Relevant bibliographies by topics / Markov numbers

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Markov numbers'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Markov numbers"

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Karpenkov, Oleg, and Matty van Son. "Generalised Markov numbers." Journal of Number Theory 213 (August 2020): 16–66. http://dx.doi.org/10.1016/j.jnt.2020.01.010.

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Hoare, Graham T. Q. "102.37 Markov numbers." Mathematical Gazette 102, no. 555 (2018): 494–96. http://dx.doi.org/10.1017/mag.2018.117.

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CRIPPA, D., K. SIMON, and P. TRUNZ. "Markov Processes Involving q-Stirling Numbers." Combinatorics, Probability and Computing 6, no. 2 (1997): 165–78. http://dx.doi.org/10.1017/s0963548397002964.

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In this paper we consider the Markov process defined byP1,1=1, Pn,[lscr ]=(1−λn,[lscr ]) ·Pn−1,[lscr ] +λn,[lscr ]−1 ·Pn−1,[lscr ]−1for transition probabilities λn,[lscr ]=q[lscr ] and λn,[lscr ]=qn−1. We give closed forms for the distributions and the moments of the underlying random variables. Thereby we observe that the distributions can be easily described in terms of q-Stirling numbers of the second kind. Their occurrence in a purely time dependent Markov process allows a natural approximation for these numbers through the normal distribution. We also show that these Markov processes desc
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Kirkland, Stephen J., Michael Neumann, and Nung-Sing Sze. "On optimal condition numbers for Markov chains." Numerische Mathematik 110, no. 4 (2008): 521–37. http://dx.doi.org/10.1007/s00211-008-0172-8.

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Huang, Huilin, and Weiguo Yang. "Limit theorems for asymptotic circular mth-order Markov chains indexed by an m-rooted homogeneous tree." Filomat 33, no. 6 (2019): 1817–32. http://dx.doi.org/10.2298/fil1906817h.

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In this paper, we give the definition of an asymptotic circularmth-order Markov chain indexed by an m rooted homogeneous tree. By applying the limit property for a sequence of multi-variables functions of a nonhomogeneous Markov chain indexed by such tree, we estabish the strong law of large numbers and the asymptotic equipartition property (AEP) for asymptotic circular mth-order finite Markov chains indexed by this homogeneous tree. As a corollary, we can obtain the strong law of large numbers and AEP about the mth-order finite nonhomogeneous Markov chain indexed by the m rooted homogeneous t
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Madritsch, Manfred G. "Non-normal numbers with respect to Markov partitions." Discrete and Continuous Dynamical Systems 34, no. 2 (2013): 663–76. http://dx.doi.org/10.3934/dcds.2014.34.663.

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Sorrentino, A., та A. P. Veselov. "Markov numbers, Mather’s β function and stable norm". Nonlinearity 32, № 6 (2019): 2147–56. http://dx.doi.org/10.1088/1361-6544/ab047d.

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Rudakov, A. N. "THE MARKOV NUMBERS AND EXCEPTIONAL BUNDLES ON P²." Mathematics of the USSR-Izvestiya 32, no. 1 (1989): 99–112. http://dx.doi.org/10.1070/im1989v032n01abeh000738.

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Rabideau, Michelle, and Ralf Schiffler. "Continued fractions and orderings on the Markov numbers." Advances in Mathematics 370 (August 2020): 107231. http://dx.doi.org/10.1016/j.aim.2020.107231.

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Huang, Huilin. "Strong Law of Large Numbers for Hidden Markov Chains Indexed by Cayley Trees." ISRN Probability and Statistics 2012 (September 23, 2012): 1–11. http://dx.doi.org/10.5402/2012/768657.

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We extend the idea of hidden Markov chains on lines to the situation of hidden Markov chains indexed by Cayley trees. Then, we study the strong law of large numbers for hidden Markov chains indexed by Cayley trees. As a corollary, we get the strong limit law of the conditional sample entropy rate.
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Dissertations / Theses on the topic "Markov numbers"

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Spalding, Kathryn. "Growth and integrability in multi-valued dynamics." Thesis, Loughborough University, 2018. https://dspace.lboro.ac.uk/2134/33483.

