Digest of the Non Linear Science Network, Volume 13, Number 18 October 1, 2013 Editor: Angel Jorba Topics: School, Modelling and Analysis of Innovation & Competition Processes Postdoc position in Brazil Clements Chair of Mathematics Position, Southern Methodist Univ Leroy Martin Chair Position, NC State Faculty Positions, Math, Applied Math, and Statistics Assistant Professor Position, Mathematical Biology 3 Academic Positions, Univ of Pretoria Contents, The Journal of Geometric Mechanics 5:3 Contents, Journal of Modern Dynamics 7:2 Contents, Discrete and Continuous Dynamical Systems - Series B 18:9 Contents, Discrete and Continuous Dynamical Systems - Series S 7:2 Contents, Mathematical Biosciences and Engineering 11:1 Contents, Mathematical Control and Related Fields 3:3 Contents, Mathematical Control and Related Fields 3:4 Contents, Communications in Mathematical Sciences 12:2 Submissions to nls-net must be addressed to: Comments and suggestions are also welcome. General information about nls-net can be found at: http://www.maia.ub.es/cgi-bin/mailman/listinfo/nls-net/ This is a service created and maintained in collaboration with the American Institute of Mathematical Sciences (AIMS) http://www.aimsciences.org/ ------ Subject: School, Modelling and Analysis of Innovation & Competition Processes From: sicc Date: Sat, 21 Sep 2013 08:38:54 -0600 9th SICC International School Topics in Nonlinear Dynamics MODELLING AND ANALYSIS OF INNOVATION AND COMPETITION PROCESSES May 26-30, 2014 Politecnico di Milano, Milano, Italy Directed by Fabio Dercole The aim of the course is to present adaptive dynamics (AD), a mathematical framework to model long-term evolution of coevolving multi-species communities, with special emphasis on the generation of diversity through evolutionary branching. Evolutionary branching takes place when a resident and a similar mutant type coexist in the same environment and natural selection favors further differentiation between the two types. The evolutionary dynamics are described as a random walk in the space of the coexisting strategies, a space with variable dimension according to evolutionary branching and extinction. Evolution proceeds in the direction of the local fitness gradient and can be approximated by deterministic continuous dynamics ruled by the AD canonical equation. Applications to relevant biological communities, as well as to social and economic sciences, where innovations and competition play the role of mutations and natural selection, will be presented. The course is part of the teaching activities organized by the PhD Program in Information Technology at Politecnico di Milano, yet it is not only addressed to PhD students, but to all researchers working in any areas of science and engineering and interested in modelling innovation and competition processes. Advanced theoretical topics and cutting-edge applications of AD will be presented in the workshop by the leading scientists in the field. All presentations will be given in English. Lecturers * Fabio Della Rossa, Department of Electronics, Information, and Bioengineering, Politecnico di Milano * Fabio Dercole, Department of Electronics, Information, and Bioengineering, Politecnico di Milano * Ulf Dieckmann, Evolution and Ecology Program, International Institute for Applied Systems Analysis (to be confirmed) * Stefan Geritz, Department of Mathematics and Statistics, University of Helsinki * Mats Gyllenberg, Department of Mathematics and Statistics, University of Helsinki * Christopher Klausmeier, W. K. Kellogg Biological Station, Michigan State University * Pietro Landi, Department of Electronics, Information and Bioengineering, Politecnico di Milano * Geza Meszena, Department of Biological Physics, Eotvos University, Budapest * Hans Metz, Mathematisch Instituut, Universitet Leiden * Kalle Parvinen, Department of Mathematics and Statistics, University of Turku * Tadeas Priklopil, Department of Mathematics and Statistics, University of Helsinki * Sergio Rinaldi, Department of Electronics, Information and Bioengineering, Politecnico di Milano For information and application visit http://maicp2014.deib.polimi.it/ ------ Subject: Postdoc position in Brazil From: Sonia Carvalho Date: Mon, 23 Sep 2013 06:49:20 -0300 The Graduate Program in Mathematics http://www.mat.ufmg.br/pgmat/en-pgmat/index.php at the Mathematics Department (www.mat.ufmg.br) of