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  Subjects -> MATHEMATICS (Total: 968 journals)
    - APPLIED MATHEMATICS (81 journals)
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    - MATHEMATICS (714 journals)
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MATHEMATICS (714 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 29)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 12)
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: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 10)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 3)
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: 19)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 3)
Advances in Materials Science     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 4)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Numerical Analysis     Open Access   (Followers: 5)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 6)
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: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 6)
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 Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 5)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 2)
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 4)
Annals of Data Science     Hybrid Journal   (Followers: 12)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription   (Followers: 1)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 3)
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)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 2)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 20)
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: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
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: 12)
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 Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
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: 19)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
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: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
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: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
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: 5)
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: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
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: 29)
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: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Combinatorics     Open Access  
Electronic Journal of Differential Equations     Open Access  
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: 4)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  

        1 2 3 4 | Last

Journal Cover
Arnold Mathematical Journal
Journal Prestige (SJR): 0.355
Number of Followers: 1  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 2199-6792 - ISSN (Online) 2199-6806
Published by Springer-Verlag Homepage  [2348 journals]
  • Two-Valued Groups, Kummer Varieties, and Integrable Billiards
    • Authors: V. M. Buchstaber; V. Dragović
      Abstract: Abstract A natural and important question of study two-valued groups associated with hyperelliptic Jacobians and their relationship with integrable systems is motivated by seminal examples of relationship between algebraic two-valued groups related to elliptic curves and integrable systems such as elliptic billiards and celebrated Kowalevski top. The present paper is devoted to the case of genus 2, to the investigation of algebraic two-valued group structures on Kummer varieties. One of our approaches is based on the theory of \(\sigma \) -functions. It enables us to study the dependence of parameters of the curves, including rational limits. Following this line, we are introducing a notion of n-groupoid as natural multivalued analogue of the notion of topological groupoid. Our second approach is geometric. It is based on a geometric approach to addition laws on hyperelliptic Jacobians and on a recent notion of billiard algebra. Especially important is connection with integrable billiard systems within confocal quadrics. The third approach is based on the realization of the Kummer variety in the framework of moduli of semi-stable bundles, after Narasimhan and Ramanan. This construction of the two-valued structure is remarkably similar to the historically first example of topological formal two-valued group from 1971, with a significant difference: the resulting bundles in the 1971 case were ”virtual”, while in the present case the resulting bundles are effectively realizable.
      PubDate: 2018-04-09
      DOI: 10.1007/s40598-018-0085-2
       
  • Cyclohedron and Kantorovich–Rubinstein Polytopes
    • Authors: Filip D. Jevtić; Marija Jelić; Rade T. Živaljević
      Abstract: Abstract We show that the cyclohedron (Bott–Taubes polytope) \(W_n\) arises as the polar dual of a Kantorovich–Rubinstein polytope \(KR(\rho )\) , where \(\rho \) is an explicitly described quasi-metric (asymmetric distance function) satisfying strict triangle inequality. From a broader perspective, this phenomenon illustrates the relationship between a nestohedron \(\Delta _{{\widehat{\mathcal {F}}}}\) (associated to a building set \({\widehat{\mathcal {F}}}\) ) and its non-simple deformation \(\Delta _{\mathcal {F}}\) , where \(\mathcal {F}\) is an irredundant or tight basis of \({\widehat{\mathcal {F}}}\) (Definition 21). Among the consequences are a new proof of a recent result of Gordon and Petrov (Arnold Math. J. 3(2):205–218, 2017) about f-vectors of generic Kantorovich–Rubinstein polytopes and an extension of a theorem of Gelfand, Graev, and Postnikov, about triangulations of the type A, positive root polytopes.
      PubDate: 2018-04-09
      DOI: 10.1007/s40598-018-0083-4
       
  • Trace Test
    • Authors: Anton Leykin; Jose Israel Rodriguez; Frank Sottile
      Abstract: Abstract The trace test in numerical algebraic geometry verifies the completeness of a witness set of an irreducible variety in affine or projective space. We give a brief derivation of the trace test and then consider it for subvarieties of products of projective spaces using multihomogeneous witness sets. We show how a dimension reduction leads to a practical trace test in this case involving a curve in a low-dimensional affine space.
      PubDate: 2018-04-05
      DOI: 10.1007/s40598-018-0084-3
       
  • Upper Bounds on Betti Numbers of Tropical Prevarieties
    • Authors: Dima Grigoriev; Nicolai Vorobjov
      Abstract: Abstract We prove upper bounds on the sum of Betti numbers of tropical prevarieties in dense and sparse settings. In the dense setting the bound is in terms of the volume of Minkowski sum of Newton polytopes of defining tropical polynomials, or, alternatively, via the maximal degree of these polynomials. In sparse setting, the bound involves the number of the monomials.
      PubDate: 2018-04-03
      DOI: 10.1007/s40598-018-0086-1
       
