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1

Chen, Xiao-Wu, and Yu Ye. "The D -standard and K -standard categories." Advances in Mathematics 333 (July 2018): 159–93. http://dx.doi.org/10.1016/j.aim.2018.05.032.

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2

Pich, Antonio, and Eduardo de Rafael. "K-K mixing in the standard model." Physics Letters B 158, no. 6 (1985): 477–84. http://dx.doi.org/10.1016/0370-2693(85)90798-1.

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3

Klemsová, Ludmila, and Katarína Žiaková. "The importance of nursing standards: elements to create a standard for sheath decannulation according to EBP." Kontakt 16, no. 1 (2014): e17-e23. http://dx.doi.org/10.1016/j.kontakt.2013.11.001.

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4

Egorov, S. A., and E. L. Kvasov. "�K-1 control standard and simulator." Chemical and Petroleum Engineering 21, no. 11 (1985): 560–61. http://dx.doi.org/10.1007/bf01149871.

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5

Coogan, P. C., J. M. Darlow, J. R. Fiander, and G. W. Small. "200 k ac resistance transfer standard." Metrologia 38, no. 6 (2001): 503–7. http://dx.doi.org/10.1088/0026-1394/38/6/5.

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6

Vincent Yang, S., Jerry H. Wagstaff, and Gordon A. McKay. "From the evaluation of the NIST Standard K-411 to the concept of a model standard in quantitative electron microprobe analysis." Proceedings, annual meeting, Electron Microscopy Society of America 48, no. 2 (1990): 222–23. http://dx.doi.org/10.1017/s0424820100134715.

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The National Institute of Standards and Technology (NIST, formally NBS) offers a wide spectrum of high quality standards. For microanalytical standards, mineral glasses SRM470 (K-411 and K-412) “provide a highly homogeneous material at microscopic spatial resolution”. Other advantages are their availability and stable compositions. At NASA-JSC, standard K-411 was evaluated along with other microprobe standards by the backward-ZAF-calculation method described by Yang and Gordon, in which no real analysis was performed. Instead, our CAMECA MBX electron microprobe was set up collecting standard r
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7

Pandey, Pooja, and Ishpreet Singh. "Comparison between Standard K-Mean Clustering and Improved K-Mean Clustering." International Journal of Computer Applications 146, no. 13 (2016): 39–42. http://dx.doi.org/10.5120/ijca2016910868.

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8

Weiss, Gunter. "Non-standard Aspects of Fibonacci Type Sequences." KoG, no. 21 (2017): 26–34. http://dx.doi.org/10.31896/k.21.4.

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Fibonacci sequence and the limit of the quotient of adjacent Fibonacci numbers, namely the Golden Mean, belong to general knowledge of almost anybody, not only of mathematicians and geometers. There were several attempts to generalize these fundamental concepts which also found applications in art and architecture, as e.g. number series and quadratic equations leading to the so-called ``Metallic means'' by V. de Spinadel [8] or the cubic ``plastic number'' by van der Laan [5] resp. the ``cubi ratio'' by L. Rosenbusch [7]. The mentioned generalisations consider series of integers or real number
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9

Marchevski, Radoslav. "The rarest particle decay ever observed." SPG Mitteilungen - Communications de la SSP 75 (April 15, 2025): 29–30. https://doi.org/10.5281/zenodo.15230162.

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10

HOMMA-TAKEDA, SHINO, KYOKO SUZUKI, KEIKO HARUMOTO, et al. "EVALUATION OF THIN SECTION STANDARDS FOR LOCAL ANALYSIS OF LIGHT ELEMENTS BY MICRO-PIXE ANALYSIS." International Journal of PIXE 21, no. 01n02 (2011): 25–30. http://dx.doi.org/10.1142/s0129083511002124.

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For quantitative measurements of light elements by micro-PIXE (particle-induced X-ray emission) analysis, suitable external standards have been expected. In this paper thin sections of polyvinyl alcohol solution containing phosphorus ( P ) and potassium ( K ) were assessed for their purpose as standards by micro-PIXE analysis. Homogeneity of P and K added to the standard materials were validated by 1 μm and 10 μm-step scanning of the standard. The relative standard deviations of the X-ray intensity of the standards P and K were < 25% and <16%, respectively. The calibration line between t
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11

Guomin, Liu, Ma Xueliang, and Li Ping. "K Ratio H-Point Standard Additions Method." Analytical Letters 26, no. 4 (1993): 801–17. http://dx.doi.org/10.1080/00032719308017409.

