Hybrid basis vector based underdetermined beamforming algorithm in optimized antenna reconfiguration

Optimized positioning of antenna to obtain the best beam forming solution is adopted in this research. Non-uniform linear array-based beamforming algorithms have the challenge of placing the array of antennas in positions that would implement best beamforming outputs. This paper attempts to obtain the optimized beam forming by tuning the sparse Bayesian learning based algorithm. The parameters used for tuning involve choosing the hybrid basis vector for creating the steering vector while at the same time developing the optimized position of the antennas. Basis vectors are the building blocks of the steering vector developed for the beamforming algorithm that finds the angle of arrival in antennas. Reconfiguration of antennas is carried out using particle swarm optimization (PSO) algorithm and the basis vectors are generated using two different ways. One by cumulating similar basis vectors and another by cumulating two different basis vectors. The performance of accurate detection of angle of arrival in the beamforming algorithm is analyzed and results are discussed. This basis vector and antenna distance optimization is adopted on the sparse Bayesian learning paradigm. Performance evaluation of these optimizations in the algorithm is realised by validating the mean square error (MSE) versus signal to noise ratio (SNR) graphs for both the cumulative basis vector and hybrid basis vector cases.

On a Certain Operator Related to Blackwell’s Markov Chain

We present an example of a densely defined, linear operator on the $$l^{1}$$ l 1 space with the property that each basis vector of the standard Schauder basis of $$l^{1}$$ l 1 does not belong to its domain. Our example is based on the construction of a Markov chain with all states instantaneous given by D. Blackwell in 1958. In addition, it turns out that the closure of this operator is the generator of a strongly continuous semigroup of Markov operators associated with Blackwell’s chain.

Three-Complex Numbers and Related Algebraic Structures

Three-complex numbers are introduced for using a geometric vector product in the three-dimensional Euclidean vector space R3 and proving its equivalence with a spherical coordinate product. Based upon the definitions of the geometric power and geometric exponential functions, some Euler-type trigonometric representations of three-complex numbers are derived. Further, a general l23−complex algebraic structure together with its matrix, polynomial and variable basis vector representations are considered. Then, the classes of lp3-complex numbers are introduced. As an application, Euler-type formulas are used to construct directional probability laws on the Euclidean unit sphere in R3.

Shape Optimum Design by Basis Vector Method Considering Partial Shape Dependence

Regarding the case of complicated structural shape optimization, there are cases where there are partial shapes such as holes and irregularities inside the structure. Concerning the complex structural optimization shape, the relationship between the external boundary shape and the internal local shape should be maintained, and how to change the internal partial shape while maintaining a subordinate relationship with the external form has become an important issue. Currently, there is no good solution to this kind of problem using general optimization design software. Therefore, this paper proposes to use the basic vector method to solve the local shape dependency problem of partial shapes. First, this paper classifies the subordinate problems of partial shape into three primary patterns, theoretically proving a method for controlling subordinate relationships of partial forms, respectively. Then, the research also provides two classical application examples: shape optimization of a steam turbine implantation section and stress distribution optimization of an engine mount bracket. The results show that the optimization method is effective for the partial shape subordination problem in complex structural shape optimization problems. Finally, the study examines the problem of making a vectorial vector, a correlation between the basis vector and the remeshing problem of the analysis model in shape optimization, and further substantiates the validity of the method proposed by the body using the analysis result of the actual structural shape optimization case.

Extraction of Quasi-Monochromatic Gravity Waves from an Airglow Imager Network

An algorithm has been developed to isolate the gravity waves (GWs) of different scales from airglow images. Based on the discrete wavelet transform, the images are decomposed and then reconstructed in a series of mutually orthogonal spaces, each of which takes a Daubechies (db) wavelet of a certain scale as a basis vector. The GWs in the original airglow image are stripped to the peeled image reconstructed in each space, and the scale of wave patterns in a peeled image corresponds to the scale of the db wavelet as a basis vector. In each reconstructed image, the extracted GW is quasi-monochromatic. An adaptive band-pass filter is applied to enhance the GW structures. From an ensembled airglow image with a coverage of 2100 km × 1200 km using an all-sky airglow imager (ASAI) network, the quasi-monochromatic wave patterns are extracted using this algorithm. GWs range from ripples with short wavelength of 20 km to medium-scale GWs with a wavelength of 590 km. The images are denoised, and the propagating characteristics of GWs with different wavelengths are derived separately.

The semi-analytical method for inversion of a weighted vector ray transform in three dimensions

An inversion of the weighted vector ray transform is performed jointly with the inversion of the scalar ray transform for the weighted function [Formula: see text]. Initially, the ray transform of the basis vector functions for the vector field [Formula: see text] is evaluated in an analytical form and then the inversion problem is reduced by the method of the least squares to a linear system of equations.

Golf Clubhead Optimization Based on Contribution of Eigenmodes

This study is aimed to optimize a golf clubhead for the purposes of maximizing the driving distance. Since the sensitivity-based approaches cannot be applied in impact problem, the authors developed an optimization system by using basis vector method. The relation between the eigenfrequencies and the coefficient of restitution is examined with finite element method (FEM) models numerically at first. Based on evaluating the contribution of eigenmodes, the authors proposed an approach to create the basis vectors using the sensitivity functions of eigenvalues. Computational results are presented for demonstrating the effectiveness of the proposed approach.

On the Orbits of One Non-Solvable 5-Dimensional Lie Algebra

This paper studies holomorphic homogeneous real hypersurfaces in C3 associated with the unique non-solvable indecomposable 5-dimensional Lie algebra 𝑔5 (in accordance with Mubarakzyanov’s notation). Unlike many other 5-dimensional Lie algebras with “highly symmetric” orbits, non-degenerate orbits of 𝑔5 are “simply homogeneous”, i.e. their symmetry algebras are exactly 5-dimensional. All those orbits are equivalent (up to holomorphic equivalence) to the specific indefinite algebraic surface of the fourth order. The proofs of those statements involve the method of holomorphic realizations of abstract Lie algebras. We use the approach proposed by Beloshapka and Kossovskiy, which is based on the simultaneous simplification of several basis vector fields. Three auxiliary lemmas formulated in the text let us straighten two basis vector fields of 𝑔5 and significantly simplify the third field. There is a very important assumption which is used in our considerations: we suppose that all orbits of 𝑔5 are Levi non-degenerate. Using the method of holomorphic realizations, it is easy to show that one need only consider two sets of holomorphic vector fields associated with 𝑔5. We prove that only one of these sets leads to Levi non-degenerate orbits. Considering the commutation relations of 𝑔5, we obtain a simplified basis of vector fields and a corresponding integrable system of partial differential equations. Finally, we get the equation of the orbit (unique up to holomorphic transformations) (𝑣 − 𝑥2𝑦1)2 + 𝑦2 1𝑦2 2 = 𝑦1, which is the equation of the algebraic surface of the fourth order with the indefinite Levi form. Then we analyze the obtained equation using the method of Moser normal forms. Considering the holomorphic invariant polynomial of the fourth order corresponding to our equation, we can prove (using a number of results obtained by A.V. Loboda) that the upper bound of the dimension of maximal symmetry algebra associated with the obtained orbit is equal to 6. The holomorphic invariant polynomial mentioned above differs from the known invariant polynomials of Cartan’s and Winkelmann’s types corresponding to other hypersurfaces with 6- dimensional symmetry algebras.