Subjects -> MATHEMATICS (Total: 1013 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: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 4)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 13)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 5)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 43)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 2)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 3)
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: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 7)
Advances in Complex Systems     Hybrid Journal   (Followers: 10)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 16)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access  
Advances in Geosciences (ADGEO)     Open Access   (Followers: 20)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 6)
Advances in Materials Science     Open Access   (Followers: 21)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 18)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 13)
Advances in Operator Theory     Hybrid Journal  
Advances in Pure Mathematics     Open Access   (Followers: 10)
Advances in Science and Research (ASR)     Open Access   (Followers: 9)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 8)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 5)
Afrika Matematika     Hybrid Journal   (Followers: 2)
Air, Soil & Water Research     Open Access   (Followers: 6)
AKSIOMATIK : Jurnal Penelitian Pendidikan dan Pembelajaran Matematika     Open Access  
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Al-Qadisiyah Journal for Computer Science and Mathematics     Open Access   (Followers: 3)
AL-Rafidain Journal of Computer Sciences and Mathematics     Open Access   (Followers: 4)
Algebra and Logic     Hybrid Journal   (Followers: 9)
Algebra Colloquium     Hybrid Journal   (Followers: 3)
Algebra Universalis     Hybrid Journal   (Followers: 3)
Algorithmic Operations Research     Open Access   (Followers: 6)
Algorithms     Open Access   (Followers: 14)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 4)
American Journal of Mathematical Analysis     Open Access   (Followers: 1)
American Journal of Mathematical and Management Sciences     Hybrid Journal  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 6)
American Mathematical Monthly     Full-text available via subscription   (Followers: 3)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 12)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access  
Analysis and Applications     Hybrid Journal   (Followers: 2)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 7)
Anargya : Jurnal Ilmiah Pendidikan Matematika     Open Access  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 3)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – 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: 15)
Annals of Functional Analysis     Hybrid Journal   (Followers: 2)
Annals of Mathematics     Full-text available via subscription   (Followers: 5)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 13)
Annals of PDE     Hybrid Journal  
Annals of Pure and Applied Logic     Open Access   (Followers: 5)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access   (Followers: 1)
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access   (Followers: 1)
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access   (Followers: 2)
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 3)
Applications of Mathematics     Hybrid Journal   (Followers: 3)
Applied Categorical Structures     Hybrid Journal   (Followers: 5)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 16)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 7)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal   (Followers: 1)
Applied Mathematics and Nonlinear Sciences     Open Access   (Followers: 1)
Applied Mathematics Letters     Full-text available via subscription   (Followers: 3)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 4)
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: 1)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 21)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Research Journal of Mathematics     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: 5)
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: 2)
Banach Journal of Mathematical Analysis     Hybrid Journal  
Basin Research     Hybrid Journal   (Followers: 6)
BIBECHANA     Open Access  
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
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  
British Journal for the History of Mathematics     Hybrid Journal   (Followers: 2)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 17)
British Journal of Mathematics & Computer Science     Full-text available via subscription   (Followers: 1)
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 2)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 3)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 3)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 4)
Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics     Open Access  
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 2)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the Iranian Mathematical Society     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Cadernos do IME : Série Matemática     Open Access  
Calculus of Variations and Partial Differential Equations     Hybrid Journal   (Followers: 1)
Canadian Journal of Mathematics / Journal canadien de mathématiques     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 20)
Canadian Mathematical Bulletin     Hybrid Journal  
Carpathian Mathematical Publications     Open Access  
Catalysis in Industry     Hybrid Journal  
CAUCHY     Open Access   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 5)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 1)
Chaos, Solitons & Fractals : X     Open Access   (Followers: 1)
ChemSusChem     Hybrid Journal   (Followers: 8)
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  
Ciencia     Open Access  
CODEE Journal     Open Access  
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Hybrid Journal   (Followers: 3)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 5)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 20)
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: 3)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 6)
Complex Analysis and its Synergies     Open Access   (Followers: 1)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Compositio Mathematica     Full-text available via subscription   (Followers: 2)
Comptes Rendus : Mathematique     Open Access  
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods     Hybrid Journal  
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 5)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 11)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 9)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 10)
Confluentes Mathematici     Hybrid Journal  
Constructive Mathematical Analysis     Open Access  
Contributions to Discrete Mathematics     Open Access  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal   (Followers: 1)
Cross Section     Full-text available via subscription   (Followers: 1)
Cryptography and Communications     Hybrid Journal   (Followers: 11)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal  
Daya Matematis : Jurnal Inovasi Pendidikan Matematika     Open Access  
Demographic Research     Open Access   (Followers: 14)
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 35)
Desimal : Jurnal Matematika     Open Access  
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Differentsial'nye Uravneniya     Open Access  
Digital Experiences in Mathematics Education     Hybrid Journal   (Followers: 3)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access   (Followers: 1)
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  
Doklady Akademii Nauk     Open Access  

