相关论文: Rational Landen transformations on the real line
We discuss first order systems of rational difference equations which have the property that lines through the origin are mapped into lines through the origin. We call such systems projective systems of rational difference equations and we…
A geometric approach to Sundman transformation defined by basic functions for systems of second-order differential equations is developed and the necessity of a change of the tangent structure by means of the function defining the Sundman…
We study cubic rational maps that take lines to plane curves. A complete description of such cubic rational maps concludes the classification of all planarizations, i.e., maps taking lines to plane curves.
The Universal Field Equations, recently constructed as examples of higher dimensional dynamical systems which admit an infinity of inequivalent Lagrangians are shown to be linearised by a Legendre transformation. This establishes the…
Elementary Algebraic Geometry can be described as study of zeros of polynomials with integer degrees, this idea can be naturally carried over to `polynomials' with rational degree. This paper explores affine varieties, tangent space and…
Let $M$ be the space of real $n\times m$ matrices which can be identified with the Euclidean space $R^{nm}$. We introduce continuous wavelet transforms on $M$ with a multivalued scaling parameter represented by a positive definite symmetric…
If we take a superintegrable Stackel system and make variables "faster" or "slower", that is equivalent to a trivial transformation of the Stackel matrix and potentials, then we obtain an infinite family of superintegrable systems with…
We use the concept of the half of a lower-triangular matrix to define a transformation on integer sequences. We explore the properties of this transformation, including in some cases a study of the Hankel transform of the transformed…
This paper introduces a differentiable semantic reasoner, where rules are presented as a relevant set of graph transformations. These rules can be written manually or inferred by a set of facts and goals presented as a training set. While…
A central objective in inverse problems arising in integral geometry is to understand the kernel characterization, inversion formulas, stability estimates, range characterization, and unique continuation properties of integral transforms.…
An effective method for generating linear equations of maximal symmetry in their much general normal form is obtained. In the said normal form, the coefficients of the equation are differential functions of the coefficient of the term of…
Elimination theory has many applications, in particular, it describes explicitly an image of a complex line under rational transformation and determines the number of common zeroes of two polynomials in one variable. We generalize classical…
Let $F$ be a local field and $n\ge 2$ an integer. We study the Radon transform as an operator $M : \mathcal C_+ \to \mathcal C_-$ from the space of smooth $K$-finite functions on $F^n \setminus \{0\}$ with bounded support to the space of…
We determine the structure of linear maps on the tensor product of matrices which preserve the numerical range or numerical radius.
We describe methods to evaluate elementary logarithmic integrals. The integrand is the product of a rational function and a linear polynomial in ln x.
$\DeclareMathOperator{\IntR}{Int{}^\text{R}}$Integer-valued rational functions are a natural generalization of integer-valued polynomials. Given a domain $D$, the collection of all integer-valued rational functions over $D$ forms a ring…
The Hankel transform of an integer sequence is a much studied and much applied mathematical operation. In this note, we extend the notion in a natural way to sequences of $d$ integer sequences. We explore links to generalized continued…
This article is written with the hope to draw attention to a method that uses integral transforms to find exact values for a large class of convergent series (and, in particular, series of rational terms). We apply the method to some series…
We give an example of infinite order rational transformation that leaves a linear differential equation covariant. This example can be seen as a non-trivial but still simple illustration of an exact representation of the renormalization…
The paper studies various properties of the V-line transform (VLT) in the plane and conical Radon transform (CRT) in $\mathbb{R}^n$. VLT maps a function to a family of its integrals along trajectories made of two rays emanating from a…