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This thesis is focused on the problem of growth and integrability in multi-valued dynamics generated by $SL_2 (\mathbb{Z})$ actions. An important example is given by Markov dynamics on the cubic surface $$x^2+ y^2 +z^2 = 3xyz,$$ generating all the integer solutions of this celebrated Diophantine equation, known as Markov triples. To study the growth problem of Markov numbers we use the binary tree representation. This allows us to define the Lyapunov exponents $\Lambda (x)$ as the function of the paths on this tree, labelled by $x \in \mathbb{R}P^1$. We prove that $\Lambda (x)$ is a $PGL_2 (\m
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Šindelková, Petra. "Fuzzy Markovovy řetězce a jejich využití v řízení rizik." Master's thesis, Vysoké učení technické v Brně. Ústav soudního inženýrství, 2015. http://www.nusl.cz/ntk/nusl-233171.

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This thesis deals with the application of Markov chains for the production of concrete products. The theoretical part is focused on clarifying the concepts of risk management and describes the procedures for dealing with classical Markov chains. There are presented basics of fuzzy logic and finally there is explained the procedure using fuzzy logic in calculating of classical Markov chains in the subsection entitled Fuzzy Markov chains. The practical part describes production process, namely concrete pavements. On this production process is applied knowledge from the theoretical part and there
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Blaha, Rebecca. "Hearing aid telecoils : current numbers in the U.S. market /." Connect to resource, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1129571996.

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Thesis (M.A.)--Ohio State University, 2004.<br>Advisor: Stephanie Davidson, Dept. of Speech and Hearing Science. Includes bibliographical references (leaves 34-37). Available online via OhioLINK's ETD Center
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Zhang, Yunyu. "Hidden Markov Model inference copy number change in array-CGH data." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33086.

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Thesis (S.M.)--Harvard-MIT Division of Health Sciences and Technology, 2005.<br>Includes bibliographical references (p. 56-57).<br>Cancer development and progression typically features genomic instability frequently resulting in genomic changes involving DNA copy number gains or losses. Identifying the genomic location of these regional alterations provides important opportunities for the discovery of potential novel oncogenes and tumor suppressors. Recently, array based competitive genomic hybridization (array-CGH) has become available as a powerful approach for genome-wide detection of DNA c
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Sögner, Leopold. "Selection of the number of states by birth-death processes." SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 2000. http://epub.wu.ac.at/200/1/document.pdf.

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In this article we use spatial birth-death processes to estimate the number of states k of a switching model. Following Preston (1976) and Stephens (1998) matching the detailed balance condition for the underlying birth-death process results in an unique invariant probability measure with the corresponding stationary distribution of the number of states. This concept could be easily integrated to Bayesian sampling to derive the marginal posterior distribution of the number of states within the sampling procedure. We apply this technique to simulated AR(1)data and to quarterly Austrian data on
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Suwardi, Eko. "Exploring the relationship between market values and accounting numbers of firms listed in an emerging market." Queensland University of Technology, 2004. http://eprints.qut.edu.au/15986/.

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Studies of the relationship between market values and accounting numbers have long been a part of an established theme in capital markets research (CMR). These studies have taken various forms, most being conducted on a cross sectional basis, tied closely with the assumptions of equilibrium behaviour and efficient markets. Explanatory variables for market value have been dominated by firm-specific variables without incorporating macroeconomic variables. Recently, however, some studies have employed macroeconomic variables and dynamic specification in assessing the relationship between market
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Yahya, Bokhari. "Discovering driver somatic mutations, copy number alterations and methylation changes using Markov Chain Monte Carlo." VCU Scholars Compass, 2013. http://scholarscompass.vcu.edu/etd/3266.

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Nowadays we have tremendous amount of genetic data needing to be interpreted. Somatic mutations, copy number variations and methylation are example of the genetics data we are dealing with. Discovering driver mutations from these combined data types is challenging. Mutations are unpredictable and have broad heterogeneity, which makes our goal hard to accomplish. Many methods have been proposed to solve the mystery of genetics of cancer. In this project we manipulate those above mentioned genetics data types and choose to use and modified an existing method utilizing Markov Chain Monte Carlo (M
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McGillivray, Annaliza. "A penalized quasi-likelihood approach for estimating the number of states in a hidden markov model." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=110634.

