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MATHEMATICS (656 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 8)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 22)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 7)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 5)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 4)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 3)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 9)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access  
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 19)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 1)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 7)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 5)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)

        1 2 3 4 | Last

Journal Cover Arnold Mathematical Journal
  [1 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 2199-6792 - ISSN (Online) 2199-6806
   Published by Springer-Verlag Homepage  [2353 journals]
  • Origami, Affine Maps, and Complex Dynamics
    • Authors: William Floyd; Gregory Kelsey; Sarah Koch; Russell Lodge; Walter Parry; Kevin M. Pilgrim; Edgar Saenz
      Pages: 365 - 395
      Abstract: Abstract We investigate the combinatorial and dynamical properties of so-called nearly Euclidean Thurston maps, or NET maps. These maps are perturbations of many-to-one folding maps of an affine two-sphere to itself. The close relationship between NET maps and affine maps makes computation of many invariants tractable. In addition to this, NET maps are quite diverse, exhibiting many different behaviors. We discuss data, findings, and new phenomena.
      PubDate: 2017-09-01
      DOI: 10.1007/s40598-017-0071-0
      Issue No: Vol. 3, No. 3 (2017)
  • Integral Geometry of Euler Equations
    • Authors: Nikolai Nadirashvili; Serge Vlăduţ
      Pages: 397 - 421
      Abstract: Abstract We develop an integral geometry of stationary Euler equations defining some function w on the Grassmannian of affine lines in \(\mathbb {R}^3\) depending on a putative compactly supported solution (v; p) of the system and deduce some linear differential equations for w. We conjecture that \(w=0\) everywhere and prove that this conjecture implies that \(v=0.\)
      PubDate: 2017-09-01
      DOI: 10.1007/s40598-017-0072-z
      Issue No: Vol. 3, No. 3 (2017)
  • On Irreducible Components of Real Exponential Hypersurfaces
    • Authors: Cordian Riener; Nicolai Vorobjov
      Pages: 423 - 443
      Abstract: Abstract Fix any real algebraic extension \(\mathbb K\) of the field \(\mathbb Q\) of rationals. Polynomials with coefficients from \(\mathbb K\) in n variables and in n exponential functions are called exponential polynomials over \({\mathbb K}\) . We study zero sets in \({\mathbb R}^n\) of exponential polynomials over \(\mathbb K\) , which we call exponential-algebraic sets. Complements of all exponential-algebraic sets in \({\mathbb R}^n\) form a Zariski-type topology on \({\mathbb R}^n\) . Let \(P \in {\mathbb K}[X_1, \ldots ,X_n,U_1, \ldots ,U_n]\) be a polynomial and denote $$\begin{aligned} V:=\{ (x_1, \ldots , x_n) \in {\mathbb R}^n \> P(x_1, \ldots ,x_n,, e^{x_1}, \ldots ,e^{x_n})=0 \}. \end{aligned}$$ The main result of this paper states that, if the real zero set of a polynomial P is irreducible over \(\mathbb K\) and the exponential-algebraic set V has codimension 1, then, under Schanuel’s conjecture over the reals, either V is irreducible (with respect to the Zariski topology) or each of its irreducible components of codimension 1 is a rational hyperplane through the origin. The family of all possible hyperplanes is determined by monomials of P. In the case of a single exponential (i.e., when P is independent of \(U_2, \ldots , U_n\) ) stronger statements are shown which are independent of Schanuel’s conjecture.
      PubDate: 2017-09-01
      DOI: 10.1007/s40598-017-0073-y
      Issue No: Vol. 3, No. 3 (2017)
  • The Geometry of Axisymmetric Ideal Fluid Flows with Swirl
    • Authors: Pearce Washabaugh; Stephen C. Preston
      Pages: 175 - 185
      Abstract: Abstract The sectional curvature of the volume preserving diffeomorphism group of a Riemannian manifold M can give information about the stability of inviscid, incompressible fluid flows on M. We demonstrate that the submanifold of the volumorphism group of the solid flat torus generated by axisymmetric fluid flows with swirl, denoted by \(\mathcal {D}_{\mu ,E}(M)\) , has positive sectional curvature in every section containing the field \(X = u(r)\partial _\theta \) iff \(\partial _r(ru^2)>0\) . This is in sharp contrast to the situation on \(\mathcal {D}_{\mu }(M)\) , where only Killing fields X have nonnegative sectional curvature in all sections containing it. We also show that this criterion guarantees the existence of conjugate points on \(\mathcal {D}_{\mu ,E}(M)\) along the geodesic defined by X.
