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1

Fleishon, Howard B. "Regular Order." Journal of the American College of Radiology 10, no. 12 (2013): 890. http://dx.doi.org/10.1016/j.jacr.2013.04.002.

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2

Hanson, Peter C. "Abandoning the Regular Order." Political Research Quarterly 67, no. 3 (2014): 519–32. http://dx.doi.org/10.1177/1065912914524485.

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3

Balonin, N., and M. Sergeev. "REGULAR HADAMARD MATRIX OF ORDER 196 AND SIMILAR MATRICES." Informatsionno-upravliaiushchie sistemy (Information and Control Systems) 74, no. 1 (2015): 2–3. http://dx.doi.org/10.15217/issn1684-8853.2015.1.2.

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4

Alves, Fraga, Laurens Haan, and Tao Lin. "Third order extended regular variation." Publications de l'Institut Math?matique (Belgrade) 80, no. 94 (2006): 109–20. http://dx.doi.org/10.2298/pim0694109a.

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5

Kemprasit, Yupaporn, and Thawhat Changphas. "Regular order-preserving transformation semigroups." Bulletin of the Australian Mathematical Society 62, no. 3 (2000): 511–24. http://dx.doi.org/10.1017/s000497270001902x.

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The semigroup OT (X) of all order-preserving total transformations of a finite chain X is known to be regular. We extend this result to subchains of Z; and we characterise when OT (X) is regular for an interval X in R. We also consider the corresponding idea for partial transformations of arbitrary chains and posets.
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6

Xu, Tao, and Heguo Liu. "Regular automorphisms of order p2." Frontiers of Mathematics in China 14, no. 6 (2019): 1367–73. http://dx.doi.org/10.1007/s11464-019-0790-8.

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7

Liu, Qing, Tiantian Mao, and Taizhong Hu. "THE SECOND-ORDER REGULAR VARIATION OF ORDER STATISTICS." Probability in the Engineering and Informational Sciences 28, no. 2 (2013): 209–22. http://dx.doi.org/10.1017/s0269964813000430.

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Let X1, …, Xn be non-negative, independent and identically distributed random variables with a common distribution function F, and denote by X1:n ≤ ··· ≤ Xn:n the corresponding order statistics. In this paper, we investigate the second-order regular variation (2RV) of the tail probabilities of Xk:n and Xj:n − Xi:n under the assumption that $\bar {F}$ is of the 2RV, where 1 ≤ k ≤ n and 1 ≤ i < j ≤ n.
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8

Butz, A. R. "Regular sets and rank order processors." IEEE Transactions on Acoustics, Speech, and Signal Processing 38, no. 2 (1990): 241–46. http://dx.doi.org/10.1109/29.103059.

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9

Tomkins, R. J. "Regular stability of large order statistics." Statistics & Probability Letters 41, no. 2 (1999): 145–51. http://dx.doi.org/10.1016/s0167-7152(98)00132-1.

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10

Peña, J. M. "Sign Regular Matrices of Order Two." Linear and Multilinear Algebra 50, no. 1 (2002): 91–97. http://dx.doi.org/10.1080/03081080290011656.

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11

Karantha, Manjunatha Prasad, and P. Divya Shenoy. "Minus partial order on regular matrices." Linear and Multilinear Algebra 64, no. 5 (2015): 929–41. http://dx.doi.org/10.1080/03081087.2015.1067667.

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12

de Haan, Laurens, and Ulrich Stadtmüller. "Generalized regular variation of second order." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 61, no. 3 (1996): 381–95. http://dx.doi.org/10.1017/s144678870000046x.

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AbstractAssume that for a measurable funcion f on (0, ∞) there exist a positive auxiliary function a(t) and some γ ∈ R such that . Then f is said to be of generalized regular variation. In order to control the asymptotic behaviour of certain estimators for distributions in extreme value theory we are led to study regular variation of second order, that is, we assume that exists non-trivially with a second auxiliary function a1(t). We study the possible limit functions in this limit relation (defining generalized regular variation of second order) and their domains of attraction. Furthermore we
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13

Uğurlu, Ekin. "Regular third-order boundary value problems." Applied Mathematics and Computation 343 (February 2019): 247–57. http://dx.doi.org/10.1016/j.amc.2018.09.046.

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14

Ungor, B., S. Halicioglu, A. Harmanci, and J. Marovt. "Minus partial order in regular modules." Communications in Algebra 48, no. 10 (2020): 4542–53. http://dx.doi.org/10.1080/00927872.2020.1766056.

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15

Miyagawa, Masashi. "Order Distance in Regular Point Patterns." Geographical Analysis 41, no. 3 (2009): 252–62. http://dx.doi.org/10.1111/j.1538-4632.2009.00737.x.

