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Journal articles on the topic 'Converge'

Author: Grafiati

Published: 4 June 2021

Last updated: 21 February 2023

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1

Luo, Xu-Ren, Chun-Hsiao Chu, and Henry C. J. Chao. "Novel Solution Method for Inventory Models with Stochastic Demand and Defective Units." Mathematical Problems in Engineering 2020 (October 10, 2020): 1–13. http://dx.doi.org/10.1155/2020/3528706.

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This paper is a response to two papers. We improve the lengthy proof for the first paper by an elegant verification. For the second paper, we point out the three-sequence approach will result in different convergent rates such that when the other two sequences are converged, the ordering quantity sequence may still not converge to the optimal solution. We construct a novel iterative method to simplify the previous approach proposed by the three-sequence approach for the optimal solution. By the same numerical examples of three published papers, we demonstrate that we can control our findings to converge more accurately than previous results. Moreover, we show that there are three distinct features of our proposed approach. (i) It converges to the desired solution within the preassigned threshold value. (ii) We estimate the convergent ratio. (iii) We find the dominant factors for our proposed convergent sequence.

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2

Cunjalo, Fikret. "Almost convergence of double subsequences." Filomat 22, no. 2 (2008): 87–93. http://dx.doi.org/10.2298/fil0802087c.

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Almost-convergence of double sequences (subsequences) is equivalent to almost Cauchy condition. If the set of all almost convergent subsequences of a sequence S = Snm is of the second category, then S is convergent in the simple sense. For the sequence S = Snm which almost converges to L, Lebesgue measure of the set of all its subsequences which almost converge to L is either 1 or 0. .

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3

Yuille, A. L. "CCCP Algorithms to Minimize the Bethe and Kikuchi Free Energies: Convergent Alternatives to Belief Propagation." Neural Computation 14, no. 7 (July 1, 2002): 1691–722. http://dx.doi.org/10.1162/08997660260028674.

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This article introduces a class of discrete iterative algorithms that are provably convergent alternatives to belief propagation (BP) and generalized belief propagation (GBP). Our work builds on recent results by Yedidia, Freeman, and Weiss (2000), who showed that the fixed points of BP and GBP algorithms correspond to extrema of the Bethe and Kikuchi free energies, respectively. We obtain two algorithms by applying CCCP to the Bethe and Kikuchi free energies, respectively (CCCP is a procedure, introduced here, for obtaining discrete iterative algorithms by decomposing a cost function into a concave and a convex part). We implement our CCCP algorithms on two- and three-dimensional spin glasses and compare their results to BP and GBP. Our simulations show that the CCCP algorithms are stable and converge very quickly (the speed of CCCP is similar to that of BP and GBP). Unlike CCCP, BP will often not converge for these problems (GBP usually, but not always, converges). The results found by CCCP applied to the Bethe or Kikuchi free energies are equivalent, or slightly better than, those found by BP or GBP, respectively (when BP and GBP converge). Note that for these, and other problems, BP and GBP give very accurate results (see Yedidia et al., 2000), and failure to converge is their major error mode. Finally, we point out that our algorithms have a large range of inference and learning applications.

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4

Cohen, Jason, Sidney Resnick, and Gennady Samorodnitsky. "Sample correlations of infinite variance time series models: an empirical and theoretical study." Journal of Applied Mathematics and Stochastic Analysis 11, no. 3 (January 1, 1998): 255–82. http://dx.doi.org/10.1155/s1048953398000227.

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When the elements of a stationary ergodic time series have finite variance the sample correlation function converges (with probability 1) to the theoretical correlation function. What happens in the case where the variance is infinite? In certain cases, the sample correlation function converges in probability to a constant, but not always. If within a class of heavy tailed time series the sample correlation functions do not converge to a constant, then more care must be taken in making inferences and in model selection on the basis of sample autocorrelations. We experimented with simulating various heavy tailed stationary sequences in an attempt to understand what causes the sample correlation function to converge or not to converge to a constant. In two new cases, namely the sum of two independent moving averages and a random permutation scheme, we are able to provide theoretical explanations for a random limit of the sample autocorrelation function as the sample grows.