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12

Kleinschmidt, Axel, and Hermann Nicolai. "Standard model fermions and K (E 10 )." Physics Letters B 747 (July 2015): 251–54. http://dx.doi.org/10.1016/j.physletb.2015.06.005.

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13

Tarr, James E. "Principles and Standards (2002): April 2002." Teaching Children Mathematics 8, no. 8 (2002): 482–87. http://dx.doi.org/10.5951/tcm.8.8.0482.

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NCTM's Principles and Standards for School Mathematics (2000) identifies Data Analysis and Probability as one of the five content standards for pre-K–12 mathematics and delineates learning expectations at each of four grade bands. This standard places much more emphasis on data analysis than on probability, particularly for grades pre-K through 5. Indeed, only one of the four goals in the standard directly addresses probability, and no probability learning expectations are explicitly stated for grades pre-K through 2. The standard states, however, that “instructional programs from prekindergar
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14

Ait Ouahra, Mohamed, Mohamed Mellouk, Hanae Ouahhabi, and Aissa Sghir. "An extension of the standard multifractional Brownian motion." Annales mathématiques Blaise Pascal 32, no. 1 (2025): 167–84. https://doi.org/10.5802/ambp.436.

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In this paper, firstly, we generalize the definition of the bifractional Brownian motion B H,K :=B H,K ; t ≥ 0, with parameters H∈(0,1) and K∈(0,1], to the case where H is no longer a constant, but a function H(·) of the time index t of the process. We denote this new process by B H(·),K . Secondly, we study its time regularities, the local asymptotic self-similarity and the long-range dependence properties.
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15

Zhang, Ting, and Xiaofei Qi. "Strong k-Skew Commutativity Preserving Maps on Standard Operator Algebras." Axioms 14, no. 2 (2025): 93. https://doi.org/10.3390/axioms14020093.

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Let A be a self-adjoint standard operator algebra on a real or complex Hilbert space of dimension ≥2, and let k∈{1,2,3}. The k-skew commutator for A,B∈A is defined by *[A,B]1=AB−BA* and *[A,B]k=*[A,*[A,B]k−1]1. Assume that Φ:A→A is a map whose range contains all rank-one projections. In this paper, we prove that Φ is strong k-skew-commutativity preserving, that is, *[Φ(A),Φ(B)]k=*[A,B]k for all A,B∈A if and only if one of the following statements holds: (i) Φ is either the identity map or the negative identity map whenever k∈{1,3}; (ii) Φ is the identity map whenever k=2.
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16

Deandrea, Aldo, Julien Welzel та Micaela Oertel. "K→πνbar nu from standard to new physics". Journal of High Energy Physics 2004, № 10 (2004): 038. http://dx.doi.org/10.1088/1126-6708/2004/10/038.

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17

Burdman, Gustavo. "Testing the standard model inB→K(*)l+l−." Physical Review D 52, no. 11 (1995): 6400–6410. http://dx.doi.org/10.1103/physrevd.52.6400.

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18

Edward A., Shirly, and Malarvizhi S. "Reduced-Complexity k-best Decoder for LTE Standard." International Journal of Multimedia and Ubiquitous Engineering 10, no. 3 (2015): 397–406. http://dx.doi.org/10.14257/ijmue.2015.10.3.36.

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19

Farke, Stefan. "Anorektaler Morbus Crohn Diagnostik: Standard- und K�rprogramm." coloproctology 26, no. 6 (2004): 391–94. http://dx.doi.org/10.1007/s00053-004-5143-7.

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20

Astrov, D. N., S. V. Korostin, and S. P. Polunin. "Thermometer working standard for temperatures below 0.5 K." Measurement Techniques 38, no. 12 (1995): 1356–59. http://dx.doi.org/10.1007/bf00990494.

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21

Tinti, G. "Physics beyond the Standard Model with NA62." Journal of Instrumentation 18, no. 12 (2023): C12018. http://dx.doi.org/10.1088/1748-0221/18/12/c12018.

