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1

Bollobás, Béla, and Graham Brightwell. "Random high-dimensional orders." Advances in Applied Probability 27, no. 1 (March 1995): 161–84. http://dx.doi.org/10.2307/1428102.

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The random k-dimensional partial order Pk(n) on n points is defined by taking n points uniformly at random from [0,1]k. Previous work has concentrated on the case where k is constant: we consider the model where k increases with n.We pay particular attention to the height Hk(n) of Pk(n). We show that k = (t/log t!) log n is a sharp threshold function for the existence of a t-chain in Pk(n): if k – (t/log t!) log n tends to + ∞ then the probability that Pk(n) contains a t-chain tends to 0; whereas if the quantity tends to − ∞ then the probability tends to 1. We describe the behaviour of Hk(n) for the entire range of k(n).We also consider the maximum degree of Pk(n). We show that, for each fixed d ≧ 2, is a threshold function for the appearance of an element of degree d. Thus the maximum degree undergoes very rapid growth near this value of k.We make some remarks on the existence of threshold functions in general, and give some bounds on the dimension of Pk(n) for large k(n).
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2

Bollobás, Béla, and Graham Brightwell. "Random high-dimensional orders." Advances in Applied Probability 27, no. 01 (March 1995): 161–84. http://dx.doi.org/10.1017/s0001867800046292.

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The random k-dimensional partial order P k (n) on n points is defined by taking n points uniformly at random from [0,1] k . Previous work has concentrated on the case where k is constant: we consider the model where k increases with n. We pay particular attention to the height H k (n) of P k (n). We show that k = (t/log t!) log n is a sharp threshold function for the existence of a t-chain in P k (n): if k – (t/log t!) log n tends to + ∞ then the probability that P k (n) contains a t-chain tends to 0; whereas if the quantity tends to − ∞ then the probability tends to 1. We describe the behaviour of H k (n) for the entire range of k(n). We also consider the maximum degree of P k (n). We show that, for each fixed d ≧ 2, is a threshold function for the appearance of an element of degree d. Thus the maximum degree undergoes very rapid growth near this value of k. We make some remarks on the existence of threshold functions in general, and give some bounds on the dimension of P k (n) for large k(n).
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3

Arévalo López, Angel M. "Multiple orders in high pressure perovskites." Journal of Physics: Conference Series 950 (October 2017): 032002. http://dx.doi.org/10.1088/1742-6596/950/3/032002.

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4

Cătinaş, Emil. "A survey on the high convergence orders and computational convergence orders of sequences." Applied Mathematics and Computation 343 (February 2019): 1–20. http://dx.doi.org/10.1016/j.amc.2018.08.006.

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5

VAN KERVEL, VINCENT, and ALBERT J. MENKVELD. "High‐Frequency Trading around Large Institutional Orders." Journal of Finance 74, no. 3 (March 21, 2019): 1091–137. http://dx.doi.org/10.1111/jofi.12759.

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6

Montes-Lamas, H. "The method LPLDE applied to high orders." Journal of Physics: Conference Series 37 (May 1, 2006): 147–53. http://dx.doi.org/10.1088/1742-6596/37/1/026.

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7

Wang, Xiaofeng, Bo Wang, and Liqun Liu. "High uniformity splitter with great inhibition of ±1st orders." Laser Physics 33, no. 10 (September 7, 2023): 106201. http://dx.doi.org/10.1088/1555-6611/acf4e6.

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Abstract A transmissive double-groove grating under vertical incidence is proposed in this paper. The grating has a total of five diffraction orders, and the effect of a three-channel beam splitter is achieved by inhibiting the diffraction efficiency of ±1st orders. This is a polarization-independent micro-nano structure that achieves triple beam splitting under both TE and TM polarization. The diffraction efficiency of the 0th order and ±2nd orders for TE polarization orders can reach 32.55% and 32.72%, respectively. And the diffraction efficiency of 0th order and ±2nd orders for TM polarization can reach 32.28% and 32.59%, respectively. Both TE and TM polarization can achieve 99% uniformity. The grating performs well in terms of manufacturing tolerances and immunity to interference.
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8

Zou, W. N., Q. S. Zheng, D. X. Du, and J. Rychlewski. "Orthogonal Irreducible Decompositions of Tensors of High Orders." Mathematics and Mechanics of Solids 6, no. 3 (June 2001): 249–67. http://dx.doi.org/10.1177/108128650100600303.