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5

RAWDON, ERIC J., and JONATHAN K. SIMON. "POLYGONAL APPROXIMATION AND ENERGY OF SMOOTH KNOTS." Journal of Knot Theory and Its Ramifications 15, no. 04 (April 2006): 429–51. http://dx.doi.org/10.1142/s0218216506004543.

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We establish a fundamental connection between smooth and polygonal knot energies, showing that the Minimum Distance Energy for polygons inscribed in a smooth knot converges to the Möbius Energy of the smooth knot as the polygons converge to the smooth knot. For this to work, the polygons must converge in a "nice" way, and the energies must be correctly regularized. We determine an explicit error bound for the convergence.

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6

Xia, Tai Wu, and Hong Jun Liu. "Multiuser Beamforming Using Weighted Orthogonal Constant Modulus Algorithm." Advanced Materials Research 204-210 (February 2011): 2162–66. http://dx.doi.org/10.4028/www.scientific.net/amr.204-210.2162.

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Beamforming is a core technique in intelligent antenna signal processing and has been receiving a prevalent focus by researchers. Common orthogonal constant modulus algorithm (OCMA) doesn’t guarantee that the weights of different beamformers converge to corresponding signals when the array of receivers takes in signals with same feature. Thereby a weighted orthogonal constant modulus algorithm (WOCMA) is proposed in which weights of different beamformers are ensured to be disparate by controlling their relevance down to a low level, which concludes different weight converges to corresponding signal. Simulation has proved that WOCMA possesses fast convergent speed and favorable facility in receiving signals.

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7

Kantrowitz, Robert, and Michael Schramm. "Series that Converge Absolutely but Don't Converge." College Mathematics Journal 43, no. 4 (September 2012): 331–33. http://dx.doi.org/10.4169/college.math.j.43.4.331.

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8

MOREIRA, DIEGO R., and EDUARDO V. O. TEIXEIRA. "Weak convergence under nonlinearities." Anais da Academia Brasileira de Ciências 75, no. 1 (March 2003): 9–19. http://dx.doi.org/10.1590/s0001-37652003000100002.

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In this paper, we prove that if a Nemytskii operator maps Lp(omega, E) into Lq(omega, F), for p, q greater than 1, E, F separable Banach spaces and F reflexive, then a sequence that converge weakly and a.e. is sent to a weakly convergent sequence. We give a counterexample proving that if q = 1 and p is greater than 1 we may not have weak sequential continuity of such operator. However, we prove that if p = q = 1, then a weakly convergent sequence that converges a.e. is mapped into a weakly convergent sequence by a Nemytskii operator. We show an application of the weak continuity of the Nemytskii operators by solving a nonlinear functional equation on W1,p(omega), providing the weak continuity of some kind of resolvent operator associated to it and getting a regularity result for such solution.

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9

Gåsemyr, J., and Terje Aven. "Asymptotic distributions for downtimes of monotone systems." Journal of Applied Probability 36, no. 3 (September 1999): 814–24. http://dx.doi.org/10.1239/jap/1032374636.

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Consider a monotone system with independent alternating renewal processes as component processes, and assume the component uptimes are exponentially distributed. In this paper we study the asymptotic properties of the distribution of the rth downtime of the system, as the failure rates of the components converge to zero. We show that this distribution converges, and the limiting function has a simple form. Thus we have established an easy computable approximation formula for the downtime distribution of the system for highly available systems. We also show that the steady state downtime distribution, i.e. the downtime distribution of a system failure occurring after an infinite run-in period, converges to the same limiting function as the failure rates converge to zero.

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10

Gåsemyr, J., and Terje Aven. "Asymptotic distributions for downtimes of monotone systems." Journal of Applied Probability 36, no. 03 (September 1999): 814–24. http://dx.doi.org/10.1017/s0021900200017599.