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Abstract The NA62 experiment at CERN took data in 2016–2018 with the main goal of measuring the K + → νν̅ decay. The NA62 dataset is also exploited to search for light feebly interacting particles produced in kaon decays. Searches for K + → e + N and K + → μ + N decays, where N is a massive invisible particle, are performed. The N particle is assumed to be a heavy neutral lepton, and the results are expressed as upper limits of 𝒪(10-8) the neutrino mixing parameter |U14|2, where l = e,μ. Dedicated trigger lines were employed to collect di-lepton final states, which allowed stringent upper limi
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22

Damet, J., P. Eerola, A. Manara, and S. E. M. Nooij. "Searching for physics beyond the Standard Model in the decay B+ ? K+K+ ??" EPJ direct 3, no. 1 (2001): 1–9. http://dx.doi.org/10.1007/s1010501c0007.

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23

Sakurai, H., and R. C. Kemp. "Intercomparison of 12 Standard Platinum Resistance Thermometers between 13.8 K and 273.15 K." Metrologia 21, no. 4 (1985): 201–6. http://dx.doi.org/10.1088/0026-1394/21/4/005.

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24

Nuraeni, Yeni, Zulela MS, and Endry Boeriswati. "A Case Study of Curriculum Implementation and K-13 Challenges in Indonesia." International Journal for Educational and Vocational Studies 1, no. 8 (2020): 14. http://dx.doi.org/10.29103/ijevs.v2i1.2263.

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The K-13 curriculum has been implemented since July 2013 in several Indonesian schools and might have been in effect in all school arround 2014. The study was aimed to obtain information regarding teachers’ difficulties in impelemnting the curriculum 2013. The research was descriptive explorative research by means of qualitative data gathering which conducted from July 2016 to January 2018. The data on teachers’ difficulties in implementing the curriculum 2013 were gathered by means of interviews, observation, and focus discussion with elementary school teachers and the vice principals of curr
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25

BOILEAU, MICHEL, YI NI, and SHICHENG WANG. "ON STANDARD FORMS OF 1-DOMINATIONS BETWEEN KNOTS WITH SAME GROMOV VOLUMES." Communications in Contemporary Mathematics 10, supp01 (2008): 857–70. http://dx.doi.org/10.1142/s0219199708003071.

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Let k and k′ be two knots in the 3-sphere. Say k 1-dominates k′, if there is a proper degree 1 map f: E(k) → E(k′). Theorem: Suppose that any companion of k is prime. If k 1-dominates k′ with the same Gromov volume, then k′ can be obtained from k by finitely many de-satellizations. The condition of "same Gromov volume" clearly cannot be removed. We also give a new construction of 1-domination between knots with the same Gromov volume to show that the condition "any companion of k is prime" cannot be removed.
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26

Kitahara, Teppei. "Standard Model and New physics for ε′k/εk". EPJ Web of Conferences 179 (2018): 01007. http://dx.doi.org/10.1051/epjconf/201817901007.

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The first result of the lattice simulation and improved perturbative calculations have pointed to a discrepancy between data on ε′k/εk and the standard-model (SM) prediction. Several new physics (NP) models can explain this discrepancy, and such NP models are likely to predict deviations of ℬ(K → πvv) from the SM predictions, which can be probed precisely in the near future by NA62 and KOTO experiments. We present correlations between ε′k/εk and ℬ(K → πvv) in two types of NP scenarios: a box dominated scenario and a Z-penguin dominated one. It is shown that different correlations are predicted
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27

Mareš, Jan, and Kateřina Vlčková. "K metodologickým standardům kvantitativních studií v pedagogice: Jak psát o výzkumných zjištěních?" Pedagogická orientace 23, no. 4 (2013): 455–77. http://dx.doi.org/10.5817/pedor2013-4-455.

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Cílem studie je přispět do debaty ohledně metodologické kvality a standardů kvantitativního výzkumu a prezentace a publikace jeho zjištění. Ve studii nejprve diskutujeme o tom, proč vlastně publikovat výsledky výzkumu, a následně pojednáváme, jak o výzkumu a jeho výsledcích psát. Teoretickým východiskem jsou zahraniční publikační standardy (např. APA, AERA) a metodologická literatura. V druhé části studie na základě analýzy obsahových požadavků českých recenzovaných časopisů a významných konferencí k pedagogickému výzkumu se věnujeme tomu, co je explicitně požadováno a co by bylo vhodné v souč
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28

McAnulty, David P., Neil B. Rappaport, and Richard D. McAnulty. "An a Posteriori Investigation of Standard MMPI Validity Scales." Psychological Reports 57, no. 1 (1985): 95–98. http://dx.doi.org/10.2466/pr0.1985.57.1.95.