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9

Weinhold, F., and C. R. Landis. "CHEMISTRY: High Bond Orders in Metal-Metal Bonding." Science 316, no. 5821 (April 6, 2007): 61–63. http://dx.doi.org/10.1126/science.1140756.

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10

Szirmai, E., and M. Lewenstein. "Exotic magnetic orders for high-spin ultracold fermions." EPL (Europhysics Letters) 93, no. 6 (March 1, 2011): 66005. http://dx.doi.org/10.1209/0295-5075/93/66005.

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11

Denuit, Michel, Claude Lefèvre, and Moshe Shaked. "On the theory of high convexity stochastic orders." Statistics & Probability Letters 47, no. 3 (April 2000): 287–93. http://dx.doi.org/10.1016/s0167-7152(99)00166-2.

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12

Li, Kun. "Do high-frequency fleeting orders exacerbate market illiquidity?" Electronic Commerce Research 18, no. 2 (November 22, 2017): 241–55. http://dx.doi.org/10.1007/s10660-017-9273-8.

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13

Gao, Shuhong. "Elements of provable high orders in finite fields." Proceedings of the American Mathematical Society 127, no. 6 (February 11, 1999): 1615–23. http://dx.doi.org/10.1090/s0002-9939-99-04795-4.

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14

Suslov, I. M. "High orders of perturbation theory. Are renormalons significant?" Journal of Experimental and Theoretical Physics 89, no. 2 (August 1999): 197–207. http://dx.doi.org/10.1134/1.558971.

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15

Levin, David C., Vijay M. Rao, and Laurence Parker. "Physician Orders Contribute To High-Tech Imaging Slowdown." Health Affairs 29, no. 1 (January 2010): 189–95. http://dx.doi.org/10.1377/hlthaff.2009.0528.

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16

Török, I. "High resolution PIXE using different orders of reflection." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 68, no. 1-4 (May 1992): 289–91. http://dx.doi.org/10.1016/0168-583x(92)96096-h.

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17

Korek, Mahmoud, and Hafez Kobeissi. "Highly accurate diatomic centrifugal distortion constants for high orders and high levels." Journal of Computational Chemistry 13, no. 9 (November 1992): 1103–8. http://dx.doi.org/10.1002/jcc.540130909.

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18

Mahmmod, Basheera M., Alaa M. Abdul-Hadi, Sadiq H. Abdulhussain, and Aseel Hussien. "On Computational Aspects of Krawtchouk Polynomials for High Orders." Journal of Imaging 6, no. 8 (August 13, 2020): 81. http://dx.doi.org/10.3390/jimaging6080081.

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Discrete Krawtchouk polynomials are widely utilized in different fields for their remarkable characteristics, specifically, the localization property. Discrete orthogonal moments are utilized as a feature descriptor for images and video frames in computer vision applications. In this paper, we present a new method for computing discrete Krawtchouk polynomial coefficients swiftly and efficiently. The presented method proposes a new initial value that does not tend to be zero as the polynomial size increases. In addition, a combination of the existing recurrence relations is presented which are in the n- and x-directions. The utilized recurrence relations are developed to reduce the computational cost. The proposed method computes approximately 12.5% of the polynomial coefficients, and then symmetry relations are employed to compute the rest of the polynomial coefficients. The proposed method is evaluated against existing methods in terms of computational cost and maximum size can be generated. In addition, a reconstruction error analysis for image is performed using the proposed method for large signal sizes. The evaluation shows that the proposed method outperforms other existing methods.
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19

Parish, Colin. "High number of treatment orders sparks call for review." Mental Health Practice 13, no. 4 (December 2009): 7. http://dx.doi.org/10.7748/mhp.13.4.7.s6.

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20

Howls, C. J., and S. A. Trasler. "High orders of Weyl series: resurgence for odd balls." Journal of Physics A: Mathematical and General 32, no. 8 (January 1, 1999): 1487–506. http://dx.doi.org/10.1088/0305-4470/32/8/015.

