相关论文: Inverse problem and Bertrand's theorem

The more then hundred years old Bernstein inequality states that the supremum norm of the derivative of a trigonometric polynomial of fixed degree can be bounded from above by supremum norm of the polynomial itself. The reversed Bernstein…

In this paper, the solution of the multi-order differential equations, by using Mellin Transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the…

Using Euler's equations of motion and the Hamiltonian formulation, we obtain the equations of motion of systems with internal angular momentum that are moving with respect to a given reference frame, when subjected to a torque which is…

In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem.

In this work we are interested in general linear inverse problems where the corresponding forward problem is solved iteratively using fixed point methods. Then one-shot methods, which iterate at the same time on the forward problem solution…

Quantum theory is formulated as the uniquely consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if the amplitude of a quantum process can be computed in two different ways, the two…

The inverse quantum scattering problem for the perturbed Bessel equation is considered. A direct and practical method for solving the problem is proposed. It allows one to reduce the inverse problem to a system of linear algebraic…

We prove a version of the classical 'generic smoothness' theorem with smooth varieties replaced by non-commutative resolutions of singular varieties. This in particular implies a non-commutative version of the Bertini theorem.

After a brief survey of the definition and the properties of Lambda-symmetries in the general context of dynamical systems, the notion of "Lambda-constant of motion'' for Hamiltonian equations is introduced. If the Hamiltonian problem is…

It is argued that, for motion in a central force field, polar reciprocals of trajectories are an elegant alternative to hodographs. The principal advantage of polar reciprocals is that the transformation from a trajectory to its polar…

In our work we give the examples using Fermat's Last Theorem for solving some problems from algebra and number theory.

Quantum and classical mechanics are derived using four natural physical principles: (1) the laws of nature are invariant under time evolution, (2) the laws of nature are invariant under tensor composition, (3) the laws of nature are…

Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…

In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…

In this paper we prove the global existence of classical static solutions of Einstein gravitational theory coupled to a real scalar field where the spacetime admits spherically symmetry. The equations of motions can then be reduced into a…

Weyl theory for a non-classical system depending rationally on the spectral parameter is treated. Borg-Marchenko-type uniqueness theorem is proved. The solution of the inverse problem is constructed. An application to sine-Gordon equation…

The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…

In this article we use the Desargues' theorem and its reciprocal to solve two problems.

Two main aims of this paper are to develop a numerical method to solve an inverse source problem for parabolic equations and apply it to solve a nonlinear coefficient inverse problem. The inverse source problem in this paper is the problem…

The so-called inverse problem of dynamics is about constructing a potential for a given family of curves. We observe that there is a more general way of posing the problem by making use of ideas of another inverse problem, namely the…