Universidade Federal de Minas Gerais (www.ufmg.br) has two immediate Postdoc open positions. The Graduate Program has several lines of research which can be checked through the link: http://www.mat.ufmg.br/pgmat/en-pgmat/pesquisa/peslin.php The stipends will be covered by PNPD - Postdoctoral National Program - a nationwide program supported by the brazilian funding agency CAPES (www.capes.gov.br). Monthly payments will be in reals, the brazilian currency, and they correspond to approximately 2.000,00 US dollars plus an additional research grant of approximately 500,00 US dollars/month. The amount is more than enough for living expenses in Belo Horizonte (http://pt.wikipedia.org/wiki/Belo_Horizonte). Scholarships will last for 12 months and may be renewed for up to an additional 48 months. Accepted applications may start in between November 1, 2013 to April 1, 2014. To those interested in applying for the positions, please send your CV to the email address pgmat@mat.ufmg.br no later then October 31, 2013. For any further questions, contact the email address montene@mat.ufmg.br Sonia Pinto de Carvalho Departamento de Matematica - ICEx - UFMG ------ Subject: Clements Chair of Mathematics Position, Southern Methodist Univ From: Tom Hagstrom thagstrom@smu.edu Date: September 17, 2013 Southern Methodist University Department of Mathematics Applications are invited for the Clements Chair of Mathematics to begin in the fall semester of 2014. The department is searching for senior scholars with outstanding records of research in computational and applied mathematics as well as a strong commitment to teaching, including an established history of advising doctoral students. We are seeking candidates whose interests align with those of the department and who would contribute in a substantial way to the university's initiatives in high performance computing and interdisciplinary research. The Department of Mathematics offers graduate degrees in Computational and Applied Mathematics and includes 16 tenured or tenure-track faculty researchers, all of whom work in application areas. Visit http://www.smu.edu/math/ for more information. To apply send a letter of application with a curriculum vitae, a list of publications, research and teaching statements, and the names of three references to: The Faculty Search Committee, Department of Mathematics, Southern Methodist University, P.O. Box 750156, Dallas, Texas, 75275-0156. The Search Committee can also be contacted by sending e-mail to mathsearch@mail.smu.edu. (Tel: (214)768-2452; Fax: (214)768-2355). Applications received by November 1, 2013 will receive full consideration, but will continue to be accepted until the position is filled. A Ph.D. in applied mathematics or a related field is required. Applicants will be notified when the search is concluded. SMU, a private university with active graduate and undergraduate programs in the sciences and engineering, is situated in a quiet residential section of Dallas. The Dallas-Fort Worth Metroplex is America's fourth largest metropolitan area, and residents enjoy access to world-class cultural and entertainment activities. SMU will not discriminate on the basis of race, color, religion, national origin, sex, age, disability, genetic information, or veteran status. SMU's commitment to equal opportunity includes nondiscrimination on the basis of sexual orientation and gender identity and expression. Hiring is contingent upon the satisfactory completion of a background check. ------ Subject: Leroy Martin Chair Position, NC State From: Tim Kelley tim_kelley@ncsu.edu Date: September 17, 2013 The Mathematics Department at North Carolina State University invites applications for the LeRoy Martin Professorship in Mathematics. We are seeking exceptionally well-qualified, world-renowned individuals with research interests compatible with those in the department. All areas of pure and applied mathematics will be considered. Candidates must have a PhD in the mathematical sciences. The successful applicant must have an internationally recognized research program, demonstrated ability to attract external funding, a strong record of mentoring PhD students and post-docs, and a commitment to effective teaching at the undergraduate and graduate levels. The Department of Mathematics has strong research programs in both pure and applied mathematics. Many members of the