        1 2 3 4 | Last

Similar Journals
Journal Cover
Complex Analysis and its Synergies
Number of Followers: 1  

  This is an Open Access Journal Open Access journal
ISSN (Print) 2524-7581 - ISSN (Online) 2197-120X
Published by SpringerOpen Homepage  [228 journals]
  • Inequalities for complex polynomials

    • Abstract: Abstract If \(P(z)=a_n\prod _{j=1}^{n}(z-z_j)\) is a complex polynomial of degree n having all its zeros in \( z \le K, ~ K\ge 1,\) it is known that $$\max _{ z =1} P^{\prime }(z) \ge \frac{2}{1+K^n}\sum _{j=1}^{n}\frac{K}{K+ z_j }\max _{ z =1} P(z) .$$ In this paper, we generalise the above inequality to the polar derivative of a polynomial. Our result includes many other interesting inequalities as special cases.
      PubDate: 2022-11-23
       
  • Constructing group-invariant CR mappings

    • Abstract: Abstract We construct CR mappings between spheres that are invariant under actions of finite unitary groups. In particular, we combine a tensoring procedure with D’Angelo’s construction of a canonical group-invariant CR mapping to obtain new invariant mappings. We also explore possible gap phenomena in this setting.
      PubDate: 2022-09-15
       
  • Two decades of finite jet determination of CR mappings

    • Abstract: Abstract This is a survey paper discussing the developments around the so-called finite jet determination problem for CR maps over the past twenty years.
      PubDate: 2022-09-09
       
  • Analysis on quadrics

    • Abstract: Abstract This paper surveys recent progress on the analysis of the \(\Box _b\) operator on quadric submanifolds of \({\mathbb {C}}^n \times {\mathbb {C}}^m \) . We focus our discussion on the (relative) fundamental solution to \(\Box _b\) on quadric submanifolds of arbitrary codimension. We summarize known results regarding \(\Box _b\) -invariance of mappings, necessary and sufficient conditions for solvability and hypoellipticity for \(\Box _b\) , and we describe the \(L^p\) regularity of the complex Green operator on quadrics with nonvanishing Levi form. We discuss the ramifications of these results for many examples of quadrics of codimension 1 and 2.
      PubDate: 2022-09-09
       
  • Cartan uniqueness theorem on nonopen sets

    • Abstract: Abstract Cartan’s uniqueness theorem does not hold in general for CR mappings, but it does hold under certain conditions guaranteeing extendibility of CR functions to a fixed neighborhood. These conditions can be defined naturally for a wide class of sets such as local real-analytic subvarieties or subanalytic sets, not just submanifolds. Suppose that V is a locally connected and locally closed subset of \({\mathbb {C}}^n\) such that the hull constructed by contracting analytic discs close to arbitrarily small neighborhoods of a point always contains the point in the interior. Then, restrictions of holomorphic functions uniquely extend to a fixed neighborhood of the point. Using this extension, we obtain a version of Cartan’s uniqueness theorem for such sets. When V is a real-analytic subvariety, we can generalize the concept of infinitesimal CR automorphism and also prove an analogue of the theorem. As an application of these two results we show that, for circular subvarieties, the only automorphisms, CR or infinitesimal, are linear.
      PubDate: 2022-09-05
       
  • Boundary behaviour of the span metric and its higher-order curvatures

    • Abstract: Abstract In this note, we use scaling principle to study the boundary behaviour of the span metric and its higher-order curvatures on finitely connected Jordan planar domains. A localization of this metric near boundary points of finitely connected Jordan domains is also obtained. Further, we obtain boundary sharp estimates for the span metric near \( C^2 \) -smooth boundary points on such domains.
      PubDate: 2022-08-27
       
