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Journal articles on the topic 'Length functions'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

KRAUSE, HENNING. "COHOMOLOGICAL LENGTH FUNCTIONS." Nagoya Mathematical Journal 223, no. 1 (2016): 136–61. http://dx.doi.org/10.1017/nmj.2016.28.

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We study certain integer valued length functions on triangulated categories, and establish a correspondence between such functions and cohomological functors taking values in the category of finite length modules over some ring. The irreducible cohomological functions form a topological space. We discuss its basic properties, and include explicit calculations for the category of perfect complexes over some specific rings.

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2

Anderson, D. D., and J. R. Juett. "Long length functions." Journal of Algebra 426 (March 2015): 327–43. http://dx.doi.org/10.1016/j.jalgebra.2014.12.016.

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3

Wilkens, David L. "Length functions on hypercentral groups." Proceedings of the Edinburgh Mathematical Society 28, no. 3 (1985): 303–4. http://dx.doi.org/10.1017/s0013091500017107.

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In [6] the structure of any real valued length function on an abelian group G is determined. It is shown there, in Theorem 6.1., that such a length function is an extension of a non-Archimedean length function l1 on N by an Archimedean length function l2 on H=G/N. Any non-Archimedean length function is given by a chain of subgroups, as described in [5], and following from results of Nancy Harrison [2], the length l2 is essentially the absolute value function on a subgroup of R. In the situation above if N≠G then N is a subgroup of G whose elements have bounded lengths. In this paper we show th

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4

Hoare, A. H. M. "Pregroups and length functions." Mathematical Proceedings of the Cambridge Philosophical Society 104, no. 1 (1988): 21–30. http://dx.doi.org/10.1017/s030500410006521x.

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Pregroups were defined by Stallings[7] who showed that the elements of the group they define have a normal form up to an equivalence called interleaving. Recently Rimlinger[5] has shown that subject to a discreteness and a boundedness condition any pregroup P defines a graph of groups. We show here that closer analysis of P makes the boundedness condition superfluous. In § 1 we give results of Stallings and Rimlinger and prove some key lemmas. In §2 we show that the discreteness condition gives an integer-valued length function in the sense of Lyndon [4]. It follows from the work of Chiswell [

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5

Chiswell, I. M. "Length functions and pregroups." Proceedings of the Edinburgh Mathematical Society 30, no. 1 (1987): 57–67. http://dx.doi.org/10.1017/s001309150001796x.

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The idea of a pregroup was introduced by Stallings and provides an axiomatic setting for a well-known argument, due to van der Waerden, used to prove normal form theorems. Details are provided in [7], Section 3.

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6

Kuznetsova, O. S., and V. G. Tkachev. "Length functions of lemniscates." manuscripta mathematica 112, no. 4 (2003): 519–38. http://dx.doi.org/10.1007/s00229-003-0411-3.

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7

Fritz, Tobias, Siddhartha Gadgil, Apoorva Khare, Pace Nielsen, Lior Silberman, and Terence Tao. "Homogeneous length functions on groups." Algebra & Number Theory 12, no. 7 (2018): 1773–86. http://dx.doi.org/10.2140/ant.2018.12.1773.

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8

Nesayef, Faisal. "Length Functions and HNN Groups." Journal of Scientific Research and Reports 14, no. 4 (2017): 1–8. http://dx.doi.org/10.9734/jsrr/2017/33282.

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9

Dreyer, Guillaume. "Length functions of Hitchin representations." Algebraic & Geometric Topology 13, no. 6 (2013): 3153–73. http://dx.doi.org/10.2140/agt.2013.13.3153.

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10

Wilkens, David L. "Minimal length functions on groups." Mathematika 39, no. 1 (1992): 56–61. http://dx.doi.org/10.1112/s0025579300006847.

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11

Anderson, David F., and Paula Pruis. "Length functions on integral domains." Proceedings of the American Mathematical Society 113, no. 4 (1991): 933. http://dx.doi.org/10.1090/s0002-9939-1991-1057742-1.

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12

Smillie, John, and Karen Vogtmann. "Length functions and outer space." Michigan Mathematical Journal 39, no. 3 (1992): 485–93. http://dx.doi.org/10.1307/mmj/1029004602.

