Related papers: Integral representation results in BVxL^p
We use thermodynamic perturbation theory to calculate the free energies and resulting phase diagrams of binary systems of spherical colloidal particles and interacting polymer coils in good solvent within an effective one-component…
This paper presents analogous results of Hua [7][8] on numbers of representations of quivers over finite fields which respect nilpotent relations under certain assumptions. A closed formula which counts isomorphism classes of absolutely…
When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor…
Representation Engineering (RepE) has emerged as a powerful paradigm for enhancing AI transparency by focusing on high-level representations rather than individual neurons or circuits. It has proven effective in improving interpretability…
In this paper we achieve some $\Gamma$-compactness results for suitable classes of integral functionals depending on a given family of Lipschitz vector fields, with respect to both the strong $L^p-$topology and the strong…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
We consider four types of representations of solutions of GKZ system: series representations, Laplace integral representations, Euler integral representations, and Residue integral representations which will be introduced in this paper. In…
The power of multivariate functions is their ability to model a wide variety of phenomena, but have the disadvantages that they lack an intuitive or interpretable representation, and often require a (very) large number of parameters. We…
Estimating individual-level treatment effect from observational data is a fundamental problem in causal inference and has attracted increasing attention in the fields of education, healthcare, and public policy.In this work, we concentrate…
We prove that Bargmann representations exist for some deformed harmonic oscillators that admit non-Fock representations. In specific cases, we explicitly obtain the resolution of the identity in terms of a true integral on the complex…
We use a combination of perturbation theory and numerical techniques to study the equilibration of two interacting fields which are initially at thermal equilibrium at different temperatures. Using standard rules of quantum field theory, we…
A representation of the sharp constant in a pointwise estimate of the gradient of a harmonic function in a multidimensional half-space is obtained under the assumption that function's boundary values belong to $L^p$. This representation is…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
The decay of the electrical energy in a resistor-vacuum capacitor circuit is shown to involve multiple relaxation processes, with dramatically different time constants. This is measured using a vacuum capacitor to eliminate the effect of a…
We develop an abstract framework for the investigation of quantization and dequantization procedures based on orthogonality relations that do not necessarily involve group representations. To illustrate the usefulness of our abstract method…
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…
Explicit expressions, for efficient application in engineering practice, are derived for generalized displacements and stresses in simply supported multi-layered wide plates and beams subjected to steady-state thermal and mechanical…
Deep learning models develop successive representations of their input in sequential layers, the last of which maps the final representation to the output. Here we investigate the informational content of these representations by observing…
In this article, we give a geometric description for any invertible operator on a finite dimensional inner--product space. With the aid of such a description, we are able to decompose any given conformal transformation as a product of…
Vector fields are a highly abstract physical concept that is often taught using visualizations. Although vector representations are particularly suitable for visualizing quantitative data, they are often confusing, especially when…