Subjects -> MATHEMATICS (Total: 1013 journals)
    - APPLIED MATHEMATICS (92 journals)
    - GEOMETRY AND TOPOLOGY (23 journals)
    - MATHEMATICS (714 journals)
    - MATHEMATICS (GENERAL) (45 journals)
    - NUMERICAL ANALYSIS (26 journals)
    - PROBABILITIES AND MATH STATISTICS (113 journals)

MATHEMATICS (714 journals)            First | 1 2 3 4     

Showing 401 - 538 of 538 Journals sorted alphabetically
Journal of mathematical and computational science     Open Access   (Followers: 2)
Journal of Mathematical and Fundamental Sciences     Open Access  
Journal of Mathematical Behavior     Hybrid Journal   (Followers: 6)
Journal of Mathematical Chemistry     Hybrid Journal   (Followers: 5)
Journal of Mathematical Finance     Open Access   (Followers: 6)
Journal of Mathematical Imaging and Vision     Hybrid Journal   (Followers: 6)
Journal of Mathematical Logic     Hybrid Journal   (Followers: 2)
Journal of Mathematical Sciences     Hybrid Journal  
Journal of Mathematical Sciences and Applications     Open Access   (Followers: 2)
Journal of Mathematical Sociology     Hybrid Journal   (Followers: 3)
Journal of Mathematics     Open Access  
Journal of Mathematics and Statistics     Open Access   (Followers: 6)
Journal of Mathematics and Statistics Studies     Open Access  
Journal of Mathematics and the Arts     Hybrid Journal   (Followers: 1)
Journal of Mathematics Education at Teachers College     Open Access   (Followers: 5)
Journal of Mathematics in Industry     Open Access  
Journal of Mathematics Research     Open Access  
Journal of Metallurgy     Open Access   (Followers: 9)
Journal of Modern Mathematics Frontier     Open Access  
Journal of Multidisciplinary Modeling and Optimization     Open Access   (Followers: 1)
Journal of Multivariate Analysis     Hybrid Journal   (Followers: 15)
Journal of Nonlinear Analysis and Optimization : Theory & Applications     Open Access   (Followers: 4)
Journal of Nonlinear Mathematical Physics     Hybrid Journal   (Followers: 2)
Journal of Nonlinear Science     Hybrid Journal   (Followers: 1)
Journal of Numerical Cognition     Open Access   (Followers: 1)
Journal of Optimization     Open Access   (Followers: 5)
Journal of Peridynamics and Nonlocal Modeling     Hybrid Journal  
Journal of Progressive Research in Mathematics     Open Access   (Followers: 1)
Journal of Pseudo-Differential Operators and Applications     Hybrid Journal  
Journal of Pure and Applied Algebra     Full-text available via subscription   (Followers: 3)
Journal of Quantitative Linguistics     Hybrid Journal   (Followers: 6)
Journal of Scientific Computing     Hybrid Journal   (Followers: 19)
Journal of Scientific Research     Open Access  
Journal of Symbolic Computation     Hybrid Journal   (Followers: 2)
Journal of the Australian Mathematical Society     Full-text available via subscription  
Journal of the Egyptian Mathematical Society     Open Access  
Journal of the Indian Mathematical Society     Hybrid Journal  
Journal of the Institute of Mathematics of Jussieu     Hybrid Journal  
Journal of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Journal of the Nigerian Mathematical Society     Open Access  
Journal of Theoretical and Applied Physics     Open Access   (Followers: 9)
Journal of Topology and Analysis     Hybrid Journal  
Journal of Transport and Supply Chain Management     Open Access   (Followers: 10)
Journal of Turbulence     Hybrid Journal   (Followers: 7)
Journal of Universal Mathematics     Open Access  
Journal of Urban Regeneration & Renewal     Full-text available via subscription   (Followers: 8)
JRAMathEdu : Journal of Research and Advances in Mathematics Education     Open Access   (Followers: 5)
JUMLAHKU : Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan     Open Access  
JURING (Journal for Research in Mathematics Learning)     Open Access  
Jurnal Didactical Mathematics     Open Access   (Followers: 5)
Jurnal Matematika     Open Access  
Jurnal Matematika, Sains, Dan Teknologi     Open Access  
Jurnal Natural     Open Access  
Jurnal Pendidikan Matematika Raflesia     Open Access  
Jurnal Penelitian Pembelajaran Matematika Sekolah     Open Access  
Jurnal Penelitian Sains (JPS)     Open Access  
Jurnal Riset Pendidikan Matematika     Open Access  
Jurnal Sains Matematika dan Statistika     Open Access  
Jurnal Tadris Matematika     Open Access  
Jurnal Teknologi dan Sistem Komputer     Open Access  
Kontinu : Jurnal Penelitian Didaktik Matematika     Open Access  
Kreano, Jurnal Matematika Kreatif-Inovatif     Open Access  