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Consider a monotone system with independent alternating renewal processes as component processes, and assume the component uptimes are exponentially distributed. In this paper we study the asymptotic properties of the distribution of the rth downtime of the system, as the failure rates of the components converge to zero. We show that this distribution converges, and the limiting function has a simple form. Thus we have established an easy computable approximation formula for the downtime distribution of the system for highly available systems. We also show that the steady state downtime distribution, i.e. the downtime distribution of a system failure occurring after an infinite run-in period, converges to the same limiting function as the failure rates converge to zero.

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11

Hubber, David A., Sam A. E. G. Falle, and Simon P. Goodwin. "Convergence of SPH and AMR simulations." Proceedings of the International Astronomical Union 6, S270 (May 2010): 429–32. http://dx.doi.org/10.1017/s1743921311000767.

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AbstractWe present the first results of a large suite of convergence tests between Adaptive Mesh Refinement (AMR) Finite Difference Hydrodynamics and Smoothed Particle Hydrodynamics (SPH) simulations of the non-linear thin shell instability and the Kelvin-Helmholtz instability. We find that the two methods converge in the limit of high resolution and accuracy. AMR and SPH simulations of the non-linear thin shell instability converge with each other with standard algorithms and parameters. The Kelvin-Helmholtz instability in SPH requires both an artificial conductivity term and a kernel with larger compact support and more neighbours (e.g. the quintic kernel) in order converge with AMR. For purely hydrodynamical problems, SPH simulations take an order of magnitude longer than the grid code when converged.

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12

Wang, Yang, Guirong Liu, and Xiong Li. "Entire solutions in a delayed nonlocal dispersal competitive system." International Journal of Biomathematics 12, no. 04 (May 2019): 1950035. http://dx.doi.org/10.1142/s1793524519500359.

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In this paper, we are concerned with the existence of an entire solution in a delayed nonlocal dispersal competitive system. This entire solution converges to two monotone fronts with different speeds, which approach each other from both sides of the [Formula: see text]-axis, as [Formula: see text] converge to [Formula: see text] and then converge to [Formula: see text] as [Formula: see text] converges to [Formula: see text]. Its global dynamic shows the superior species invade the inferior ones from both sides of the [Formula: see text]-axis and then the inferior ones become extinct, which is a new invading way. In fact, our conclusions extend this invading way into a more general competitive system. Furthermore, we show several properties of this entire solution.

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13

Vo, Thi Van Anh. "Complete Convergence for M-Pairwise Negatively Dependent Random Variables." Journal of Technical Education Science, no. 72A (October 28, 2022): 28–33. http://dx.doi.org/10.54644/jte.72a.2022.1135.

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Hsu and Robbins (1947) introduce the concept complete convergence as follows. A sequence of random variables is said to converge completely to a constant if for all The converse is true if the are independent. They also show that the sequence of arithmetic means of independent and identically distributed random variables converges completely to the expected value if the variance of the summands is finite. Erdös proved the converse. The result of Hsu-Robbins-Erdös is a fundamental theorem in probability theory and has been generalized and extended in several directions by many authors. In this paper, let be a sequence of positive constants with and be a sequence of m-pairwise negatively dependent random variables. We study the complete convergence for m-pairwise negatively dependent random variables under mild condition . Our results obtained in the paper generalize the corresponding ones for pairwise independent and identically distributed random variables and also pairwise negatively dependent random variables.

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14

Klei, Heinz-Albrecht. "Measure convergent sequences in Lebesgue spaces and Fatou's lemma." Bulletin of the Australian Mathematical Society 54, no. 2 (October 1996): 197–202. http://dx.doi.org/10.1017/s0004972700017652.

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Let (fn) be a sequence of positive P-integrable functions such that (∫ fndP)n converges. We prove that (fn) converges in measure to if and only if equality holds in the generalised Fatou's lemma. Let f∞ be an integrable function such that (∥fn − f∞∥1)n converges. We present in terms of the modulus of uniform integrability of (fn) necessary and sufficient conditions for (fn) to converge in measure to f∞.

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15

Kash, I. A., E. J. Friedman, and J. Y. Halpern. "Multiagent Learning in Large Anonymous Games." Journal of Artificial Intelligence Research 40 (March 22, 2011): 571–98. http://dx.doi.org/10.1613/jair.3213.

