相关论文: Four-divergence as a paravector operator. Invarian…
Symmetry is present in many tasks in computer vision, where the same class of objects can appear transformed, e.g. rotated due to different camera orientations, or scaled due to perspective. The knowledge of such symmetries in data coupled…
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…
In present paper, the equivalence problem for fourth order differential operators with one variable under general fiber-preserving transformation using the Cartan method of equivalence is applied. Two versions of equivalence problems are…
The momentum operator $ {\bf p} = - i {\bx \nabla} $ has radial component $ {\bf \tilde p} \equiv - i {\bf \hat{r}} ({1 \over r} \partial_r r).$ We show that ${\bf \tilde p} $ is the space part of a 4-vector operator, the zero component of…
Refraction, interference, and diffraction serve as distinguishing features for wave-like phenomena. While they are normally associated only with a purely spatial wave-propagation pattern, analogs to interference and diffraction involving…
We continue to derive spacetime quantities and spin 1/2 propagators from rotations. Rotation-invariant projection operators are found for each element of a four element basis, i.e. a basis for four component quantities with specific…
Variational inference is an umbrella term for algorithms which cast Bayesian inference as optimization. Classically, variational inference uses the Kullback-Leibler divergence to define the optimization. Though this divergence has been…
Operational definition of space-time in light of quantum mechanics and general relativity inevitably indicates an intrinsic imprecision in space-time structure which has to do with space-time dimension as well. The operational dimension of…
In this paper, a pointwise weighted identity for some stochastic partial differential operators (with complex principal parts) is established. This identity presents a unified approach in studying the controllability, observability and…
This work is concerned with the classical wave equation with a high-contrast coefficient in the spatial derivative operator. We first treat the periodic case, where we derive a new limit in the one-dimensional case. The behavior is…
A simple, though rarely considered, thought experiment on relativistic rotation is described in which internal inconsistencies in the theory of relativity seem to arise. These apparent inconsistencies are resolved by appropriate insight…
By solving the two variable differential equations which arise from finding the eigenfunctions for the Casimir operator for $O(d,2)$ succinct expressions are found for the functions, conformal partial waves, representing the contribution of…
We analyze the parabolic Dirac operator $D \pm i\partial_t$ in a biquaternionic setting, characterizing its kernel via generalized div-curl systems and Cauchy-Riemann-type relations between the real and imaginary parts. Using the machinery…
Over n-dimensional manifolds, I classify ternary differential operators acting on the spaces of weighted densities and invariant with respect to the Lie algebra of vector fields. For n=1, some of these operators can be expressed in terms of…
We consider an inverse boundary value problem for diffusion equations with multiple fractional time derivatives. We prove the uniqueness in determining a number of fractional time-derivative terms, the orders of the derivatives and…
Accurately forecasting the long-term evolution of turbulence represents a grand challenge in scientific computing and is crucial for applications ranging from climate modeling to aerospace engineering. Existing deep learning methods,…
We develop a theoretical framework for computer-assisted proofs of the existence of invariant objects in semilinear PDEs. The invariant objects considered in this paper are equilibrium points, traveling waves, periodic orbits and invariant…
For For a given PDE system, or an exterior differential system possessing a Lie group of internal symmetries the orbit reduction procedure is introduced. It is proved that the solutions of the reduced exterior differential system are in…
The aim of this paper is to show some examples of matrix-valued orthogonal functions on the real line which are simultaneously eigenfunctions of a second-order differential operator of Schr\"{o}dinger type and an integral operator of…
We have found a new class of time dependent partial waves which are solutions of time dependent Schr\"odinger equation for three dimensional harmonic oscillator. We also showed the decomposition of coherent states of harmonic oscillator…