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This study investigated the standard MMPI validity scales alone and in combination, i.e., F—K, L+K, in discriminating subjects who deny faking good from those who report faking good. The design of the study was unique in that determination of faking was made after the test was administered. The validity scales and the F—K index in particular do not differentiate effectively between subjects who dissimulate and others. These results are interpreted in light of previous research.
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29

Sukmawati and Achmad Budiman. "Analysis of The Reliability of The 20kV Distribution System of PT PLN (Persero) ULP Tarakan Using Root Cause Problem Solving Methods." Journal of Emerging Supply Chain, Clean Energy, and Process Engineering 2, no. 2 (2023): 145–59. http://dx.doi.org/10.57102/jescee.v2i2.70.

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The distribution system is one of the components of the power system that cannot be separated from the occurrence of interference or damage, which causes factors from within the equipment and factors from outside that can cause blackouts. In this final project, the reliability problems of SAIDI, SAIFI and CAIDI in 2021 at PT PLN (Persero) ULP Tarakan will be discussed using the RCPS (Root Cause Problem Solving) method. The parameters used to see the reliability of the distribution network are SAIDI (System Average Interruption Duration Index), SAIFI (System Average Interruption Frequency Index
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30

Jacob, K. T., V. S. Saji, and Y. Waseda. "Standard Gibbs energy of formation of Pb2Ru2O6.5." Journal of Materials Research 22, no. 5 (2007): 1174–81. http://dx.doi.org/10.1557/jmr.2007.0171.

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Lead ruthenate is used as a bifunctional electrocatalyst for both oxygen evolution and reduction and as a conducting component in thick-film resistors. It also has potential applications in supercapacitors and solid oxide fuel cells. However, thermodynamic properties of the compound have not been reported in the literature. The standard Gibbs energy of formation has now been determined in the temperature range from 873 to 1123 K using a solid-state cell incorporating yttria-stabilized zirconia (YSZ) as the electrolyte, a mixture of PbO + Pb2Ru2O6.5 + Ru as the measuring electrode, and Ru + RuO
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31

Adanta, Dendy, I. M. Rizwanul Fattah, and Nura Musa Muhammad. "COMPARISON OF STANDARD k-epsilon AND SST k-omega TURBULENCE MODEL FOR BREASTSHOT WATERWHEEL SIMULATION." Journal of Mechanical Science and Engineering 7, no. 2 (2020): 039–44. http://dx.doi.org/10.36706/jmse.v7i2.44.

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Currently, Computational Fluid Dynamics (CFD) was utilized to predict the performance, geometry optimization or physical phenomena of a breastshot waterwheel. The CFD method requires the turbulent model to predict the turbulent flow. However, until now there is special attention on the effective turbulent model used in the analysis of breastshot waterwheel. This study is to identify the suitable turbulence model for a breatshot waterwheel. The two turbulence models investigated are: standard k-epsilon model and shear stress transport (SST) k-omega. Pressure based and one degrees of freedom (on
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32

De Almeida, Maria Candida Moreira, Jose Ubiratan Delgado, Ronaldo Lins Silva, Roberto Poledna, Regio S. Gomes, and Alfredo L. Ferreira Filho. "Uncertainty evaluation in activity measurements with HPGe using two relative methods." Brazilian Journal of Radiation Sciences 10, no. 4 (2022): 1–13. http://dx.doi.org/10.15392/2319-0612.2022.2070.

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Radionuclide metrology laboratories aim to provide radioactive standards for detector calibrations in nuclear safety areas with low uncertainties. Such standards are applied in nuclear industries, according to the requirements of monitoring programmes. The standard radionuclides of 133Ba, 152Eu and 166mHo are suitable to the determination of efficiency curves in HPGe detectors due to their multi-gamma emissions, which are intense and well separate in the spectrum. With efficiency curves it is possible to do the measurements without needing to use standards. In this work was made a verifying of
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33

Velásquez, Laura, Ainhoa Rubio-Clemente, and Edwin Chica. "Numerical and Experimental Analysis of Vortex Profiles in Gravitational Water Vortex Hydraulic Turbines." Energies 17, no. 14 (2024): 3543. http://dx.doi.org/10.3390/en17143543.