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In large systems, it is important for agents to learn to act effectively, but sophisticated multi-agent learning algorithms generally do not scale. An alternative approach is to find restricted classes of games where simple, efficient algorithms converge. It is shown that stage learning efficiently converges to Nash equilibria in large anonymous games if best-reply dynamics converge. Two features are identified that improve convergence. First, rather than making learning more difficult, more agents are actually beneficial in many settings. Second, providing agents with statistical information about the behavior of others can significantly reduce the number of observations needed.

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16

Gonzalez, Gilbert. "DIVIDE OR CONVERGE?" Muma Case Review 1 (2016): 1–23. http://dx.doi.org/10.28945/3581.

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Gilbert Gonzalez, founder and CEO of Mission Critical Solutions (MCS), was reflecting on the path forward for his company. MCS maintained and updated a five-year strategic plan each year since its inception in 1990. In the early years, the strategic plan focused on the key strategic factors (KSFs) and resulted in a narrow mission. Year after year, that focus on the KSFs was rewarded by the market. Doing the most important things well kept the organization focused and efficient. The consistently evolving mission of the organization necessitated adding new products, services, and solutions. In the early 1990s, deploying PCs, implementing local area networks (LANs), and providing onsite support met the challenges their customers faced. A few years later, the company’s clients’ needs led to the addition of a Wide Area Network (WAN) solution to aggregate offices and link applications. By 1996, information technologies (IT) and telecommunications began to converge. Common structured cable plants and digital trunks sharing voice and data traffic were new and mandatory elements of the clients’ solutions. Subtly, the technologies evolved and converged. Internet Protocol (IP) Telephony and Unified Communications converged onto the clients’ LAN/WAN networks. It was clear that most technology would speak IP in the future. In the early 2000s, building automation, audio video (AV), security, surveillance, and control system endpoints converged onto the network. The trend of unusual devices converging onto the network, also known as “the Internet of things,” will continue. Wireless innovations and mobility meant that technology could move not just around the facility, but also around the world. For MCS, the end result of this phenomenon was a group of specialized departments and teams: information technologies, passive cabling systems, electrical systems, building automation and controls, audio video, security and surveillance, and unified communications. All of these departments, staffed 200 associates strong, were coordinated by the project management team, and collaborated to meet the requirements of the company’s clients. Thus, the marketing elevator speech for MCS required a tall building! Their clients expressed surprise and confusion at the breadth of services offered. While the devices had converged, the clients’ perception of their vendors and providers had not. The question at hand was whether MCS should stay converged in a functional organization strategy with capability-based teams, or organize into separate standalone entities with unique identities and separate overheads, focusing more on the individual capability-based technology specialization.

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17

Gonzalez, Gilbert. "DIVIDE OR CONVERGE?" Journal of Information Technology Education: Discussion Cases 5 (2016): 07. http://dx.doi.org/10.28945/3599.

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Should Mission Critical Solutions (MCS) stay converged in a functional organization strategy with capability-based teams, or organize into separate standalone entities with unique identities and separate overheads, focusing more on the individual capability-based technology specialization?

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18

Kolb, Holger. "When Extremes Converge." Comparative Migration Studies 2, no. 1 (March 2014): 57–75. http://dx.doi.org/10.5117/cms2014.1.kolb.

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19

Blow, Julian. "Many strands converge." Nature 326, no. 6112 (April 1987): 441–42. http://dx.doi.org/10.1038/326441a0.

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20

Greenstein, S. "When technologies converge." IEEE Micro 19, no. 1 (1999): 8–9. http://dx.doi.org/10.1109/40.748790.

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21

Whalley, Katherine. "Inhibitory signals converge." Nature Reviews Neuroscience 8, no. 4 (April 2007): 245. http://dx.doi.org/10.1038/nrn2116.

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22

Willison, James. "Invitation to converge." Infosecurity 4, no. 8 (November 2007): 17. http://dx.doi.org/10.1016/s1754-4548(07)70197-3.