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16

Uğurlu, Ekin. "Regular Fifth-Order Boundary Value Problems." Bulletin of the Malaysian Mathematical Sciences Society 43, no. 3 (2019): 2105–21. http://dx.doi.org/10.1007/s40840-019-00794-w.

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17

Wang, Fu Rong, and Shao Fei Du. "Möbius Regular Maps of Order pq." Acta Mathematica Sinica, English Series 35, no. 5 (2018): 690–702. http://dx.doi.org/10.1007/s10114-018-5744-7.

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18

Feng, Yan-Quan, Jin Ho Kwak, and Ming-Yao Xu. "Cubics-regular graphs of order 2p3." Journal of Graph Theory 52, no. 4 (2006): 341–52. http://dx.doi.org/10.1002/jgt.20169.

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19

Chen, Zi Li, Ying Feng, and Jin Xi Chen. "The Order Continuity of the Regular Norm on Regular Operator Spaces." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/183786.

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20

Ungor, Burcu, Sait Halicioglu, and Abdullah Harmanci. "The direct sum order in regular modules." Journal of Algebra and Its Applications 19, no. 09 (2019): 2050178. http://dx.doi.org/10.1142/s0219498820501789.

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In this paper, we define the direct sum relation on a module and prove that this is a partial order when the module is regular. We also focus on a regular support and a strong regular support of an element in a module, which are extensions of a generalized inverse and a reflexive generalized inverse of an element in a ring, respectively. Using regular supports and strong regular supports, we present various characterizations of the direct sum order as an application. We obtain some decompositions of a module via the direct sum order.
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21

Namnak, C., and E. Laysirikul. "Right regular and left regular elements of E-order-preserving transformation semigroups." International Journal of Algebra 7 (2013): 289–96. http://dx.doi.org/10.12988/ija.2013.13029.

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22

Mattingly, R. Bruce. "Even Order Regular Magic Squares Are Singular." American Mathematical Monthly 107, no. 9 (2000): 777. http://dx.doi.org/10.2307/2695733.

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23

Gao, Zhenlin, and Guijie Zhang. "ON SOME CLASSES OF REGULAR ORDER SEMIGROUPS." Communications of the Korean Mathematical Society 23, no. 1 (2008): 29–40. http://dx.doi.org/10.4134/ckms.2008.23.1.029.

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24

Cotsakis, Spiros, Seifedine Kadry, and Dimitrios Trachilis. "The regular state in higher order gravity." International Journal of Modern Physics A 31, no. 23 (2016): 1650130. http://dx.doi.org/10.1142/s0217751x1650130x.

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We consider the higher-order gravity theory derived from the quadratic Lagrangian [Formula: see text] in vacuum as a first-order (ADM-type) system with constraints, and build time developments of solutions of an initial value formulation of the theory. We show that all such solutions, if analytic, contain the right number of free functions to qualify as general solutions of the theory. We further show that any regular analytic solution which satisfies the constraints and the evolution equations can be given in the form of an asymptotic formal power series expansion.
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25

Feng, Yan-Quan, Klavdija Kutnar, Dragan Marusic, and Cui Zhang. "Tetravalent one-regular graphs of order 4p2." Filomat 28, no. 2 (2014): 285–303. http://dx.doi.org/10.2298/fil1402285f.

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26

Kutsia, Temur, and Mircea Marin. "Regular expression order-sorted unification and matching." Journal of Symbolic Computation 67 (March 2015): 42–67. http://dx.doi.org/10.1016/j.jsc.2014.08.002.

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27

Makarenko, N. Yu. "On almost regular automorphisms of prime order." Siberian Mathematical Journal 33, no. 5 (1992): 932–34. http://dx.doi.org/10.1007/bf00971002.

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28

Mattingly, R. Bruce. "Even Order Regular Magic Squares Are Singular." American Mathematical Monthly 107, no. 9 (2000): 777–82. http://dx.doi.org/10.1080/00029890.2000.12005272.

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29

Yoshikawa, Masayoshi. "On regular association schemes of order pq." Discrete Mathematics 338, no. 1 (2015): 111–13. http://dx.doi.org/10.1016/j.disc.2014.08.027.

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30

Fronček, Dalibor, Petr Kovář, Tereza Kovářová, et al. "On regular handicap graphs of even order." Electronic Notes in Discrete Mathematics 60 (July 2017): 69–76. http://dx.doi.org/10.1016/j.endm.2017.06.010.

