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Relevant bibliographies by topics / Two Numbers

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Academic literature on the topic 'Two Numbers'

Author: Grafiati

Published: 5 June 2025

Last updated: 24 June 2025

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Journal articles on the topic "Two Numbers"

1

Adédji, Kouèssi Norbert, Japhet Odjoumani, and Alain Togbé. "Padovan and Perrin numbers as products of two generalized Lucas numbers." Archivum Mathematicum, no. 4 (2023): 315–37. http://dx.doi.org/10.5817/am2023-4-315.

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Finney, David J. "On Comparing Two Numbers." Teaching Statistics 29, no. 1 (2007): 17–20. http://dx.doi.org/10.1111/j.1467-9639.2007.00251.x.

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Shen, Jian. "On two Turán Numbers." Journal of Graph Theory 51, no. 3 (2006): 244–50. http://dx.doi.org/10.1002/jgt.20141.

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BuxDPI, BNYuldashev. "PROBLEMS OF FINDING THESE NUMBERS ACCORDING TO THE SUM (OR DIFFERENCE) AND MULTIPLE RATIO OF TWO NUMBERS." European International Journal of Pedagogics 4, no. 12 (2024): 65–70. https://doi.org/10.55640/eijp-04-12-13.

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Xu, Aimin. "Ramanujan’s Harmonic Number Expansion and Two Identities for Bernoulli Numbers." Results in Mathematics 72, no. 4 (2017): 1857–64. http://dx.doi.org/10.1007/s00025-017-0748-7.

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Honwei, Shi, Mi Zhou, Zhang Delong, Jiang Xingyi, and He Songting. "Even numbers are the sum of two prime numbers." Greener Journal of Science, Engineering and Technological Research 9, no. 1 (2019): 8–11. http://dx.doi.org/10.15580/gjsetr.2019.1.040919068.

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Luca, Florian, Japhet Odjoumani, and Alain Togbé. "Tribonacci Numbers That Are Products of Two Fibonacci Numbers." Fibonacci Quarterly 61, no. 4 (2023): 298–304. http://dx.doi.org/10.1080/00150517.2023.12427384.

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Ddamulira, Mahadi, Florian Luca, and Mihaja Rakotomalala. "Fibonacci Numbers which are Products of two Pell Numbers." Fibonacci Quarterly 54, no. 1 (2016): 11–18. http://dx.doi.org/10.1080/00150517.2016.12427833.

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Murat, Alan. "Mersenne numbers as a difference of two Lucas numbers." Commentationes Mathematicae Universitatis Carolinae 63, no. 3 (2023): 269–76. http://dx.doi.org/10.14712/1213-7243.2022.027.

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Daşdemir, Ahmet, and Mehmet Varol. "Lucas Numbers Which Are Products of Two Pell Numbers." Fibonacci Quarterly 63, no. 1 (2025): 78–83. https://doi.org/10.1080/00150517.2024.2412958.

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Dissertations / Theses on the topic "Two Numbers"

1

McNamara, James N. "Two new Ramsey numbers /." Online version of thesis, 1992. http://hdl.handle.net/1850/11146.

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Lin, Wensong. "Circular chromatic numbers and distance two labelling numbers of graphs." HKBU Institutional Repository, 2004. http://repository.hkbu.edu.hk/etd_ra/591.

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Kong, Yafang, and 孔亚方. "On linear equations in primes and powers of two." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50533769.

