Related papers: A note on some fiber-integrals

In this paper, a new class of optical fibers is studied, i.e. microstructured fibers or photonic crystal fibers (PCF). The main objective is to characterize these fibers using different dispersion diagrams and present an interface that…

A one-parameter generalized fermion algebra ${\cal B}_{\kappa}(1)$ is introduced. The Fock representation is studied. The associated coherent states are constructed and the polynomial representation, in the Bargmann sense, is derived. A…

We identify all uniform limits of polynomials on the closed unit disc with respect to the chordal metric \c{hi} . One such limit is f=oo. The other limits are holomorphic functions f:-->C so that for every {\zeta} in the boundary of unit…

For a germ $f$ on a complex manifold $X$, we introduce a complex derived from the Liouville form acting on logarithmic differential forms, and give an exactness criterion. We use this Liouville complex to connect properties of the…

We consider foliations of compact complex manifolds by analytic curves. We suppose that the line bundle tangent to the foliation is negative. We show that in a generic case there exists a finitely smooth homeomophism, holomorphic on the…

We study the semigroup of non-injective monoid endomorphisms of the semigroup $\boldsymbol{B}_{\omega}^{\mathscr{F}}$ with a two-elements family $\mathscr{F}$ of inductive nonempty subsets of $\omega$. We describe the structure of elements…

Let $F$ be a local non-archimedean field and $\mathcal{O}_F$ its ring of integers. Let $\Omega$ be a Bernstein component of the category of smooth representations of $GL_n(F)$, let $(J, \lambda)$ be a Bushnell-Kutzko $\Omega$-type, and let…

We determine, up to exponentiating, the polar locus of the multivariable archimedean zeta function associated to a finite collection of polynomials F. The result is the monodromy support locus of F, a topological invariant. We give a…

Let f be a polynomial over the complex numbers with an isolated singularity at 0. We show that the multiplicity and the log canonical threshold of f at 0 are invariants of the link of f viewed as a contact submanifold of the sphere. This is…

We show that the absolute value $|f|$ of an invertible holomorphic function $f$ on the Drinfeld symmetric space $\OM^r$ $(r \geq 2)$ is constant on fibers of the building map to the Bruhat-Tits building $\MB\MT$. Its logarithm $\log|f|$ is…

We present an example of a compact connected F-space with a continuous real-valued function f for which the union of the interiors of its fibers is not dense. This indirectly answers a question from Abramovich and Kitover in the negative.

On any odd-dimensional oriented Riemannian manifold we define a volume form, which we call the odd Pfaffian, through a certain invariant polynomial with integral coefficients in the curvature tensor. We prove an intrinsic Chern-Gauss-Bonnet…

In this paper, we will evaluate integrals that define the conditional expectation, variance and characteristic function of stochastic processes with respect to fractional Brownian motion (fBm) for all relevant Hurst indices, i.e. $H \in…

An $F$-manifold is complex manifold with a multiplication on the holomorphic tangent bundle with a certain integrability condition. Important examples are Frobenius manifolds and especially base spaces of universal unfoldings of isolated…

This paper considers some work done by the author and Catlin [CD1,CD2,CD3] concerning positivity conditions for bihomogeneous polynomials and metrics on bundles over certain complex manifolds. It presents a simpler proof of a special case…

For a holomorphic function $f$ on a complex manifold $X$, the Brian\c{c}on-Skoda exponent $e^{\rm BS}(f)$ is the smallest integer $k$ with $f^k\in(\partial f)$ (replacing $X$ with a neighborhood of $f^{-1}(0)$), where $(\partial f)$ denotes…

Let $\boldsymbol{B}_{\omega}^{\mathscr{F}}$ be the bicyclic semigroup extension for the family $\mathscr{F}$ of ${\omega}$-closed subsets of $\omega$ which is introduced in \cite{Gutik-Mykhalenych=2020}. We study topologizations of the…

We show that non-flatness of a morphism f of complex-analytic spaces with a locally irreducible target Y of dimension n manifests in the existence of vertical components in the n-fold fibred power of the pull-back of f to the…

We make quantitative improvements to recently obtained results on the structure of the image of a large difference set under certain quadratic forms and other homogeneous polynomials. Previous proofs used deep results of Benoist-Quint on…

In this paper, we address the full discretization of Friedrichs' systems with a two-field structure, such as Maxwell's equations or the acoustic wave equation in div-grad form, cf. [14]. We focus on a discontinuous Galerkin space…