department participate in interdisciplinary programs and research groups on campus and in the broader Research Triangle community. More information about the department can be found at http://www.math.ncsu.edu. To submit your application materials, go to http://www.mathjobs.org/jobs/ncsu. Include a vita, at least four letters of recommendation, and a description of current and planned research. You will then be given instructions to go to http://jobs.ncsu.edu/postings/4072 and complete a Faculty Profile for the position. Write to math-jobs@math.ncsu.edu or tim_kelley@ncsu.edu for questions concerning this position. NC State University is an Equal Opportunity and Affirmative Action Employer. NC State welcomes all persons without regard to sexual orientation. The College of Sciences welcomes the opportunity to work with candidates to identify suitable employment opportunities for spouses or partners. ------ Subject: Faculty Positions, Math, Applied Math, and Statistics From: Nadine Rizk nr04@aub.edu.lb Date: September 20, 2013 The Department of Mathematics at the American University of Beirut (AUB) invites applications for positions in Mathematics at the Assistant Professor level. Employment will begin September 1, 2014. Visiting appointments at other ranks may be possible. Only applicants holding a Ph.D. in Mathematics, Statistics or Applied Mathematics and showing a strong commitment to teaching and research will be considered. Anticipated vacancies are in any of the following areas: (1) Analysis, (2) Partial Differential Equations and Differential Geometry, (3) Numerical Analysis and Computing, (4) Statistics and Probability. Strong candidates in other areas of mathematics may be considered. AUB is a teaching-centered research university. Its mission is to enhance education, primarily for the people of the Middle East, and to participate in the advancement of knowledge. The beautiful campus is located on a hill in Beirut overlooking the Mediterranean Sea, with pleasant weather year-round. The language of instruction is English. All interested applicants should send a letter of application with a current CV, research and teaching statements, and arrange for three letters of reference. Electronic submissions may be sent by e-mail to: as_dean@aub.edu.lb , or can be sent through the Mathjobs website at https://www.mathjobs.org , or may be sent by post to the address listed on our advertisement at the Mathjobs website. Applicants should indicate whether they are planning to attend the AMS-MAA joint mathematics meetings on January 15-18, 2014 in Baltimore, Maryland. The deadline for applications is December 1, 2013. The American University of Beirut is an Equal Opportunity Employer. ------ Subject: Assistant Professor Position, Mathematical Biology From: Cindy Moulton cindy.moulton@usu.edu Date: September 16, 2013 Assistant Professor in Mathematical Biology Utah State University The Department of Mathematics and Statistics seeks an Assistant Professor of Mathematical Biology who will extend and enhance Utah State University's interdisciplinary research and education programs in mathematical and biological/ecological sciences (broadly interpreted). The position is a 9-month, tenure track position in mathematical biology/ecology. Postdoctoral experience is preferred; a PhD in Mathematics, Applied Mathematics or related discipline is required. The candidate will work toward tenure in Mathematics and Statistics but will be expected to interact with existing, and develop new, interdisciplinary teams, particularly in the Department of Biology, College of Science, and the University-wide Ecology Center (http://www.usu.edu/ecology/). Duties in Mathematics & Statistics include teaching graduate and undergraduate classes in applied mathematics (such as numerical methods, stochastic processes, nonlinear dynamics, partial differential equations, asymptotic analysis, applied math in biology) and supervising research students in the interdisciplinary masters and PhD programs. We are particularly interested in applicants who are excited about opportunities to interact with quantitatively oriented biologists and ecologists on campus and who have experience modeling/simulating ecological processes. Applicants with background in applied probability or numerical solution of partial/stochastic differential equations are particularly welcome. Utah State University