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It is known that the binary Goldbach problem is one of the open problems on linear equations in primes, and it has the Goldbach-Linnik problem, that is, representation of an even integer in the form of two odd primes and powers of two, as its approximate problem. The theme of my research is on linear equations in primes and powers of two. Precisely, there are two cases: one pair of linear equations in primes and powers of two, and one class of pairs of linear equations in primes and powers of two, in this thesis. In 2002, D.R. Heath-Brown and P.C. Puchta obtained that every sufficiently large even integer is the sum of two odd primes and k powers of two. Here k = 13, or = 7 under the generalized Riemann hypothesis. In 2010, B. Green and T. Tao obtained that every pair of linear equations in four prime variables with coefficients matrix A = (a_ij)s×t with s ≤ t, satisfying nondegenerate condition, that is, A has full rank and the only elements of the row-space of A over Q with two or fewer nonzero entries is the zero vector, is solvable. The restriction on the coefficient matrix means that they excluded the case of the binary Goldbach problem. Motivated by the above results, it is obtained that for every pair of sufficiently large positive even integers B1, B2, the simultaneous equation {█({B1 = p1 + p2 + 2v1 + 2v2 + · · · + 2vk ,@B2 = p3 + p4 + 2v1 + 2v2 + · · · + 2vk ,)┤ (1) is solvable, where p1, · · · , p4 are odd primes, each vi is a positive integer, and the positive integer k ≥ 63 or ≥ 31 under the generalized Riemann hypothesis. Note that, in 1989, M.C. Liu and K.M. Tsang have obtained that subject to some natural conditions on the coefficients, every pair of linear equations in five prime variables is solvable. Therefore one class of pairs of linear equations in four prime variables with special coefficient matrix and powers of two is considered. Indeed, it is deduced that every pair of integers B1 and B2 satisfying B1 ≡ 0 (mod 2), 3BB1 > e^(eB^48 ), B2 ≡ ∑_1^4▒= 1^(a_i ) (mod 2) and |B2| < BB1, where B = max1≤j≤4(2, |aj|), can be represented as {█(B1 = 〖p1〗_1 + p2 + 2^(v_1 ) + 2^(v_2 )+ · · · + 2^(v_k )@B2 = a1p1 + a2p2 + a3p3 + a4p4 + 2^(v_1 )+ 2^(v_2 )+ · · · + 2^(v_k ) )┤ (2) with k being a positive integer. Here p1, · · · p4 are odd primes, each 〖v 〗_iis a positive integer and the integral coefficients ai (i = 1, 2, 3, 4) satisfy {█((〖a 〗_1- 〖a 〗_2, 〖a 〗_3, 〖a 〗_4) = 1,@〖a 〗_1 〖a 〗_2< 0, 〖a 〗_3 〖a 〗_4<0,)┤ Moreover it is calculated that the positive integer k ≥ g(〖a 〗_1- 〖a 〗_2, 〖a 〗_3, 〖a 〗_4) where g(〖a 〗_21- 〖a 〗_22, 〖a 〗_23, 〖a 〗_24) = [(log⁡〖G(〖a 〗_21, …, 〖a 〗_24 〗)-log⁡〖F (〖a 〗_21, …, 〖a 〗_24)〗)/log0.975805-84.0285], (3) G(〖a 〗_21, 〖a 〗_22, 〖a 〗_23, 〖a 〗_24) = (min(1/(|a_24 |), 1/(|a_23 |)) - (〖|a〗_(21 )- a_22 |)/(|〖a_23 a〗_24 |) 〖(3B)〗^(-1) ×〖(3B)〗^(-1) (1-0.000001)- 〖(3B)〗^(-1-4), with B = max1≤j≤4(2, |a2j|), and F(a_21, …, a_24) = √(f(a_21)f〖(a〗_22 )) with f(a_2i) = {█(4414.15h (a_21-1)+5.088331 if a_21≠1@59.8411 if a_21=1,)┤ for i = 1, 2, and h(n) =∏_(p|n,p>2)▒(p-1)/(p-2). This result, if without the powers of two, can make up some of the cases excluded in Green and Tao’s paper.<br>published_or_final_version<br>Mathematics<br>Doctoral<br>Doctor of Philosophy

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Armulik, Villem-Adolf. "Ramsey Numbers and Two-colorings ofComplete Graphs." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-44610.