  • Equivariant Oka theory: survey of recent progress

    • Abstract: Abstract We survey recent work, published since 2015, on equivariant Oka theory. The main results described in the survey are as follows. Homotopy principles for equivariant isomorphisms of Stein manifolds on which a reductive complex Lie group G acts. Applications to the linearisation problem. A parametric Oka principle for sections of a bundle E of homogeneous spaces for a group bundle \({{\mathscr {G}}}\) , all over a reduced Stein space X with compatible actions of a reductive complex group on E, \({{\mathscr {G}}}\) , and X. Application to the classification of generalised principal bundles with a group action. Finally, an equivariant version of Gromov’s Oka principle based on a notion of a G-manifold being G-Oka.
      PubDate: 2022-08-24
       
  • The 1-jet determination of stationary discs attached to generic CR
           submanifolds

    • Abstract: Abstract The existence of a non-defective stationary disc attached to a non-degenerate model quadric in \({\mathbb {C}}^N\) is a necessary condition to ensure the unique 1-jet determination of the lifts of a key family of stationary discs [6]. In this paper, we give an elementary proof of the equivalence when the model quadric is strongly pseudoconvex, recovering a result of Tumanov [14]. Our proof is based on the explicit expression of stationary discs, and opens up a conjecture for the unique 1-jet determination to hold when the model is not necessarily strongly pseudoconvex.
      PubDate: 2022-08-04
       
  • Normal form for pseudo-Einstein contact forms and intrinsic CR normal
           coordinates

    • Abstract: Abstract We give a normal form for pseudo-Einstein contact forms and apply it to construct intrinsic CR normal coordinates parametrized by the structure group of CR geometry. The proof is based on the construction of parabolic normal coordinates by Jerison and Lee.
      PubDate: 2022-08-02
       
  • Squeezing function corresponding to polydisk

    • Abstract: Abstract In the present article, we define squeezing function corresponding to polydisk and study its properties. We investigate relationship between squeezing function and squeezing function corresponding to polydisk.
      PubDate: 2022-07-29
       
  • On exotic symmetries of finite type models

    • Abstract: Abstract We study the infinitesimal CR automorphisms of polynomial model hypersurfaces of finite multitype, which violates 2-jet determination. We give an exposition of some recent results, which provide explicit description of such “exotic” symmetries in complex dimension three. The results are illustrated by numerous examples.
      PubDate: 2022-07-06
       
  • Totally geodesic discs in bounded symmetric domains

    • Abstract: Abstract In this paper, we characterize \(C^2\) -smooth totally geodesic isometric embeddings \(f:\Omega \rightarrow \Omega '\) between bounded symmetric domains \(\Omega \) and \(\Omega '\) which extend \(C^1\) -smoothly over some open subset in the Shilov boundaries and have nontrivial normal derivatives on it. In particular, if \(\Omega \) is irreducible, there exist totally geodesic bounded symmetric subdomains \(\Omega _1\) and \(\Omega _2\) of \(\Omega '\) such that \(f = (f_1, f_2)\) maps into \(\Omega _1\times \Omega _2\subset \Omega \) where \(f_1\) is holomorphic and \(f_2\) is anti-holomorphic totally geodesic isometric embeddings. If \(\text {rank}(\Omega ')<2\text {rank}(\Omega )\) , then either f or \({\bar{f}}\) is a standard holomorphic embedding.
      PubDate: 2022-06-17
       
  • On weighted Bergman spaces of a domain with Levi-flat boundary II

    • Abstract: Abstract Holomorphic functions on the maximal Grauert tube of a hyperbolic compact Riemann surface are studied. It is shown that their weighted Bergman spaces are infinite dimensional for arbitrary weight order greater than \(-1\) in spite of the fact that they do not admit any non-constant bounded holomorphic functions. The key ingredient of the proof is a computation of weighted norms of analytic continuations of eigenfunctions of the Laplacian in terms of the hypergeometric function. This result complements our previous work (Adachi in Trans Am Math Soc 374(10):7499–7524, 2021) where it was shown that the space of geodesic segments on the Riemann surface has exactly the same property.
      PubDate: 2022-04-16
       