has an excellent climate for interdisciplinary research, with a history of interdisciplinary education and grantsmanship. The state of Utah was recently given EPSCoR status by the National Science Foundation, offering young faculty an advantage when seeking funding opportunities. Publications in biological and ecological journals are encouraged and will count with equal weight toward tenure as those in mathematical or statistical journals. Candidates should submit a cover letter, three letters of recommendation, and curriculum vitae on USU????????s employment website (https://jobs.usu.edu). At least one of the letters should address teaching qualifications. A separate, brief (two pages or less) statement of research interests and capabilities, indicating how the candidate envisions enhancing the university's interdisciplinary research programs in quantitative biology and ecology, must also be submitted. Full position and application details appear on the USU employment website and on the Department of Mathematics and Statistics website (http://www.math.usu.edu/). Utah State University is an AA/EO employer, sensitive to the needs of dual-career applicants. The university is open to considering dual-career appointments for suitable professional partners and is dedicated to recruiting stellar candidates from a diverse pool including women, minorities, veterans and people with disabilities. Qualified couples should note that the department also has a faculty search in differential geometry and mathematical physics. USU offers competitive salaries with outstanding medical, retirement and professional benefits (for details visit http://www.usu.edu/hr/). The main campus is in Logan, Utah, a semi-rural city in a mountain valley with a community of 100,000 people, offering ample opportunities for family-friendly professional life. Local ski resorts, lakes, rivers, and mountains create an excellent recreation environment. Applicants should apply at http://jobs.usu.edu/applicants/Central?quickFind=59244 or https://jobs.usu.edu (Req. ID 054096). Details about requirements for the application process are explained on this site. Review of applications begins January 14, 2014, with the position open until filled. Email inquiries should be directed to jim.powell@usu.edu. ------ Subject: 3 Academic Positions, Univ of Pretoria From: Roumen Anguelov roumen.anguelov@up.ac.za Date: September 23, 2013 The Department of Mathematics and Applied Mathematics at University of Pretoria invites applications for three academic posts at the level of Lecturer/Senior Lecturer/Associate Professor/Professor. For more information visit "Positions" at http://www.up.ac.za/maths. Closing date: 14 October 2013 Enquiries: Roumen Anguelov (roumen.anguelov@up.ac.za) ------ Subject: Contents, The Journal of Geometric Mechanics 5:3 From: Susan Cummins Date: Fri, 27 Sep 2013 16:49:51 -0500 The Journal of Geometric Mechanics (JGM) Volume: 5, Number: 3 September 2013 http://aimsciences.org/journals/contentsListnew.jsp?pubID=629 1. A setting for higher order differential equation fields and higher order Lagrange and Finsler spaces Pages : 257 - 279 Ioan Bucataru 2. Smooth perfectness for the group of diffeomorphisms Pages : 281 - 294 Stefan Haller, Tomasz Rybicki and Josef Teichmann 3. Multi-symplectic method to simulate Soliton resonance of (2+1)-dimensional Boussinesq equation Pages : 295 - 318 Weipeng Hu, Zichen Deng and Yuyue Qin 4. On Euler's equation and 'EPDiff' Pages : 319 - 344 David Mumford and Peter W. Michor 5. The Kadomtsev-Petviashvili hierarchy and the Mulase factorization of formal Lie groups Pages : 345 - 364 Anahita Eslami Rad and Enrique G. Reyes 6. Variational formulation of commuting Hamiltonian flows: Multi-time Lagrangian 1-forms Pages : 365 - 379 Yuri B. Suris ------ Subject: Contents, Journal of Modern Dynamics 7:2 From: Susan Cummins Date: Fri, 27 Sep 2013 16:01:11 -0500 Journal of Modern Dynamics (JMD) Volume: 7, Number: 2 June 2013 http://aimsciences.org/journals/contentsListJMDnew.jsp?pubID=627 1. On cyclicity-one elliptic islands of the standard map Pages : 153 - 208 Jacopo De Simoi 2. Weierstrass filtration on Teichmuller curves and Lyapunov exponents Pages : 209 - 237 Fei Yu and Kang Zuo 3. Infinitely many lattice surfaces with special pseudo-Anosov maps Pages : 239 - 254 Kariane Calta and Thomas A. Schmidt 4. Robustly invariant sets in fiber