Le Matematiche     Open Access  
Lettera Matematica     Hybrid Journal  
Lietuvos Matematikos Rinkinys     Open Access  
Limits : Journal of Mathematics and Its Applications     Open Access  
Linear Algebra and its Applications     Full-text available via subscription   (Followers: 22)
Linear and Multilinear Algebra     Hybrid Journal   (Followers: 7)
Lithuanian Mathematical Journal     Hybrid Journal  
Lobachevskii Journal of Mathematics     Open Access  
Logic Journal of the IGPL     Hybrid Journal   (Followers: 1)
Logica Universalis     Hybrid Journal  
manuscripta mathematica     Hybrid Journal   (Followers: 1)
MaPan : Jurnal Matematika dan Pembelajaran     Open Access  
Marine Genomics     Hybrid Journal   (Followers: 1)
Matemáticas, Educación y Sociedad     Open Access  
Matematicheskie Zametki     Full-text available via subscription  
Mathematica Scandinavica     Full-text available via subscription   (Followers: 1)
Mathematical Analysis and its Contemporary Applications     Open Access   (Followers: 1)
Mathematical Communications     Open Access  
Mathematical Computation     Open Access   (Followers: 1)
Mathematical Geosciences     Hybrid Journal   (Followers: 4)
Mathematical Journal of Interdisciplinary Sciences     Open Access   (Followers: 1)
Mathematical Medicine and Biology: A Journal of the IMA     Hybrid Journal   (Followers: 1)
Mathematical Methods in the Applied Sciences     Hybrid Journal   (Followers: 3)
Mathematical Methods of Statistics     Hybrid Journal   (Followers: 4)
Mathematical Modelling and Analysis     Open Access   (Followers: 1)
Mathematical Modelling of Natural Phenomena     Open Access   (Followers: 1)
Mathematical Models and Methods in Applied Sciences     Hybrid Journal   (Followers: 1)
Mathematical Notes     Hybrid Journal  
Mathematical Proceedings of the Cambridge Philosophical Society     Full-text available via subscription   (Followers: 2)
Mathematical Programming Computation     Hybrid Journal   (Followers: 2)
Mathematical Sciences     Open Access  
Mathematical Social Sciences     Hybrid Journal   (Followers: 1)
Mathematical Theory and Modeling     Open Access   (Followers: 6)
Mathematical Thinking and Learning     Hybrid Journal   (Followers: 4)
Mathematics and Statistics     Open Access   (Followers: 2)
Mathematics Education Forum Chitwan     Open Access   (Followers: 2)
Mathematics Education Journal     Open Access   (Followers: 4)
Mathematics Education Research Journal     Partially Free   (Followers: 16)
Mathematics of Control, Signals, and Systems (MCSS)     Hybrid Journal   (Followers: 5)
Mathematics Teacher: Learning and Teaching PK-12     Full-text available via subscription   (Followers: 9)
Mathematics Teaching in the Middle School     Full-text available via subscription   (Followers: 8)
Mathematische Annalen     Hybrid Journal   (Followers: 2)
Mathematische Nachrichten     Hybrid Journal   (Followers: 1)
Mathematische Semesterberichte     Hybrid Journal  
Mathematische Zeitschrift     Hybrid Journal   (Followers: 2)
MATICS     Open Access  
Matrix Science Mathematic     Open Access   (Followers: 1)
Measurement Science Review     Open Access   (Followers: 3)
Mediterranean Journal of Mathematics     Hybrid Journal  
Memetic Computing     Hybrid Journal  
Mendel : Soft Computing Journal     Open Access  
Metaheuristics     Hybrid Journal  
Metals and Materials International     Hybrid Journal   (Followers: 1)
Metascience     Hybrid Journal   (Followers: 1)
Metrology and Instruments / Метрологія та прилади     Open Access  
Milan Journal of Mathematics     Hybrid Journal  
MLQ- Mathematical Logic Quarterly     Hybrid Journal   (Followers: 1)
Modelling in Civil and Environmental Engineering     Open Access   (Followers: 4)
MONA : Matematik- og Naturfagsdidaktik     Hybrid Journal  
Monatshefte fur Mathematik     Hybrid Journal  
Moroccan Journal of Pure and Applied Analysis     Open Access  
Moscow University Mathematics Bulletin     Hybrid Journal  
MSOR Connections     Open Access   (Followers: 1)
Multiscale Modeling and Simulation     Hybrid Journal   (Followers: 2)
MUST : Journal of Mathematics Education, Science and Technology     Open Access   (Followers: 4)
Nagoya Mathematical Journal     Hybrid Journal   (Followers: 1)
Nano Research     Hybrid Journal   (Followers: 4)
Nanotechnologies in Russia     Hybrid Journal  
Natural Resource Modeling     Hybrid Journal  
New Mathematics and Natural Computation     Hybrid Journal   (Followers: 1)
Nonlinear Analysis     Hybrid Journal   (Followers: 1)