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Ramsey theory has to do with order within disorder. This thesis studies two Ramsey numbers, R(3; 3) and R(3; 4), to see if they can provide insight into finding larger Ramsey numbers. The numbers are studied with the help of computer programs. In the second part of the thesis we try to create a coloring of K45 which lacks monochromatic K5 and where each vertex has an equal degree for both color of edges. The results from studying R(3; 3) and R(3; 4) fail to give any further insight into larger Ramsey numbers. Every coloring of K45 we produce contains a monochromatic K5.

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Coward, Daniel R. "Sums of two rational cubes." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320587.

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Fernandez, Manuel Franco. "Local root numbers of two-dimensional symplectic representations." Thesis, University of Southampton, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.432725.

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Djang, Claire. "Two-Coloring Cycles In Complete Graphs." Oberlin College Honors Theses / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1370618319.

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Han, Sang-Geun. "Two applications of p-adic L-functions /." The Ohio State University, 1987. http://rave.ohiolink.edu/etdc/view?acc_num=osu148733154171079.

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Straw, N. A. "Resource limitation and competition in two tephritid flies attacking the flowerheads of lesser burdock (Arctium minus)." Thesis, University of Cambridge, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384516.

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Stone, Megan Elizabeth, and Megan Elizabeth Stone. "Eigenvalue Densities for the Hermitian Two-Matrix Model and Connections to Hurwitz Numbers." Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/626370.

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This dissertation investigates the limiting distribution of eigenvalues of pairs of matrices (M_1,M_2) belonging to the Hermitian two-matrix model. This model is an example of a larger class of models, "multi-matrix models", which aim to generalize the Hermitian one-matrix model. The interaction between matrices in multi-matrix models makes the analysis of the eigenvalue distributions more difficult than those for the one-matrix model. This dissertation makes use of a recent result which connects the interaction term for the two-matrix model to a combinatorial geometry problem. In particular, the interaction term is written as the Harish-Chandra-Itzykson-Zuber integral, which is expanded in a neighborhood of \tau=0, where \tau is the coupling constant appearing in the interaction term. The expansion involves monotone double Hurwitz numbers, which count a collection of ramified coverings of the two-sphere. Using this expansion, and its connection to monotone double Hurwitz numbers, this dissertation purports to describe a variational problem which describes the joint eigenvalue densities for the two-matrix model up to order \tau^2.

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Books on the topic "Two Numbers"

1

Nunn, Daniel. Numbers in English: One, two, three... Heinemann Library, 2012.

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2

Kinney, Gilbert Ford. Primes: The first two thousand four hundred prime numbers. Naval Postgraduate School, 1990.

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3

Micklethwait, Lucy. I spy two eyes: Numbers in art. Greenwillow Books, 1993.

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4

Steve, Henry, ed. Two enormous elephants: God's wonderful world of numbers. Chariot Books, 1993.

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Williams, B. C. Qualitative research without numbers: Two alternatives for auditing. School ofInformation Systems, University of East Anglia, 1989.

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Neusner, Jacob. Comparative midrash: Sifre to Numbers and Sifre Zutta to Numbers : two rabbinic readings of the Book of Numbers. University Press of America, 2009.

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7

Joselovitz, Ernest. Love by the numbers: A romance in two acts. S. French, 1995.

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8

Page, Donna. Two, three, four: Multiples in African art : essay. L. Kahan Gallery, African Arts, 1987.

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Hicks, R. M. An evaluation of three two-dimensional computational fluid dynamics codes including low Reynolds numbers and transonic Mach numbers. Ames Research Center, 1991.

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Papageorgiou, D. T. The stability of two-dimensional wakes and shear-layers at high Mach numbers. National Aeronautics and Space Administration, Langley Research Center, 1990.

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Book chapters on the topic "Two Numbers"

1

Erdman, Nikolai, Vladimir Mass, and John Freedman. "Two Music Hall Numbers." In A Meeting About Laughter. Routledge, 2021. http://dx.doi.org/10.4324/9781315077413-10.

