相关论文: On exceptional terminal singularities
For a finite field of odd number of elements we construct families of permutation binomials and permutation trinomials with one fixed-point (namely zero) and remaining elements being permuted as disjoint cycles of same length. Binomials and…
Let $T$ be a countable complete first-order theory with a definable, infinite, discrete linear order. We prove that $T$ has continuum-many countable models. The proof is purely first-order, but raises the question of Borel completeness of…
New exceptional (i.e. non-repeating) prime number multiplets are given and formulated in terms of arithmetic progressions, along with laws governing them. Accompanying repeating prime number multiplets are pointed out. Prime number…
We construct an example of a real plane analytic singular metric, degenerating only at the origin, such that any gradient trajectory (respectively to this singular metric) of some well chosen function spirals around the origin. The…
Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.
Exceptional points (EPs) are degeneracies in open wave systems where at least two energy levels and their corresponding eigenstates coalesce. We report evidence of the existence of EPs in 3D plasmonic nanostructures. The systems are…
Necessary and sufficient conditions for the exactness (in the algebraic sense) of certain sequences of continuous group homomorphisms are established.
The class of abelian $p$-groups are an example of some very interesting phenomena in computable structure theory. We will give an elementary first-order theory $T_p$ whose models are each bi-interpretable with the disjoint union of an…
We construct and classify, in the case of two complex dimensions, the possible tangent cones at points of limit spaces of non-collapsed sequences of K\"ahler-Einstein metrics with cone singularities.
In this chapter we characterize Askey-Wilson polynomials including specific and limiting cases of them by some structure relations of the first type.
New cases of the multiplicity conjecture are considered.
Covering space theory is used to construct new examples of buildings.
We construct equisingular semiuniversal deformations of Legendrian curves.
Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…
Despite much recent theoretical and observational progress in our knowledge of the early universe, many fundamental questions remain only partially answered. Here, we review the latest achievements and persisting problems in the…
Matter collapsing to a singularity in a gravitational field is still an intriguing question. Similar situation arises when discussing the very early universe or a universe recollapsing to a singularity. It is suggested that inclusion of…
We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.
We consider the group property of being icc. We give several examples of icc groups and study its stability under usual algebraic constructions.
Recent results on finite open group transformations are reviewed.
This is a survey on recent results regarding singularities that occur on higher dimensional stable varieties.