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In statistical applications of hidden Markov models (HMMs), one may have no knowledge of the number of hidden states (or order) of the model needed to be able to accurately represent the underlying process of the data. The problem of estimating the number of states of the HMM is thus a task of major importance. We begin with a literature review of the major developments in the problem of order estimation for HMMs. We then propose a new penalized quasi-likelihood method for estimating the number of hidden states, which makes use of the fact that the marginal distribution of the HMM observations
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Mujumdar, Monali. "Estimation of the number of syllables using hidden Markov models and design of a dysarthria classifier using global statistics of speech." Laramie, Wyo. : University of Wyoming, 2006. http://proquest.umi.com/pqdweb?did=1283963331&sid=6&Fmt=2&clientId=18949&RQT=309&VName=PQD.

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Clout, Victoria Jane. "Investigating the relationship between market values and accounting numbers for 30 selected Australian listed companies." Queensland University of Technology, 2007. http://eprints.qut.edu.au/16515/.

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In capital market research (CMR) studies of the value relevance of accounting numbers are founded upon the concept that, in equilibrium, the book values are equal to or have some long-term relationship with the market value and that market returns are related to book returns. This thesis seeks to resolve a gap in the CMR by examining 30 selected individual firms listed on the Australian stock market during the period 1950 to 2004, using equilibrium correction modelling techniques. Even these limited prior works used cross-sectional techniques rather than the long-run, time-series, analysis
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Books on the topic "Markov numbers"

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Benjamin, Arthur. Discrete mathematics. The Teaching Company, 2009.

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Jerrum, Mark. A very simple algorithm for estimating the numberof k-colourings of a low-degree graph. LFCS, Dept. of Computer Science, University of Edinburgh, 1994.

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The trading game: Playing by the numbers to make millions. Wiley, 1999.

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Cooney, Kieran V. Sophisticated or naive: How efficient is the Irish equity market in it's interpretation of accounting numbers? University College Dublin, 1993.

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Morrison Institute for Public Policy. How Arizona compares: Real numbers and hot topics. Morrison Institute for Public Policy, School of Public Affairs, College of Public Programs, Arizona State University, 2005.

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Oyen, Renate. Schlagwortliste Arbeitsmarkt, Beruf und Berufsbildung: Arbeitsgrundlage für die Dokumentationsdatenbanken des Instituts für Arbeitsmarkt- und Berufsforschung und des Bundesinstituts für Berufsbildung. 2nd ed. Institut für Arbeitsmarkt- und Berufsforschung der Bundesanstalt für Arbeit (IAB), 2003.

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Oyen, Renate. Schlagwortliste Arbeitsmarkt und Beruf. Institut für Arbeitsmarkt- und Berufsforschung der Bundesanstalt für Arbeit, 1988.

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Oyen, Renate. Schlagwortliste Arbeitsmarkt und Beruf. Institut für Arbeitsmarkt- und Berufsforschung der Bundesanstalt für Arbeit, 1990.

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Koli︠a︡da, S. F. Dynamics and numbers: A special program, June 1-July 31, 2014, Max Planck Institute for Mathematics, Bonn, Germany : international conference, July 21-25, 2014, Max Planck Institute for Mathematics, Bonn, Germany. Edited by Max-Planck-Institut für Mathematik. American Mathematical Society, 2016.

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Trade What You See: How To Profit from Pattern Recognition (Wiley Trading). Wiley, 2007.

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Book chapters on the topic "Markov numbers"

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Krieger, Wolfgang. "On Subshifts and Topological Markov Chains." In Numbers, Information and Complexity. Springer US, 2000. http://dx.doi.org/10.1007/978-1-4757-6048-4_38.

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Geist, Robert, and Robert Reynolds. "The Most Likely Steady State for Large Numbers of Stochastic Traveling Salesmen." In Numerical Solution of Markov Chains. CRC Press, 2021. http://dx.doi.org/10.1201/9781003210160-28.

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Hertling, Peter. "A Banach-Mazur Computable But Not Markov Computable Function on the Computable Real Numbers." In Automata, Languages and Programming. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45465-9_82.