Nonlinear Analysis : Modelling and Control     Open Access   (Followers: 1)
Nonlinear Analysis: Hybrid Systems     Hybrid Journal  
Nonlinear Analysis: Real World Applications     Hybrid Journal   (Followers: 1)
Nonlinear Differential Equations and Applications NoDEA     Hybrid Journal  
North Carolina Journal of Mathematics and Statistics     Open Access  
Note di Matematica     Open Access  
NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin     Hybrid Journal   (Followers: 3)
Numeracy : Advancing Education in Quantitative Literacy     Open Access   (Followers: 1)
Numerical Analysis and Applications     Hybrid Journal   (Followers: 1)
Numerical Functional Analysis and Optimization     Hybrid Journal   (Followers: 3)
Numerical Linear Algebra with Applications     Hybrid Journal   (Followers: 7)
Numerische Mathematik     Hybrid Journal  
Open Journal of Discrete Mathematics     Open Access   (Followers: 3)
Open Journal of Modelling and Simulation     Open Access   (Followers: 2)
Operations Research Letters     Hybrid Journal   (Followers: 11)
Optimization Letters     Hybrid Journal   (Followers: 2)
Optimization Methods and Software     Hybrid Journal   (Followers: 6)
Opuscula Mathematica     Open Access  
Order     Hybrid Journal  
ORiON     Open Access  
P-Adic Numbers, Ultrametric Analysis, and Applications     Hybrid Journal  
PAMM : Proceedings in Applied Mathematics and Mechanics     Free  
Parallel Processing Letters     Hybrid Journal   (Followers: 3)
Peking Mathematical Journal     Hybrid Journal  
Periodica Mathematica Hungarica     Full-text available via subscription   (Followers: 1)
Petroleum Science     Open Access  
Philosophia Mathematica     Hybrid Journal   (Followers: 1)
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences     Full-text available via subscription   (Followers: 9)
PNA. Revista de Investigación en Didáctica de la Matemática     Open Access  
Polar Science     Hybrid Journal   (Followers: 3)
Positivity     Hybrid Journal  
Press Start     Open Access   (Followers: 1)
Prime Number     Full-text available via subscription  
Probability in the Engineering and Informational Sciences     Hybrid Journal   (Followers: 1)
Problemy Peredachi Informatsii     Full-text available via subscription  
Proceedings - Mathematical Sciences     Open Access   (Followers: 5)
Proceedings of the American Mathematical Society, Series B     Open Access   (Followers: 4)
Proceedings of the Edinburgh Mathematical Society     Hybrid Journal  
Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics     Hybrid Journal   (Followers: 2)
Proceedings of the Latvian Academy of Sciences. Section B: Natural, Exact and Applied Sciences     Open Access   (Followers: 1)
Proceedings of the London Mathematical Society     Hybrid Journal   (Followers: 5)
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences     Full-text available via subscription   (Followers: 6)
Proceedings of the Royal Society of Edinburgh Section A Mathematics     Full-text available via subscription  
Proceedings of the Steklov Institute of Mathematics     Hybrid Journal  
Progress in Photovoltaics: Research & Applications     Hybrid Journal   (Followers: 6)
Proyecciones : Revista de Matematica     Open Access   (Followers: 1)
Publications Mathématiques de Besançon : Algèbre et Théorie des Nombres     Open Access  
Publications Mathématiques de L'IHÉS     Hybrid Journal   (Followers: 4)
Punjab University Journal of Mathematics     Open Access   (Followers: 1)
Pure Mathematics and Applications     Open Access  
Pythagoras     Open Access  
Quaestiones Mathematicae     Hybrid Journal  
Qualitative Theory of Dynamical Systems     Hybrid Journal  
Quantum Studies : Mathematics and Foundations     Hybrid Journal   (Followers: 2)
Quarterly Journal of Mathematics     Hybrid Journal  
Rare Metals     Hybrid Journal   (Followers: 2)
Recreational Mathematics Magazine     Open Access  
REDIMAT : Journal of Research in Mathematics Education     Open Access   (Followers: 6)
REMAT : Revista Eletrônica da Matemática     Open Access  
Rendiconti del Circolo Matematico di Palermo     Hybrid Journal  
Reportes Científicos de la FaCEN     Open Access  
Research in Mathematics Education     Hybrid Journal   (Followers: 13)
Research in Nondestructive Evaluation     Hybrid Journal   (Followers: 7)
Research in Number Theory     Hybrid Journal   (Followers: 1)
Research in the Mathematical Sciences     Open Access  
Research Journal of Pure Algebra     Open Access   (Followers: 1)
Researches in Mathematics     Open Access  

