Search
Search Results
-
An elementary proof of the dual representation of Expected Shortfall
We provide an elementary proof of the dual representation of Expected Shortfall on the space of integrable random variables over a general...
-
Proof of the Brunn–Minkowski Theorem by Elementary Methods
In this paper, we propose new proofs of the classical Brunn—Minkowski theorem on the volume of the sum of convex polyhedra P 0 and P 1 of the same n -dim...
-
An elementary proof of the Brouwer’s fixed point theorem
We provide an elementary proof of the Brouwer’s fixed point theorem based solely on introductory topological concepts such as compactness and...
-
A Short Elementary Proof of the Gearhart–Prüss Theorem for Bounded Semigroups
We present a short elementary proof of the Gearhart–Prüss theorem for bounded...
-
An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces
We revisit Yudovich’s well-posedness result for the 2-dimensional Euler equations for an inviscid incompressible fluid on either a sufficiently...
-
A simple proof of second-order sufficient optimality conditions in nonlinear semidefinite optimization
In this note, we present an elementary proof for a well-known second-order sufficient optimality condition in nonlinear semidefinite optimization...
-
An elementary proof of Lelli-Chiesa’s theorem on constancy of second coordinate of gonality sequence
Let X be a K 3 surface and L be an ample line bundle on it. In this article, we will give an alternative and elementary proof of Lelli-Chiesa’s...
-
Elementary Covering Numbers in Odd-Dimensional Unitary Groups
Let (K, Δ) be a field of Hermitian forms and n ≥ 3. It is proved that if σ ∈ U 2n+1 (K, Δ) is a unitary matrix of level (K, Δ), then any short root...
-
An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor
Based on the Cayley-Hamilton theorem and fixed-point method, we provide an elementary proof for the representation theorem of analytic isotropic...
-
A Proof of Fatou’s Interpolation Theorem
For Fatou’s interpolation theorem of 1906 we suggest a new elementary proof.
-
Galois closures and elementary components of Hilbert schemes of points
Bhargava and the first-named author of this paper introduced a functorial Galois closure operation for finite-rank ring extensions, generalizing...
-
Disjoint Linear Dynamical Properties of Elementary Operators
In this paper, we characterize disjoint hypercyclic finite sequences of elementary operators. We provide sufficient conditions for a finite sequence...
-
On the geometry of elementary flux modes
Elementary flux modes (EFMs) play a prominent role in the constraint-based analysis of metabolic networks. They correspond to minimal functional...
-
Elementary Invariants for Quantified Probability Logic
AbstractLet QPL be the two-sorted probabilistic language proposed in [8], which expands the well-known ‘polynomial’ language described in [3],...
-
A short proof of the existence of master test plans
The aim of this brief note is to provide a quick and elementary proof of the following known fact: on a metric measure space whose Sobolev space is...
-
Mathematical Elements of Elementary Education
AbstractIn recent decades, several Russian schools have been implementing a world-unique education program of mathematics for elementary schools. In...
-
Some Theorems from Elementary Geometry
In this chapter we compile the necessary preliminaries from elementary geometry. They are mainly about some well-known concepts and theorems,...