contracting bundle flows Pages : 255 - 267 Oliver Butterley and Carlangelo Liverani 5. Growth of quotients of groups acting by isometries on Gromov-hyperbolic spaces Pages : 269 - 290 Stephane Sabourau 6. On the deviation of ergodic averages for horocycle flows Pages : 291 - 328 Andreas Strombergsson ------ Subject: Contents, Discrete and Continuous Dynamical Systems - Series B 18:9 From: Susan Cummins Date: Mon, 30 Sep 2013 09:14:19 -0500 Discrete and Continuous Dynamical Systems - Series B (DCDS-B) Volume: 18, Number: 9 November 2013 http://aimsciences.org/journals/contentsListnew.jsp?pubID=628 1. A mixed discontinuous Galerkin, convex splitting scheme for a modified Cahn-Hilliard equation and an efficient nonlinear multigrid solver Pages : 2211 - 2238 Andreas C. Aristotelous, Ohannes Karakashian and Steven M. Wise 2. Epidemic models with age of infection, indirect transmission and incomplete treatment Pages : 2239 - 2265 Liming Cai, Maia Martcheva and Xue-Zhi Li 3. Evolutionary branching patterns in predator-prey structured populations Pages : 2267 - 2282 Marcello Delitala and Tommaso Lorenzi 4. Dynamics of a ratio-dependent predator-prey system with a strong Allee effect Pages : 2283 - 2313 Yujing Gao and Bingtuan Li 5. Blow-up results for semilinear wave equations in the superconformal case Pages : 2315 - 2329 Mohamed-Ali Hamza and Hatem Zaag 6. On the dynamics of two-consumers-one-resource competing systems with Beddington-DeAngelis functional response Pages : 2331 - 2353 Sze-Bi Hsu, Shigui Ruan and Ting-Hui Yang 7. The infected frontier in an SEIR epidemic model with infinite delay Pages : 2355 - 2376 Zhigui Lin, Yinan Zhao and Peng Zhou 8. Nonlinear dynamics of a mathematical model on action potential duration and calcium transient in paced cardiac cells Pages : 2377 - 2396 Jiying Ma and Dongmei Xiao 9. Strong and weak Allee effects and chaotic dynamics in Richards' growths Pages : 2397 - 2425 J. Leonel Rocha, Daniele Fournier-Prunaret and Abdel-Kaddous Taha 10. Advantages for controls imposed in a proper subset Pages : 2427 - 2439 Gengsheng Wang and Yashan Xu 11. Spreading speed and traveling waves for a two-species weak competition system with free boundary Pages : 2441 - 2455 Chang-Hong Wu 12. A study on the positive nonconstant steady states of nonlocal chemotaxis systems Pages : 2457 - 2485 Tian Xiang 13. On positive solutions and the Omega limit set for a class of delay differential equations Pages : 2487 - 2503 Changjing Zhuge, Xiaojuan Sun and Jinzhi Lei ------ Subject: Contents, Discrete and Continuous Dynamical Systems - Series S 7:2 From: Susan Cummins Date: Mon, 23 Sep 2013 01:26:15 -0500 Discrete and Continuous Dynamical Systems - Series S (DCDS-S) Volume: 7, Number: 2 April 2014 http://aimsciences.org/journals/contentsListnew.jsp?pubID=626 1. Preface: Workshop in fluid mechanics and population dynamics Pages : i - i Alain Miranville, Mazen Saad and Raafat Talhouk 2. Study of degenerate parabolic system modeling the hydrogen displacement in a nuclear waste repository Pages : 191 - 205 Florian Caro, Bilal Saad and Mazen Saad 3. From particles scale to anomalous or classical convection-diffusion models with path integrals Pages : 207 - 238 Catherine Choquet and Marie-Christine Neel 4. Shallow water asymptotic models for the propagation of internal waves Pages : 239 - 269 Vincent Duchene, Samer Israwi and Raafat Talhouk 5. Some mathematical models in phase transition Pages : 271 - 306 Alain Miranville 6. Two-dimensional individual clustering model Pages : 307 - 316 Elissar Nasreddine 7. Numerical analysis of a non equilibrium two-component two-compressible flow in porous media Pages : 317 - 346 Bilal Saad and Mazen Saad 8. Asymptotics of wave models for non star-shaped geometries Pages : 347 - 362 Farah Abou Shakra ------ Subject: Contents, Mathematical Biosciences and Engineering 11:1 From: Susan Cummins Date: Fri, 20 Sep 2013 10:31:08 -0500 Mathematical Biosciences and Engineering (MBE) Volume: 11, Number: 1 February 2014 http://aimsciences.org/journals/contentsListnew.jsp?pubID=622 1. Preface Pages : i - ii Susanne Ditlevsen and Petr Lansky 2. A simple algorithm to generate firing times for leaky integrate-and-fire neuronal model Pages : 1 - 10 Aniello Buonocore, Luigia Caputo, Enrica Pirozzi and Maria Francesca Carfora 3. Diffusion approximation of neuronal models revisited Pages : 11 - 25 Jakub Cupera 4. Cross