Yoo. "Packing A-paths of length zero modulo a prime." Journal of Combinatorial Theory, Series B 160 (May 2023): 114–43. http://dx.doi.org/10.1016/j.jctb.2022.12.007.

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31

Jer Hwang, Yu, Joseph Granelli, Jillian Larsen, and Julia G. Lyubovitsky. "The Effects of Zero-Length and Non-Zero Length Cross-Linking Reagents on the Optical Spectral Properties and Structures of Collagen Hydrogels." Biophysical Journal 102, no. 3 (January 2012): 202a. http://dx.doi.org/10.1016/j.bpj.2011.11.1098.

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32

Zhang, Lei, Ayesha Ijaz, Pei Xiao, Kezhi Wang, Deli Qiao, and Muhammad Ali Imran. "Optimal Filter Length and Zero Padding Length Design for Universal Filtered Multi-Carrier (UFMC) System." IEEE Access 7 (2019): 21687–701. http://dx.doi.org/10.1109/access.2019.2898322.

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33

Cheng, Wang-Yau, Chun Yi Hu, and Jow-Tsong Shy. "Portable 543 nm length standard and magnetic-induced zero-crossing shift on length standard transition." Review of Scientific Instruments 76, no. 5 (May 2005): 053110. http://dx.doi.org/10.1063/1.1898216.

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34

Hart, Sarah B., and Peter J. Rowley. "Maximal length elements of excess zero in finite Coxeter groups." Journal of Group Theory 21, no. 5 (September 1, 2018): 817–37. http://dx.doi.org/10.1515/jgth-2018-0016.

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Abstract In this paper we prove that for W a finite Coxeter group and C a conjugacy class of W, there is always an element of C of maximal length in C which has excess zero. An element {w\in W} has excess zero if there exist elements {\sigma,\tau\in W} such that {\sigma^{2}=\tau^{2}=1,w=\sigma\tau} and {\ell(w)=\ell(\sigma)+\ell(\tau)} , {\ell} being the length function on W.
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35

Shen, Caixia, Li-meng Xia, and Yuanlin Li. "On the index of length four minimal zero-sum sequences." Colloquium Mathematicum 135, no. 2 (2014): 201–9. http://dx.doi.org/10.4064/cm135-2-4.

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36

Congero, Spencer, and Kenneth Zeger. "Hexagonal Run-Length Zero Capacity Region—Part I: Analytical Proofs." IEEE Transactions on Information Theory 68, no. 1 (January 2022): 130–52. http://dx.doi.org/10.1109/tit.2021.3120090.

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37

Congero, Spencer, and Kenneth Zeger. "Hexagonal Run-Length Zero Capacity Region—Part II: Automated Proofs." IEEE Transactions on Information Theory 68, no. 1 (January 2022): 153–77. http://dx.doi.org/10.1109/tit.2021.3120088.

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38

Cirillo, M., U. Gambardella, S. Pace, and B. Savo. "Zero-field singularities in Josephson tunnel junctions of intermediate length." IEEE Transactions on Magnetics 21, no. 2 (March 1985): 618–21. http://dx.doi.org/10.1109/tmag.1985.1063872.

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39

Sasegbon, Ayodeji, and Klaus Hellgardt. "Flux response technology applied in zero length column diffusivity measurements." Adsorption 18, no. 5-6 (October 10, 2012): 403–15. http://dx.doi.org/10.1007/s10450-012-9424-0.

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40

SCHLUENTZ, EMILY J., and JAMES F. STEFFE. "CONVERGENCE ANGLE OF WHEAT DOUGH IN A ZERO LENGTH DIE." Journal of Food Process Engineering 22, no. 4 (October 1999): 331–35. http://dx.doi.org/10.1111/j.1745-4530.1999.tb00489.x.

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41

Joyce, Helen, and Peter Mörters. "A Set with Finite Curvature and Projections of Zero Length." Journal of Mathematical Analysis and Applications 247, no. 1 (July 2000): 126–35. http://dx.doi.org/10.1006/jmaa.2000.6831.

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42

Grabarek, Zenon, and John Gergely. "Zero-length crosslinking procedure with the use of active esters." Analytical Biochemistry 185, no. 1 (February 1990): 131–35. http://dx.doi.org/10.1016/0003-2697(90)90267-d.

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43

Seow, C. Y., and N. L. Stephens. "Velocity-length-time relations in canine tracheal smooth muscle." Journal of Applied Physiology 64, no. 5 (May 1, 1988): 2053–57. http://dx.doi.org/10.1152/jappl.1988.64.5.2053.

