Related papers: Finsleroids with three axes in dimension $N=3$

In this paper, we give a necessary and sufficient condition for an even order three dimensional strongly symmetric circulant tensor to be positive semi-definite. In some cases, we show that this condition is also sufficient for this tensor…

Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…

A standard theorem in nonsmooth analysis states that a piecewise affine function $F:\mathbb R^n\rightarrow\mathbb R^n$ is surjective if it is coherently oriented in that the linear parts of its selection functions all have the same nonzero…

Given an extriangulated category $(\mathcal{C},\mathbb{E},\mathfrak{s})$, we introduce the $3 \times 3$-lemma property for subfunctors of $\mathbb{E}$ and prove that an additive subfunctor $\mathbb{F}$ of $\mathbb{E}$ is closed if, and only…

In an abstract Hilbert space setting, we discuss many linear phenomena of mathematical physics. The functional analytic framework presented is used to address continuous dependence of the solution operators $\mathcal{S}(\mathcal{M})$ of…

We prove that the number of combinatorially distinct causal 3-dimensional triangulations homeomorphic to the 3-dimensional sphere is bounded by an exponential function of the number of tetrahedra. It is also proven that the number of…

We prove that the metric tensor $g$ of a complete Riemannian manifold is uniquely determined, up to isometry, from the knowledge of a local source-to-solution operator. This later is associated to a fractional power of the Laplace-Belrami…

We provide a necessary and sufficient condition for the validity of the following Landsberg-Thirring theorem: for a real-valued function on a convex set, any two of the properties of superadditivity, concavity and homogeneity implies the…

In classical function theory, a function is holomorphic if and only if it is complex analytic. For higher dimensional spaces it is natural to work in the context of Clifford algebras. The structures of these algebras depend on the parity of…

We study a class of mechanisms known as Kokotsakis polyhedra with a quadrangular base. These are $3\times3$ quadrilateral meshes whose faces are rigid bodies and joined by hinges at the common edges. In contrast to existing work, the…

We determine a positive real number (weight), which corresponds to a vertex of a tetrahedron and it depends on the three weights which correspond to the other three vertices and an infinitesimal number $\epsilon.$ As a limiting case, for…

In this paper we first study some global properties of the energy functional on a non-reversible Finsler manifold. In particular we present a fully detailed proof of the Palais--Smale condition under the completeness of the Finsler metric.…

We define a function by refining Stern's diatomic sequence. We name it the {\it assembly function}. It is strictly increasing continuous. The first and the second main theorems are on an action to the function. The third theorem is on…

We have shown that the Beltrami Theorem in Riemannian geometry is still true for square metrics if the dimension $n\ge 3$, namely, an $n(\ge 3)$-dimensional square metric is locally projectively flat if and only if it is of scalar flag…

Let $k$ be an infinite finitely generated field of characteristic $p>0$. Fix a separated scheme $X$ smooth, geometrically connected, and of finite type over $k$ and a smooth proper morphism $f:Y\rightarrow X$. The main result of this paper…

Finite trigonometric Fourier series on a set of discrete equidistant points are considered. A finite system of orthogonal functions that have interpolation and certain differential properties on the period is introduced. Finite Fourier…

We present a theorem of resolution of singularities for real analytic constrained differential systems $A(x)\dot{x} = F(x)$ defined on a 2-manifold with corners having impasse set $\{x; \det A(x) = 0\}$. This result can be seen as a…

We characterize a holomorphic positive definite function $f$ defined on a horizontal strip of the complex plane as the Fourier-Laplace transform of a unique exponentially finite measure on $\mathbb{R}$. The classical theorems of Bochner on…

Let $X$ be an $F$-finite smooth scheme of essentially finite type over a perfect field. This article proves the existence of $b$-functions for locally finitely generated unit $F$-modules when equipped with their induced…

In this paper, we study some basic analytic properties of the boundary term of Fesenko's two-dimensional zeta integrals. In the case of the rational number field, we show that this term is the Laplace transform of certain infinite series…