Academic literature on the topic 'Prob.-Math'

Although a variational iteration algorithm was proposed by Yildirim (Math. Prob. Eng. 2008 (2008), Article ID 869614) that successfully solves differential-difference equations, the method involves some repeated and unnecessary iterations in each step. An alternative iteration algorithm (variational iteration algorithm-II) is constructed in this paper that overcomes this shortcoming and promises to provide a universal mathematical tool for many differential-difference equations.

Let (Xi)i?1 be a sequence of positive independent identically distributed random variables with regularly varying distribution tail of index 0 < ? < 1 and define Tn = X1?+X2?+???+Xn?/(X1+X2+???+ Xn)?.In this note we simplify an expression for lim n?? E(T kn ), which was obtained by Albrecher and Teugels: Asymptotic analysis of a measure of variation. Theory Prob. Math. Stat., 74 (2006), 1-9, in terms of coefficients of a continued fraction expansion. The new formula establishes an unexpected link to an enumeration problem for rooted maps on orientable surfaces that was studied in Arqu?s and B?raud: Rooted maps of orientable surfaces, Riccati's equation and continued fractions. Discrete Mathematics, 215 (2000), 1-12.

The inclusion of technology in the academic processes has led to constant innovation and investment of resources to offer a first-level educational service, with international standards, methodologies, study plans, and last generation laboratories. This paper focuses on how teachers can make use of an educational technology tool that will allow them to identify patterns that are associated with learning based on human-computer interaction. We present evidence of learning outcomes based on the detection of behaviors in Intelligent Tutoring Systems. These patterns pave the way for the auto-matic identification of patterns in association to students’ learning while using an educational technological tool. The results suggest a model for student’s behavior identification when interacting with the technological tool “Scooter”. This model identifies students with prospective better learning outcomes as well as students with difficulties to solve math prob-lems. Work for the future will analyze data that comes from different set-tings apart from solving exercises in Scooter to prove the hypothesis that there are patterns of behavior associated to learning outcomes in different problem-solving situations presented by educational technology.

Classical Ornstein–Uhlenbeck (ou) processes are Lévy-driven linear stochastic models with exponentially decaying autocorrelation functions which do not always fit more slowly decaying real time series data. A superposition of ou processes (known as a supou process) is proposed to overcome this issue for application to river discharge time series data. The discharge data has a sub-exponential autocorrelation function and this is captured by the supou process based on the mean reversion speed generated by a Gamma distribution. All the parameters of the supou process are identified by matching the autocorrelation and the first to fourth statistical moments of the discharge data. The empirical and modelled histograms of the discharge data are comparable with each other. References O. E. Barndorff-Nielsen. Superposition of Ornstein–Uhlenbeck type processes. Theory Prob. Appl. 45.2 (2001), pp. 175–194. doi: 10.1137/S0040585X97978166 O. E. Barndorff-Nielsen, F. E. Benth, and A. E. D. Veraart. Modelling energy spot prices by volatility modulated Lévy-driven Volterra processes. Bernoulli 19.3 (2013), pp. 803–845. doi: 10.3150/12-BEJ476 O. E. Barndorff-Nielsen and N. N. Leonenko. Burgers’ turbulence problem with linear or quadratic external potential. J. Appl. Prob. 42.2 (2001), pp. 550–565. url: http://www.jstor.org/stable/30040809 J. Beran, Y. Feng, S. Ghosh, and R. Kulik. Long-Memory Processes. Springer-Verlag, Berlin, Heidelberg, 2016. doi: 10.1007/978-3-642-35512-7 F. Fuchs and R. Stelzer. Mixing conditions for multivariate infinitely divisible processes with an application to mixed moving averages and the supOU stochastic volatility model. ESAIM: Prob. Stat. 17 (2013), pp. 455–471. doi: 10.1051/ps/2011158 Y. Kabanov and S. Pergamenshchikov. Ruin probabilities for a Lévy-driven generalised Ornstein–Uhlenbeck process. Fin. Stoch. 