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Zero-load velocity (V0) as a function of the length of canine tracheal smooth muscle was obtained by applying zero-load clamps to isotonically contracting muscle under various loads. The load clamps were applied at a specific time after onset of contraction. The magnitude of the isotonic load therefore determines the length of the muscle at the moment of release or at the moment the unloaded shortening velocity was measured. A family of such V0-muscle length (L) curves was obtained at 1-s intervals in the time course of contraction. The V0-L curve was fitted by a parabolic function with satisfactory goodness of fit. The maximum shortening velocity at optimum muscle length varied with time, but the minimum length at which V0 diminished to zero was time independent.
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44

Zhao, Pin, and Jian Shu Ye. "Research on the Installation Lengths of Zero Block Concrete Segment in Prestressed Concrete Box-Girder Beams with Corrugated Steel Webs." Advanced Materials Research 255-260 (May 2011): 1147–53. http://dx.doi.org/10.4028/www.scientific.net/amr.255-260.1147.

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In order to study the reasonable installation lengths of zero block concrete segment in prestressed concrete box-girder beams with corrugated steel webs, a numerical analysis on the length of different zero blocks in PC box girder beams with corrugated steel webs is made by the finite element software ANSYS. The influence of the installation lengths of zero block concrete segment on the structure control section's internal forces and deformation is discussed. The results indicate: the impact of length changes of zero block on box girder deflection is greater than its impact on internal forces; in terms of deflection, the displacement influence in quarter-section in middle span is the largest; and in terms of internal forces, the internal forces influence of the junction section formed by zero block concrete segment and beam segment with corrugated steel webs is the largest. According to the above results and the relevant information of constructed bridges, the reasonable setting length of zero block concrete segment has been provided, that the ratio L0/L of installation lengths and span for zero block of box girder should be in the range of 0.05 to 0.10.
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45

Vargas-Bustamante, Jaquebet, Pedro Martínez-Ortiz, Daniel Alvarado-Alvarado, Ulises Torres-Herrera, and Jorge Balmaseda. "Experimental Setup and Graphical User Interface for Zero-Length Column Chromatography." Applied Sciences 12, no. 13 (July 1, 2022): 6694. http://dx.doi.org/10.3390/app12136694.

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This work describes the design and implementation of a Zero-Length Column system to measure: diffusion coefficients, adsorption isotherm parameters of pure components and mixtures. In addition, a graphical user interface (GUI) was developed in LabVIEW for the semi-automatic operation of the system. The system is novel because it integrates all the aforementioned functionalities without using mass spectrometry. Two adsorbents, zeolite 5A and Basolite® C300 (Copper benzene-1,3,5-tricarboxylate) and two adsorbates methane and ethane were used to perform the validation of adsorption and diffusion experiments. The Henry constants and diffusion coefficients obtained reproduce those previously reported. The combination of the experimental setup and the GUI significantly reduce the amount of sample and measurement time needed in the characterization of the molecular sieves by conventional volumetric and gravimetric systems. The proposed system is relatively inexpensive, robust, easy to build, and capable of reproducing the results of other techniques.
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46

Zeng, Xiangneng, and Xiaoxia Qi. "On minimal zero-sum sequences of length four over cyclic groups." Colloquium Mathematicum 146, no. 2 (2017): 157–63. http://dx.doi.org/10.4064/cm6702-1-2016.

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47

Mattila, Pertti. "A class of sets with positive length and zero analytic capacity." Annales Academiae Scientiarum Fennicae. Series A. I. Mathematica 10 (1985): 387–95. http://dx.doi.org/10.5186/aasfm.1985.1043.

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48

Delissen, Arnoud A. T. M., Giuseppe Radaelli, and Just L. Herder. "Design and optimization of a general planar zero free length spring." Mechanism and Machine Theory 117 (November 2017): 56–77. http://dx.doi.org/10.1016/j.mechmachtheory.2017.07.002.

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49

Pavšič, Matej. "A non-trivial zero length limit of the Nambu–Goto string." Physics Letters B 740 (January 2015): 329–34. http://dx.doi.org/10.1016/j.physletb.2014.12.009.

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50

Wang, Chunlin, and Kevin Zhao. "On zero-sum subsequences of length not exceeding a given number." Journal of Number Theory 176 (July 2017): 365–74. http://dx.doi.org/10.1016/j.jnt.2016.12.019.

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