Results 11 to 20 of about 11,083 (123)

Singularities and Topology of Meromorphic Functions

, 2002
We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of polynomial functions.
A Dimca, A Dimca, A Dold, A Parusiriski, AH Durfee, B Teissier, B Teissier, C Sabbah, C Sabbah, D Burghelea, D Siersma, D. Siersma, D.T. Lê, DT Lê, DT Lê, E Brieskorn, EH Spanier, F Pham, H Hamm, HV Ha, J Briançon, J Briançon, J-L Verdier, JP Henry, L Fourrier, M Tibàr, M Tibár, M Tibár, M Tibár, M. Morse, N A’Campo, N A’Campo, O Zariski, P Deligne, R García López, R García López, R Switzer, R Thom, S Gusein, S Gusein-Zade, S Gusein-Zade, SA Broughton, SA Broughton, T Gaffney, VA Vassiliev, VI Arnol’d, VI Arnol’d, W Ebeling, WD Neumann, WD Neumann   +49 more
core   +1 more source

On solutions of certain compatible systems of quadratic trinomial Partial differential-difference equations

Математичні Студії
This paper has involved the use of a variety of variations of the Fermat-type equation $f^n(z)+g^n(z)=1$, where $n(\geq 2)\in\mathbb{N}$. Many researchers have demonstrated a keen interest to investigate the Fermat-type equations for entire and ...
R. Mandal, R. Biswas
doaj   +1 more source

Matrix Models, Complex Geometry and Integrable Systems. I

, 2006
We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric properties of planar ...
A. A. Migdal, A. Gerasimov, A. M. Polyakov, A. Marshakov, A. V. Marshakov, A. V. Marshakov, B. Eynard, B. Wit de, E. Brézin, E. Witten, F. David, G. Bonnet, G. Felder, G. Hooft ’t, I. Krichever, I. Krichever, J. Fay, J. Polchinski, J. Polchinski, L. A. Takhtajan, L. Chekhov, L. Chekhov, M. Fukuma, M. Kontsevich, M. Mineev-Weinstein, R. Dijkgraaf, S. Kharchev, S. Kharchev, S. Kharchev, S. Kharchev, T. Miwa, V. A. Kazakov, V. A. Kazakov   +32 more
core   +2 more sources

The Mathematical History Behind the Granger–Johansen Representation Theorem

Oxford Bulletin of Economics and Statistics, EarlyView.
ABSTRACT When can a vector time series that is integrated once (i.e., becomes stationary after taking first differences) be described in error correction form? The answer to this is provided by the Granger–Johansen representation theorem. From a mathematical point of view, the theorem can be viewed as essentially a statement concerning the geometry of ...
Johannes M. Schumacher
wiley   +1 more source

A fractional residue theorem and its applications in calculating real integrals

Bulletin of the London Mathematical Society, Volume 58, Issue 4, April 2026.
Abstract As part of an ongoing effort to fractionalise complex analysis, we present a fractional version of the residue theorem, involving pseudo‐residues calculated at branch points. Since fractional derivatives are non‐local and fractional powers necessitate branch cuts, each pseudo‐residue depends on a line segment in the complex plane rather than a
Egor Zaytsev, Arran Fernandez
wiley   +1 more source

The description of entire solutions for some class of complex nonlinear partial differential equation (systems) in C2 ${\mathbb{C}}^{2}$

Demonstratio Mathematica
This article focuses on describing the entire solutions of complex nonlinear partial differential equation (systems) with two variables. Utilizing Nevanlinna theory along with the Hadamard factorization theory of meromorphic functions, we derive several ...
Chen Yu Bin, Jiao Xin, Xu Hong Yan
doaj   +1 more source

Bloch's principle

, 2005
A heuristic principle attributed to A. Bloch says that a family of holomorphic functions is likely to be normal if there is no nonconstant entire functions with this property. We discuss this principle and survey recent results that have been obtained in
Bergweiler, Walter
core   +2 more sources

A Miyaoka–Yau inequality for hyperplane arrangements in CPn$\mathbb {CP}^n$

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract Let H$\mathcal {H}$ be a hyperplane arrangement in CPn$\mathbb {CP}^n$. We define a quadratic form Q$Q$ on RH$\mathbb {R}^{\mathcal {H}}$ that is entirely determined by the intersection poset of H$\mathcal {H}$. Using the Bogomolov–Gieseker inequality for parabolic bundles, we show that if a∈RH$\mathbf {a}\in \mathbb {R}^{\mathcal {H}}$ is ...
Martin de Borbon, Dmitri Panov
wiley   +1 more source

Moments of L$L$‐functions via a relative trace formula

Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.
Abstract We prove an asymptotic formula for the second moment of the GL(n)×GL(n−1)$\mathrm{GL}(n)\times \mathrm{GL}(n-1)$ Rankin–Selberg central L$L$‐values L(1/2,Π⊗π)$L(1/2,\Pi \otimes \pi)$, where π$\pi$ is a fixed cuspidal representation of GL(n−1)$\mathrm{GL}(n-1)$ that is tempered and unramified at every place, while Π$\Pi$ varies over a family of
Subhajit Jana, Ramon Nunes
wiley   +1 more source

Graph potentials and topological quantum field theories

Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.
Abstract We introduce a new functional equation in birational geometry, whose solutions can be used to construct two‐dimensional topological quantum field theories (2d TQFTs), infinite‐dimensional in many interesting examples. The solutions of the equation give rise to a hierarchy of graph potentials, which, in the simplest setup, are Laurent ...
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay   +2 more
wiley   +1 more source