24.1 (2020), pp. 39–69. doi: 10.1007/s00780-019-00413-3 R. Kawai and H. Masuda. On simulation of tempered stable random variates. J. Comput. Appl. Math. 235.8 (2011), pp. 2873–2887. doi: 10.1016/j.cam.2010.12.014 S. Pelacani and F. G. Schmitt. Scaling properties of the turbidity and streamflow time series at two different locations of an intra-Apennine stream: Case study. J. Hydro. 603.B (2021), p. 126943. doi: 10.1016/j.jhydrol.2021.126943 R. Stelzer, T. Tosstorff, and M. Wittlinger. Moment based estimation of supOU processes and a related stochastic volatility model. Stat. Risk Model. 32.1 (2015), pp. 1–24. doi: 10.1515/strm-2012-1152 S. Suweis, E. Bertuzzo, G. Botter, A. Porporato, I. Rodriguez-Iturbe, and A. Rinaldo. Impact of stochastic fluctuations in storage-discharge relations on streamflow distributions. Water Resource. Res. 46.3 (2010), W03517. doi: 10.1029/2009WR008038 M. Tamborrino and P. Lansky. Shot noise, weak convergence and diffusion approximations. Physica D: Nonlinear Phenomena 418 (2021), p. 132845. doi: 10.1016/j.physd.2021.132845 E. Taufer and N. Leonenko. Simulation of Lévy-driven Ornstein–Uhlenbeck processes with given marginal distribution. In: Comput. Stat. Data Anal. 53.6 (2009), pp. 2427–2437. doi: 10.1016/j.csda.2008.02.026 C. Van Den Broeck. On the relation between white shot noise, Gaussian white noise, and the dichotomic Markov process. J. Stat. Phys. 31 (1983), pp. 467–483. doi: 10.1007/BF01019494 H. Yoshioka and Y. Yoshioka. Designing cost-efficient inspection schemes for stochastic streamflow environment using an effective Hamiltonian approach. Opt. Eng. (2021), pp. 1–33. doi: 10.1007/s11081-021-09655-7

We present an efficient Bayesian algorithm for identifying the shape of an object from noisy far field data. The data is obtained by illuminating the object with one or more incident waves. Bayes' theorem provides a framework to find a posterior distribution of the parameters that determine the shape of the scatterer. We compute the distribution using the Markov Chain Monte Carlo (MCMC) method with a Gibbs sampler. The principal novelty of this work is to replace the forward far-field-ansatz wave model (in an unbounded region) in the MCMC sampling with a neural-network-based surrogate that is hundreds of times faster to evaluate. We demonstrate the accuracy and efficiency of our algorithm by constructing the distributions, medians and confidence intervals of non-convex shapes using a Gaussian random circle prior. References Y. Chen. Inverse scattering via Heisenberg’s uncertainty principle. Inv. Prob. 13 (1997), pp. 253–282. doi: 10.1088/0266-5611/13/2/005 D. Colton and R. Kress. Inverse acoustic and electromagnetic scattering theory. 4th Edition. Vol. 93. Applied Mathematical Sciences. References C112 Springer, 2019. doi: 10.1007/978-3-030-30351-8 R. DeVore, B. Hanin, and G. Petrova. Neural Network Approximation. Acta Num. 30 (2021), pp. 327–444. doi: 10.1017/S0962492921000052 M. Ganesh and S. C. Hawkins. A reduced-order-model Bayesian obstacle detection algorithm. 2018 MATRIX Annals. Ed. by J. de Gier et al. Springer, 2020, pp. 17–27. doi: 10.1007/978-3-030-38230-8_2 M. Ganesh and S. C. Hawkins. Algorithm 975: TMATROM—A T-matrix reduced order model software. ACM Trans. Math. Softw. 