  First | 1 2 3 4     

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Research in the Mathematical Sciences
Number of Followers: 0  

  This is an Open Access Journal Open Access journal
ISSN (Print) 2522-0144 - ISSN (Online) 2197-9847
Published by SpringerOpen Homepage  [228 journals]
  • Infinite families of crank functions, Stanton-type conjectures, and
           unimodality

    • Abstract: Dyson’s rank function and the Andrews–Garvan crank function famously give combinatorial witnesses for Ramanujan’s partition function congruences modulo 5, 7, and 11. While these functions can be used to show that the corresponding sets of partitions split into 5, 7, or 11 equally sized sets, one may ask how to make the resulting bijections between partitions organized by rank or crank combinatorially explicit. Stanton recently made conjectures which aim to uncover a deeper combinatorial structure along these lines, where it turns out that minor modifications of the rank and crank are required. Here, we prove two of these conjectures. We also provide abstract criteria for quotients of polynomials by certain cyclotomic polynomials to have non-negative coefficients based on unimodality and symmetry. Furthermore, we extend Stanton’s conjecture to an infinite family of cranks. This suggests further applications to other combinatorial objects. We also discuss numerical evidence for our conjectures, connections with other analytic conjectures such as the distribution of partition ranks.
      PubDate: 2022-06-06
       
  • Deep solution operators for variational inequalities via proximal neural
           networks

    • Abstract: Abstract Following Bauschke and Combettes (Convex analysis and monotone operator theory in Hilbert spaces, Springer, Cham, 2017), we introduce ProxNet, a collection of deep neural networks with ReLU activation which emulate numerical solution operators of variational inequalities (VIs). We analyze the expression rates of ProxNets in emulating solution operators for variational inequality problems posed on closed, convex cones in real, separable Hilbert spaces, covering the classical contact problems in mechanics, and early exercise problems as arise, e.g., in valuation of American-style contracts in Black–Scholes financial market models. In the finite-dimensional setting, the VIs reduce to matrix VIs in Euclidean space, and ProxNets emulate classical projected matrix iterations, such as projected Jacobi and projected SOR methods.
      PubDate: 2022-06-04
       
  • Linearity of free resolutions of monomial ideals

    • Abstract: Abstract We study monomial ideals with linear presentation or partially linear resolution. We give combinatorial characterizations of linear presentation for square-free ideals of degree 3, and for primary ideals whose resolutions are linear except for the last step (the “almost linear” case). We also give sharp bounds on Castelnuovo–Mumford regularity and numbers of generators in some cases. It is a basic observation that linearity properties are inherited by the restriction of an ideal to a subset of variables, and we study when the converse holds. We construct fractal examples of almost linear primary ideals with relatively few generators related to the Sierpiński triangle. Our results also lead to classes of highly connected simplicial complexes \(\Delta \) that cannot be extended to the complete \(\mathrm{dim}\Delta \) -skeleton of the simplex on the same variables by shelling.
      PubDate: 2022-05-29
       
