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In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present some important results of uniformly convergent sequences of…
The existence of a semiconjugate relation permits the transformation of a higher order difference equation on a group into an equivalent triangular system of two difference equations of lower orders. Introducing time-dependent form…
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation of nonclassical symmetries for differential equations can…
For nonautonomous linear difference equations, we introduce the notion of the so-called nonuniform dichotomy spectrum and prove a spectral theorem. Moreover, we introduce the notion of weak kinematical similarity and prove a reducibility…
In the statistical inference for long range dependent time series the shape of the limit distribution typically depends on unknown parameters. Therefore, we propose to use subsampling. We show the validity of subsampling for general…
A classical problem of statistical inference is the valid specification of a model that can account for the statistical dependencies between observations when the true structure is dense, intractable, or unknown. To address this problem, a…
Improved local and global versions of the effective Nullstellensatz for ideal sheaves on non-singular complex varieties are obtained, based on a new invariant motivated by the notion of finite type from the theory of several complex…
Motivated by the intermediate Lang conjectures on hyperbolicity and rational points, we prove new finiteness results for non-constant morphisms from a fixed variety to a fixed variety defined over a number field by applying Faltings's…
Many results on the convex order in the literature were stated for random variables with finite mean. For instance, a fundamental result in dependence modeling is that the sum of a pair of random random variables is upper bounded in convex…
Two dynamical models that have been proposed to describe transitions between low and high confinement states (L-H transitions) in confined plasmas are analysed using singularity theory and stability theory. It is shown that the…
The use of terms from natural and social scientific titles and abstracts is studied from the perspective of sublanguages and their specialized dictionaries. Different notions of sublanguage distinctiveness are explored. Objective methods…
Few-shot semantic segmentation (FSS) aims to segment objects of unseen classes in query images with only a few annotated support images. Existing FSS algorithms typically focus on mining category representations from the single-view support…
For Hilbert, the consistency of a formal theory T is an infinite series of statements "D is free of contradictions" for each derivation D and a consistency proof is i) an operation that, given D, yields a proof that D is free of…
Session types are behavioural types for guaranteeing that concurrent programs are free from basic communication errors. Recent work has shown that asynchronous session subtyping is undecidable. However, since session types have become…
We present compact semi-implicit finite difference schemes on structured grids for numerical solutions of the advection by an external velocity and by a speed in normal direction that are applicable in level set methods. The most involved…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
Correlation filters are special classifiers designed for shift-invariant object recognition, which are robust to pattern distortions. The recent literature shows that combining a set of sub-filters trained based on a single or a small group…
This paper concerns the tilt stability of local optimal solutions to a class of nonlinear semidefinite programs, which involves a twice continuously differentiable objective function and a convex feasible set. By leveraging the second…
Consistency regularization describes a class of approaches that have yielded ground breaking results in semi-supervised classification problems. Prior work has established the cluster assumption - under which the data distribution consists…
In this paper, we give precise rates of convergence in the strong invariance principle for stationary sequences of bounded real-valued random variables satisfying weak dependence conditions. One of the main ingredients is a new Fuk-Nagaev…