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This work compared the suitability of the k-ϵ standard, k-ϵ RNG, k-ω SST, and k-ω standard turbulence models for simulating a gravitational water vortex hydraulic turbine using ANSYS Fluent. This study revealed significant discrepancies between the models, particularly in predicting vortex circulation. While the k-ϵ RNG and standard k-ω models maintained relatively constant circulation values, the k-ϵ standard model exhibited higher values, and the k-ω SST model showed irregular fluctuations. The mass flow rate stabilization also varied, with the k-ϵ RNG, k-ω SST, and k-ω standard models being
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34

Landsberg, L. G. "Rare K-meson decays, standard model, and new physics." Physics of Atomic Nuclei 64, no. 10 (2001): 1729–95. http://dx.doi.org/10.1134/1.1414926.

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35

Takemitsu, N. "An Analytical Study of the Standard k–ε Model". Journal of Fluids Engineering 112, № 2 (1990): 192–98. http://dx.doi.org/10.1115/1.2909387.

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An asymptotic solution of the standard k–ε model for two-dimensional turbulent channel flow is found. Using this solution, five model constants in the model are all determined reasonably with the aid of experimental data. If an asymptotic solution with the logarithmic law as the leading term is sought for, the standard k–ε model is shown to be ill-posed since the second-order solution has divergent terms.
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36

Markwig, Thomas. "Standard bases in K[[t1,…,tm]][x1,…,xn]s." Journal of Symbolic Computation 43, no. 11 (2008): 765–86. http://dx.doi.org/10.1016/j.jsc.2008.03.003.

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37

Feutelais, Y., B. Legendre, M. Guymont, and P. Ochin. "Standard enthalpy of formation of Al0.28Fe0.72 at 298 K." Journal of Alloys and Compounds 322, no. 1-2 (2001): 184–89. http://dx.doi.org/10.1016/s0925-8388(01)01175-6.

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38

GROSSMAN, Y. "BEYOND THE STANDARD MODEL WITH B AND K PHYSICS." International Journal of Modern Physics A 19, no. 06 (2004): 907–17. http://dx.doi.org/10.1142/s0217751x04018865.

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In the first part of the talk the flavor physics input to models beyond the Standard Model is described. One specific example of such a new physics model is given: a model with bulk fermions in one non-factorizable extra dimension. In the second part of the talk we discuss several observables that are sensitive to new physics. We explain what type of new physics can produce deviations from the Standard Model predictions in each of these observables.
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39

Hou, Jinchuan, and Xiaofei Qi. "Strong k-commutativity preservers on complex standard operator algebras." Linear and Multilinear Algebra 66, no. 5 (2017): 902–18. http://dx.doi.org/10.1080/03081087.2017.1330868.

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40

HENG, S. H. "k-Resilient Identity-Based Encryption in the Standard Model." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E89-A, no. 1 (2006): 39–46. http://dx.doi.org/10.1093/ietfec/e89-a.1.39.

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41

Guberina, Branko, Antonio Pich та Eduardo de Rafael. "The decay K+→φ+φ0 in the standard model". Physics Letters B 163, № 1-4 (1985): 198–202. http://dx.doi.org/10.1016/0370-2693(85)90220-5.

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42

Büchler, Andrin, Lars Bülow, and Nicolai Rawyler. "Welchen Einfluss nimmt der Bildungsgrad auf die k-Affrizierung im Schweizer Standard?" Zeitschrift für Dialektologie und Linguistik 89, no. 1 (2022): 3. http://dx.doi.org/10.25162/zdl-2022-0001.

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43

Kardena, Sucinda, Fildza Izzati, and Rusdah Rusdah. "Classification of Coconut Fruit Quality Using The K-Nearest Neighbour (K-NN) Method Based on Feature Extraction: Color, Shape, and Texture." JURNAL TEKNIK INFORMATIKA 18, no. 1 (2025): 143–56. https://doi.org/10.15408/jti.v18i1.41225.

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In 2021, Indonesia was the world's largest coconut producer, with production reaching 17.1 million tons, according to the Food and Agriculture Organization (FAO). However, due to the long distribution time from farmers to consumers, the quality of coconuts often decreases, mainly due to manual classification. Coconuts that meet consumption standards are considered suitable, while coconuts that are overripe, damaged, or unripe are considered Non-standard. To overcome this problem, an automatic classification system was developed using machine learning with the K-Nearest Neighbor (K-NN) algorith
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44

Jeppsson, Lennart. "A new latest Telychian, Sheinwoodian and Early Homerian (Early Silurian) Standard Conodont Zonation." Transactions of the Royal Society of Edinburgh: Earth Sciences 88, no. 2 (1997): 91–114. http://dx.doi.org/10.1017/s0263593300006854.