  • Explicit transformations of certain Lambert series

    • Abstract: Abstract An exact transformation, which we call the master identity, is obtained for the first time for the series \(\sum _{n=1}^{\infty }\sigma _{a}(n)e^{-ny}\) for \(a\in {\mathbb {C}}\) and Re \((y)>0\) . New modular-type transformations when a is a nonzero even integer are obtained as its special cases. The precise obstruction to modularity is explicitly seen in these transformations. These include a novel companion to Ramanujan’s famous formula for \(\zeta (2m+1)\) . The Wigert–Bellman identity arising from the \(a=0\) case of the master identity is derived too. When a is an odd integer, the well-known modular transformations of the Eisenstein series on \(SL _{2}\left( {\mathbb {Z}}\right) \) , that of the Dedekind eta function as well as Ramanujan’s formula for \(\zeta (2m+1)\) are derived from the master identity. The latter identity itself is derived using Guinand’s version of the Voronoï summation formula and an integral evaluation of N. S. Koshliakov involving a generalization of the modified Bessel function \(K_{\nu }(z)\) . Koshliakov’s integral evaluation is proved for the first time. It is then generalized using a well-known kernel of Watson to obtain an interesting two-variable generalization of the modified Bessel function. This generalization allows us to obtain a new modular-type transformation involving the sums-of-squares function \(r_k(n)\) . Some results on functions self-reciprocal in the Watson kernel are also obtained.
      PubDate: 2022-05-19
       
  • Learning generative neural networks with physics knowledge

    • Abstract: Abstract Deep generative neural networks have enabled modeling complex distributions, but incorporating physics knowledge into the neural networks is still challenging and is at the core of current physics-based machine learning research. To this end, we propose a physics generative neural network (PhysGNN), a new class of generative neural networks for learning unknown distributions in a physical system described by partial differential equations (PDE). PhysGNN couples PDE systems with generative neural networks. It is a fully differentiable model that allows back-propagation of gradients through both numerical PDE solvers and generative neural networks, and is trained by minimizing the discrete Wasserstein distance between generated and observed probability distributions of the PDE outputs using the stochastic gradient descent method. Moreover, PhysGNN does not require adversarial training like standard generative neural networks, which offers better stability than adversarial training. We show that PhysGNN can learn complex distributions in stochastic inverse problems, where conventional methods such as maximum likelihood estimation and momentum matching methods may be inapplicable when little knowledge is known about the form of unknown distributions or the physical model is too complex. Our method allows physics-based generative neural network training for learning complex distributions in the context of differential equations.
      PubDate: 2022-05-17
       
  • On the occurrence of complete intersections in shifted families of
           numerical semigroups

    • Abstract: Abstract We give a necessary and sufficient condition for the existence of infinitely many complete intersections in the shifted family of a numerical semigroup.
      PubDate: 2022-05-11
       
  • Powers of graphs & applications to resolutions of powers of
           monomial ideals

    • Abstract: Abstract This paper is concerned with the question of whether geometric structures such as cell complexes can be used to simultaneously describe the minimal free resolutions of all powers of a monomial ideal. We provide a full answer in the case of square-free monomial ideals of projective dimension one by introducing a combinatorial construction of a family of (cubical) cell complexes whose 1-skeletons are powers of a graph that supports the resolution of the ideal.
      PubDate: 2022-05-09
       
  • Algebraic properties of Levi graphs associated with curve arrangements

    • Abstract: Abstract In the present paper, we study algebraic properties of edge ideals associated with plane curve arrangements via their Levi graphs. Using combinatorial properties of such Levi graphs, we are able to describe those monomial algebras being Cohen–Macaulay, Buchsbaum, and sequentially Cohen–Macaulay. We also consider the projective dimension and the Castelnuovo-Mumford regularity for these edge ideals. We provide effective lower and upper bounds on them. As a by-product of our study, we connect, in general, various Buchsbaum properties of squarefree modules.
      PubDate: 2022-05-07
       
  • A glimpse to most of the old and new results on very well-covered graphs
           from the viewpoint of commutative algebra

    • Abstract: Abstract A very well-covered graph is a well-covered graph without isolated vertices such that the height of its edge ideal is half of the number of vertices. In this survey article, we gather together most of the old and new results on the edge and cover ideals of these graphs.
      PubDate: 2022-05-06
       