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31

Hou, Dong-Dong, Yan-Quan Feng, and Dimitri Leemans. "On Regular Polytopes of 2-Power Order." Discrete & Computational Geometry 64, no. 2 (2019): 339–46. http://dx.doi.org/10.1007/s00454-019-00119-5.

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32

Zhou, Jin Xin, and Yan Quan Feng. "Regular maps of graphs of order 4p." Acta Mathematica Sinica, English Series 28, no. 5 (2011): 989–1012. http://dx.doi.org/10.1007/s10114-011-9528-6.

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33

Zhou, Jin-Xin, and Yan-Quan Feng. "Tetravalent one-regular graphs of order 2pq." Journal of Algebraic Combinatorics 29, no. 4 (2008): 457–71. http://dx.doi.org/10.1007/s10801-008-0146-z.

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34

Das, Bikramjit, and Marie Kratz. "Risk concentration under second order regular variation." Extremes 23, no. 3 (2020): 381–410. http://dx.doi.org/10.1007/s10687-020-00382-3.

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35

Drazin, Michael P. "A partial order in completely regular semigroups." Journal of Algebra 98, no. 2 (1986): 362–74. http://dx.doi.org/10.1016/0021-8693(86)90003-7.

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36

Li, Yantao, and Yan-Quan Feng. "Pentavalent One-regular Graphs of Square-free Order." Algebra Colloquium 17, no. 03 (2010): 515–24. http://dx.doi.org/10.1142/s1005386710000490.

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A graph is one-regular if its automorphism group acts regularly on the set of its arcs. Let n be a square-free integer. It is shown in this paper that a pentavalent one-regular graph of order n exists if and only if n = 2 · 5tp1p2 … ps ≥ 62, where t ≤ 1, s ≥ 1, and pi's are distinct primes such that 5|(pi-1). For such an integer n, there are exactly 4s-1 non-isomorphic pentavalent one-regular graphs of order n, which are Cayley graphs on dihedral groups constructed by Kwak et al. This work is a continuation of the classification of cubic one-regular graphs of order twice a square-free integer
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37

Jitjankarn, Phichet, and Thitarie Rungratgasame. "A GENERALIZATION OF NONSINGULAR REGULAR MAGIC SQUARES." Matematički Vesnik 74, no. 4 (2022): 272–79. http://dx.doi.org/10.57016/mv-aqsi1967.

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A generalization of regular magic squares with magic sum $\mu$ is an sq-corner (or square corner) magic square. It is a magic square satisfying the condition that the sum of 4 entries, square symmetrically placed with respect to the center, equals $\frac{4\mu}{n}$. Using the sq-corner magic squares of order $n$, a construction of sq-corner magic squares of order {$n+2$} is derived. Moreover, this construction provides some nonsingular classical sq-corner magic squares of all orders. In particular, a nonsingular regular magic square of any odd order can be constructed under this new method, as
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38

Cabello Sánchez, Javier. "Order isomorphisms between bases of topologies." Extracta Mathematicae 37, no. 1 (2022): 139–51. http://dx.doi.org/10.17398/2605-5686.37.1.139.

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In this paper we will study the representations of isomorphisms between bases of topological spaces. It turns out that the perfect setting for this study is that of regular open subsets of complete metric spaces, but we have been able to show some results about arbitrary bases in complete metric spaces and also about regular open subsets in Hausdorff regular topological spaces.
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39

Vostrikov, Anton. "Matrix vitrages and regular Hadamard matrices." Information and Control Systems, no. 5 (October 26, 2021): 2–9. http://dx.doi.org/10.31799/1684-8853-2021-5-2-9.

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Introduction: The Kronecker product of Hadamard matrices when a matrix of order n replaces each element in another matrix of order m, inheriting the sign of the replaced element, is a basis for obtaining orthogonal matrices of order nm. The matrix insertion operation when not only signs but also structural elements (ornamental patterns of matrix portraits) are inherited provides a more general result called a "vitrage". Vitrages based on typical quasi-orthogonal Mersenne (M), Seidel (S) or Euler (E) matrices, in addition to inheriting the sign and pattern, inherit the value of elements other t
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40

Silber, Adam, Petr Kovář, Pavla Kabelíková–Hrušková, and Michal Kravčenko. "On Regular Distance Magic Graphs of Odd Order." Journal of Combinatorial Mathematics and Combinatorial Computing 117 (December 31, 2023): 55–64. http://dx.doi.org/10.61091/jcmcc117-06.

