Synopses & Reviews
The emphasis of the two volumes is on complex analysis with classical topics such as value distribution, and modern topics such as complex dynamics, both in one and several complex variables; the application of complex analysis to partial differential equations and integral equations and its generalization to quaternionic and Clifford analysis; new results from real and functional analysis, numerical and computational mathematics; and areas in applied mathematics such as acoustics and computational biology. Audience: Researchers, especially those working in real and complex analysis, in numerical analysis, and in mathematical physics.
Synopsis
Let 8 be a Riemann surface of analytically finite type (9, n) with 29 - 2+n> O. Take two pointsP1, P2 E 8, and set 8,1>2= 8 \ {P1' P2}. Let PI Homeo+(8;P1, P2) be the group of all orientation preserving homeomor- phismsw: 8 -+ 8 fixingP1, P2 and isotopic to the identity on 8. Denote byHomeot(8;Pb P2) the set of all elements ofHomeo+(8;P1, P2) iso- topic to the identity on 8, P2' ThenHomeot(8;P1, P2) is a normal sub- pl group ofHomeo+(8;P1, P2). We setIsot(8;P1, P2) =Homeo+(8;P1, P2)/ Homeot(8;p1, P2). The purpose of this note is to announce a result on the Nielsen- Thurston-Bers type classification of an element w] ofIsot+(8;P1, P2). We give a necessary and sufficient condition for thetypeto be hyperbolic. The condition is described in terms of properties of the pure braid b ] w induced by w]. Proofs will appear elsewhere. The problem considered in this note and the form ofthe solution are suggested by Kra's beautiful theorem in 6], where he treats self-maps of Riemann surfaces with one specified point. 2 TheclassificationduetoBers Let us recall the classification of elements of the mapping class group due to Bers (see Bers 1]). LetT(R) be the Teichmiiller space of a Riemann surfaceR, andMod(R) be the Teichmtiller modular group of R. Note that an orientation preserving homeomorphism w: R -+ R induces canonically an element (w) EMod(R). Denote by&.r(R)(-, .) the Teichmiiller distance onT(R). For an elementXEMod(R), we define a(x)= inf &.r(R)(r, x(r)).
Table of Contents
Volume 1: Preface.
1. A central limit theorem for the Simple random walk on a crystal lattice;
M. Kotani, T. Sunada. 2. Level Statistics for Quantum Hamiltonians - Some Preliminary Ideas toward Mathematical Justification of the Theory of Berry and Tabor;
N. Minami. 3. Fermion process and Fredholm determinant;
T. Shirai, Y. Takahashi. 4. Strong type estimation from weak type estimates for some integral operators;
N. Fujii. 5. Conjugate Fourier Series and Integrals of Several Variables in the
l - 1 Sense;
Z. Li. 6. Admissible wavelets and Siegel domains;
H. Liu. 7. Some results on a class of oscillatory Integrals;
S. Lu. 8. Weighted Hardy spaces on a domain;
A. Miyachi. 9. Commutators of singular integral operators on Morrey spaces with some growth functions;
T. Mizuhara. 10. On generalized fractional integrals in the Orlicz spaces;
E. Nakai. 11. Weak (1,1) estimates for Littlewood-Paley functions with rough kernels;
S. Sato. 12. A Note on average densities of Brownian intersection measures;
N.-R. Shieh. 13. Problem of integral geometry on paraboloids with perturbation;
A.H. Begmatov. 14. The connection between discrete and continuous realisations of least squares method;
Y.V. Chebrakov, V.V. Shmagin. 15. An Eigenvalue Problem for Analytic Functions;
D.Q. Dai, M.S. Liu. 16. On quadrature formulae of hypersingular integrals;
J.Y. Du, J.C. Hu. 17. Theoretical and numerical analysis of inversion of satellite remote sensing;
S.-x. Huang, J. Li. 18. Optimization of vector-valued integral equations for a class; C.G. Hu, L.X. Ma. 19. Nonlinear Riemann-Hilbert problems of first order quasi-linear elliptic system; M.Z. Li. 20. The algorithm implementation of Cauchy singular integral in Daubechies wavelets on the interval; W. Lin, Q. Li. 21. Closed form solution for a hypersingular integral equation of order n + 1; X. Li. 22. Cyclically symmetric crack problems of different media II; J. Lu. 23. Linear conjugate boundary value problems for first order ordinary system of linear differential equations with singular or super singular coefficients; N. Rajabov. 24. Initial-mixed boundary value problems for parabolic equations of second order with measurable coeeficients in a higher dimensional domain; G.C. Wen. 25. Stability estimates in states-estimation for a heat process; D. Xu, M. Yamamoto. 26. Plastic zone and opening displacement for an asymmetrical fast propagating semi-infinite crack in a strip; X.-C. Yang, T.-Y. Fan. 27. Certain class of hyperanalytic Haseman boundary value problems; Y.S. Zeng. 28. On compound boundary value problems for non linear elliptic systems of first order; C. Zhao. 29. On the integral of Cauchy type and the generalized Harnack theorem for bianalytic functions; Z. Zhao. 30. The growth of spirallike mappings; H. Hamada, G. Kohr. 31. Subordination principle to functions of several complex variables; K.H. Shon, G.M. Son. 32. &rgr;-adic Nevanlinna Theory and Functional Equations; A. Boutabaa, A. Escassut. 33. Unique range sets in p-adic and complex analysis; A. Escassut, A. Boutabaa. 34. On uniqueness of meromorphic functions sharing finite sets; H. Fujimoto. 35. Defect relations for moving targets; P.-C. Hu, C.-C. Yang. 36. The Green-residue theorem and the Nevanlinna's second theorem on small functions in Banach spaces; C.-G. Hu, X.-F. Ye. 37. Dynamics of Transcendental Functions; X. Hua, et al. 38. On the Growth of Meromorphic Solutions of Algebraic Differential Equations; L. Liao. 39. Numerical conformal mapping by the charge simulation method and its application to potential flow analysis; K. Amano, et al. 40. Hénon mapping of complex n-space in complex n-space; Y. Fukushima. 41. The Carathéodory convergence of Fatou components of polynomials to Baker domains or wandering domains; S. Morosawa. 42. DE-type quadrature formulae for Cauchy principal-value integrals and for Hadamard finite-part integrals; H. Ogata, et al. 43. Mathematical models used for sound synthesis; K. Ohya, K. Shinjo. 44. An integral equation method of numerical conformal mapping onto parallel, circular and radial slit domains; D. Okano, K. Amano. 45. Uniformly perfect sets, rational semigroups, Kleinian Groups and Iterated functions systems; R.Stankewitz. 45 More Chapters.
