相关论文: Landen survey
As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.
In this paper, we study how certain vector bundles on an elliptic surface are changed under logarithmic transformations.
The Cartan development takes a Lie algebra valued 1-form satisfying the Maurer-Cartan equation on a simply connected manifold $M$ to a smooth mapping from $M$ into the Lie group. In this paper this is generalized to infinite dimensional $M$…
The quantum entanglements are studied in terms of the invariants under local unitary transformations. A generalized formula of concurrence for $N$-dimensional quantum systems is presented. This generalized concurrence has potential…
In this paper we consider a transformation $L_a$ of sequences of complex numbers. We find the inverse transformation of $L_a$ as well as the inverse of a related transformation $\tilde{L}_a$. We explore a connection to the binomial…
Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum…
This article studies the possible degenerations of plane Cremona transformations of some degree into maps of smaller degree.
Functional integrals are defined in terms of locally compact topological groups and their associated Banach-valued Haar integrals. This approach generalizes the functional integral scheme of Cartier and DeWitt-Morette. The definition allows…
Manin transformations are maps of the plane that preserve a pencil of cubic curves. They are the composition of two involutions. Each involution is constructed in terms of an involution point that is required to be one of the base points of…
We develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of…
We describe for any Riemannian manifold a certain infinitesimal neighbourhood of the diagonal. Semi-conformal maps are analyzed as those that preserve such neighbourhoods; harmonic maps are analyzed as those that preserve mirror image…
We give unique recovery guarantees for matrices of bounded rank that have undergone permutations of their entries. We even do this for a more general matrix structure that we call ladder matrices. We use methods and results of commutative…
We discuss the conditions for mapping the geometric description of the kinematics of particles that probe a given Hamiltonian in phase space to a description in terms of Finsler geometry (and vice-versa).
The monograph contains a systematic treatment of a circle of problems in analysis and integral geometry related to inversion of the Radon transform on the space of real rectangular matrices. This transform assigns to a function $f$ on the…
A classification of upper semicontinuous, translation and dually epi-translation invariant valuations is established on the space of convex Lipschitz function on $\mathbb{R}$ with compact domain.
Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency…
Many known Radon-type transforms of symmetric (radial or zonal) functions are represented by one-dimensional Riemann-Liouville fractional integrals or their modifications. The present article contains new examples of such transforms in the…
We propose an integral transform, called metamorphism, which allow us to reduce the order of a differential equation. For example, the second order Helmholtz equation is transformed into a first order equation, which can be solved by the…
Logarithmic integrals revisited. We consider integrals of the form $\int_0^1 \ln{\ln{(\frac{1}{x})}}R{(x)}{\rm d}x$ again, where $R{(x)}$ is a rational function, and we will explain a way to obtain their values.
It will be shown that transformations of order one on the Wiener space give rise to quadratic forms as exponents of change of variables formulas, and conversely every exponentially integrable quadratic form has a transformation of order one…