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13

Nunokawa, Mamoru, Janusz Sokół, and Huo Tang. "Length problems for Bazilevič functions." Demonstratio Mathematica 52, no. 1 (2019): 56–60. http://dx.doi.org/10.1515/dema-2019-0007.

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Abstract Let C(r) denote the curve which is image of the circle |z| = r < 1 under the mapping f . Let L(r) be the length of C(r) and A(r) the area enclosed by the curve C(r). Furthermore M(r) = max|z|=r |f (z)|.We present some relations between these notions for Bazilevič functions.

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14

Niemenmaa, Markku. "Length functions and fuzzy groups." Journal of Mathematical Analysis and Applications 123, no. 1 (1987): 292–96. http://dx.doi.org/10.1016/0022-247x(87)90310-6.

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15

Faisal, H. Nesayef. "Length Functions and HNN Groups." Journal of Scientific Research & Reports 14, no. 4 (2017): 1–8. https://doi.org/10.9734/JSRR/2017/33282.

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The concept of length functions on groups is first introduced by Lyndon. This is used to give direct proofs of many other results in combinatorial group theory. Two important sets called M and N satisfying some certain axioms of length functions are considered. Finally investigations of the nature and the structures of the sets M and N in relation to the elements of HNN group were carried out.

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16

McGarvey, Richard, and John E. Feenstra. "Estimating length-transition probabilities as polynomial functions of premoult length." Marine and Freshwater Research 52, no. 8 (2001): 1517. http://dx.doi.org/10.1071/mf01172.

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In length-based lobster stock-assessment models where the population is subdivided into discrete length classes, growth is represented as a matrix of length-transition probabilities. At specific times during the model year, the length-transition probabilities specify the proportions growing into larger length classes. These probabilities are calculated by integration of gamma or normal distributions over the length intervals of each larger length class. The mean growth from any given length category is commonly modelled by a von Bertalanffy or other continuous growth curve. The coefficients of

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17

Gavish, A., and A. Lempel. "Match-length functions for data compression." IEEE Transactions on Information Theory 42, no. 5 (1996): 1375–80. http://dx.doi.org/10.1109/18.532879.

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18

Wu, Jang-Mei. "Length of Paths for Subharmonic Functions." Journal of the London Mathematical Society s2-32, no. 3 (1985): 497–505. http://dx.doi.org/10.1112/jlms/s2-32.3.497.

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19

Spirito, Dario. "Decomposition and classification of length functions." Forum Mathematicum 32, no. 5 (2020): 1109–29. http://dx.doi.org/10.1515/forum-2018-0168.

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AbstractWe study decompositions of length functions on integral domains as sums of length functions constructed from overrings. We find a standard representation when the integral domain admits a Jaffard family, when it is Noetherian and when it is a Prüfer domains such that every ideal has only finitely many minimal primes. We also show that there is a natural bijective correspondence between singular length functions and localizing systems.

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20

Arnold, Dirk V., and Alexander MacLeod. "Step Length Adaptation on Ridge Functions." Evolutionary Computation 16, no. 2 (2008): 151–84. http://dx.doi.org/10.1162/evco.2008.16.2.151.

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Step length adaptation is central to evolutionary algorithms in real-valued search spaces. This paper contrasts several step length adaptation algorithms for evolution strategies on a family of ridge functions. The algorithms considered are cumulative step length adaptation, a variant of mutative self-adaptation, two-point adaptation, and hierarchically organized strategies. In all cases, analytical results are derived that yield insights into scaling properties of the algorithms. The influence of noise on adaptation behavior is investigated. Similarities and differences between the adaptation

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21

Luo, Feng. "Geodesic length functions and Teichmüller spaces." Journal of Differential Geometry 48, no. 2 (1998): 275–317. http://dx.doi.org/10.4310/jdg/1214460797.

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22

Barrett, David E., and Michael Bolt. "Laguerre Arc Length from Distance Functions." Asian Journal of Mathematics 14, no. 2 (2010): 213–34. http://dx.doi.org/10.4310/ajm.2010.v14.n2.a3.

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23

Deng, Youjin, Timothy M. Garoni, Jens Grimm, and Zongzheng Zhou. "Unwrapped two-point functions on high-dimensional tori." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 5 (2022): 053208. http://dx.doi.org/10.1088/1742-5468/ac6a5c.