44.9 (2017), pp. 1–18. doi: 10.1145/3054945 M. Ganesh and S. C. Hawkins. Scattering by stochastic boundaries: hybrid low- and high-order quantification algorithms. ANZIAM J. 56 (2016), pp. C312–C338. doi: 10.21914/anziamj.v56i0.9313 M. Ganesh, S. C. Hawkins, and D. Volkov. An efficient algorithm for a class of stochastic forward and inverse Maxwell models in R3. J. Comput. Phys. 398 (2019), p. 108881. doi: 10.1016/j.jcp.2019.108881 L. Lamberg, K. Muinonen, J. Ylönen, and K. Lumme. Spectral estimation of Gaussian random circles and spheres. J. Comput. Appl. Math. 136 (2001), pp. 109–121. doi: 10.1016/S0377-0427(00)00578-1 T. Nousiainen and G. M. McFarquhar. Light scattering by quasi-spherical ice crystals. J. Atmos. Sci. 61 (2004), pp. 2229–2248. doi: 10.1175/1520-0469(2004)061<2229:LSBQIC>2.0.CO;2 A. Palafox, M. A. Capistrán, and J. A. Christen. Point cloud-based scatterer approximation and affine invariant sampling in the inverse scattering problem. Math. Meth. Appl. Sci. 40 (2017), pp. 3393–3403. doi: 10.1002/mma.4056 M. Raissi, P. Perdikaris, and G. E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378 (2019), pp. 686–707. doi: 10.1016/j.jcp.2018.10.045 A. C. Stuart. Inverse problems: A Bayesian perspective. Acta Numer. 19 (2010), pp. 451–559. doi: 10.1017/S0962492910000061 B. Veihelmann, T. Nousiainen, M. Kahnert, and W. J. van der Zande. Light scattering by small feldspar particles simulated using the Gaussian random sphere geometry. J. Quant. Spectro. Rad. Trans. 100 (2006), pp. 393–405. doi: 10.1016/j.jqsrt.2005.11.053

Based on the results of the analysis of research on mathematical thinking, its creative nature has been ascertained. The results of research on creative mathematical thinking were analyzed and the expediency of studying the psychological essence of the interaction of thought processes of understanding and forecasting when solving creative mathematical problems was ascertained.The aim of the article is to find out the psychological essence of the inte­raction of thought processes of understanding and forecasting in creative ma­thematical thinking. To study the interaction of the processes of understanding and forecasting in mathematical thinking, the method of analyzing students’ search actions du­ring solving creative mathematical problems of different classes was used.the results of the research. It was established that creative mathematical thinking is a complete system of interrelated actions, with the help of which the thinking mathematical result is achieved.It was established that the processes of understanding mathematical prob-lems and predicting thinking results function throughout the entire process of solving mathematical problems.It was found that the content of search actions aimed at understanding the problem and predicting thinking results depend on the stages of solving the problem (study of the condition, search for a solution, verification of the found solution), in which their procedural and dynamic side is not only manifested, but is also being formed. At the same time, the process of understanding a creative mathematical problem and the process of forecasting are complementary.It is established that the understanding of the condition of the problem forms the content of forecasting actions, and the process of forecasting cont­ributes to the formation of understanding of the mathematical problem. It was established that in the search mathematical process it is not possible to record such a state of understanding of the problem that would ensure the emergence of a hypothesis regarding the solution.It has been found that forecasting, which takes place throughout the en-tire search process, can generate a solution hypothesis at different stages of the solution, with different states of understanding of the mathematical problem.The hypothesis of solving the problem is an indicator of the state of un-derstanding of the problem, and its approbation contributes to deepening the understanding of the essence of the problem itself. At the same time, the content of the hypothesis, its approval determines the state of understanding of the problem.conclusion. The process of the subject’s understanding of a creative math-ematical problem and the process of prediction take place throughout all stages of the solution process and are mutually complementary.

