The principles of behavior of the system with discrete interactions are applied to description of motion of a relativistic particle. The apparently covariant equation of motion of a particle (Klein-Gordon) is defined without explicit use of the principle of correspondence. Based on the assumption that the form of the equation has to be invariant in inertial frames of reference, the principle of...

We compare two methods for visualising contingency tables and develop a method called the ratio map which combines the good properties of both. The first is a biplot based on the logratio approach to compositional data analysis. This approach is founded on the principle of subcompositional coherence, which assures that results are invariant to considering subsets of the composition. The second ...

Hamilton’s variation principle can be shown to correspond to Fermat’s Principle for a wave propagation in configuration space (q-space), and the Hamilton-Jacobi equation expresses Huygens’ Principle for this wave propagation. Unfortunately this powerful and momentous conception of Hamilton, is deprived, in most modern reproductions, of its beautiful raiment as a superfluous accessory, in favour...

This paper proposes a principle of one-to-one correspondence in performance evaluation of a general class of detection and recognition algorithms. Such a correspondence between ground-truth entities and algorithm declared entities is essential in accurately computing objective performance measures such as the detection, recognition, and false alarm rates. We mathematically de ne the corresponde...

The motion of a magnetic spin particle in electromagnetic fields is considered on the basis of general principles of the classical relativistic theory. Alternative approaches in derivation of the equations of charge motion and spin precession, the problem of noncollinearity of the momentum and velocity of a particle with spin, the origin and the meaning of Thomas precession in dynamics of the s...

We consider string theory corrections to 4D black holes which are solutions of the 5D vacuum Einstein equations. We find that the corrections vanish only for the extremal electric solution. We also show that for the non-extremal electric black hole the mass corrections are related to the charge corrections. The implications to string states counting and the correspondence principle for black ho...

Characteristic length scale of the post-Newtonian corrections to the gravitational field of a body is given by its gravitational radius rg. The role of this scale in quantum domain is discussed in the context of the low-energy effective theory. The question of whether quantum gravity effects appear already at rg leads to the question of correspondence between classical and quantum theories, whi...

We use the Litvinov-Maslov correspondence principle to reduce and hybridize networks of biochemical reactions. We apply this method to a cell cycle oscillator model. The reduced and hybridized model can be used as a hybrid model for the cell cycle. We also propose a practical recipe for detecting quasi-equilibrium QE reactions and quasi-steady state QSS species in biochemical models with ration...

Descriptions of the mechanical behaviors of articular cartilage and their correlations with collagen, proteoglycan, water, and ions are summarized, with particular emphasis on understanding the osmotic effect inside the tissue. First, a descriptive explanation is presented of the biphasic theory required to understand how interstitial water contributes toward the viscoelastic behavior of any hy...

In a one-good world, there is a nice correspondence between the Pigou-Dalton principle of transfer and social welfare dominance. In this paper we study the case of multiple goods (without using prices as a means to come back to one dimension), and show that many results of the onedimensional setting carry over to the multidimensional case when individuals are assumed to have identical preferenc...