We develop a new setting for the exponential principle in the context of multisort species, where indecomposable objects are generated intrinsically instead of being given in advance. Our approach uses the language of functors and natural transformations (composition operators), and we show that, somewhat surprisingly, a single axiom for the composition already suffices to guarantee validity of...

A modification of the variational configuration interaction functional in the first-order interacting space for molecular electronic structure is presented. The modified functional is a fully linked expression that by construction is extensive and invariant to transformations of the underlying orbital basis and is exact for an ensemble of separated two-electron subsystems. In addition, an appro...

Pure spinor formalism and non-integrable exponential factors are used for constructing the conformal-invariant wave equation and Lagrangian density for massive fermion. It is proved that canonical Dirac Lagrangian for massive fermion is invariant under induced projective conformal transformations.

This paper explores applications of the exponential splitting method for approximating highly oscillatory solutions of the n-dimensional paraxial Helmholtz equation. An eikonal transformation is introduced for oscillation-free platforms and matrix operator decompositions. It is found that the sequential, parallel and combined exponential splitting formulas possess not only anticipated algorithm...

Various soil texture schemes are in current use. These differ in the size ranges of their particle fractions. There is a need to establish simple methods to correlate these conventional schemes. Therefore I have defined closed-form exponential and power law functions to fit models to cumulative particle-size distribution data. I have tested the functions for their suitability (i) to represent c...

Motivated by insights from the maxout-units-based deep Convolutional Neural Network (CNN) that "non-maximal features are unable to deliver" and "feature mapping subspace pooling is insufficient," we present a novel mixed variant of the recently introduced maxout unit called a mixout unit. Specifically, we do so by calculating the exponential probabilities of feature mappings gained by applying ...

A characterization of the space L2[−σ, σ] in terms of its image under the Fourier transformation has been given by the Paley-Wiener theorem [5]. The theorem asserts that f ∈ L2[−σ, σ] if and only if its Fourier transform f̂(ω) can be continued analytically to the whole complex plane as an entire function of exponential type at most σ whose restriction to the real axis belongs to L2(R). This char...

Image enhancement plays an important role in image processing. This paper proposed method using a nonlinear(exponential) function. Firstly, we use the exponential function to construct gray transformation equation. Then, depending on position of each pixel, scale obtained by is further adjusted based compression factor. In section 3, comparative experiment shows that could achieve good performa...

The Gibbs distribution of statistical physics is an exponential family of probability distributions, which has a mathematical basis of duality in the form of the Legendre transformation. Recent studies of complex systems have found lots of distributions obeying the power law rather than the standard Gibbs type distributions. The Tsallis q-entropy is a typical example capturing such phenomena. W...