  • Hilbert series of parallelogram polyominoes

    • Abstract: Abstract We present a conjecture about the reduced Hilbert series of the coordinate ring of a simple polyomino in terms of particular arrangements of non-attacking rooks that can be placed on the polyomino. By using a computational approach, we prove that the above conjecture holds for all simple polyominoes up to rank 11. In addition, we prove that the conjecture holds true for the class of parallelogram polyominoes, by looking at those as simple planar distributive lattices. Finally, we give a combinatorial interpretation of the Gorensteinness of parallelogram polyominoes.
      PubDate: 2022-04-28
       
  • Powers of monomial ideals with characteristic-dependent Betti numbers

    • Abstract: Abstract We explore the dependence of the Betti numbers of monomial ideals on the characteristic of the field. A first observation is that for a fixed prime p either the i-th Betti number of all high enough powers of a monomial ideal differs in characteristic 0 and in characteristic p or it is the same for all high enough powers. In our main results, we provide constructions and explicit examples of monomial ideals all of whose powers have some characteristic-dependent Betti numbers or whose asymptotic regularity depends on the field. We prove that, adding a monomial on new variables to a monomial ideal allows to spread the characteristic dependence to all powers. For any given prime p, this produces an edge ideal such that all its powers have some Betti numbers that are different over \(\mathbb {Q}\) and over \(\mathbb {Z}_p\) . Moreover, we show that, for every \(r \ge 0\) and \(i \ge 3\) there is a monomial ideal I such that some coefficient in a degree \(\ge r\) of the Kodiyalam polynomials \({\mathfrak {P}}_3(I),\ldots ,{\mathfrak {P}}_{i+r}(I)\) depends on the characteristic. We also provide a summary of related results and speculate about the behavior of other combinatorially defined ideals.
      PubDate: 2022-04-18
       
  • Computational graph completion

    • Abstract: Abstract We introduce a framework for generating, organizing, and reasoning with computational knowledge. It is motivated by the observation that most problems in Computational Sciences and Engineering (CSE) can be described as that of completing (from data) a computational graph (or hypergraph) representing dependencies between functions and variables. In that setting nodes represent variables and edges (or hyperedges) represent functions (or functionals). Functions and variables may be known, unknown, or random. Data come in the form of observations of distinct values of a finite number of subsets of the variables of the graph (satisfying its functional dependencies). The underlying problem combines a regression problem (approximating unknown functions) with a matrix completion problem (recovering unobserved variables in the data). Replacing unknown functions by Gaussian processes and conditioning on observed data provides a simple but efficient approach to completing such graphs. Since the proposed framework is highly expressive, it has a vast potential application scope. Since the completion process can be automatized, as one solves \(\sqrt{\sqrt{2}+\sqrt{3}}\) on a pocket calculator without thinking about it, one could, with the proposed framework, solve a complex CSE problem by drawing a diagram. Compared to traditional regression/kriging, the proposed framework can be used to recover unknown functions with much scarcer data by exploiting interdependencies between multiple functions and variables. The computational graph completion (CGC) problem addressed by the proposed framework could therefore also be interpreted as a generalization of that of solving linear systems of equations to that of approximating unknown variables and functions with noisy, incomplete, and nonlinear dependencies. Numerous examples illustrate the flexibility, scope, efficacy, and robustness of the CGC framework and show how it can be used as a pathway to identifying simple solutions to classical CSE problems. These examples include the seamless CGC representation of known methods (for solving/learning PDEs, surrogate/multiscale modeling, mode decomposition, deep learning) and the discovery of new ones (digital twin modeling, dimension reduction).
      PubDate: 2022-04-18
       
  • Cohomological supports of tensor products of modules over commutative
           rings

    • Abstract: Abstract This works concerns cohomological support varieties of modules over commutative local rings. The main result is that the support of a derived tensor product of a pair of differential graded modules over a Koszul complex is the join of the supports of the modules. This generalizes, and gives another proof of, a result of Dao and the third author dealing with Tor-independent modules over complete intersection rings. The result for Koszul complexes has a broader applicability, including to exterior algebras over local rings.
      PubDate: 2022-04-15
       
  • Stability for quantitative photoacoustic tomography revisited

    • Abstract: Abstract This paper deals with the issue of stability in determining the absorption and the diffusion coefficients in quantitative photoacoustic imaging. We establish a global conditional Hölder stability inequality from the knowledge of two internal data obtained from optical waves, generated by two point sources in a region where the optical coefficients are known.
      PubDate: 2022-04-12
       