A wavelength resolved measurement technique used in neutron imaging applications is known as energy-resolved neutron transmission imaging. This technique of reconstructing residual strain maps provides high spatial resolution measurements of strain distribution in polycrystalline materials from sets of Bragg edge measurement images. Strain field reconstructions obtained from both triangular and quadrilateral finite element meshes are compared. The reconstruction is approached via a least square method and relies on the inversion of the longitudinal ray transform, which has uniqueness issues. References B. Abbey, S. Y. Zhang, W. J. J. Vorster, and A. M. Korsunsky. Feasibility study of neutron strain tomography. Proc. Eng., 1:185–188, 2009. doi:10.1016/j.proeng.2009.06.043. R. Aggarwal, M. H. Meylan, B. P. Lamichhane, and C. M. Wensrich. Energy resolved neutron imaging for strain reconstruction using the finite element method. J. Imag., 6(3):13, 2020a. doi:10.3390/jimaging6030013. R. Aggarwal, M. H. Meylan, C. M. Wensrich, and B. P. Lamichhane. Finite element approach to Bragg edge neutron strain tomography. In B. Lamichhane, T. Tran, and J. Bunder, editors, Proceedings of the 18th Biennial Computational Techniques and Applications Conference, CTAC-2018, volume 60 of ANZIAM J., pages C279–C294, June 2020b. doi:10.21914/anziamj.v60i0.14054. M. E. Fitzpatrick and A. Lodini. Analysis of residual stress by diffraction using neutron and synchrotron radiation. CRC Press, 2003. URL https://www.routledge.com/Analysis-of-Residual-Stress-by-Diffraction-using-Neutron-and-Synchrotron/Fitzpatrick-Lodini/p/book/9780367446802. A. W. T. Gregg, J. N. Hendriks, C. M. Wensrich, A. Wills, A. S. Tremsin, V. Luzin, T. Shinohara, O. Kirstein, M. H. Meylan, and E. H. Kisi. Tomographic reconstruction of two-dimensional residual strain fields from Bragg-edge neutron imaging. Phys. Rev. Appl., 10:064034, Dec 2018. doi:10.1103/PhysRevApplied.10.064034. J. N. Hendriks, A. W. T. Gregg, C. M. Wensrich, A. S. Tremsin, T. Shinohara, M. Meylan, E. H. Kisi, V. Luzin, and O. Kirsten. Bragg-edge elastic strain tomography for in situ systems from energy-resolved neutron transmission imaging. Phys. Rev. Mat., 1:053802, 2017. doi:10.1103/PhysRevMaterials.1.053802. E. H. Kisi and C. J. Howard. Applications of neutron powder diffraction, volume 15 of Neutron Scattering in Condensed Matter. Oxford University Press, 2012. URL https://global.oup.com/academic/product/applications-of-neutron-powder-diffraction-9780199657421. W. R. B. Lionheart and P. J. Withers. Diffraction tomography of strain. Inv. Prob., 31:045005, 2015. doi:10.1088/0266-5611/31/4/045005. C. C. Paige and M. A. Saunders. LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Software, 8:43–71, 1982. doi:10.1145/355984.355989. J. R. Santisteban, L. Edwards, M. E. Fitzpatrick, A. Steuwer, P. J. Withers, M. R. Daymond, M. W. Johnson, N. Rhodes, and E. M. Schooneveld. Strain imaging by Bragg edge neutron transmission. Nucl. Inst. Meth. Phys. Res., 481:765–768, 2002. doi:10.1016/S0168-9002(01)01256-6. T. Shinohara and T. Kai. Commissioning start of energy-resolved neutron imaging system, RADEN in J-PARC. Neut. News, 26(2):11–14, 2015. doi:10.1080/10448632.2015.1028271. T. Shinohara, T. Kai, K. Oikawa, M. Segawa, M. Harada, T. Nakatani, M. Ooi, K. Aizawa, H. Sato, T. Kamiyama, H. Yokota, T. Sera, K. Mochiki, and Y. Kiyanagi. Final design of the energy-resolved neutron imaging system RADEN at J-PARC. J. Phys., 746, 2016. doi:10.1088/1742-6596/746/1/012007. A. S. Tremsin, J. B. McPhate, W. Kockelmann, J. V. Vallerga, O. H. W. Siegmund, and W. B. Feller. High resolution Bragg edge transmission spectroscopy at pulsed neutron sources: proof of principle experiments with a neutron counting MCP detector. Nucl. Inst. Meth. Phys. Res., 633:S235–S238, 2011. doi:10.1016/j.nima.2010.06.176. R. Woracek, J. Santisteban, A. Fedrigo, and M. Strobl. Diffraction in neutron imaging—A review. Nucl. Inst. Meth. Phys. Res., 878:141–158, 2018. doi:10.1016/j.nima.2017.07.040.