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Abstract We study unwrapped two-point functions for the Ising model, the self-avoiding walk (SAW) and a random-length loop-erased random walk on high-dimensional lattices with periodic boundary conditions. While the standard two-point functions of these models have been observed to display an anomalous plateau behaviour, the unwrapped two-point functions are shown to display standard mean-field behaviour. Moreover, we argue that the asymptotic behaviour of these unwrapped two-point functions on the torus can be understood in terms of the standard two-point function of a random-length random wa

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24

Virili, Simone. "On the relation between length functions and exact Sylvester rank functions." Topological Algebra and its Applications 7, no. 1 (2019): 69–74. http://dx.doi.org/10.1515/taa-2019-0006.

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AbstractInspired by the work of Crawley-Boevey on additive functions in locally finitely presented Grothendieck categories, we describe a natural way to extend a given exact Sylvester rank function on the category of finitely presented left modules over a given ring R, to the category of all left R-modules.

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25

Nunokawa, Mamoru, Janusz Sokół, and Nak Cho. "On a Length Problem for Univalent Functions." Mathematics 6, no. 11 (2018): 266. http://dx.doi.org/10.3390/math6110266.

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Let g be an analytic function with the normalization in the open unit disk. Let L ( r ) be the length of g ( { z : | z | = r } ) . In this paper we present a correspondence between g and L ( r ) for the case when g is not necessary univalent. Furthermore, some other results related to the length of analytic functions are also discussed.

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26

Clontz, Steven, and Alan Dow. "Almost compatible functions and infinite length games." Rocky Mountain Journal of Mathematics 48, no. 2 (2018): 463–83. http://dx.doi.org/10.1216/rmj-2018-48-2-463.

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27

Promislow, David. "Equivalence Classes of Length Functions on Groups." Proceedings of the London Mathematical Society s3-51, no. 3 (1985): 449–77. http://dx.doi.org/10.1112/plms/s3-51.3.449.

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28

Abbasiyan-Motlaq, M., and P. Pedram. "The minimal length and quantum partition functions." Journal of Statistical Mechanics: Theory and Experiment 2014, no. 8 (2014): P08002. http://dx.doi.org/10.1088/1742-5468/2014/08/p08002.

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29

Wilkens, David L. "Group actions on trees and length functions." Michigan Mathematical Journal 35, no. 1 (1988): 141–50. http://dx.doi.org/10.1307/mmj/1029003688.

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30

KHARLAMPOVICH, OLGA, ALEXEI MYASNIKOV, and DENIS SERBIN. "ACTIONS, LENGTH FUNCTIONS, AND NON-ARCHIMEDEAN WORDS." International Journal of Algebra and Computation 23, no. 02 (2013): 325–455. http://dx.doi.org/10.1142/s0218196713400031.

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In this paper we survey recent developments in the theory of groups acting on Λ-trees. We are trying to unify all significant methods and techniques, both classical and recently developed, in an attempt to present various faces of the theory and to show how these methods can be used to solve major problems about finitely presented Λ-free groups. Besides surveying results known up to date we draw many new corollaries concerning structural and algorithmic properties of such groups.

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31

Yamashita, Shinji. "Area and length maxima for univalent functions." Bulletin of the Australian Mathematical Society 41, no. 3 (1990): 435–39. http://dx.doi.org/10.1017/s0004972700018311.

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Let S be the family of functions f(z) = z + a2z2 + … which are analytic and univalent in |z| < 1. We find the valueas a function of r 0 < r < 1. The known lower estimate ofis improved. Relations with the growth theorem are considered and the radius of univalence of f(z)/z is discussed.

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32

Mazo, Loïc, and Étienne Baudrier. "Non-local length estimators and concave functions." Theoretical Computer Science 690 (August 2017): 73–90. http://dx.doi.org/10.1016/j.tcs.2017.06.005.

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33

Gilpin, Michael, and Robert Shelton. "Predicates whose maximal length functions increase periodically." Discrete Mathematics 84, no. 1 (1990): 15–21. http://dx.doi.org/10.1016/0012-365x(90)90268-m.

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34

Wolpert, Scott A. "Geodesic length functions and the Nielsen problem." Journal of Differential Geometry 25, no. 2 (1987): 275–96. http://dx.doi.org/10.4310/jdg/1214440853.