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21

Appel, Jacob M. "Ethics: English High Court Orders Separation of Conjoined Twins." Journal of Law, Medicine & Ethics 28, no. 3 (2000): 312–13. http://dx.doi.org/10.1111/j.1748-720x.2000.tb00678.x.

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22

Fradkin, Eduardo, Steven A. Kivelson, and John M. Tranquada. "Colloquium: Theory of intertwined orders in high temperature superconductors." Reviews of Modern Physics 87, no. 2 (May 26, 2015): 457–82. http://dx.doi.org/10.1103/revmodphys.87.457.

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23

Meyer, Daniel R., Yoonsook Ha, and Mei‐Chen Hu. "Do High Child Support Orders Discourage Child Support Payments?" Social Service Review 82, no. 1 (March 2008): 93–118. http://dx.doi.org/10.1086/526503.

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24

Loewen, E., D. Maystre, E. Popov, and L. Tsonev. "Diffraction efficiency of echelles working in extremely high orders." Applied Optics 35, no. 10 (April 1, 1996): 1700. http://dx.doi.org/10.1364/ao.35.001700.

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25

Guilbaud, Fabien, and Huyên Pham. "Optimal high-frequency trading with limit and market orders." Quantitative Finance 13, no. 1 (January 2013): 79–94. http://dx.doi.org/10.1080/14697688.2012.708779.

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26

Bijnens, Johan, and Lisa Carloni. "The massive non-linear sigma model at high orders." Nuclear Physics B 843, no. 1 (February 2011): 55–83. http://dx.doi.org/10.1016/j.nuclphysb.2010.09.019.

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27

Wang, Zewen, and Rongsheng Wen. "Numerical differentiation for high orders by an integration method." Journal of Computational and Applied Mathematics 234, no. 3 (June 2010): 941–48. http://dx.doi.org/10.1016/j.cam.2010.01.056.

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28

Travěnec, Igor, and Ladislav Šamaj. "High orders of Weyl series for the heat content." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 467, no. 2133 (March 16, 2011): 2479–99. http://dx.doi.org/10.1098/rspa.2010.0502.

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This article concerns the Weyl series of spectral functions associated with the Dirichlet Laplacian in a d -dimensional domain with a smooth boundary. In the case of the heat kernel, Berry and Howls predicted the asymptotic form of the Weyl series characterized by a set of parameters. Here, we concentrate on another spectral function, the (normalized) heat content. We show on several exactly solvable examples that, for even d , the same asymptotic formula is valid with different values of the parameters. The considered domains are d -dimensional balls and two limiting cases of the elliptic domain with eccentricity ε : a slightly deformed disk ( ε →0) and an extremely prolonged ellipse ( ε →1). These cases include two-dimensional domains with circular symmetry and those with only one shortest periodic orbit for the classical billiard. We also analyse the heat content for the balls in odd dimensions d for which the asymptotic form of the Weyl series changes significantly.
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29

Lenczewski, Martins Carlos Jorge. "Hidden and Fast Liquidity - Hidden Orders and High-Frequency Trading." e-Finanse 16, no. 1 (March 1, 2020): 27–35. http://dx.doi.org/10.2478/fiqf-2020-0004.

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AbstractThis work focuses on two of the more frequent practices in financial (especially capital) markets -the use of hidden orders and High-Frequency Trading (HFT). Although the use of each of them may reach 40% of the market turnover - even 60% for HFT, the actual knowledge on how they affect liquidity, prices, and market structure is still limited - especially if they are combined. The presence of both of these practices may look controversial, as it seems to be going in the opposite direction to what some of the goals that market regulators try to reach - transparency and increase of market liquidity. Additionally, their use suggests first, to give a clear advantage to some traders while not knowing the exact consequences to others. The aim of this paper is, by performing a literature study, to structure the current knowledge on a very specific topic in the area of market microstructure - the use of hidden orders and High-Frequency Trading. This paper tries to show the motivations, strategies, and eventual price effects behind hidden orders and High-Frequency Trading. It is also important to mention that this paper is based on scarce empirical research available (mainly for the US market) and as such, it is intended to encourage further analysis and research on this important topic.
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30

Shao, Yue, and Jianping Fu. "Engineering multiscale structural orders for high-fidelity embryoids and organoids." Cell Stem Cell 29, no. 5 (May 2022): 722–43. http://dx.doi.org/10.1016/j.stem.2022.04.003.