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Tichy, Robert F. "Two Distribution Problems for Polynomials." In Applications of Fibonacci Numbers. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2058-6_55.

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Ramaré, Olivier. "Sums of two squarefree numbers." In Arithmetical Aspects of the Large Sieve Inequality. Hindustan Book Agency, 2009. http://dx.doi.org/10.1007/978-93-86279-40-8_20.

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Dimovski, Ivan H., and Virginia S. Kiryakova. "Discrete Operational Calculi for Two-sided Sequences." In Applications of Fibonacci Numbers. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2058-6_15.

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Harborth, Heiko, and Lothar Piepmeyer. "Two-Distance Sets and the Golden Ratio." In Applications of Fibonacci Numbers. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2058-6_27.

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Şiar, Zafer. "Lucas Numbers Which are Products of Two Balancing Numbers." In Notes from the International Autumn School on Computational Number Theory. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12558-5_8.

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Long, Calvin, and Shiro Ando. "Two Generalizations of Gould’s Star of David Theorem." In Applications of Fibonacci Numbers. Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3586-3_25.

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Cohn, P. M. "Algebraic function fields in two variables." In Algebraic Numbers and Algebraic Functions. Springer US, 1991. http://dx.doi.org/10.1007/978-1-4899-3444-4_5.

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Holte, Robert, Louis Rosier, Igor Tulchinsky, and Donald Varvel. "Pinwheel scheduling with two distinct numbers." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-51486-4_75.

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Bartz, Jeremiah, Bruce Dearden, Joel Iiams, and Julia Peterson. "Powers of Two as Sums of Two Balancing Numbers." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-52969-6_32.

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Conference papers on the topic "Two Numbers"

1

Agrawal, Anita B., Amar Biswas, Shruti Singh, and Sayan Neogy. "Design of a Floating-Point ALU for Calculating Shortest Distance Between Two Floating Point Numbers." In 2024 4th International Conference on Sustainable Expert Systems (ICSES). IEEE, 2024. https://doi.org/10.1109/icses63445.2024.10763154.

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IZMAILOVA, YULIA, and ILIA K. MARCHEVSKY. "ON MESHLESS LAGRANGIAN VORTEX METHODS FOR TWO-DIMENSIONAL FLOW SIMULATION AT MODERATE AND HIGH REYNOLDS NUMBERS." In BEM/MRM 47. WIT Press, 2024. http://dx.doi.org/10.2495/be470101.

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Gao, Yun'e, and Xuegang Yu. "Two Kinds of Hypercomplex Numbers." In 2010 International Conference on Computing, Control and Industrial Engineering. IEEE, 2010. http://dx.doi.org/10.1109/ccie.2010.222.

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Ehrlichman, Samuel M. T., and Shane G. Henderson. "Comparing two systems: Beyond common random numbers." In 2008 Winter Simulation Conference (WSC). IEEE, 2008. http://dx.doi.org/10.1109/wsc.2008.4736074.

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Banasik, K., D. E. Woodward, and R. Hawkins. "Curve Numbers for Two Agro-Forested Watersheds." In World Environmental and Water Resources Congress 2014. American Society of Civil Engineers, 2014. http://dx.doi.org/10.1061/9780784413548.223.

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Muramatsu, Akinori, and Tatsuo Motohashi. "Two Dimensional Jet at Low Reynolds Numbers." In ASME/JSME 2007 5th Joint Fluids Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/fedsm2007-37221.

