Related papers: A generalized Join theorem for real analytic singu…
We prove a generalized version of Renault's theorem for Cartan subalgebras. We show that the original assumptions of second countability and separability are not needed. This weakens the assumption of topological principality of the…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
We prove a generic Torelli theorem for Jacobian elliptic surfaces, provided that the geometric genus is large compared to the irregularity. The result is effective to the extent that defining equations for the base curve are recovered from…
We generalize certain arguments in Zariski's irregularity theorem on cyclic multiple planes.
We give a geometric proof of Conn's linearization theorem for analytic Poisson structures, without using the fast convergence method.
We prove a generalisation of the Grothendieck-Riemann-Roch theorem, which is valid for any proper and flat morphism between noetherian and separated schemes of odd characteristic.
The celebrated Thistlethwaite theorem relates the Jones polynomial of a link with the Tutte polynomial of the corresponding planar graph. We give a generalization of this theorem to virtual links. In this case, the graph will be embedded…
In the theory of generalized cluster algebras, we build the so-called cluster formula and $D$-matrix pattern. Then as applications, some fundamental conjectures of generalized cluster algebras are solved affirmatively.
For a complete noncompact connected Riemannian manifold with bounded geometry, we prove a compactness result for sequences of finite perimeter sets with uniformly bounded volume and perimeter in a larger space obtained by adding limit…
We introduce the notion of a pro-fusion system on a pro-p group, which generalizes the notion of a fusion system on a finite p-group. We also prove a version of Alperin's Fusion Theorem for pro-fusion systems.
We settle the fusion product decomposition theorem for higher-level affine Demazure modules for the cases $E^{(1)}_{6, 7, 8}, F^{(1)}_4$ and $E^{(2)}_{6}$, thus completing the main theorems of Chari et al. (J. Algebra, 2016) and Kus et al.…
In the long paper "Family Blowup formula, Admissible Graphs and the Enumeration of Singular Curves (I)" (appearing in JDG), the author solved the enumeration problem of nodal (or general singular) curve counting on algebraic surfaces by…
We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension of Bestvina and Feighn's Combination Theorem for hyperbolic…
The idea of generating integrals analogous to generating functions is first introduced in this paper. A new proof of the well-known Finite Harmonic Series Theorem in Analysis and Analytical Number Theory is then obtained by the method of…
Determination of linear combination of exponential functions with unknown rate constants from its sampled values is a problem of considerable interest. Here we present a constructive and explicit solution to this problem. Moments of such…
The global analytic hypoellipticity is proved for a class of second order partial differential equations with non-negative characteristic form globally defined on the torus. The class considered in this work generalizes at some degree the…
The generalized symmetry method is applied to a class of completely discrete equations including the Adler-Bobenko-Suris list. Assuming the existence of a generalized symmetry, we derive a few integrability conditions suitable for testing…
This is an exposition of the combinatorial proof of the density Hales--Jewett theorem, due to D.\,H.\,J. Polymath in 2012. The theorem says that for given $\de>0$ and $k$, for every $n>n_0$ every set $A\sus\{1,2,\ds,k\}^n$ with $|A|\ge\de…
We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…
The aim of this paper is to establish some metrical coincidence and common fixed point theorems with an arbitrary relation under an implicit contractive condition which is general enough to cover a multitude of well known contraction…