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31

Burkardt, M. "Trivial vacua, high orders in perturbation theory, and nontrivial condensates." Physical Review D 53, no. 2 (January 15, 1996): 933–38. http://dx.doi.org/10.1103/physrevd.53.933.

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32

Zha, Guo-Qiao, Jing-Chao Wang, Li-Jing Jin, Lin Wen, Ling-Feng Zhang, Hao Meng, Liang-Ma Shi, Hong-Wei Zhao, and Shi-Ping Zhou. "Modulations of orders around magnetic impurities in high-temperature superconductors." Solid State Communications 150, no. 35-36 (September 2010): 1605–9. http://dx.doi.org/10.1016/j.ssc.2010.06.048.

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33

Ussyukina, N. I. "Calculation of multiloop diagrams in high orders of perturbation theory." Physics Letters B 267, no. 3 (September 1991): 382–88. http://dx.doi.org/10.1016/0370-2693(91)90950-u.

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34

Kuz'mina, G. V. "On existence of quadratic differentials with poles of high orders." Journal of Mathematical Sciences 83, no. 6 (March 1997): 772–78. http://dx.doi.org/10.1007/bf02439204.

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35

Török, I., and T. Bondár. "High resolution PIXE using different orders of reflection, Part II." Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms 79, no. 1-4 (June 1993): 413–14. http://dx.doi.org/10.1016/0168-583x(93)95375-f.

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36

Kazaure, Hadiza. "High Mortality in Surgical Patients With Do-Not-Resuscitate Orders." Archives of Surgery 146, no. 8 (August 1, 2011): 922. http://dx.doi.org/10.1001/archsurg.2011.69.

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37

Schneider, G. "Zone plates with high efficiency in high orders of diffraction described by dynamical theory." Applied Physics Letters 71, no. 16 (October 20, 1997): 2242–44. http://dx.doi.org/10.1063/1.120069.

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38

Lakner, Peter, Josh Reed, and Sasha Stoikov. "High Frequency Asymptotics for the Limit Order Book." Market Microstructure and Liquidity 02, no. 01 (June 2016): 1650004. http://dx.doi.org/10.1142/s2382626616500040.

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We study the one-sided limit order book corresponding to limit sell orders and model it as a measure-valued process. Limit orders arrive to the book according to a Poisson process and are placed on the book according to a distribution which varies depending on the current best price. Market orders to buy periodically arrive to the book according to a second, independent Poisson process and remove from the book the order corresponding to the current best price. We consider the above described limit order book in a high frequency regime in which the rate of incoming limit and market orders is large and traders place their limit sell orders close to the current best price. Our first set of results provide weak limits for the unscaled price process and the properly scaled measure-valued limit order book process in the high frequency regime. In particular, we characterize the limiting measure-valued limit order book process as the solution to a measure-valued stochastic differential equation. We then provide an analysis of both the transient and long-run behavior of the limiting limit order book process.
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39

BOULWARE, C. H., J. D. JARVIS, H. L. ANDREWS, and C. A. BRAU. "NEEDLE CATHODES FOR HIGH-BRIGHTNESS BEAMS." International Journal of Modern Physics A 22, no. 22 (September 10, 2007): 3784–93. http://dx.doi.org/10.1142/s0217751x07037421.

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At the tips of sharp needles, the surface electric field is enhanced by many orders of magnitude. This intensifies thermionic emission and photoemission of electrons through the Schottky effect, and reduces the effect of space charge. The increased current density improves the brightness of electron sources by orders of magnitude. In addition, at very high fields (>109 V/m ), field emission and photo-field emission produce very high current density. Arrays of needles can be used to achieve high total current.
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40

Saliba, Pamela. "The information content of high-frequency traders aggressive orders: recent evidence." Quantitative Finance 20, no. 11 (May 13, 2020): 1779–94. http://dx.doi.org/10.1080/14697688.2020.1748700.

