CLASSIFICATION OF SEISMIC PHASES BASED ON MACHINE LEARNING

In the course of recent years, progresses in sensor innovation has lead to increments in the interest for automated strategies for investigating seismological signals. Fundamental to the comprehension of the components creating seismic signals is the information on the phases of seismic waves. Having the option to indicate the kind of wave prompts better performing seismic forecasting frameworks. In this article, we propose another strategy for the characterization of seismic waves quantification from a three-channel seismograms. The seismograms are isolated into covering time windows, where each time-window is mapped to a lot of multi-scale three-dimensional unitary vectors that portray the direction of the seismic wave present in the window at a few physical scales. The issue of arranging seismic waves gets one of ordering focuses on a few two-dimensional unit circles. We take care of this issue by utilizing kernel based machine learning that are remarkably adjusted to the geometry of the circle. The grouping of the seismic wave depends on our capacity to gain proficiency with the limits between sets of focuses on the circles related with the various kinds of seismic waves. At each signal scale, we characterize a thought of vulnerability connected to the order that considers the geometry of the dissemination of tests on the circle. At long last, we join the grouping results acquired at each scale into a unique label.

Possible principles of mathematical music analysis

The text is a summary of many years of research in the domains of micro-intervals, metric-rhythmic projection of the spectrum harmonics, and the establishment of a link with mathematics, more precisely, geometry, with a special focus on the application of the Pythagorean Theorem. Mathematical music analysis enables the establishment of methods for constructing right, obtuse, and acute musical triangles as well as projections of their edges (sides), which are recognized in trigonometry as the functions of angles: the sine, cosine, and so on; as well as the establishment of methods for constructing spectral and scalar (intonative-temporal) trigonometric unit circles with their function graphs.

On Pure Quasi-Quantum Quadratic Operators of 𝕄2(ℂ) II

In this paper we study quasi quantum quadratic operators (QQO) acting on the algebra of [Formula: see text] matrices [Formula: see text]. We consider two kinds of quasi QQO the corresponding quadratic operator maps from the unit circle into the sphere and from the sphere into the unit circle, respectively. In our early paper we have defined a q-purity of quasi QQO. This notion is equivalent to the invariance of the unit sphere in [Formula: see text]. But to check this condition, in general, is tricky. Therefore, it would be better to find weaker conditions to check the q-purity. One of the main results of this paper is to provide a criterion of q-purity of quasi QQO in terms of the unit circles. Moreover, we are able to classify all possible kinds of quadratic operators which can produce q-pure quasi QQO. We think that such result will allow one to check whether a given mapping is a pure channel or not. This finding suggests us to study such a class of nonpositive mappings. Correspondingly, the complement of this class will be of potential interest for physicist since this set contains all completely positive mappings.

Unit Circles and Inverse Trigonometric Functions

A method to determine all the inverse trigonometric functions directly from the unit circle.

Covering Discs in Minkowski Planes

We investigate the following version of the circle covering problem in strictly convex (normed or) Minkowski planes: to cover a circle of largest possible diameter by k unit circles. In particular, we study the cases k = 3, k = 4, and k = 7. For k = 3 and k = 4, the diameters under consideration are described in terms of side-lengths and circumradii of certain inscribed regular triangles or quadrangles. This yields also simple explanations of geometric meanings that the corresponding homothety ratios have. It turns out that basic notions from Minkowski geometry play an essential role in our proofs, namely Minkowskian bisectors, d-segments, and the monotonicity lemma.