Related papers: On the Decomposition of Forces
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
We prove that any complete metric space has a unique decomposition as a direct product of a possibly finite or zero-dimensional Hilbert space and a space that does not split off lines.
The classical approach to solvability of a mathematical problem is to define a method which includes certain rules of operation or algorithms. Then using the defined method, one can show that some problems are solvable or not solvable or…
We put forward a theory on the optical force exerted upon a dipolar particle by a stationary and ergodic partially coherent light field. We show through a rigorous analysis that the ensemble averaged electromagnetic force is given in terms…
A mechanical covariant equation is introduced which retains all the effectingness of the Lagrange equation while being able to describe in a unified way other phenomena including friction, non-holonomic constraints and energy radiation…
The long-standing resolution of the Abraham--Minkowski electromagnetic momentum controversy is predicated on a decomposition of the total momentum of a closed continuum electrodynamic system into separate field and matter components. Using…
The classical Dedekind sums $s(d, c)$ can be represented as sums over the partial quotients of the continued fraction expansion of the rational $\frac{d}{c}$. Hardy sums, the analog integer-valued sums arising in the transformation of the…
Over a real field which is an extension of transcendence degree 1 of a hereditarily pythagorean base field, every quadratic form which is torsion decomposes into an orthogonal sum of 2-dimensional torsion forms. This is obtained from a more…
There are significant differences between Helmholtz and Hodge's decomposition theorems, but both share a common flavor. This paper is a first step to bring them together. We here produce Helmholtz theorems for differential 1-forms and…
It is proved that the set of geodesic circles in two dimensions may be given a variational description and the explicit form of it is presented. In the limit case of the Euclidean geometry a certain claim of uniqueness of such description…
Consider $k\ge 2$ distinct, linearly independent, homogeneous linear recurrences of order $k$ satisfying the same recurrence relation. We prove that the recurrences are related to a decomposable form of degree $k$, and there is a very broad…
We prove a uniqueness result for the broken ray transform acting on the sums of functions and $1$-forms on surfaces in the presence of an external force and a reflecting obstacle. We assume that the considered twisted geodesic flows have…
We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings; that is, we study the number of ways a permutation can be decomposed into a product of a given number of 2-cycles, 3-cycles, etc.…
Monsky's celebrated equidissection theorem follows from his more general proof of the existence of a polynomial relation $f$ among the areas of the triangles in a dissection of the unit square. More recently, the authors studied a different…
From a new perspective, this paper rederives Lagrange's equations. By applying the chain rule of differentiation, the intrinsic relationship between the momentum theorem and the kinetic energy theorem is first established. Subsequently,…
This paper is devoted to discrete mechanical systems subject to external forces. We introduce a discrete version of systems with Rayleigh-type forces, obtain the equations of motion and characterize the equivalence for these systems.…
On compact Riemannian manifolds, we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.
This paper reviews a class of univariate piecewise polynomial functions known as discrete splines, which share properties analogous to the better-known class of spline functions, but where continuity in derivatives is replaced by (a…
The properties of a one space-dimension, one particle dynamical system under the influence of a purely dissipative force are investigated. Assuming this force depends only on the velocity, it is demonstrated, in contrast to the case of…
We establish the coarse relative trace formulae of Jacquet-Rallis for linear and unitary groups. Both formulae are of the form: a sum of spectral distributions equals a sum of geometric distributions. In order to obtain the spectral…