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Walrand, Jean. "PageRank: B." In Probability in Electrical Engineering and Computer Science. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-49995-2_2.

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AbstractIn this chapter, we take a second look at the concepts that we introduced in PageRank-A. The main ideas concern the long-term behavior of Markov chains and, in particular, the significance of the invariant distribution. As explained in the Introduction, part B of each chapter can be omitted in an introductory course.Section 2.1 discusses the sample space of a Markov chain: the outcomes and their probability. Section 2.2 explains the meaning of the weak and strong laws of large numbers. Section 2.3 proves these results for independent and identically distributed random variables. Section 2.4 proves the strong law of large numbers for Markov chains. Section 2.5 concludes the chapter by proving the Big Theorem for Markov chains.
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Hirano, Katuomi, Sigeo Aki, and Masayuki Uchida. "Distributions of Numbers of Success-Runs Until the First Consecutive k Successes in Higher Order Markov Dependent Trials." In Advances in Combinatorial Methods and Applications to Probability and Statistics. Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-4140-9_23.

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Joffe, A., and W. A. O’N Waugh. "Exact distribution of kin number in multitype Galton-Watson process." In Semi-Markov Models. Springer US, 1986. http://dx.doi.org/10.1007/978-1-4899-0574-1_22.

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Anatassova, Vassia K., and J. C. Turner. "On Triangles and Squares Marked with Goldpoints—Studies of Golden Tiles." In Applications of Fibonacci Numbers. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4271-7_2.

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Boyd, David. "Best Approximation of Real Numbers by Pisot Numbers." In Number Theory with an Emphasis on the Markoff Spectrum. CRC Press, 2017. http://dx.doi.org/10.4324/9780203747018-3.

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Koralov, Leonid, and Yakov G. Sinai. "Markov Chains with a Finite Number of States." In Theory of Probability and Random Processes. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-540-68829-7_5.

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Schmidt, Klaus D. "The Claim Number Process as a Markov Process." In Teubner Skripten zur Mathematischen Stochastik. Vieweg+Teubner Verlag, 1996. http://dx.doi.org/10.1007/978-3-322-90570-3_4.

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Conference papers on the topic "Markov numbers"

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Novitasari, Dian Candra Rini, Nurul Ardhiyah, and Nanang Widodo. "Flare Identification by Forecasting Sunspot Numbers Using Fuzzy Time Series Markov Chain Model." In 2019 International Seminar on Intelligent Technology and Its Applications (ISITIA). IEEE, 2019. http://dx.doi.org/10.1109/isitia.2019.8937242.

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Shaohua, Jin, Zhong Yanyan, Wan Yanping, and Chen Xiuyin. "A Strong Law of Large Numbers for Markov Chain Fields on a Special Non-homogeneous Tree." In 2009 International Conference on Computational Intelligence and Natural Computing (CINC). IEEE, 2009. http://dx.doi.org/10.1109/cinc.2009.103.

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Sivaramakrishnan, Jayaram, and Gareth Lee. "Application of a Hidden Markov Model for consistency checking of process plant facility tag numbers: A case study." In 2018 5th International Conference on Industrial Engineering and Applications (ICIEA). IEEE, 2018. http://dx.doi.org/10.1109/iea.2018.8387117.

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Czapla, Dawid, Katarzyna Horbacz, and Hanna Wojewódka. "The strong law of large numbers for certain piecewise-deterministic Markov processes with application to a gene expression model." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5044078.

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Alvin, Kenneth F., and Lee D. Peterson. "Determination of Modal Residues and Residual Flexibility for Time-Domain System Realization." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0667.

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Abstract A linear least-squares procedure for the determination of modal residues using time-domain system realization theory is presented. The present procedure is shown to be theoretically equivalent to residue determination in realization algorithms such as the Eigen-system Realization Algorithm (ERA) and Q-Markov COVER. However, isolating the optimal residue estimation problem from the general realization problem affords several advantages over standard realization algorithms for structural dynamics identification. Primary among these are the ability to identify data sets with large number
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Chrigui, M., A. Sadiki, J. Gounder, and A. Masri. "Numerical and Experimental Study of Polydispersed Acetone Spray Dispersion and Evaporation in Turbulent Flow." In ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/gt2011-46301.