nearest-spike interval based method to measure synchrony dynamics Pages : 27 - 48 Aldana M. Gonzalez Montoro, Ricardo Cao, Christel Faes, Geert Molenberghs, Nelson Espinosa, Javier Cudeiro and Jorge Mari\~no 5. Estimating nonstationary inputs from a single spike train based on a neuron model with adaptation Pages : 49 - 62 Hideaki Kim and Shigeru Shinomoto 6. The effect of interspike interval statistics on the information gain under the rate coding hypothesis Pages : 63 - 80 Shinsuke Koyama and Lubomir Kostal 7. Non-Markovian spiking statistics of a neuron with delayed feedback in presence of refractoriness Pages : 81 - 104 Kseniia Kravchuk and Alexander Vidybida 8. Fano factor estimation Pages : 105 - 123 Kamil Rajdl and Petr Lansky 9. Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators Pages : 125 - 138 Ryotaro Tsuneki, Shinji Doi and Junko Inoue 10. Structural phase transitions in neural networks Pages : 139 - 148 Tatyana S. Turova 11. Network inference with hidden units Pages : 149 - 165 Joanna Tyrcha and John Hertz ------ Subject: Contents, Mathematical Control and Related Fields 3:3 From: Susan Cummins Date: Mon, 23 Sep 2013 00:38:25 -0500 Mathematical Control and Related Fields (MCRF) Volume: 3, Number: 3 September 2013 http://aimsciences.org/journals/contentsListnew.jsp?pubID=624 1. Preface Pages : i - ii J.-B. Caillau, Monique Chyba, Dominique Sugny and Emmanuel Trelat 2. Estimates on trajectories in a closed set with corners for (t,x) dependent data Pages : 245 - 267 Piernicola Bettiol and Richard Vinter 3. On the motion planning of the ball with a trailer Pages : 269 - 286 Nicolas Boizot and Jean-Paul Gauthier 4. The Serret-Andoyer Riemannian metric and Euler-Poinsot rigid body motion Pages : 287 - 302 Bernard Bonnard, Olivier Cots and Nataliya Shcherbakova 5. Phantom tracking method, homogeneity and rapid stabilization Pages : 303 - 322 Jean-Michel Coron 6. Asymptotic stability of uniformly bounded nonlinear switched systems Pages : 323 - 345 Philippe Jouan and Said Naciri 7. Affine-quadratic problems on Lie groups Pages : 347 - 374 Velimir Jurdjevic ------ Subject: Contents, Mathematical Control and Related Fields 3:4 From: Susan Cummins Date: Mon, 23 Sep 2013 00:42:42 -0500 Mathematical Control and Related Fields (MCRF) Volume: 3, Number: 4 December 2013 http://aimsciences.org/journals/contentsListnew.jsp?pubID=625 1. On the application of geometric optimal control theory to Nuclear Magnetic Resonance Pages : 375 - 396 Elie Assemat, Marc Lapert, Dominique Sugny and Steffen J. Glaser 2. Algebraic geometric classification of the singular flow in the contrast imaging problem in nuclear magnetic resonance Pages : 397 - 432 Bernard Bonnard, Monique Chyba, Alain Jacquemard and John Marriott 3. Controllability with quadratic drift Pages : 433 - 446 Roger Brockett 4. Sparse stabilization and optimal control of the Cucker-Smale model Pages : 447 - 466 Marco Caponigro, Massimo Fornasier, Benedetto Piccoli and Emmanuel Trelat 5. Ricci curvatures in Carnot groups Pages : 467 - 487 Ludovic Rifford ------ Subject: Contents, Communications in Mathematical Sciences 12:2 From: Communications in Math Sciences Date: Sat, 21 Sep 2013 09:45:49 -0500 Communications in Mathematical Sciences (CMS) Vol 12, No. 2, 2014 Table of Contents full articles are online at http://intlpress.com/site/pub/pages/journals/items/cms/content/_home/index.html Quantitative photoacoustic imaging in the radiative transport regime Alexander V. Mamonov and Kui Ren On convergence of the projective integration method for stiff ordinary differential equations Georg A. Gottwald and John MacLean On a system coupling two-crystallization Allen-Cahn equations and a singular Navier-Stokes system Bianca Morelli Rodolfo Calsavara and Josi Luiz Boldrini Sub-linear estimate of large velocities in a collisionless plasma Zili Chen and Xianwen Zhang Scattering of solutions and stability of solitary waves for the generalized BBM-ZK equation Amin Esfahani Evolution of non-isothermal Landau-de Gennes nematic liquid crystals flows with singular potential Eduard Feireisl, Elisabetta Rocca, Giulio Schimperna, and Arghir Zarnescu Homogenization of stochastic semilinear parabolic equations with non-Lipschitz forcings in domains with finegrained boundaries Mamadou Sango Asymptotic expansion of the stokes solutions at small viscosity: The case of non-compatible initial data Gung-Min Gie