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A numerical simulation of two-dimensional jets was carried out using a SOLA method. The two-dimensional jets were discharged from a slit in a wall at Reynolds numbers below 50. The difference between the calculated flow fields and those of the Bickley jet is due to the non-uniformity of the pressure field near the jet exit at the wall. The jet spreads faster than the Bickley jet. The decay of the streamwise velocity on the center line is more rapid than that of the Bickley jet. The streamwise velocity profile is different from that of the Bickley jet, and a reversed flow is generated in the outer part of the jet. The jet develops instability through two processes. First, small fluctuations grow exponentially. Second, vortical motion such as so-called ‘flapping motion’ of the jet develops in the downstream region. The critical Reynolds number, as determined by the growth of an integral of kinetic energy, is approximately 16.5. Integrals of momentum and pressure are calculated on a control surface in order to confirm the momentum conservation law. When the Reynolds number exceeds 20, the generation of fluctuations contributes to streamwise variations in the integrals of momentum and pressure.

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Wang, Bai-Sheng, and Lei Xie. "Operations on Fuzzy Numbers with Two Fuzziness Sources." In 2009 Sixth International Conference on Fuzzy Systems and Knowledge Discovery. IEEE, 2009. http://dx.doi.org/10.1109/fskd.2009.293.

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Kan, Igor D., Nikolay G. Moshchevitin, Jonathan Chaika, Masaaki Amou, and Masanori Katsurada. "On Minkowski diagonal functions for two real numbers." In DIOPHANTINE ANALYSIS AND RELATED FIELDS 2011: DARF - 2011. AIP, 2011. http://dx.doi.org/10.1063/1.3630039.

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Krasnobayev, Victor, Alexandr Kuznetsov, Mykhaylo Bagmut, and Yelyzaveta Kuznetsova. "Design of the Residual Adder of Two Numbers." In 2021 IEEE 8th International Conference on Problems of Infocommunications, Science and Technology (PIC S&T). IEEE, 2021. http://dx.doi.org/10.1109/picst54195.2021.9772132.

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Buchnev, S., and N. Pyshnograev. "SYNTHESIS OF A COMPARATOR OF TWO TWO-BIT NUMBERS WITH THREE OUTPUTS." In CHALLENGING ISSUES IN SYSTEMS MODELING AND PROCESSES. FSBE Institution of Higher Education Voronezh State University of Forestry and Technologies named after G.F. Morozov, 2025. https://doi.org/10.58168/cismp2024_678-681.

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This article considers the process of synthesizing a comparator for comparing two two-bit numbers with three output signals indicating the relationships between the numbers (greater, less, or equal). Truth tables and logical expressions for each function are provided. The structure of the comparator circuit is described, and possible optimization paths through the minimization of logical expressions are proposed.

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Reports on the topic "Two Numbers"

1

Kinney, Gilbert F. Primes: The First Two Thousand Four Hundred Prime Numbers. Defense Technical Information Center, 1990. http://dx.doi.org/10.21236/ada233979.

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Ermak, D. L., and J. S. Nasstrom. A method for generating skewed random numbers using two overlapping uniform distributions. Office of Scientific and Technical Information (OSTI), 1995. http://dx.doi.org/10.2172/32589.

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Townsley, W. Layer Two Tunneling Protocol (L2TP) Internet Assigned Numbers Authority (IANA) Considerations Update. RFC Editor, 2002. http://dx.doi.org/10.17487/rfc3438.

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Sjaardema, G. D. NUMBERS: A collection of utilities for pre- and postprocessing two- and three-dimensional EXODUS finite element models. Office of Scientific and Technical Information (OSTI), 1989. http://dx.doi.org/10.2172/6274525.

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Haering, S., R. Balakrishnan, and R. Kotamarthi. A computational study of turbulent separated flow over a wall-mounted cube at two different Reynolds numbers and incoming velocity profiles. Office of Scientific and Technical Information (OSTI), 2021. http://dx.doi.org/10.2172/1810324.

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El Hamamsy, Laila. Early Marriage and Reproduction in Two Egyptian Villages. Population Council, 1994. http://dx.doi.org/10.31899/pgy1994.1009.