  • Affine Hecke Algebras via DAHA
    • Authors: Ivan Cherednik
      Abstract: Abstract A method is suggested for obtaining the Plancherel measure for Affine Hecke Algebras as a limit of integral-type formulas for inner products in the polynomial and related modules of Double Affine Hecke Algebras. The analytic continuation necessary here is a generalization of “picking up residues” due to Arthur, Heckman, Opdam and others, which can be traced back to Hermann Weyl. Generally, it is a finite sum of integrals over double affine residual subtori; a complete formula is presented for \(A_1\) in the spherical case.
      PubDate: 2018-04-03
      DOI: 10.1007/s40598-018-0082-5
       
  • Semiconjugate Rational Functions: A Dynamical Approach
    • Authors: F. Pakovich
      Abstract: Abstract Using dynamical methods we give a new proof of the theorem saying that if A, B, X are rational functions of complex variable z of degree at least two such that \(A\circ X=X\circ B\) and \({\mathbb C}(B,X)={\mathbb C}(z)\) , then the Galois closure of the field extension \({\mathbb C}(z)/{\mathbb C}(X)\) has genus zero or one.
      PubDate: 2018-02-12
      DOI: 10.1007/s40598-018-0081-6
       
  • Open Problems on Configuration Spaces of Tensegrities
    • Authors: Oleg Karpenkov
      Abstract: Abstract In this small paper we bring together some open problems related to the study of the configuration spaces of tensegrities, i.e. graphs with stresses on edges. These problems were announced in Doray et al. (Discrete Comput Geom 43:436–466, 2010), Karpenkov et al. (ARS Math Contemp 6:305–322, 2013), Karpenkov (The combinatorial geometry of stresses in frameworks. arXiv:1512.02563 [math.MG], 2017), and Karpenkov (Geometric Conditions of Rigidity in Nongeneric settings, 2016) (by F. Doray, J. Schepers, B. Servatius, and the author), for more details we refer to the mentioned articles.
      PubDate: 2018-02-02
      DOI: 10.1007/s40598-018-0080-7
       
  • Modular Periodicity of the Euler Numbers and a Sequence by Arnold
    • Authors: Sanjay Ramassamy
      Abstract: Abstract For any positive integer q, the sequence of the Euler up/down numbers reduced modulo q was proved to be ultimately periodic by Knuth and Buckholtz. Based on computer simulations, we state for each value of q precise conjectures for the minimal period and for the position at which the sequence starts being periodic. When q is a power of 2, a sequence defined by Arnold appears, and we formulate a conjecture for a simple computation of this sequence.
      PubDate: 2018-01-22
      DOI: 10.1007/s40598-018-0079-0
       
  • 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)
       
  • Secant Degeneracy Index of the Standard Strata in The Space of Binary
           Forms
    • Authors: Gleb Nenashev; Boris Shapiro; Michael Shapiro
      Abstract: Abstract The space \(Pol_d\simeq \mathbb {C}P^d\) of all complex-valued binary forms of degree d (considered up to a constant factor) has a standard stratification, each stratum of which contains all forms whose set of multiplicities of their distinct roots is given by a fixed partition \(\mu \vdash d\) . For each such stratum \(S_\mu ,\) we introduce its secant degeneracy index \(\ell _\mu \) which is the minimal number of projectively dependent pairwise distinct points on \(S_\mu \) , i.e., points whose projective span has dimension smaller than \(\ell _\mu -1\) . In what follows, we discuss the secant degeneracy index \(\ell _\mu \) and the secant degeneracy index \(\ell _{{{\bar{\mu }}}}\) of the closure \({{\bar{S}}}_\mu \) .
      PubDate: 2017-12-06
      DOI: 10.1007/s40598-017-0077-7
       
  • The Number $$\pi $$ π and a Summation by $$SL(2,{\mathbb {Z}})$$ S L ( 2
           , Z )
    • Authors: Nikita Kalinin; Mikhail Shkolnikov
      Abstract: Abstract The sum (resp. the sum of squares) of the defects in the triangle inequalities for the area one lattice parallelograms in the first quadrant has a surprisingly simple expression. Namely, let \(f(a,b,c,d)=\sqrt{a^2+b^2}+\sqrt{c^2+d^2}-\sqrt{(a+c)^2+(b+d)^2}\) . Then, where the sum runs by all \(a,b,c,d\in {\mathbb {Z}}_{\ge 0}\) such that \(ad-bc=1\) . We present a proof of these formulae and list several directions for the future studies.
      PubDate: 2017-11-02
      DOI: 10.1007/s40598-017-0075-9
       
  • Orbifold Jacobian Algebras for Exceptional Unimodal Singularities
    • Authors: Alexey Basalaev; Atsushi Takahashi; Elisabeth Werner
      Abstract: Abstract This note shows that the orbifold Jacobian algebra associated to each invertible polynomial defining an exceptional unimodal singularity is isomorphic to the (usual) Jacobian algebra of the Berglund–Hübsch transform of an invertible polynomial defining the strange dual singularity in the sense of Arnold.
      PubDate: 2017-11-02
      DOI: 10.1007/s40598-017-0076-8
       
  • 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
       
  • 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
       
  • 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
       
 
 
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