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23

KEMSLEY, JYLLIAN. "192 LASERS CONVERGE." Chemical & Engineering News 87, no. 13 (March 30, 2009): 30–33. http://dx.doi.org/10.1021/cen-v087n013.p030.

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24

Martin, Kevan A. C. "Parallel pathways converge." Current Biology 2, no. 10 (October 1992): 555–57. http://dx.doi.org/10.1016/0960-9822(92)90037-b.

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25

Apergis, Nicholas, and Yannis Georgellis. "Does Happiness Converge?" Journal of Happiness Studies 16, no. 1 (January 9, 2014): 67–76. http://dx.doi.org/10.1007/s10902-013-9495-y.

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26

Bartels, Larry M. "Failure to Converge." ANNALS of the American Academy of Political and Social Science 667, no. 1 (August 17, 2016): 143–65. http://dx.doi.org/10.1177/0002716216661145.

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The logic of electoral competition suggests that candidates should have to adopt moderate issue positions to win majority support. But U.S. presidential candidates consistently take relatively extreme positions on a variety of important issues. Some observers have attributed these “polarized” positions to the extreme views of the parties’ core supporters. I characterize the issue preferences of core Republicans, core Democrats, and swing voters over the past three decades and assess how well the positions of presidential candidates reflect those preferences. I find that Republican candidates have generally been responsive to the positions of their base. However, Democratic candidates have often been even more extreme than the Democratic base, suggesting that electoral polarization is due in significant part to candidates’ own convictions rather than the need to mollify core partisans. Neither party’s presidential candidates have been more than minimally responsive to the views of swing voters.

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27

Januchowski-Hartley, Stephanie R. "Two Rivers Converge." BioScience 69, no. 5 (April 3, 2019): 398–99. http://dx.doi.org/10.1093/biosci/biz028.

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28

Clay, Keith. "Parallel worlds converge." Trends in Ecology & Evolution 13, no. 1 (January 1998): 38–39. http://dx.doi.org/10.1016/s0169-5347(97)01265-2.

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29

Meyer, Helen. "Security, management converge." Computers & Security 17, no. 6 (January 1998): 518–19. http://dx.doi.org/10.1016/s0167-4048(98)80082-5.

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30

Skipper, Magdalena. "Converge and diversify." Nature Reviews Genetics 7, no. 11 (November 2006): 828. http://dx.doi.org/10.1038/nrg2001.

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31

Moroni, Lorenzo, and Clemens A. van Blitterswijk. "Converge and regenerate." Nature Materials 5, no. 6 (June 2006): 437–38. http://dx.doi.org/10.1038/nmat1665.

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32

INOUE, D., and K. TANAKA. "Conditional Converge Cast." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E91-A, no. 6 (June 1, 2008): 1537–40. http://dx.doi.org/10.1093/ietfec/e91-a.6.1537.

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33

Tadj, Lotfi. "Converge, Version 3.0." Journal of Applied Mathematics and Stochastic Analysis 6, no. 3 (January 1, 1993): 281–85. http://dx.doi.org/10.1155/s1048953393000243.

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Although intended for college teachers/students, Converge presents a feature that may interest all scientists: it allows an easy export of graphic files to most known word processors, specifically to the 𝔼𝕏ℙ, Version 2.1, a powerful WYSIWYG mathematical word processor.

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34

Hansen, Jo-Ida C. "To Converge or Not to Converge: That Is the Question." Contemporary Psychology: A Journal of Reviews 40, no. 9 (September 1995): 904–5. http://dx.doi.org/10.1037/003987.

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35

Cohen, T. "Medical and information technologies converge medical and information technologies converge." IEEE Engineering in Medicine and Biology Magazine 23, no. 3 (May 2004): 59–65. http://dx.doi.org/10.1109/memb.2004.1317983.

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36

Thirring, W. "ENTROPY INCREASE AND K-SYSTEMS IN QUANTUM THEORY." International Journal of Modern Physics B 04, no. 05 (April 1990): 1119–26. http://dx.doi.org/10.1142/s0217979290000553.