Volume 2: A characterization of analytic functionals on the sphere II; M. Morimoto, M. Suwa. 92. An algorithm for the local residues with the viewpoint of D-module; Y. Nakamura, S. Tajima. 93. On non quasi-analytic classes of functions and the space of Whitney jets of class M; Y.S. Park. 94. Algebraic analysis of multivariate Hermite interpolation formulas; S. Tajima. 95. Deformation of singularities via quivers; M. Tsuji. 96. Fuchsian Cauchy problem for entire functions; H. Yamane. 97. Imbedding theorems in Sobolev-Orlicz spaces; A.F. Chuvenkov. 98. Unbounded C*-seminorms on *-algebras; S.J. Bhatt, et al. 99. A remark on the Bers type of some self-maps of Riemann surfaces with two specified points; Y. Imayoshi, et al. 100. Some results concerning the determination of the polynomials on E by the dual space E'; S. Lassalle. 101. A note on Strebel differentials; Z. Li. 102. A pseudo-metric on the space of generalized quasisymmetric automorphisms of a Jordan curve; D. Partykai, K. Sakan. 103. Fatou sets of permutable functions satisfying functional equations; Y. Wang. 104. Hamilton sequences and point shift differentials; Y. Qi, S. Wu. 105. Chaos in Two-dimensional Mappings; J. Zhou. 106. Round-off error of optimal control problems in floating-point number systems; K. Tsuji. 107. Some codes determined by their weight enumerators; E.J. Cheon, S.J. Kim. 108. Goppa codes supported by two points on a curve; M. Homma, S.J. Kim. 109. The most symmetric non-singular plane curves; H. Kaneta, et al. 110. Variety of special nets of degree g &endash; 1 on double coverings of a smooth plane quartic of genus 9; K.-H. Cho, et al. 111. Cohomologies of elliptic curves; U. Narzullaev. 112. Non-cyclic Weierstrass semigroups; S.J. Kim, J. Komeda. <> Finite group actions on compact Riemann surfaces of genus 4;
H. Kimura. 114. Discreteness of the mapping class group for Riemann surfaces of infinite analytic type;
E. Fujikawa, et al. 115. Schottky groups and Bers boundary of Teichmüller space;
K. Ito. 116. The asymptotic behavior of Eisenstein series and a comparison of the Weil-Pettersson and the Zograf-Takhtajan metrics;
K. Obitsu. 117. Asplund operators on locally convex spaces;
C. Boyd, et al. 118. Three dimensional shift-like mappings of dynamical degree golden ratio;
K. Maegawa. 119. Iteration of some birational polynomial maps in
Pn^{2};
T. Shinohara. 120. On the Fatou component of polynomial maps on
C^{2};
M. Suzuki. 121. Closure of Drinfeld's associator and the Kontsevich integral for (2,
n)-torus knots;
S.D. Tyurina. 122. Extremal quasiconformal extension and quadrilateral modulus;
X. Huang. 123. On the non-linearizability of analytic germs and irrationally independent fixed points;
Y. Okuyama. 124. A note on a paper of Saski;
Y. Komori. 125. Unified approach to conformally invariant metrics on Riemann surfaces;
T. Sugawa. 126. A remark on a normal domain;
T. Kanemaru. 127. Extension theorems for Sobolev and more general spaces for degenerate open sets;
V.I. Burenkov. 128. Behavior of the higher order derivatives of solutions of a class of nonhypoelliptic equations in the infinite cylinder;
G.H. Hakobyan, V.N. Markarjan. 129. Generalized isometric spheres of elements of PU(1,n;C);
S. Kamiya. 130. Aymptotic formula for minimal eigenvalues of Hilbert type matrices;
G.A. Kalyabin. 39 Other Chapters.