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Characteristics of acetone spray in a turbulent flow were numerically predicted and compared to experimental measurements. The focus was on the effect of polydispersity on the dispersion and evaporation of a relatively volatile fuel that featured a wide range of Stokes numbers in a turbulent two phase flow. Droplets were generated using an ultrasonic atomizer. It produced a relatively uniform velocity distribution with a moderate carrier to fuel velocities ratio. The simulations were performed in the framework of Reynolds Averaging Navier Stokes equations along with the Eulerian-Lagrangian app
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Johnson, Derek, Marc Besch, Robert Heltzel, and Sashank Jammalamadaka. "Effects of Fuel Quality on Gaseous Emissions From an 8.9L Spark-Ignited Natural Gas Engine Operated Over Prime-Mover Cycles for Unconventional Well Development." In ASME 2017 Internal Combustion Engine Division Fall Technical Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icef2017-3556.

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Technology developments in directional drilling and hydraulic fracturing have led to increased natural gas reserves. Development of these unconventional resources is an energy intensive process. Prime-movers of unconventional well development were previously identified to be over-the-road trucks, drilling engines, and hydraulic stimulation engines. Diesel engines dominate these markets but industry is attempting to cut costs by using dual fuel and dedicated natural gas engines. On-road engines are subject to the transient FTP cycle for certification and off-road engines are subject to the 5-mo
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Zhou, Hui. "The Effect of Number Portability on Telecommunication Market." In 2008 4th International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM). IEEE, 2008. http://dx.doi.org/10.1109/wicom.2008.2054.

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Yang Zhao. "The optimization method of Markov chain usage model based on three-parameter interval number." In 2015 IEEE International Conference on Grey Systems and Intelligent Services (GSIS). IEEE, 2015. http://dx.doi.org/10.1109/gsis.2015.7301913.

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Huang, You-lan, and Yan Yu. "The influence of number portability commercialization on telecommunication market." In 2013 International Conference of Information Science and Management Engineering. WIT Press, 2013. http://dx.doi.org/10.2495/isme130381.

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Reports on the topic "Markov numbers"

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Chassamboulli, Andri, and Giovanni Peri. The Labor Market Effects of Reducing the Number of Illegal Immigrants. National Bureau of Economic Research, 2014. http://dx.doi.org/10.3386/w19932.

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Tschoppa, Daniel, Zhiyong Tianb, Magdalena Berberichc, Jianhua Fand, Bengt Perersd, and Simon Furbo. LSEVIER paper: Large Scale Solar Thermal Systems in Leading Countries. IEA SHC Task 55, 2020. http://dx.doi.org/10.18777/ieashc-task55-2020-0001.

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Large-scale solar thermal systems are a cost-efficient technology to provide renewable heat. The rapid market growth in the last decade has been concentrated on a small number of countries, with the outstanding position of Denmark followed by China, Germany and Austria. This paper provides a comprehensive overview of the market and common technological solutions for large-scale solar thermal systems in these countries.
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Rincón-Torres, Andrey Duván, Kimberly Rojas-Silva, and Juan Manuel Julio-Román. The Interdependence of FX and Treasury Bonds Markets: The Case of Colombia. Banco de la República, 2021. http://dx.doi.org/10.32468/be.1171.

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We study the interdependence of FX and Treasury Bonds (TES) markets in Colombia. To do this, we estimate a heteroskedasticity identified VAR model on the returns of the COP/USD exchange rate (TRM) and bond prices, as well as event-analysis models for return volatilities, number of quotes, quote volume, and bid/ask spreads. The data under analysis consists of 5-minute intraday bid/ask US dollar prices and bond quotes, for an assortment of bond species. For these species we also have the number of bid/ask quotes as well as their volume. We found, also, that the exchange rate conveys information
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Resch, Alois. 2020 Subsidies for PVT collectors in selected countries. IEA SHC Task 60, 2020. http://dx.doi.org/10.18777/ieashc-task60-2020-0005.