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35

Sánchez-Larios, Hérica, and Servio Guillén-Burguete. "Arc length associated with generalized distance functions." Journal of Mathematical Analysis and Applications 370, no. 1 (2010): 49–56. http://dx.doi.org/10.1016/j.jmaa.2010.04.030.

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36

Nunokawa, Mamoru, and Janusz Sokół. "On some length problems for univalent functions." Mathematical Methods in the Applied Sciences 39, no. 7 (2016): 1662–66. http://dx.doi.org/10.1002/mma.3552.

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37

Arnold, Dirk V., and Hans-Georg Beyer. "On the Behaviour of Evolution Strategies Optimising Cigar Functions." Evolutionary Computation 18, no. 4 (2010): 661–82. http://dx.doi.org/10.1162/evco_a_00023.

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This paper studies the performance of multi-recombinative evolution strategies using isotropically distributed mutations with cumulative step length adaptation when applied to optimising cigar functions. Cigar functions are convex-quadratic objective functions that are characterised by the presence of only two distinct eigenvalues of their Hessian, the smaller one of which occurs with multiplicity one. A simplified model of the strategy's behaviour is developed. Using it, expressions that approximately describe the stationary state that is attained when the mutation strength is adapted are der

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38

Gaster, Jonah. "Infima of length functions and dual cube complexes." Algebraic & Geometric Topology 17, no. 2 (2017): 1041–57. http://dx.doi.org/10.2140/agt.2017.17.1041.

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39

CHANG, BO-HYUN. "SOME APPLICATIONS OF EXTREMAL LENGTH TO ANALYTIC FUNCTIONS." Communications of the Korean Mathematical Society 21, no. 1 (2006): 135–43. http://dx.doi.org/10.4134/ckms.2006.21.1.135.

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40

Bridgeman, Martin. "Higher derivative of length functions along earthquake deformations." Michigan Mathematical Journal 64, no. 2 (2015): 421–33. http://dx.doi.org/10.1307/mmj/1434731931.

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41

Zanardo, Paolo. "Multiplicative invariants and length functions over valuation domains." Journal of Commutative Algebra 3, no. 4 (2011): 561–87. http://dx.doi.org/10.1216/jca-2011-3-4-561.

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42

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

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43

Crane, Edward, and Dinesh Markose. "On Keogh’s Length Estimate for Bounded Starlike Functions." Computational Methods and Function Theory 5, no. 2 (2006): 263–74. http://dx.doi.org/10.1007/bf03321098.

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44

Vlad, Marcel O., and E. Segal. "Age-length distribution functions for linear chain reactions." Chemical Physics Letters 136, no. 2 (1987): 171–76. http://dx.doi.org/10.1016/0009-2614(87)80436-0.

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45

Mardešić, Pavao, Dmitry Novikov, Laura Ortiz-Bobadilla, and Jessie Pontigo-Herrera. "Infinite orbit depth and length of Melnikov functions." Annales de l'Institut Henri Poincaré C, Analyse non linéaire 36, no. 7 (2019): 1941–57. http://dx.doi.org/10.1016/j.anihpc.2019.07.003.

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46

Valstyn, E. P., and C. R. Bond. "Williams-Comstock model with finite-length transition functions." IEEE Transactions on Magnetics 35, no. 2 (1999): 1070–76. http://dx.doi.org/10.1109/20.748855.

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47

Wolpert, S. A. "Behavior of geodesic-length functions on Teichmüller space." Journal of Differential Geometry 79, no. 2 (2008): 277–334. http://dx.doi.org/10.4310/jdg/1211512642.

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48

Marc Deléglise and Andrew Markoe. "On the Maximum Arc Length of Monotonic Functions." American Mathematical Monthly 121, no. 8 (2014): 689. http://dx.doi.org/10.4169/amer.math.monthly.121.08.689.

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49

Knudsen, Lars R., Xuejia Lai, and Bart Preneel. "Attacks on Fast Double Block Length Hash Functions." Journal of Cryptology 11, no. 1 (1998): 59–72. http://dx.doi.org/10.1007/s001459900035.

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50

Globevnik, Josip. "Holomorphic functions unbounded on curves of finite length." Mathematische Annalen 364, no. 3-4 (2015): 1343–59. http://dx.doi.org/10.1007/s00208-015-1253-5.

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