      PubDate: 2017-06-01
      DOI: 10.1007/s40598-016-0058-2
      Issue No: Vol. 3, No. 2 (2017)
  • Flows in Flatland: A Romance of Few Dimensions
    • Authors: Gabriel Katz
      Pages: 281 - 317
      Abstract: Abstract This paper is about gradient-like vector fields and flows they generate on smooth compact surfaces with boundary. We use this particular 2-dimensional setting to present and explain our general results about non-vanishing gradient-like vector fields on n-dimensional manifolds with boundary. We take advantage of the relative simplicity of 2-dimensional worlds to popularize our approach to the Morse theory on smooth manifolds with boundary. In this approach, the boundary effects take the central stage.
      PubDate: 2017-06-01
      DOI: 10.1007/s40598-016-0059-1
      Issue No: Vol. 3, No. 2 (2017)
  • Internal Addresses of the Mandelbrot Set and Galois Groups of Polynomials
    • Authors: Dierk Schleicher
      Pages: 1 - 35
      Abstract: Abstract We describe an interesting interplay between symbolic dynamics, the structure of the Mandelbrot set, permutations of periodic points achieved by analytic continuation, and Galois groups of certain polynomials. Internal addresses are a convenient and efficient way of describing the combinatorial structure of the Mandelbrot set, and of giving geometric meaning to the ubiquitous kneading sequences in human-readable form (Sects. 3 and 4). A simple extension, angled internal addresses, distinguishes combinatorial classes of the Mandelbrot set and in particular distinguishes hyperbolic components in a concise and dynamically meaningful way. This combinatorial description of the Mandelbrot set makes it possible to derive existence theorems for certain kneading sequences and internal addresses in the Mandelbrot set (Sect. 6) and to give an explicit description of the associated parameters. These in turn help to establish some algebraic results about permutations of periodic points and to determine Galois groups of certain polynomials (Sect. 7). Through internal addresses, various areas of mathematics are thus related in this manuscript, including symbolic dynamics and permutations, combinatorics of the Mandelbrot set, and Galois groups.
      PubDate: 2017-04-01
      DOI: 10.1007/s40598-016-0042-x
      Issue No: Vol. 3, No. 1 (2017)
  • Building Thermodynamics for Non-uniformly Hyperbolic Maps
    • Authors: Vaughn Climenhaga; Yakov Pesin
      Pages: 37 - 82
      Abstract: Abstract We briefly survey the theory of thermodynamic formalism for uniformly hyperbolic systems, and then describe several recent approaches to the problem of extending this theory to non-uniform hyperbolicity. The first of these approaches involves Markov models such as Young towers, countable-state Markov shifts, and inducing schemes. The other two are less fully developed but have seen significant progress in the last few years: these involve coarse-graining techniques (expansivity and specification) and geometric arguments involving push-forward of densities on admissible manifolds.
      PubDate: 2017-04-01
      DOI: 10.1007/s40598-016-0052-8
      Issue No: Vol. 3, No. 1 (2017)
  • On Tangent Cones of Schubert Varieties
    • Authors: Dmitry Fuchs; Alexandre Kirillov; Sophie Morier-Genoud; Valentin Ovsienko
      Abstract: Abstract We consider tangent cones of Schubert varieties in the complete flag variety, and investigate the problem when the tangent cones of two different Schubert varieties coincide. We give a sufficient condition for such coincidence, and formulate a conjecture that provides a necessary condition. In particular, we show that all Schubert varieties corresponding to the Coxeter elements of the Weyl group have the same tangent cone. Our main tool is the notion of pillar entries in the rank matrix counting the dimensions of the intersections of a given flag with the standard one. This notion is a version of Fulton’s essential set. We calculate the dimension of a Schubert variety in terms of the pillar entries of the rank matrix.
      PubDate: 2017-08-22
      DOI: 10.1007/s40598-017-0074-x
  • When is the Intersection of Two Finitely Generated Subalgebras of a
           Polynomial Ring Also Finitely Generated?
    • Authors: Pinaki Mondal
      Abstract: Abstract We study two variants of the following question: “Given two finitely generated \(\mathbb {C}\) -subalgebras \(R_1, R_2\) of \(\mathbb {C}[x_1, \ldots , x_n]\) , is their intersection also finitely generated?” We show that the smallest value of n for which there is a counterexample is 2 in the general case, and 3 in the case that \(R_1\) and \(R_2\) are integrally closed. We also explain the relation of this question to the problem of constructing algebraic compactifications of \(\mathbb {C}^n\) and to the moment problem on semialgebraic subsets of \(\mathbb {R}^n\) . The counterexample for the general case is a simple modification of a construction of Neena Gupta, whereas the counterexample for the case of integrally closed subalgebras uses the theory of normal analytic compactifications of \(\mathbb {C}^2\) via key forms of valuations centered at infinity.