  • The Hodge star operator and the Beltrami equation

    • Abstract: Abstract An essentially unique homeomorphic solution to the Beltrami equation with measurable coefficients was found in the 1930s by Morrey. The most well-known proof from the 1960s uses the theory of Calderón–Zygmund and singular integral operators in \(L^p(\mathbb {C})\) . We will present an alternative method to solve the Beltrami equation using the Hodge star operator and standard elliptic PDE theory. We will also discuss a different method to prove the regularity of the solution. This approach is partially based on work by Dittmar.
      PubDate: 2022-04-12
       
  • Symmetries, rational sphere maps, and complete polynomial sequences

    • Abstract: Abstract We consider the set S of possible target dimensions for rational sphere maps whose Hermitian-invariant group is the unitary group. In each source dimension, we show that S is co-finite by applying a classical theorem of Ron Graham on complete polynomial sequences. We establish several results, some computer assisted, finding the largest exceptional value. We close by posing a purely number-theoretic question about these exceptional values.
      PubDate: 2022-03-09
       
  • Subharmonic functions, conformal metrics, and CAT(0)

    • Abstract: Abstract We present an analytical proof that certain natural metric universal covers are Hadamard metric spaces. If \(\rho \,\mathrm{{d}}s\) induces a complete distance d on a plane domain \(\Omega \) , and \(\rho =\varphi \circ u\) where u is (locally Lipschitz and) subharmonic in \(\Omega \) , \(\varphi \) is positive and increasing on an interval containing \(u(\Omega )\) with \(\log \varphi \) convex, then \((\Omega ,d)\) has a universal cover \(({\tilde{\Omega }},{\tilde{d}})\) which is a Hadamard metric space (with geodesics that have Lipschitz continuous first derivatives).
      PubDate: 2022-02-16
       
  • The fundamental solutions of the curve shortening problem via the Schwarz
           function

    • Abstract: Abstract Curve shortening in the z-plane in which, at a given point on the curve, the normal velocity of the curve is equal to the curvature, is shown to satisfy \(S_tS_z=S_{zz}\) , where S(z, t) is the Schwarz function of the curve. This equation is shown to have a parametric solution from which the known explicit solutions for curve shortening flow; the circle, grim reaper, paperclip and hairclip, can be recovered.
      PubDate: 2022-02-15
       
  • A Tauberian approach to an analog of Weyl’s law for the Kohn Laplacian
           on compact Heisenberg manifolds

    • Abstract: Abstract Let \(M= \Gamma \setminus \mathbb {H}_d\) be a compact quotient of the d-dimensional Heisenberg group \(\mathbb {H}_d\) by a lattice subgroup \(\Gamma \) . We show that the eigenvalue counting function \(N^\alpha \left( \lambda \right) \) for any fixed element of a family of second order differential operators \(\left\{ \mathcal {L}_\alpha \right\} \) on M has asymptotic behavior \(N^\alpha \left( \lambda \right) \sim C_{d,\alpha } {\text {vol}}\left( M\right) \lambda ^{d + 1}\) , where \(C_{d,\alpha }\) is a constant that only depends on the dimension d and the parameter \(\alpha \) . As a consequence, we obtain an analog of Weyl’s law (both on functions and forms) for the Kohn Laplacian on M. Our main tools are Folland’s description of the spectrum of \({\mathcal {L}}_{\alpha }\) and Karamata’s Tauberian theorem.
      PubDate: 2022-02-14
       
  • Intrinsic metrics in ring domains

    • Abstract: Abstract Three hyperbolic-type metrics including the triangular ratio metric, the \(j^*\) -metric, and the Möbius metric are studied in an annular ring. The Euclidean midpoint rotation is introduced as a method to create upper and lower bounds for these metrics, and their sharp inequalities are found. A new Möbius-invariant lower bound is proved for the conformal capacity of a general ring domain by using a symmetric quantity defined with the Möbius metric.
      PubDate: 2022-02-07
       
  • Complex solutions to Maxwell’s equations

    • Abstract: Abstract This expository paper provides a view of Maxwell’s equations from the perspective of complex differential forms and the Hodge star operator in \(\mathbb {C}^2\) with respect to the Euclidean and the Minkowski metrics. The electric field and the magnetic field are complex 3-dimensional in this case. The paper shows that holomorphic functions naturally give rise to nontrivial solutions to the equations. A simple necessary and sufficient condition regarding wavelike solutions to the equations is also obtained. In the end, the paper gives an interpretation of the Lorenz gauge condition in terms of the co-differential operator.
      PubDate: 2022-02-05
       
 
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