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 Showing 1 - 200 of 538 Journals sorted alphabetically Abakós       (Followers: 3) Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg       (Followers: 3) Academic Voices : A Multidisciplinary Journal       (Followers: 2) Accounting Perspectives       (Followers: 8) ACM Transactions on Algorithms (TALG)       (Followers: 16) ACM Transactions on Computational Logic (TOCL)       (Followers: 4) ACM Transactions on Mathematical Software (TOMS)       (Followers: 6) ACS Applied Materials & Interfaces       (Followers: 22) Acta Applicandae Mathematicae       (Followers: 1) Acta Mathematica       (Followers: 11) Acta Mathematica Hungarica       (Followers: 2) Acta Mathematica Scientia       (Followers: 5) Acta Mathematica Sinica, English Series       (Followers: 5) Acta Mathematica Vietnamica Acta Mathematicae Applicatae Sinica, English Series Advanced Science Letters       (Followers: 7) Advances in Applied Clifford Algebras       (Followers: 3) Advances in Calculus of Variations       (Followers: 2) Advances in Catalysis       (Followers: 5) Advances in Complex Systems       (Followers: 7) Advances in Computational Mathematics       (Followers: 15) Advances in Decision Sciences       (Followers: 5) Advances in Difference Equations       (Followers: 1) Advances in Fixed Point Theory       (Followers: 5) Advances in Geosciences (ADGEO)       (Followers: 10) Advances in Linear Algebra & Matrix Theory       (Followers: 2) Advances in Materials Sciences       (Followers: 16) Advances in Mathematical Physics       (Followers: 5) Advances in Mathematics       (Followers: 10) Advances in Numerical Analysis       (Followers: 4) Advances in Operations Research       (Followers: 11) Advances in Porous Media       (Followers: 4) Advances in Pure and Applied Mathematics       (Followers: 6) Advances in Pure Mathematics       (Followers: 4) Advances in Science and Research (ASR)       (Followers: 6) Aequationes Mathematicae       (Followers: 2) African Journal of Educational Studies in Mathematics and Sciences       (Followers: 5) African Journal of Mathematics and Computer Science Research       (Followers: 4) Afrika Matematika       (Followers: 1) Air, Soil & Water Research       (Followers: 8) AKSIOMA Journal of Mathematics Education       (Followers: 1) Al-Jabar : Jurnal Pendidikan Matematika Algebra and Logic       (Followers: 4) Algebra Colloquium       (Followers: 4) Algebra Universalis       (Followers: 2) Algorithmic Operations Research       (Followers: 5) Algorithms       (Followers: 11) Algorithms Research       (Followers: 1) American Journal of Biostatistics       (Followers: 9) American Journal of Computational and Applied Mathematics       (Followers: 4) American Journal of Mathematical Analysis American Journal of Mathematics       (Followers: 7) American Journal of Operations Research       (Followers: 5) American Mathematical Monthly       (Followers: 6) An International Journal of Optimization and Control: Theories & Applications       (Followers: 7) Analele Universitatii Ovidius Constanta - Seria Matematica       (Followers: 1) Analysis       (Followers: 2) Analysis and Applications       (Followers: 1) Analysis and Mathematical Physics       (Followers: 3) Analysis Mathematica Annales Mathematicae Silesianae Annales mathématiques du Québec       (Followers: 4) Annales UMCS, Mathematica       (Followers: 1) Annales Universitatis Paedagogicae Cracoviensis. 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 Arnold Mathematical Journal   [1 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 2199-6792 - ISSN (Online) 2199-6806    Published by Springer-Verlag  [2352 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
Points
• 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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