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Report D6: PVT collectors can be still considered as young technology, but with significant growing tendency in terms of market development and number of manufacturers on a worldwide point of view. Nevertheless, PVT is definitely in an early stage of its product life cycle, where economic competitiveness among other renewable technologies providing heat and electricity is challenging.
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Gasparotto, Thatyanne, and Julia Ambrosano. Opportunities for Sustainable Infrastructure Investments at City Level in Brazil. Inter-American Development Bank, 2020. http://dx.doi.org/10.18235/0002639.

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This policy brief was developed in order to identify preliminary green /sustainable infrastructure opportunities for cities in Brazil. The rapidly growing green bond market can help local authorities to attract new sources of capital for financing subnational infrastructure. Water and sanitation, waste to energy and urban mobility were the sectors selected for an inicial assessment, given the investment needs in Brazilian municipalities and their alignment with low carbon development and resilience. This brief was also used to raise awareness across key infrastructure stakeholders in Brazil, a
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Enfield, Sue. Covid-19 Impact on Employment and Skills for the Labour Market. Institute of Development Studies (IDS), 2021. http://dx.doi.org/10.19088/k4d.2021.081.

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This literature review draws from academic and grey literature, published largely as institutional reports and blogs. Most information found considered global impacts on employment and the labour market with the particular impact for the very high numbers of youth, women, migrant workers, and people with disabilities who are more likely to be employed in the informal sector. There has been a high negative impact on the informal sector and for precariously employed groups. The informal labour market is largest in low and middle-income countries and engages 2 billion workers (62 percent) of the
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Ayala-García, Jhorland, and Sandy Dall’Erba. The impact of preemptive investment on natural disasters. Banco de la República, 2021. http://dx.doi.org/10.32468/dtseru.301.

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Extreme rainfall events are expected to become more frequent and more intense in the future. Because their mitigation is a challenge and their cost to human life is large, this paper studies the impact of preemptive investment against natural disasters on the future occurrence of landslides and the losses associated with it. Based on a panel of 746 Colombian municipalities with medium and high risk of landslides and an instrumental variable approach, we find that preemptive public investment can reduce the number of landslides, the number of people who die, are injured, or disappear after a la
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Altantuya, Jigjidsuren,, Oyun Bayar, and Habib Najibullah. Rationalizing Mongolia’s Hospital Services: Experiences, Lessons Learned, and Future Directions. Asian Development Bank, 2021. http://dx.doi.org/10.22617/wps210305-2.

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Before the 1990s, Mongolia had a health care system that largely depended on hospital-based services. The country’s hospital sector was characterized by the extensive use of an excessive number of acute beds, a large number of medically unjustified admissions, and lengthy hospital stays. In the early 1990s, the Government of Mongolia started socioeconomic reforms as part of the transition to a market economy. It requested the Asian Development Bank (ADB) to support health sector reforms in the country. This paper describes the hospital sector in Mongolia along with the reforms and results achi
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Strachan, Anna Louise. Potential Private Sector Involvement in Supporting Refugee Livelihoods and Self-reliance in Uganda: Annotated Bibliography. Institute of Development Studies (IDS), 2021. http://dx.doi.org/10.19088/k4d.2021.072.

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There is some evidence of the private sector playing a role in supporting refugee livelihoods and self-reliance in Uganda during the period 2016-2020. However, a number of evaluations and research reports highlight the potential for greater private sector involvement, if existing constraints are addressed. Key lessons identified in the literature include the need for more research, especially on market potential, to address the existing knowledge gaps on the role the private sector can play in supporting refugee livelihoods and self-reliance in Uganda. The literature notes that limited access
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Nolan, Brian, Brenda Gannon, Richard Layte, Dorothy Watson, Christopher T. Whelan, and James Williams. Monitoring Poverty Trends in Ireland: Results from the 2000 Living in Ireland survey. ESRI, 2002. http://dx.doi.org/10.26504/prs45.

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This study is the latest in a series monitoring the evolution of poverty, based on data gathered by The ESRI in the Living in Ireland Surveys since 1994. These have allowed progress towards achieving the targets set out in the National Anti Poverty Strategy since 1997 to be assessed. The present study provides an updated picture using results from the 2000 round of the Living in Ireland survey. The numbers interviewed in the 2000 Living in Ireland survey were enhanced substantially, to compensate for attrition in the panel survey since it commenced in 1994. Individual interviews were conducted
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