Background. At the beginning of the 1920’s, after establishing the borders of the restored Polish State, its eastern territories were dominated by the Ukrainian, Belarusian and Lithuanian populations, and in the western part, a significant percentage were Germans. Accordingly, the state faced the problem of developing a constructive policy towards national minorities. Purpose. The article analyzes the attitude of the Polish intellectual elite to the prob-lem of national minorities, whose opinions were partially reflected in a poll conducted in July and August 1924 by the liberal Warsaw newspaper “Kurjer Polski”. The discussion intensified, in particular, due to the expiration of the government’s commitment to give Eastern Galicia autonomy, the preparation of a government law on education (known as Lex Grabski). Results. The opening of a Ukrainian university was a part of the problem. At the request of the government, the academic community of the Jagiellonian University expressed its views in June, which generally welcomed the idea of opening a separate Ukrainian university in Lviv, Warsaw or Krakow. “Kurjer Polski” published reflections of intellectuals representing different regions of the country and political currents: socialists (A. Śliwiński – Warsaw), nationalists (S. Bukowiecki – Vilno), conservatives (Fr. Bossowsky, T. Dembowsky – Vilno; E. Hauswald – Lviv ). The basis for solving the problem at that time, most authors called the provisions of the March 1921 Constitution on the main democratic rights of citizens, unanimously called for creating opportunities for cultural and national development of national minorities, hoping for the consolidation of the state. It was emphasized the need to take into account the individual characteristics of each minority and regional specifics. In particular, E. Hauswald considered the experience of the Austro-Hungarian monarchy of the early twentieth century as an example of solving the problem (Moravian Compensation 1905 and The Bukovinian Compromise 1910). Quite controversial about the essence of Belarusian (Belarusians are not a nation that encompasses all segments of society, but only the mass of the peasantry is devoid of any political ambitions; Belarusian language is a set of dialects that makes a gradual transition from Russian to Polish; literary Belarusian lan-guage is artificially created, the population does not understand it) and Ukrainian (did not deny the existence of political ambitions, but emphasized the significant differences in Volhynia and Eastern Galicia and dependence on external support) national movements were the reflections of Fr. Bossovsky, who, however, supported the idea of granting national minorities freedom of cultural development. Lviv lawyer J. Makarewicz (representative of the Christian Democrats) called for a policy of state assimilation towards Ukrainians and Belarusians, tactics of “state indifference” towards Jews, Russians and Germans. However, despite the existence of such ideas in the Polish intellectual environment, government circles have chosen the concept of a unitary mono-national state. As early as July 1924, a law on education was passed, many articles of which were aimed at discriminating against national minorities. And further changes in the political life of the country only exacerbated the problem, which was not solved throughout the interwar period. Keywords: Fr. Bossowski, S. Bukowiecki, T. Dembowski, interwar Poland, E. Hauswald, Kurjer Polski, J. Makarewicz, national question, A. Śliwiński. A never-extinguishing volcano, 1924. Kurjer Polski, May 31, р.2. (In Polish) Announcement of the National Electoral Commission on November 24, 1930, s. 1. [online] Avialable at: http://isap.sejm.gov.pl/isap.nsf/download.xsp/ WMP19302720369/ O/M19300369. pdf [Accessed 15 march 2021]. (In Polish) Baran, Z., 1998. On the question of the agrarian policy of the governments of interwar Poland towards Western Ukraine. Visnyk of the Lviv University, 33. Series History. Lviv, pp.146–153. (In Ukrainian) Baran, Z., 2011. Julian Makarevich’s socio-political views. In: Historical sights of Galicia. Proceedings of the fifth scientific conference on local history, 12 november 2010. Lviv, рр.188–198. (In Ukrainian) Bezuk, O., 2019. The reaction of the Western Ukrainian and world community to the death of Olga Levitska-Basarab. In: The modern movement of science: theses add. VII In-ternational Scientific and Practical Internet Conference, 6–7 june 2019. Dnipro, pp.75–81. (In Ukrainian) Bojarski, Р., 2015. Piłsudski’s May Coup in commentaries of “Dziennik Wileński” journalists. The Scientific Journals of the Learned Society of Ostrołęka, 29, рр.101–114. (In Polish) Bohachevsky-Chomiak, М., 1981. The Ukrainian university in Galicia. Harvard Ukrainian Studies, 5(4). Published by Harvard Ukrainian Research Institute, pp.497–545. (In English) Bossowski, F., 1924. Any irritating policy must be abandoned. Kurjer Polski, August 24, р.3. (In Polish) Bukowiecki, S., 1922. The policy of independent Poland. Essay of the program. War-saw: Ignis S.A. (In Polish) Bukowiecki, S., 1924. Providing cultural development for minorities unites them with the State. Kurjer Polski, July 4, р.2. (In Polish) Czekaj, К., 2011. Artur Śliwiński (1877–1953). Politician, publicist, historian. Warsaw. (In Polish) Dąbrowski, P., 2020. Belarussian and Jewish issues in the political and legal thought of polish groups in Vilnius in the first years of independence – selected issues. Studia juridica Lublinensia, 29(4). Pomeranian University in Slupsk, pp.59–70. (In English) Dembowski, T., 1924. May everyone in Poland be fine. Kurjer Polski, August 10, р.4. (In Polish) Do you know who it is?, 1938. S. Łozа, ed. Warsaw: Wydawnictwo Głównej księgarni wojskowej. [online] Avialable at: https://prokuratoria.gov.pl/index.php?p=m&idg=m3,113 [Accessed 23 march 2021] (In Polish) Hauswald, Е., 1924. It is necessary to adhere to the principles of fairness and compre-hensive tolerance. Kurjer Polski, August 7, р.2. (In Polish) Hud, B., 2018. From the history of ethnosocial conflicts. Ukrainians and Poles in the Dnieper region, Volhynia and Eastern Galicia in the XIX–first half of the XX century. Harkiv: Akta. (In Ukrainian) Holzer, J. 1974. Political mosaic of the Second Polish Republic. Warsaw: Książka і Wiedza. (In Polish) Jászi, O., 1929. The Dissolution of the Habsburg Monarchy. Chicago–Illinois: The University of Chicago Press. [online] Avialable at: https://ia801603.us.archive.org/33/ items/in.ernet.dli.2015.151077/2015.151077.The-Dissolution-Of-The-Habsburg Monar-chy.pdf [Accessed 15 march 2021]. (In English) Kakareko, A., 2002. To restore the state myth: reception of the Jagiellonian heritage in the environment of the Club of Tramps Seniors in Vilnius in the 1930s. In: Poles and neighbors – distances and the interpenetration of cultures: a collection of studies, part 3. R. Wapiński, еd. Ostaszewo Gdańskie: Stepan design. (In Polish) Krykun, M. and Zashkilnyak, L., 2002. History of Poland. From ancient times to the present days. Lviv: Ivan Franko National University in Lviv. (in Ukrainian). Krzywobłocka, B., 1974. Christian Democrats 1918–1937. Warsaw: Książka і Wiedza. (In Polish) Kurjer Polski, 1924a. May 21. (In Polish) Kurjer Polski, 1924b. May 23. (In Polish) Kurjer Polski, 1924c. July 4. (In Polish) Makarewicz, J., 1924. Minorities. Lviv: Chrześcijańska Spółka Wydawnicza, 1924. (In Polish) Malycka, K., 1924. About Olga Levitsky Bessarabova. Dilo. February 23. (In Ukraini-an) Minutes