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It is shown that the relative entropy converges to its equilibrium value when the states converge strongly. This can happen only for subalgebras for which the clustering is uniform. It happens for K-systems for which this uniformity in clustering has the maximal extent which is possible.

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37

MAŁYSZ, ROBERT. "A GENERALIZATION OF FRACTAL INTERPOLATION STOCHASTIC PROCESSES TO HIGHER DIMENSIONS." Fractals 09, no. 04 (December 2001): 415–28. http://dx.doi.org/10.1142/s0218348x01000907.

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We generalize the notion of fractal interpolation functions (FIFs) to stochastic processes. We prove that the Minkowski dimension of trajectories of such interpolations for self-similar processes with stationary increments converges to 2-α. We generalize the notion of vector-valued FIFs to stochastic processes. Trajectories of such interpolations based on an equally spaced sample of size n on the interval [0,1] converge to the trajectory of the original process. Moreover, for fractional Brownian motion and, more generally, for self-similar processes with stationary increments (α-sssi) processes, upper bounds of the Minkowski dimensions of the image and the graph converge to the Hausdorff dimension of the image and the graph of the original process, respectively.

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38

Martynyuk, Eduard. "The convergent processes of the religious life of our time." Ukrainian Religious Studies, no. 35 (September 9, 2005): 45–54. http://dx.doi.org/10.32420/2005.35.1595.

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The most common tendencies in religious life of the second half of the twentieth century, which I propose to call "convergent processes". The term "convergence" (from the Latin. Convergentio, convergo - converge, approach) was first used by German scholar Henry Frick in his work Comparative Religion. In seeking to approximate the terminology of the natural sciences and social sciences, begun by DF Schlemmacher, G. Frick used the term in the sense in which it was already used primarily in biology, where this concept characterizes the process of appearance of similarities in the structure and functions in distant the origin of the organisms as a result of their adaptation to the same conditions of existence. The term was used by the researcher to refer to similar processes in different religions

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39

MOON, WOOJIN. "Party Activists, Campaign Resources and Candidate Position Taking: Theory, Tests and Applications." British Journal of Political Science 34, no. 4 (September 8, 2004): 611–33. http://dx.doi.org/10.1017/s0007123404000213.

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Electoral competition is here specified as revolving around both candidate policy positions and non-policy issues.Two candidates spend their resources on non-policy issues to sway citizens' ideological voting decisions but they are constrained by their party activists who provide them with electoral resources. In this setting, a candidate with a resource advantage converges more towards the centre, but a candidate with a resource disadvantage diverges more from the centre. This asymmetry in two candidates' incentives to converge generates the result that the two candidates do not converge towards each other. To test these theoretical results, two-stage estimation is used in this article to solve the reciprocal relationship between policy moderation and campaign resources. This analysis produces strong empirical support for the model in the context of US Senate elections between 1974 and 2000.

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40

Fukuda, Naohiro, Tamotu Kinoshita, and Toshio Suzuki. "On the unconditional convergence of wavelet expansions for continuous functions." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 01 (January 2016): 1650007. http://dx.doi.org/10.1142/s0219691316500077.

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In this paper, we study the unconditional convergence of wavelet expansions with Lipschitz wavelets. Especially with the Strömberg wavelet, we shall construct a counter example which shows that uniformly convergent wavelet expansions even for continuous functions do not always converge unconditionally in [Formula: see text].

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41

Hemker, Pieter W., Gregorii I. Shishkin, and Lidia P. Shishkin. "Novel Defect-correction High-order, in Space and Time, Accurate Schemes for Parabolic Singularly Perturbed Convection-diffusion Problems." Computational Methods in Applied Mathematics 3, no. 3 (2003): 387–404. http://dx.doi.org/10.2478/cmam-2003-0025.

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AbstractNew high-order accurate finite difference schemes based on defect correction are considered for an initial boundary-value problem on an interval for singularly perturbed parabolic PDEs with convection; the highest space derivative in the equation is multiplied by the perturbation parameter ε. Solutions of the well-known classical numerical schemes for such problems do not converge ε-uniformly (the errors of such schemes depend on the value of the parameter ε and are comparable with the solution itself for small values of ε). The convergence order of the existing ε-uniformly convergent schemes does not exceed 1 in space and time. In this paper, using a defect correction technique, we construct a special difference scheme that converges ε-uniformly with the second (up to a logarithmic factor) order of accuracy with respect to x and with the second order of accuracy and higher with respect to t.

