Related papers: Representation Theorem for Multivariable Totally S…
In this paper, the theory of functions of one complex variable is explored to study linearly full unramified holomorphic two-spheres with constant curvature in $G(2,n)$ satisfying that the generated harmonic sequence degenerates at position…
This paper establishes an extended representation theorem for unit-root VARs. A specific algebraic technique is devised to recover stationarity from the solution of the model in the form of a cointegrating transformation. Closed forms of…
A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…
The dominant theme of this thesis is the construction of matrix representations of finite solvable groups using a suitable system of generators. For a finite solvable group $G$ of order $N = p_{1}p_{2}\dots p_{n}$, where $p_{i}$'s are…
The main objective of this paper is to extend Morse-Forman theory to vector-valued functions. This is mostly motivated by the need to develop new tools and methods to compute multiparameter persistence. To generalize the theory, in addition…
The Kolmogorov-Arnold representation is a proven adequate replacement of a continuous multivariate function by an hierarchical structure of multiple functions of one variable. The proven existence of such representation inspired many…
In the conventional formulation of N=1 supersymmetry, a vector multiplet is supposed to be in the adjoint representation of a given gauge group. We present a new formulation with a vector multiplet in the non-adjoint representation of SO(N)…
We deploy algebraic complexity theoretic techniques for constructing symmetric determinantal representations of for00504925mulas and weakly skew circuits. Our representations produce matrices of much smaller dimensions than those given in…
We use the law of total variance to generate multiple expressions for the posterior predictive variance in Bayesian hierarchical models. These expressions are sums of terms involving conditional expectations and conditional variances. Since…
It is well known that over an infinite field the ring of symmetric functions in a finite number of variables is isomorphic to the one of polynomial functions on matrices that are invariants by the action of conjugation by general linear…
We consider a general regularised interpolation problem for learning a parameter vector from data. The well known representer theorem says that under certain conditions on the regulariser there exists a solution in the linear span of the…
This work proposes a unified theory of regularity in one hypercomplex variable: the theory of $T$-regular functions. In the special case of quaternion-valued functions of one quaternionic variable, this unified theory comprises…
In this paper, we consider mixed sums of generalized polygonal numbers. Specifically, we obtain a finiteness condition for universality of such sums; this means that it suffices to check representability of a finite subset of the positive…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
A map between manifolds induces stratifications of both the source and the target according to the occurring multisingularities. In this paper, we study universal expressions-called higher Thom polynomials-that describe the…
This paper is devoted to proving a general invariant representation theorem for generators of general time interval backward stochastic differential equations, where the generator $g$ has a quadratic growth in the unknown variable $z$ and…
Consider complex semisimple Lie algebras of a given dimension specified by their structure constants. We describe a finite collection of rational functions in the structure constants that form a complete set of invariants: two sets of…
We discuss representations of monogenic functions over very regular groups.
Following the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with Bounded Deformation. Mild additional continuity assumptions…
Functorial semi-norms are semi-normed refinements of functors such as singular (co)homology. We investigate how different types of representability affect the (non-)triviality of finite functorial semi-norms on certain functors or classes.…