of a conference held 11–12 july 1924, at the polish Ministry of Religions and Education, 1981. In: Bohachevsky-Chomiak, М., 1981. The Ukrainian university in Gali-cia. Harvard Ukrainian Studies, 5(4). Published by Harvard Ukrainian Research Institute, doc.3, pp.524–527. (In Polish) More than independence, 2001. Polish political thought 1918–1939. J. Jachymek and W. Paruch, ed. science. Lublin: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej. (In Polish) Mudryj, V., 1948. Ukrainian University in Lviv in 1921–1925. Nurenberg: Czas. (In Ukrainian) National-State Union, 1922. Program declaration. June 28. [online] Avialable at: https://polona.pl/item/deklaracja-programowa-inc-polska-jako-narod-ani-na-chwile-nie-przestawala-istniec,NjIxNjY2NzE/0/#info:metadata [Accessed 15 march 2021]. (In Polish) Orman, E., 1989–1991. Rosner Ignacy Juliusz (1865–1926). Polish Biographical Dictionary, Vol.32. Romiszewski Aleksander – Rudowski Jan. Wrocław: National Institute of Ossolińskich – Publishing House of the Polish Academy of Sciences, рр.106–110. [online] Avialable at: https://www.ipsb.nina.gov.pl/ a/biografia/ignacy-juliusz-rosner [Ac-cessed 3 december 2021] (In Polish) Renner, K., 2005. State and nation (1899). In: National Cultural Autonomy and its Contemporary Critics. Ephraim Nimni, ed. London and New York: Routledge, рр.13–40. (In English) Reports of the faculties at the Jagellonian about the plans for Ukrainian university studies, 1981. In: Bohachevsky-Chomiak, М., 1981. The Ukrainian university in Galicia. Harvard Ukrainian Studies, 5(4). Published by Harvard Ukrainian Research Institute, doc.2, pp.521–524. (In Polish) Shabuldo, F.M., 2004. The Union of Horodło 1413. Encyclopedia of History of Ukraine: Vol.2: G-D. Kyiv: Naukova Dumka. [online] Avialable at: http://www.history. org.ua/?termin=Gorodelska_uniya_1413 [Accessed 15 march 2021] (In Ukrainian) Shvaguliak, M., 2013. Historical studies. Ukrainians at the crossroads and sharp turns of history (second half of the XIX – first half of the XX century). Lviv: Triada plus. (In Ukrainian) Smith, A. D., 1994. National Identity. Translate from English by P. Tarashchuk. Kyiv: Osnovy. (In Ukrainian) Stourzh, G., 2019. Equality of nationalities in the constitution and public administration of Austria (1848–1918). S. Paholkiv, ed. Lviv: Piramida. (In Ukrainian) Śliwiński, А., 1924. Nationalist chauvinism is the greatest obstacle to solving the matter. Kurjer Polski, August 19, р.4. (In Polish) The results of the census, 1910. Vom 31. In the Kingdoms and Countries represented in the Imperial Council – The summary results of the census. [online] Avialable at: https://anno.onb.ac.at/cgi-content/anno-plus?aid=ost&datum =0001&page=168 [Ac-cessed 12 april 2021]. (In German) Zashkilnyak, L., 1997. Genesis and consequences of the Ukrainian-Polish normaliza-tion in 1935. In: Poland and Ukraine – the Alliance of 1920 and its aftermath. Materials from the scientific conference “Poland and Ukraine – the Alliance of 1920 and its after-math”. Toruń, on November 16–18, 1995. Toruń, рр.431–454. (In Ukrainian)

AbstractWe derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold.

AbstractThis paper incorporates fairness constraints into the classic single-unit reduced-form implementation problem (Border in Economet J Econ Soc, 59(4):1175–1187, 1991, Econ Theory 31(1):167–181, 2007; Che et al. in Econometrica 81(6): 2487–2520, 2013; Manelli and Vincent in Econometrica, 78(6):1905–1938, 2010) with two agents. To do so, I use a new approach that utilizes the results from Kellerer (Math Ann 144(4):323–344, 1961) and Gutmann et al. (Ann Prob 19:1781–1797, 1991). Under realistic assumptions on the constraints, the conditions are transparent and can be verified in polynomial time.