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AbstractThe new standard conodont zonation includes, in succession from below: Lower Ps. bicornis Zone, Upper Ps. bicornis Zone, Lower P. procerus Zone, Upper P. procerus Zone, Lower K. ranuliformis Zone, Upper K. ranuliformis Zone, 0. s. rhenana Zone, Lower K. walliseri Zone, Middle K. walliseri Zone, K. patula Zone, uppermost K. walliseri range, post K. walliseri interregnum, K. o. ortus Zone and 0. s. sagitta Zone. Lower boundaries for each zone are defined or redefined. A less detailed biostratigraphic nomenclature at the superzone level is suggested for use where collections are inadequat
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45

Travina, S. N. "Evaluation of potato varieties from the Republic of Belarus from the doublet world collection of VIR in the Murmansk region." Vegetable crops of Russia, no. 2 (April 18, 2025): 45–53. https://doi.org/10.18619/2072-9146-2025-2-45-53.

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Relevance, Materials and Methods. The potato collection, represented by varieties from the Republic of Belarus in the amount of 40 samples, was studied in the Murmansk region. The study was conducted from 2000 to 2023, the duration of the study according to the samples ranged from 3 to 9 years. The study of potato samples was carried out according to the methodological guidelines for the maintenance and study of the world potato collection in Russia. The standards for the early ripening group were the Hibinskiy ranniy variety and the percentage of the average yield standard for the collection
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46

Bay-Williams, Jennifer M. "Principles and Standards: What is Algebra in Elementary School." Teaching Children Mathematics 8, no. 4 (2001): 196–200. http://dx.doi.org/10.5951/tcm.8.4.0196.

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Patterns have long been part of early mathematics experiences. The K–4 Patterns and Relationships Standard in Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) was replaced in Principles and Standards for School Mathematics (NCTM 2000) with a K–12 Algebra Standard. This Standard encompasses patterns, functions, and some topics that are beyond what traditionally was considered to be algebra. However, the word algebra, often associated with content covered in a traditional middle school or high school course, can evoke feelings of anxiety and raise questions of appropriatene
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47

Bohan, Harry, Beverly Irby, and Dolly Vogel. "Problem Solving: Dealing With Data in The Elementary School." Teaching Children Mathematics 1, no. 5 (1995): 256–60. http://dx.doi.org/10.5951/tcm.1.5.0256.

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Standard 11 of the K-4 recommendations of the National Council of Teachers of Mathematics's Curriculum and Evaluation Standards for School Mathematics and Standard 10 of the grades 5-8 portion of this document suggest that students be given opportunities to—
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48

Jourdan, Fred, and Paul R. Renne. "Age calibration of the Fish Canyon sanidine 40Ar/39Ar dating standard using primary K–Ar standards." Geochimica et Cosmochimica Acta 71, no. 2 (2007): 387–402. http://dx.doi.org/10.1016/j.gca.2006.09.002.

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POTY, VIRGINIE, and STÉPHANE UBEDA. "A PARALLEL THINNING ALGORITHM USING K×K MASKS." International Journal of Pattern Recognition and Artificial Intelligence 07, no. 05 (1993): 1183–202. http://dx.doi.org/10.1142/s0218001493000583.

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Abstract:
Thinning is a standard kernel in pattern recognition. Both serial and parallel algorithms have been investigated. Two classes of thinning algorithms can be defined: thinning techniques that use a raster-scanning of the whole image and a mask applied on each pixel, and thinning techniques that use a contour generation of the whole image as a basic operation of the thinning operation. The goal of this paper is to increase the speed of mask thinning algorithms by increasing the size of the thinning window.
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Saghafi, S., M. J. Withford, and Z. Ghoranneviss. "Characterizing flat-top laser beams using standard beam parameters." Canadian Journal of Physics 84, no. 3 (2006): 223–40. http://dx.doi.org/10.1139/p06-012.

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We examine the correspondence between various models describing flat-top laser beam profiles using two standard parameters; namely, the M2 factor and the kurtosis parameter. Numerical expressions for M2, based on the second moment of the beam irradiance distribution in the near and far fields and for the kurtosis parameter, k, based on the fourth moment at the near field, are obtained. Plots of k in the near field versus M2 demonstrate the similarities between the different analytical models used to describe flat-top profiles. Using the Padé approximation, a relationship between k and M2, a ne
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