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Let G=(V,E) be a graph with n vertices. A bijection f:V→{1,2,…,n} is called a distance magic abeling f G if there exists an integer k such that ∑u∈N(v)f(u)=k for all v∈V, where N(v) is the set of all ertices adjacent to v. Any graph which admits a distance magic labeling is a distance magic graph. The existence of regular distance magic graphs of even order was solved completely in a paper by ronček, Kovář, and Kovářová. In two recent papers, the existence of 4-regular and of (n−3)-regular distance magic graphs of odd order was also settled completely. In this paper, we provide a similar class
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41

Rabei, Eqab M., and Mo’az M. Tarawneh. "The Quantization of Higher Order Regular Lagrangians as First Order Singular Lagrangians." International Journal of Theoretical Physics 46, no. 4 (2007): 884–97. http://dx.doi.org/10.1007/s10773-006-9248-3.

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42

Connelly, Robert, and Balázs Csikós. "Cassification of first-order flexible regular bicycle polygons." Studia Scientiarum Mathematicarum Hungarica 46, no. 1 (2009): 37–46. http://dx.doi.org/10.1556/sscmath.2008.1074.

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A bicycle ( n , k )-gon is an equilateral n -gon whose k -diagonals are equal. S. Tabach-nikov proved that a regular n -gon is first-order flexible as a bicycle ( n , k )-gon if and only if there is an integer 2 ≦ r ≦ n -2 such that tan (π/ n ) tan ( kr π/ n ) = tan ( k π/ n ) tan ( r π/ n ). In the present paper, we solve this trigonometric diophantine equation. In particular, we describe the family of first order flexible regular bicycle polygons.
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43

Yost, William A., and William P. Shofner. "Regular interval stimuli: Are higher‐order intervals necessary?" Journal of the Acoustical Society of America 102, no. 5 (1997): 3162. http://dx.doi.org/10.1121/1.420753.

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44

Favini, A., A. Lorenzi, and H. Tanabe. "First-Order Regular and Degenerate Identification Differential Problems." Abstract and Applied Analysis 2015 (2015): 1–42. http://dx.doi.org/10.1155/2015/393624.

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We are concerned with both regular and degenerate first-order identification problems related to systems of differential equations of weakly parabolic type in Banach spaces. Several applications to partial differential equations and systems will be given in a subsequent paper to show the fullness of our abstract results.
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45

Sadlej, Andrzej J. "Infinite-Order Regular Approximation by the Metric Perturbation." Collection of Czechoslovak Chemical Communications 70, no. 5 (2005): 677–88. http://dx.doi.org/10.1135/cccc20050677.

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The regular approximation methods for the reduction of the Dirac equation to a fully equivalent two-component form are considered in the framework of the perturbation theory. The usual Dirac hamiltonian is first transformed with the change of metric. Then, the change of metric is considered as a perturbation to the zeroth-order (ZORA) problem. General formulae for perturbation corrections to the ZORA wave function and energy are expressed solely in terms of the two-component solutions. The method presented in this paper gives the energy- independent scheme for the step-by-step generation of th
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46

Hiraki, Akira, and Jack Koolen. "The Regular Near Polygons of Order (s, 2)." Journal of Algebraic Combinatorics 20, no. 2 (2004): 219–35. http://dx.doi.org/10.1023/b:jaco.0000047296.94830.e7.

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47

Mathur, Umang, David Mestel, and Mahesh Viswanathan. "The Decision Problem for Regular First Order Theories." Proceedings of the ACM on Programming Languages 9, POPL (2025): 986–1012. https://doi.org/10.1145/3704870.

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The Entscheidungsproblem , or the classical decision problem, asks whether a given formula of first-order logic is satisfiable. In this work, we consider an extension of this problem to regular first-order theories , i.e., (infinite) regular sets of formulae. Building on the elegant classification of syntactic classes as decidable or undecidable for the classical decision problem, we show that some classes (specifically, the EPR and Gurevich classes), which are decidable in the classical setting, become undecidable for regular theories. On the other hand, for each of these classes, we identify
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48

Choe, W., and J. K. Lee. "Analysis of higher order regular polygonal loop antennas." IEEE Transactions on Antennas and Propagation 38, no. 7 (1990): 1114–17. http://dx.doi.org/10.1109/8.55626.

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49

Lee, Michael Z., Elizabeth Love, Sivaram K. Narayan, Elizabeth Wascher, and Jordan D. Webster. "On nonsingular regular magic squares of odd order." Linear Algebra and its Applications 437, no. 6 (2012): 1346–55. http://dx.doi.org/10.1016/j.laa.2012.04.004.

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50

Bodlaender, Hans L., Richard B. Tan та Jan van Leeuwen. "Finding a Δ-regular supergraph of minimum order". Discrete Applied Mathematics 131, № 1 (2003): 3–9. http://dx.doi.org/10.1016/s0166-218x(02)00413-4.

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