Short-Term Economic Forecasting by Complex-Valued Autoregressions

One of the directions that can expand the instrumental base for modeling the economy is complex-valued economics – ​a section of economic and mathematical modeling devoted to the use of models and methods of the theory of the function of a complex variable in economics. The article discusses the possibility of short-term economic forecasting using autoregressive models of complex variables. A classification of possible modifications of complex-valued autoregressive models is given, and the main properties of each of the classes of these models are shown. One of the varieties of these complex-valued models uses current and past errors of approximation, which means that it can be compared with the widely used model of autoregressive real variables ARIMA(p, d, q). The article makes such a comparison, both on a theoretical level and on a practical example.

Holographic M5 branes in AdS7 × S4

We study classical M5 brane solutions in the probe limit in the AdS7× S4 background geometry that preserve the minimal amount of supersymmetry. These solutions describe the holography of codimension-2 defects in the 6d boundary dual $$ \mathcal{N} $$ N = (0, 2) supersymmetric gauge theories. The general solution is described in terms of holomorphic functions that satisfy a scaling condition. We show the behavior of the world-volume of a special class of BPS solutions near the AdS boundary region can be characterized by general equations, which describe it as intersections of the zeros of holomorphic functions in three complex variables with a 5-sphere.

Complex Spacetimes and the Newman-Janis Trick

<p>In this thesis, we explore the subject of complex spacetimes, in which the mathematical theory of complex manifolds gets modified for application to General Relativity. We will also explore the mysterious Newman-Janis trick, which is an elementary and quite short method to obtain the Kerr black hole from the Schwarzschild black hole through the use of complex variables. This exposition will cover variations of the Newman-Janis trick, partial explanations, as well as original contributions.</p>

Complex Spacetimes and the Newman-Janis Trick

<p>In this thesis, we explore the subject of complex spacetimes, in which the mathematical theory of complex manifolds gets modified for application to General Relativity. We will also explore the mysterious Newman-Janis trick, which is an elementary and quite short method to obtain the Kerr black hole from the Schwarzschild black hole through the use of complex variables. This exposition will cover variations of the Newman-Janis trick, partial explanations, as well as original contributions.</p>

The Spectrum of Mapping Ideals of Type Variable Exponent Function Space of Complex Variables with Some Applications

The topological and geometric behaviors of the variable exponent formal power series space, as well as the prequasi-ideal construction by s -numbers and this function space of complex variables, are investigated in this article. Upper bounds for s -numbers of infinite series of the weighted n th power forward and backward shift operator on this function space are being investigated, with applications to some entire functions.