  • Powers of componentwise linear ideals: the Herzog–Hibi–Ohsugi
           conjecture and related problems

    • Abstract: Abstract In 1999, Herzog and Hibi introduced componentwise linear ideals. A homogeneous ideal I is componentwise linear if for all nonnegative integers d, the ideal generated by the homogeneous elements of degree d in I has a linear resolution. For square-free monomial ideals, componentwise linearity is related via Alexander duality to the property of being sequentially Cohen–Macaulay for the corresponding simplicial complexes. In general, the property of being componentwise linear is not preserved by taking powers. In 2011, Herzog, Hibi, and Ohsugi conjectured that if I is the cover ideal of a chordal graph, then \(I^s\) is componentwise linear for all \(s \ge 1\) . We survey some of the basic properties of componentwise linear ideals and then specialize to the progress on the Herzog–Hibi–Ohsugi conjecture during the last decade. We also survey the related problem of determining when the symbolic powers of a cover ideal are componentwise linear
      PubDate: 2022-04-07
       
  • On gluing semigroups in $${\pmb {\mathbb {N}}}^n$$ N n and the
           consequences

    • Abstract: Abstract A semigroup \(\langle C\rangle \) in \(\mathbb {N}^n\) is a gluing of \(\langle A\rangle \) and \(\langle B\rangle \) if its finite set of generators C splits into two parts, \(C=k_1A\sqcup k_2B\) with \(k_1,k_2\ge 1\) , and the defining ideals of the corresponding semigroup rings satisfy that \(I_C\) is generated by \(I_A+I_B\) and one extra element. Two semigroups \(\langle A\rangle \) and \(\langle B\rangle \) can be glued if there exist positive integers \(k_1,k_2\) such that for \(C=k_1A\sqcup k_2B\) , \(\langle C\rangle \) is a gluing of \(\langle A\rangle \) and \(\langle B\rangle \) . Although any two numerical semigroups, namely semigroups in dimension \(n=1\) , can always be glued, it is no longer the case in higher dimensions. In this paper, we give necessary and sufficient conditions on A and B for the existence of a gluing of \(\langle A\rangle \) and \(\langle B\rangle \) , and give examples to illustrate why they are necessary. These generalize and explain the previous known results on existence of gluing. We also prove that the glued semigroup \(\langle C\rangle \) inherits the properties like Gorenstein or Cohen–Macaulay from the two parts \(\langle A\rangle \) and \(\langle B\rangle \) .
      PubDate: 2022-04-07
       
  • Boundary and Eisenstein cohomology of $$G_2(\mathbb {Z})$$ G 2 ( Z )

    • Abstract: Abstract In this article, Eisenstein cohomology of the arithmetic group \(G_2(\mathbb {Z})\) with coefficients in any finite dimensional highest weight irreducible representation has been determined. This is accomplished by studying the cohomology of the boundary of the Borel–Serre compactification.
      PubDate: 2022-04-05
       
  • Automorphism groups and normal forms in Normaliz

    • Abstract: Abstract We discuss the computation of automorphism groups and normal forms of cones and polyhedra in Normaliz and indicate its implementation via nauty. The types of automorphisms include integral, rational, Euclidean and combinatorial, as well as algebraic for polytopes defined over real algebraic number fields. Examples treated in detail are the icosahedron and linear-ordering polytopes whose Euclidean automorphism groups are determined.
      PubDate: 2022-04-01
       
  • Uniqueness of conservative solutions for the Hunter–Saxton equation

    • Abstract: Abstract We show that the Hunter–Saxton equation \(u_t+uu_x=\frac{1}{4}\big (\int _{-\infty }^x \hbox {d}\mu (t,z)- \int ^{\infty }_x \hbox {d}\mu (t,z)\big )\) and \(\mu _t+(u\mu )_x=0\) has a unique, global, weak, and conservative solution \((u,\mu )\) of the Cauchy problem on the line.
      PubDate: 2022-03-19
       
  • On Lyapunov functions and particle methods for regularized minimax
           problems

    • Abstract: Abstract We study the two-player zero-sum game with mixed strategies. For a class of commonly used regularizers and a class of metrics, we show the existence of a Lyapunov function of the gradient ascent descent dynamics. We also propose for a new particle method for a specific combination of regularizers and metrics.
      PubDate: 2022-03-03
       
 
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