      PubDate: 2017-06-06
      DOI: 10.1007/s40598-017-0068-8
  • Moduli Space of a Planar Polygonal Linkage: A Combinatorial Description
    • Authors: Gaiane Panina
      Abstract: Abstract We describe and study an explicit structure of a regular cell complex \(\mathcal {K}(L)\) on the moduli space M(L) of a planar polygonal linkage L. The combinatorics is very much related (but not equal) to the combinatorics of the permutohedron. In particular, the cells of maximal dimension are labeled by elements of the symmetric group. For example, if the moduli space M is a sphere, the complex \(\mathcal {K}\) is dual to the boundary complex of the permutohedron.The dual complex \(\mathcal {K}^*\) is patched of Cartesian products of permutohedra. It can be explicitly realized in the Euclidean space via a surgery on the permutohedron.
      PubDate: 2017-05-29
      DOI: 10.1007/s40598-017-0070-1
  • Dynamics of Polynomial Diffeomorphisms of $$\mathbb {C}^2$$ C 2 :
           Combinatorial and Topological Aspects
    • Authors: Yutaka Ishii
      Abstract: Abstract The Fig. 1 was drawn by Shigehiro Ushiki using his software called HenonExplorer. This complicated object is the Julia set of a complex Hénon map \(f_{c, b}(x, y)=(x^2+c-by, x)\) defined on \(\mathbb {C}^2\) together with its stable and unstable manifolds, hence it is a fractal set in the real 4-dimensional space! The purpose of this paper is to survey some results, questions and problems on the dynamics of polynomial diffeomorphisms of \(\mathbb {C}^2\) including complex Hénon maps with an emphasis on the combinatorial and topological aspects of their Julia sets.
      PubDate: 2017-04-25
      DOI: 10.1007/s40598-017-0066-x
  • Vanishing Cycles and Cartan Eigenvectors
    • Authors: Laura Brillon; Revaz Ramazashvili; Vadim Schechtman; Alexander Varchenko
      Abstract: Abstract Using the ideas coming from the singularity theory, we study the eigenvectors of the Cartan matrices of finite root systems, and of q-deformations of these matrices
      PubDate: 2017-04-13
      DOI: 10.1007/s40598-017-0065-y
  • Proof of the Broué–Malle–Rouquier Conjecture in Characteristic Zero
           (After I. Losev and I. Marin—G. Pfeiffer)
    • Authors: Pavel Etingof
      Abstract: Abstract We explain a proof of the Broué–Malle–Rouquier conjecture on Hecke algebras of complex reflection groups, stating that the Hecke algebra of a finite complex reflection group W is free of rank W over the algebra of parameters, over a field of characteristic zero. This is based on previous work of Losev, Marin– Pfeiffer, and Rains and the author.
      PubDate: 2017-04-12
      DOI: 10.1007/s40598-017-0069-7
  • On a Triply Periodic Polyhedral Surface Whose Vertices are Weierstrass
    • Authors: Dami Lee
      Abstract: Abstract In this paper, we will construct an example of a closed Riemann surface X that can be realized as a quotient of a triply periodic polyhedral surface \(\Pi \subset \mathbb {R}^3\) where the Weierstrass points of X coincide with the vertices of \(\Pi .\) First we construct \(\Pi \) by attaching Platonic solids in a periodic manner and consider the surface of this solid. Due to periodicity we can find a compact quotient of this surface. The symmetries of X allow us to construct hyperbolic structures and various translation structures on X that are compatible with its conformal type. The translation structures are the geometric representations of the holomorphic 1-forms of X. Via the basis of 1-forms we find an explicit algebraic description of the surface that suggests the Fermat’s quartic. Moreover the 1-forms allow us to identify the Weierstrass points.