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41

Kim, H. H., S. M. Souliou, M. E. Barber, E. Lefrançois, M. Minola, M. Tortora, R. Heid, et al. "Uniaxial pressure control of competing orders in a high-temperature superconductor." Science 362, no. 6418 (November 29, 2018): 1040–44. http://dx.doi.org/10.1126/science.aat4708.

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Cuprates exhibit antiferromagnetic, charge density wave (CDW), and high-temperature superconducting ground states that can be tuned by means of doping and external magnetic fields. However, disorder generated by these tuning methods complicates the interpretation of such experiments. Here, we report a high-resolution inelastic x-ray scattering study of the high-temperature superconductor YBa2Cu3O6.67under uniaxial stress, and we show that a three-dimensional long-range-ordered CDW state can be induced through pressure along theaaxis, in the absence of magnetic fields. A pronounced softening of an optical phonon mode is associated with the CDW transition. The amplitude of the CDW is suppressed below the superconducting transition temperature, indicating competition with superconductivity. The results provide insights into the normal-state properties of cuprates and illustrate the potential of uniaxial-pressure control of competing orders in quantum materials.
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42

Ren, Yu-Jiun, Muhammad F. Farooqui, and Kai Chang. "A Compact Dual-Frequency Rectifying Antenna With High-Orders Harmonic-Rejection." IEEE Transactions on Antennas and Propagation 55, no. 7 (July 2007): 2110–13. http://dx.doi.org/10.1109/tap.2007.900275.

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43

Khonina, S. N., S. V. Karpeev, S. V. Alferov, and V. A. Soifer. "Generation of cylindrical vector beams of high orders using uniaxial crystals." Journal of Optics 17, no. 6 (May 1, 2015): 065001. http://dx.doi.org/10.1088/2040-8978/17/6/065001.

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44

Berger, N. K., B. Levit, and B. Fischer. "Delay lines with tailored high-dispersion orders for periodic optical pulses." IEEE Photonics Technology Letters 18, no. 14 (July 2006): 1485–87. http://dx.doi.org/10.1109/lpt.2006.877550.

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45

Gupta, Sourendu, and Prakash Mathews. "χ1and polarization asymmetries for quarkonia at high orders in nonrelativistic QCD." Physical Review D 56, no. 11 (December 1, 1997): 7341–49. http://dx.doi.org/10.1103/physrevd.56.7341.

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46

Hong, Ka H., Elena Solana-Madruga, Mauro Coduri, and J. Paul Attfield. "Complex Cation and Spin Orders in the High-Pressure Ferrite CoFe3O5." Inorganic Chemistry 57, no. 22 (November 2018): 14347–52. http://dx.doi.org/10.1021/acs.inorgchem.8b02458.

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47

Zakharov, Valentin. "High orders perturbation theory and dual models for Yang-Mills theories." Nuclear Physics B - Proceedings Supplements 207-208 (October 2010): 306–11. http://dx.doi.org/10.1016/j.nuclphysbps.2010.10.076.

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48

Scholz, G., R. Stösser, J. Klein, G. Silly, J. Y. Buzaré, Y. Laligant, and B. Ziemer. "Local structural orders in nanostructured Al2O3prepared by high-energy ball milling." Journal of Physics: Condensed Matter 14, no. 8 (February 15, 2002): 2101–17. http://dx.doi.org/10.1088/0953-8984/14/8/335.

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49

Hare, M. P. "High Intron Sequence Conservation Across Three Mammalian Orders Suggests Functional Constraints." Molecular Biology and Evolution 20, no. 6 (April 25, 2003): 969–78. http://dx.doi.org/10.1093/molbev/msg111.

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50

KIM, Hyung Taek, and Hyeok YUN. "Principle of High-order Harmonic Generation." Physics and High Technology 32, no. 12 (December 29, 2023): 2–6. http://dx.doi.org/10.3938/phit.32.032.

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High-order harmonic generation (HHG) is a highly nonlinear phenomenon that produces a numerous orders of harmonics. The generated harmonic orders can range from tens to several hundreds, depending on the ionization potential of the target medium and the intensity of the laser. The high harmonics generate a broad spectrum that is evenly distributed in frequency, enabling the production of extremely short light pulses within the attosecond time range. This article provides a brief overview of the key mechanisms involved in high-order harmonic generation from both gaseous mediums and condensed matters.
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