Time series forecasting using amplitude-frequency analysis of STL components

The problem of economic time series analysis and forecasting using amplitude-frequency analysis of STL decomposition is considered. An amplitude-phase operator was chosen as an apparatus for extraction the series harmonic components, the advantages of which (compared to the Fourier transform) are: calculations speed, result accuracy, simplicity and interpretability of software implementation. The forecast quality was carried out using the MAPE metric. Significantly higher prediction quality was achieved compared to Facebook Prophet forecasting package.

Multiple Solutions for Double Phase Problems with Hardy Type Potential

In this paper, we are concerned with the singular elliptic problems driven by the double phase operator and and Dirichlet boundary conditions. In view of the variational approach, we establish the existence of at least one nontrivial solution and two distinct nontrivial solutions under some general assumptions on the nonlinearity f. Here we use Ricceri’s variational principle and Bonanno’s three critical points theorem in order to overcome the lack of compactness.

Tan-concavity property for Lagrangian phase operators and applications to the tangent Lagrangian phase flow

We explore the tan-concavity of the Lagrangian phase operator for the study of the deformed Hermitian Yang–Mills (dHYM) metrics. This new property compensates for the lack of concavity of the Lagrangian phase operator as long as the metric is almost calibrated. As an application, we introduce the tangent Lagrangian phase flow (TLPF) on the space of almost calibrated [Formula: see text]-forms that fits into the GIT framework for dHYM metrics recently discovered by Collins–Yau. The TLPF has some special properties that are not seen for the line bundle mean curvature flow (i.e. the mirror of the Lagrangian mean curvature flow for graphs). We show that the TLPF starting from any initial data exists for all positive time. Moreover, we show that the TLPF converges smoothly to a dHYM metric assuming the existence of a [Formula: see text]-subsolution, which gives a new proof for the existence of dHYM metrics in the highest branch.

Existence results for double phase implicit obstacle problems involving multivalued operators

In this paper we study implicit obstacle problems driven by a nonhomogenous differential operator, called double phase operator, and a multivalued term which is described by Clarke’s generalized gradient. Based on a surjectivity theorem for multivalued mappings, Kluge’s fixed point principle and tools from nonsmooth analysis, we prove the existence of at least one solution.

Generalized graph states and mutually unbiased bases from multi-qudits phase states

The description of qudits in a formalism based on a generalized variant of Weyl–Heisenberg algebras is discussed. The unitary phase operators for a multi-qudit system and the corresponding phase states (the eigenstates of the phase operator) are constructed. We discuss the dynamics of multi-qudit phase states governed by a generalized Hamiltonian involving one- and two-body interactions which offer a remarkable connection between phase states, generalized graph states and the mutually unbiased bases. The entangled phase states are shown to possess the following properties simultaneously, namely the mutually unbiasedness of phase states resulting from the one-body generalized oscillator Hamiltonian and the entanglement properties of generalized graph states resulting from the two-body interaction Hamiltonian.