J. B. Kelly † American Mathematical Monthly 73 (1966) 464–471 1. The associated polynomial. Let S be a finite set of lattice points (i.e. points with integral coordinates) in k-dimensional Euclidean space, Ek. There will be no loss in generality in assuming that S is contained in E′ k, where E ′ k is that portion of Ek in which all points have nonnegative coordinates. With the point p of S havi...

A method for robot indoor automatic positioning and orientating based on two-dimensional (2D) barcode landmark is proposed. By using the scheme of the 2D barcode for reference, a special landmark is designed which is convenient to operate and easy to recognize, contain coordinates of their absolute positions and have some ability to automatically correct errors. Landmarks are placed over the “c...

We consider a class of Hamiltonian systems in 3 degrees freedom, with particular type quadratic integral and which includes the rational Calogero-Moser system as case. For general class, we introduce separation coordinates to find separable (and therefore Liouville integrable) system, two integrals. This gives coupling large potentials, generalising series potentials are parabolic coordinates. ...

We suggest a way to study possible conformal symmetries on black hole horizons. We do this by carrying out a Kaluza-Klein like reduction of the Einstein-Hilbert action along the ignorable coordinates of stationary and axisymmetric black holes. Rigid diffeomorphism invariance of the m-ignorable coordinates then becomes a global SL(m,R) gauge symmetry of the reduced action. Related to each non-va...

The one-dimensional modified shallow water equations in Lagrangian coordinates are considered. It is shown the relationship between symmetries and conservation laws coordinates, mass variables, Eulerian coordinates. For an invariant finite-difference scheme constructed for all cases which exist differential model. Such schemes possess difference analogues of mass, momentum, energy, law center m...

Abstract This paper introduces 3D modeling and application based on virtual technology. paper’s drawing of SOR can obtain the differential equation linear segments composed pixel points. The resulting output data constitute an image unit. Then this uses visual difference theory effect to realize production reality animation Finally, carries simulation test three-dimensional model. results show ...

The author shows that a systematic application of thickness-weighted averaging to the Boussinesq equations of motion results in averaged equations of motion written entirely in terms of the thickness-weighted velocity; that is, the unweighted average velocity and the eddy-induced velocity do not appear in the averaged equations of motion. This thickness-weighted average (TWA) formulation is ide...

Recovering the three-dimensional structure of molecules is important for understanding their functionality. We describe a spectral graph algorithm for reconstructing the three-dimensional structure of molecules from their cryo-electron microscopy images taken at random unknown orientations.We first identify a one-to-one correspondence between radial lines in three-dimensional Fourier space of t...

Reaction coordinates are widely used throughout chemical physics to model and understand complex chemical transformations. We introduce a definition of the natural reaction coordinate, suitable for condensed phase and biomolecular systems, as a maximally predictive one-dimensional projection. We then show that this criterion is uniquely satisfied by a dominant eigenfunction of an integral opera...

Time does not obviously appear amongst the coordinates on the constrained phase space of general relativity in the Hamiltonian formulation. Recent work in finite-dimensional models claims that topological obstructions generically make the global definition of time impossible. It is shown here that a time coordinate can be globally defined on a constrained phase space by patching together local ...