相关论文: Isolating Cardinal Invariants
We study solutions to conformally invariant equations with isolated singularties.
Suppose that kappa is a singular cardinal of cofinality omega and GCH holds. Assume that for every n<omega the set of alphas with o(alpha)>= alpha^{+n} is unbounded in kappa.Then there is a cardinal preserving extension satisfying…
Given a function on diagonal matrices, there is a unique way to extend this to an invariant (by conjugation) function on symmetric matrices. We show that the extension preserves regularity -- that is, if the original function is k times…
We study and classify topologically invariant sigma-ideals with an analytic base on Euclidean spaces and evaluate the cardinal characteristics of such ideals.
We cardinally and ordinally rank distribution functions (CDFs). We present a new class of statistics, maximal adjusted quantiles, and show that a statistic is invariant with respect to cardinal shifts, preserves least upper bounds with…
We suggest an invariant way to enumerate nodal and nodal-cuspidal real deformations of real plane curve singularities. The key idea is to assign Welschinger signs to the counted deformations. Our invariants can be viewed as a local version…
The optimum interval method for finding an upper limit of a one-dimensionally distributed signal in the presence of an unknown background is extended to the case of high statistics. There is also some discussion of how the method can be…
We obtain necessary optimality conditions for higher-order infinite horizon problems of the calculus of variations via discrete quantum operators.
Cantor's algebraic calculation of the power of the continuum contains an easily repairable error related to Cantor own way of defining the addition of cardinal numbers. The appropriate correction is suggested.
We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new ${<}\kappa$-sequences (for some regular $\kappa$). As an application, we show that consistently the following cardinal characteristics…
We construct canonical heights of subvarieties for dynamical system of several morphisms associated with line bundles defined over a number field, and study some of their properties. We also construct invariant currents for such systems…
The purpose of this article is to motivate the study of invariant, and especially conformally invariant, differential pairings. Since a general theory is lacking, this work merely presents some interesting examples of these pairings,…
In this work, we investigate the optimal map-making technique for the linear system $d=Ax+n$ while carefully taking into account singularities that may come from either the covariance matrix $C = \langle nn^t \rangle$ or the main matrix…
We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case many things simplify and we are thus able to prove a more precise structure theorem than in…
The article investigates the behaviour of the characteristic zero resolution invariant when transcribed suitably to the case of surfaces in positive characteristic. By Moh's jumping phenomenon -- or the occurrence of kangaroo singularities…
We study the behavior of a general gravitational action, including quadratic terms in the curvature, supplemented by a compact scalar field in 4+1 dimensions. The generalized Einstein equation for this system admits solutions which are…
We give new upper bounds for the number of nonconstant holomorphic maps depending only on the genus. Our estimates improve previously known bounds. The proof is based on the study of pullbacks of holomorphic differentials, together with…
We introduce combinatorial principles that characterize strong compactness and supercompactness for inaccessible cardinals but also make sense for successor cardinals. Their consistency is established from what is supposedly optimal.…
We study more general variational problems on time scales. Previous results are generalized by proving necessary optimality conditions for (i) variational problems involving delta derivatives of more than the first order, and (ii) problems…
We give a necessary and sufficient condition for the existence of a local solution of the inverse problem of calculus of variations in terms of the identical vanishing of the variation of a functional on an extended space (with the number…