Related papers: Free basis consisting of strictly small sections
This note is to show the effectiveness of the notion of pseudoalgebra in the theory of conformal algebras. We adduce very simple construction of free associative conformal algebra and find its linear basis. There is no any new result but we…
Given a morphism between smooth projective varieties $f: W \to X$, we study whether $f$-relatively free rational curves imply the existence of $f$-relatively very free rational curves. The answer is shown to be positive when the fibers of…
Neighborhood is an important concept in covering based rough sets. That under what condition neighborhoods form a partition is a meaningful issue induced by this concept. Many scholars have paid attention to this issue and presented some…
It is shown that a Wishart matrix of standard complex normal random variables is asymptotically freely independent of an independent random matrix, under minimal conditions, in two different sense of asymptotic free independence.
This paper revisits the simple, but empirically salient, problem of inference on a real-valued parameter that is partially identified through upper and lower bounds with asymptotically normal estimators. A simple confidence interval is…
This article is devoted to obtain new sufficient conditions for an extremum in problems of classical calculus of variations. The concept of a set of integrands is introduced. Using this concept, first and second order sufficient conditions…
We discuss the birational geometry of singular surfaces in positive characteristic. More precisely, we establish the minimal model program and the abundance theorem for Q-factorial surfaces and for log canonical surfaces. Moreover, in the…
Consider a domain D in R^3 which is convex (possibly all R^3) or which is smooth and bounded. Given any open surface M, we prove that there exists a complete, proper minimal immersion f : M --> D. Moreover, if D is smooth and bounded, then…
We discuss the extent to which solutions to one-phase free boundary problems can be characterized according to their topological complexity. Our questions are motivated by fundamental work of Luis Caffarelli on free boundaries and by…
We provide a sufficient condition for sets of mobile sampling in terms of the surface density of the set.
In this article, we study the continuous mild solutions to the Boltzmann equation in a bounded spatial domain, under either angular cutoff assumption or non-cutoff assumption. Without assuming convexity of the spatial domain, we establish a…
We give an explicit upper bound for the algebraic degree and an explicit lower bound for the absolute value of the minimum of a polynomial function on a compact connected component of a basic closed semialgebraic set when this minimum is…
Integrable models are often constructed with real systems in mind. The exact solvability of the models leads to results which are unambiguous and provide the correct physical picture. In this review, we discuss the physical basis of some…
The artefact is dedicated towards the inspection of nonlinear fractional differential systems involving Riemann-Liouville derivative with higher order and fixed lower limit, including non-instantaneous impulses for existence and uniqueness…
We give a sufficient condition for the existence of a holomorphic tubular neighborhood of a compact Riemann surface holomorphically embedded in a non-singular complex surface. Our sufficient condition is described by an arithmetical…
Given a probability distribution P, what is the minimum amount of bits needed to store a value x sampled according to P, such that x can later be recovered (except with some small probability)? Or, what is the maximum amount of uniform…
Partial spread is important in finite geometry and can be used to construct linear codes. From the results in (Designs, Codes and Cryptography 90:1-15, 2022) by Xia Li, Qin Yue and Deng Tang, we know that if the number of the elements in a…
We characterize those $k$-automatic sets $S$ of natural numbers that form an additive basis for the natural numbers, and we show that this characterization is effective. In addition, we give an algorithm to determine the smallest $j$ such…
Building on the work of K. Chiba (J. Algebra 263 (2003), 75-87), we present sufficient conditions for the completion of a division ring with respect to the metric defined by a discrete valuation function to contain a free field, i.e. the…
We study a free boundary problem arising from the theory of thermal insulation. The outstanding feature of this set optimization problem is that the boundary of the set being optimized is not a level surface of a harmonic function, but…