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As noted in this monograph, marriage forms a central element of social life for Egyptians. Marriage in Egypt is nearly universal, and parents invest heavily to establish their children in married life. Once married, couples are faced with social pressures to begin childbearing immediately, a reflection of the high value placed on parenthood and children. But not all marriages begin with the same prospects for stability and satisfaction. This study draws attention to the problems faced by women who marry at very early ages in parts of rural Egypt. Despite a legal minimum age of 16, significant numbers of young girls marry below that age, and many experience social, emotional, and health-related difficulties. This study tells why these young women married early and how that decision affected their later life. The study points to areas where the aspirations of these girls have been clearly thwarted—to go to school, delay marriage, and postpone childbearing until they feel physically and psychologically ready. A related picture emerges of the social and economic forces that propel rural girls into marriage at very young ages. Each of these problems suggest areas for policy attention.

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Holmgren, Amanda, Robert Wilkerson, Rodney Siegel, and Jason Ransom. North Coast and Cascades Network landbird monitoring: Report for the 2022 field season. National Park Service, 2023. http://dx.doi.org/10.36967/2301415.

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The North Coast and Cascades Network (NCCN) continued to implement the Network?s Landbird Monitoring Protocol in 2022, in partnership with The Institute for Bird Populations. The protocol was initially field-tested with data collected from the annual panel only, as part of protocol development during 2005?2006, and has subsequently been implemented fully (including data collection on the annual panel as well as five alternating panels) for the past 15 years (2007?2021), except for 2017 when data collection was temporarily suspended to reallocate resources for a 5-year data synthesis. In 2022, we conducted 1,189 point counts at point count survey stations along 68 transects in the large wilderness parks of the NCCN, including Mount Rainier National Park (MORA), North Cascades National Park Complex (NOCA), and Olympic National Park (OLYM). We also conducted 72 point counts at Lewis and Clark National Historical Park (LEWI), including 36 at Cape Disappointment, 28 at Fort Clatsop, 5 at Sunset Beach, and 3 at Yeon. Across the three large parks, we documented the presence of 130 species and one hybrid, 105 of which were detected during point counts. For 57 species (all species for which we amassed at least 96 point count detections over the period 2005?2022), we present the total number of detections of each species on each park?s annual panel transects during the 2005?2022 field seasons. We caution, however, that these detection totals have not been adjusted for differences in survey effort, observer effects, or potential differences in detectability of birds between years; such adjustments will be made in conjunction with trend analyses in a future multi-year report. The number of bird detections on annual-panel transects across all three large parks decreased by 650 between 2021 and 2022, though the magnitude of change varied among the parks. At both MORA and OLYM detections decreased between 2021 and 2022. When factoring in the number of point counts conducted each year, both parks saw a decrease in the average number of birds per count (a decrease of 9% at MORA and 24% at OLYM). At NOCA there was very little change in the number of detections between 2021 and 2022. A measurable part of the overall decrease in detections across the Network in 2022 was due to a high number of red crossbill detections in 2021, particularly at MORA and OLYM. We detected them in higher numbers in both of these parks than in any of the previous 15 years, but in 2022 our detections dropped to numbers more similar to previous years. Several other species were also detected in slightly lower numbers in the three large parks in 2022 than in 2021, which contributed to the overall decrease in detections. Golden-crowned kinglet and Pacific wren detections in particular decreased across all three parks between 2021 and 2022. Despite these slight changes, overall detection numbers of most species across the parks were not markedly different between the two years. Interpretation of these results will be completed as part of the next multi-year trend analysis, which will account for annual variation in survey effort, observer effects, and detection probability.

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Holmgren, Amanda, Jason Ransom, Rodney Siegel, et al. North Coast and Cascades Network landbird monitoring: Report for the 2023 field season. National Park Service, 2024. http://dx.doi.org/10.36967/2306475.