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42

Magri, Giorgio. "Convergence of error-driven ranking algorithms." Phonology 29, no. 2 (August 2012): 213–69. http://dx.doi.org/10.1017/s0952675712000127.

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AbstractAccording to the OT error-driven ranking model of language acquisition, the learner performs a sequence of slight re-rankings triggered by mistakes on the incoming stream of data, until it converges to a ranking that makes no more mistakes. Two classical examples are Tesar & Smolensky's (1998) Error-Driven Constraint Demotion (EDCD) and Boersma's (1998) Gradual Learning Algorithm (GLA). Yet EDCD only performs constraint demotion, and is thus shown to predict a ranking dynamics which is too simple from a modelling perspective. The GLA performs constraint promotion too, but has been shown not to converge. This paper develops a complete theory of convergence of error-driven ranking algorithms that perform both constraint demotion and promotion. In particular, it shows that convergent constraint promotion can be achieved (with an error-bound that compares well to that of EDCD) through a proper calibration of the amount by which constraints are promoted.

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43

Diewald, Gabriele, and Katerina Stathi. "Two distinct sources – one target." Functions of Language 26, no. 2 (August 2, 2019): 177–215. http://dx.doi.org/10.1075/fol.15062.sta.

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Abstract Cross-linguistic diachronic studies have focused on the parallel or divergent development of cognate or functionally equivalent items. This paper traces the diachronic convergent development of two unrelated items by means of a case study, the development of the German verb scheinen ‘shine, emit light’ and English seem ‘(originally) befit, beseem’. Despite their different source meanings, the two verbs have grammaticalized into evidential markers, as is evidenced by the constructions scheinen + zu + infinitive and seem + to + infinitive. We use historical corpus data to show that the two verbs have converged both semantically and syntactically. Semantically the verbs converge when they acquire the sense ‘appear, become visible’, a well-known source of evidentials. Syntactically, scheinen and seem come to occur in the same range of constructional patterns. This development is more advanced in English, so that it is ahead of German by at least four centuries.

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van Ginkel, Bart, and Frank Redig. "Hydrodynamic Limit of the Symmetric Exclusion Process on a Compact Riemannian Manifold." Journal of Statistical Physics 178, no. 1 (November 11, 2019): 75–116. http://dx.doi.org/10.1007/s10955-019-02420-2.

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Abstract We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these random grids converge to Brownian motion on the manifold. We then consider the empirical density field of the symmetric exclusion process and prove that it converges to the solution of the heat equation on the manifold.

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Cesari, Francesca. "Signalling and transport converge." Nature Reviews Molecular Cell Biology 9, no. 4 (April 2008): 265. http://dx.doi.org/10.1038/nrm2386.

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Antzoulatos, Angelos A., Ekaterini Panopoulou, and Chris Tsoumas. "Do Financial Systems Converge?" Review of International Economics 19, no. 1 (January 18, 2011): 122–36. http://dx.doi.org/10.1111/j.1467-9396.2010.00936.x.

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Knights, M. "The urge to converge." Engineering & Technology 5, no. 14 (September 25, 2010): 48–51. http://dx.doi.org/10.1049/et.2010.1412.

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Whiteman, Noah K., and Kailen A. Mooney. "Insects converge on resistance." Nature 489, no. 7416 (September 2012): 376–77. http://dx.doi.org/10.1038/489376a.

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Roeder, John L. "Discrepant cosmic ages converge." Physics Teacher 36, no. 1 (January 1998): 49. http://dx.doi.org/10.1119/1.1539793.

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RABER, LINDA. "CHEMISTS CONVERGE IN ATLANTA." Chemical & Engineering News 84, no. 14 (April 3, 2006): 11. http://dx.doi.org/10.1021/cen-v084n014.p011.

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