Fingerprinting/indoor positioning using complex planar splines

The rapid development of various LBS-based applications and services that operate on the basis of the user’s current location, both global GPS and local LBS, today require the development of new and improved methods. This concerns, first of all, methods for determining the local location of LPS users in premises, if there is a high concentration of users and the presence of difficulties in the propagation of radio signals. the use of local methods of location determination based on the fingerprinting method is considered. It is shown that to improve the user positioning accuracy, it is expedient to use a combination of several methods. to determine the local location of the user, a method based on the finite element method and linear complex planar splines is proposed. the construction of linear complex planar splines is considered, their coefficients are found. finding the error in determining the coordinates of the user’s UE location is shown. The use of the proposed method will improve the accuracy of determining the coordinates of the user’s location and will ensure the provision of LBS services and applications to users in the premises under various conditions of their provision.

A real expectation value of the time-dependent non-Hermitian Hamiltonians

With the aim to solve the time-dependent Schr ̈odinger equation associated to a time-dependent non-Hermitian Hamiltonian, we introduce a unitary transformation that maps the Hamiltonian to a time-independent PT-symmetric one. Consequently, the solution of time-dependent Schrödinger equation becomes easily deduced and the evolution preserves the C(t)PT -inner product, where C(t) is a obtained from the charge conjugation operator C through a time dependent unitary transformation. Moreover, the expectation value of the non-Hermitian Hamiltonian in the C(t)PT normed states is guaranteed to be real. As an illustration, we present a specific quantum system given by a quantum oscillator with time-dependent mass subjected to a driving linear complex time-dependent potential.

Further study on solutions of some non-linear homogeneous differential equations in connection to Brück conjecture

In this paper, using the theory of complex differential equations, we study the solution of some non-linear complex differential equations in connection to Brück conjecture which generalized some earlier results due to Pramanik, D. C. and Biswas, M., On solutions of some non-linear differential equations in connection to Bruck conjecture, Tamkang J. Math., 48 (2017), No. 4, 365–375; and Wang, H., Yang, L-Z. and Xu, H-Y., On some complex differential and difference equations concerning sharing function, Adv. Diff. Equ., 2014, 2014:274.

Bosonic and fermionic Gaussian states from Kähler structures

We show that bosonic and fermionic Gaussian states (also known as ``squeezed coherent states’’) can be uniquely characterized by their linear complex structure JJ which is a linear map on the classical phase space. This extends conventional Gaussian methods based on covariance matrices and provides a unified framework to treat bosons and fermions simultaneously. Pure Gaussian states can be identified with the triple (G,\Omega,J)(G,Ω,J) of compatible Kähler structures, consisting of a positive definite metric GG, a symplectic form \OmegaΩ and a linear complex structure JJ with J^2=-\mathbb{1}J2=−1. Mixed Gaussian states can also be identified with such a triple, but with J^2\neq -\mathbb{1}J2≠−1. We apply these methods to show how computations involving Gaussian states can be reduced to algebraic operations of these objects, leading to many known and some unknown identities. We apply these methods to the study of (A) entanglement and complexity, (B) dynamics of stable systems, (C) dynamics of driven systems. From this, we compile a comprehensive list of mathematical structures and formulas to compare bosonic and fermionic Gaussian states side-by-side.

Developing A Conceptual Model that Illuminates the Dynamics of Performativity within Technological Innovation

Technological innovation is a process that involves the intertwining of social, cognitive, and material elements. The relationship among these features is non-linear, complex, and possesses the ability to transform as well as inform the configuration of markets, tools, users, and social environments. The concept of performativity can be used to explain this phenomenon. This paper identifies the performative elements present in the context of technological innovation and maps the social factors and the use of cognitive features in the innovation process. This identification explicitly addresses the entanglement of the material and social influences in the process, defines the agency of technological change, and focuses on the impact the nature of a technology has on the configuration of a market. A conceptual model of performativity in the innovation process is proposed.

Blind signal separation based on widely linear complex autoregressive process of order one

In this paper, the blind signal separation problem of complex baseband signal is addressed. A widely linear complex autoregressive process of order one is employed to represent the temporal structure of complex sources. We formulate a new contrast function by a convex combination of generalized autocorrelations and the statistics of the innovation. And the proposed contrast function is optimized by gradient method. Simulation results show that the proposed algorithm is better than the comparison algorithm in convergence speed and convergence accuracy.