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The North Coast and Cascades Network (NCCN) continued to implement the network?s Landbird Monitoring Protocol in 2023, in partnership with The Institute for Bird Populations. The protocol was initially field-tested with data collected from the annual panel only, as part of protocol development during 2005?2006, and has subsequently been implemented fully (including data collection on the annual panel as well as five alternating panels) for the past 16 years (2007?2023), except for 2017 when data collection was temporarily suspended to reallocate resources for a 5-year data synthesis. In 2023, we conducted surveys at 1,174 point count stations along 68 transects in the large wilderness parks of the NCCN, including Mount Rainier National Park (MORA), North Cascades National Park Complex (NOCA), and Olympic National Park (OLYM); and 54 point counts at San Juan Island National Historical Park (SAJH). Lewis and Clark National Historical Park (LEWI) was not surveyed in 2023 as SAJH and LEWI are surveyed in alternating years. Across the three large parks, we documented the presence of 158 species, 100 of which were detected during point counts. The remaining 58 species were recorded only as incidental detections or on ?Rare Bird Report Forms.? For the most frequently detected species over the 2005?2023 field seasons, we present the total number of detections of each species on each park?s annual panel transects over that period of time. The number of bird detections on annual-panel transects across all three large parks increased by 2,239 between 2022 and 2023. When factoring in the number of point counts conducted each year, all three parks saw an increase in the average number of birds per count (an increase of 17% at MORA, 42% at OLYM, and 21% at NOCA). This overall increase in detections across the network is in part due to a high number of Red Crossbill detections in 2023, particularly at OLYM. We detected them at higher numbers in OLYM than any other year since the start of the monitoring program. Several other species (Red-breasted Nuthatch, Townsend?s/Hermit Warbler, American Robin, and Hammond?s Flycatcher) were also detected in higher numbers in the three large parks in 2023 than in 2022, which contributed to the overall increase in detections. Despite these changes, overall detection numbers of most species across the parks were not markedly different between the two years. We caution that these detection totals have not been adjusted for differences in survey effort, observer effects, or potential differences in detectability of birds between years; such adjustments will be made in conjunction with trend analyses in a future multi-year report.

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Cooper, Rachel. Water in Sustainable Agriculture Standards. Institute of Development Studies (IDS), 2021. http://dx.doi.org/10.19088/k4d.2021.037.

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This review synthesises evidence on water in sustainable agriculture standards. Sustainable agricultural standards, hereafter standards, is a broad term encompassing certification schemes, tools, and programmes. The International Trade Centre’s Sustainability Standards Map includes 166 agricultural standards . However, there is a smaller number of prominent standards that are popularly used by major retailers or for particular commodities. Two studies looking at how water is considered in standards selected smaller numbers: Morgan (2017) benchmarks 25 popular use conventional agricultural standards and organic standards, whilst Vos & Boelens (2014) selected eight prominent standards for their analysis. The evidence base for this request was limited. Whilst water is included in individual standards, there is limited research on the efficacy or impact of standards on water issues. This review identified an extremely small number of studies that either assessed or benchmarked standards’ water related requirements or the impacts of certification and water requirements on water resources.

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Rosero-Bixby, Luis, and Tim Miller. The mathematics of the reproduction number R for Covid-19: A primer for demographers. Verlag der Österreichischen Akademie der Wissenschaften, 2021. http://dx.doi.org/10.1553/populationyearbook2022.res1.3.

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The reproduction number R is a key indicator used to monitor the dynamics of Covid-19 and to assess the effects of infection control strategies that frequently have high social and economic costs. Despite having an analog in demography’s “net reproduction rate” that has been routinely computed for a century, demographers may not be familiar with the concept and measurement of R in the context of Covid-19. This article is intended to be a primer for understanding and estimating R in demography. We show that R can be estimated as a ratio between the numbers of new cases today divided by the weighted average of cases in previous days. We present two alternative derivations for these weights based on how risks have changed over time: constant vs. exponential decay. We then provide estimates of these weights, and demonstrate their use in calculating R to trace the course of the first pandemic year in 53 countries.

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