      PubDate: 2017-04-12
      DOI: 10.1007/s40598-017-0067-9
  • Polynomial Splitting Measures and Cohomology of the Pure Braid Group
    • Authors: Trevor Hyde; Jeffrey C. Lagarias
      Abstract: Abstract We study for each n a one-parameter family of complex-valued measures on the symmetric group \(S_n\) , which interpolate the probability of a monic, degree n, square-free polynomial in \(\mathbb {F}_q[x]\) having a given factorization type. For a fixed factorization type, indexed by a partition \(\lambda \) of n, the measure is known to be a Laurent polynomial. We express the coefficients of this polynomial in terms of characters associated to \(S_n\) -subrepresentations of the cohomology of the pure braid group \(H^{\bullet }(P_n, \mathbb {Q})\) . We deduce that the splitting measures for all parameter values \(z= -\frac{1}{m}\) (resp. \(z= \frac{1}{m}\) ), after rescaling, are characters of \(S_n\) -representations (resp. virtual \(S_n\) -representations).
      PubDate: 2017-03-06
      DOI: 10.1007/s40598-017-0064-z
  • Combinatorics of the Lipschitz Polytope
    • Authors: J. Gordon; F. Petrov
      Abstract: Abstract Let \(\rho \) be a metric on the set \(X=\{1,2,\dots ,n+1\}\) . Consider the n-dimensional polytope of functions \(f:X\rightarrow \mathbb {R}\) , which satisfy the conditions \(f(n+1)=0\) , \( f(x)-f(y) \leqslant \rho (x,y)\) . The question on classifying metrics depending on the combinatorics of this polytope have been recently posed by (Vershik, Arnold Math J 1(1):75–81, 2015). We prove that for any “generic” metric the number of \((n-m)\) -dimensional faces, \(0\leqslant m\leqslant n\) , equals \(\left( {\begin{array}{c}n+m\\ m,m,n-m\end{array}}\right) =(n+m)!/m!m!(n-m)!\) . This fact is intimately related to regular triangulations of the root polytope (convex hull of the roots of \(A_n\) root system). Also we get two-sided estimates for the logarithm of the number of Vershik classes of metrics: \(n^3\log n\) from above and \(n^2\) from below.
      PubDate: 2017-02-09
      DOI: 10.1007/s40598-017-0063-0
  • Convex Shapes and Harmonic Caps
    • Authors: Laura DeMarco; Kathryn Lindsey
      Abstract: Abstract Any planar shape \(P\subset {\mathbb {C}}\) can be embedded isometrically as part of the boundary surface S of a convex subset of \(\mathbb {R}^3\) such that \(\partial P\) supports the positive curvature of S. The complement \(Q = S {\setminus } P\) is the associated cap. We study the cap construction when the curvature is harmonic measure on the boundary of \(({\hat{{\mathbb {C}}}}{\setminus } P, \infty )\) . Of particular interest is the case when P is a filled polynomial Julia set and the curvature is proportional to the measure of maximal entropy.
      PubDate: 2017-01-31
      DOI: 10.1007/s40598-016-0061-7
  • Random Chain Complexes
    • Authors: Viktor L. Ginzburg; Dmitrii V. Pasechnik
      Abstract: Abstract We study random, finite-dimensional, ungraded chain complexes over a finite field and show that for a uniformly distributed differential a complex has the smallest possible homology with the highest probability: either zero or one-dimensional homology depending on the parity of the dimension of the complex. We prove that as the order of the field goes to infinity the probability distribution concentrates in the smallest possible dimension of the homology. On the other hand, the limit probability distribution, as the dimension of the complex goes to infinity, is a super-exponentially decreasing, but strictly positive, function of the dimension of the homology.
      PubDate: 2017-01-25
      DOI: 10.1007/s40598-016-0062-6
  • The $$4n^2$$ 4 n 2 -Inequality for Complete Intersection Singularities
    • Authors: Aleksandr V. Pukhlikov
      Abstract: Abstract The famous \(4n^2\) -inequality is extended to generic complete intersection singularities: it is shown that the multiplicity of the self-intersection of a mobile linear system with a maximal singularity is greater than \(4n^2\mu \) , where \(\mu \) is the multiplicity of the singular point.
      PubDate: 2016-11-30
      DOI: 10.1007/s40598-016-0060-8
  • On Postsingularly Finite Exponential Maps
    • Abstract: Abstract We consider parameters \(\lambda \) for which 0 is preperiodic under the map \(z\mapsto \lambda e^z\) . Given k and l, let n(r) be the number of \(\lambda \) satisfying \(0< \lambda \le r\) such that 0 is mapped after k iterations to a periodic point of period l. We determine the asymptotic behavior of n(r) as r tends to \(\infty \) .
      PubDate: 2016-09-19
      DOI: 10.1007/s40598-016-0056-4
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