scholarly journals On the Inverse Degree Polynomial

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1490
Author(s):  
Paul Bosch ◽  
José Manuel Rodríguez ◽  
Omar Rosario ◽  
José María Sigarreta
Keyword(s):  
Symmetry Property ◽  
Degree Polynomial ◽  
Cyclomatic Number ◽  
Inverse Degree ◽  
Mathematical Relations

Using the symmetry property of the inverse degree index, in this paper, we obtain several mathematical relations of the inverse degree polynomial, and we show that some properties of graphs, such as the cardinality of the set of vertices and edges, or the cyclomatic number, can be deduced from their inverse degree polynomials.

scholarly journals f-Polynomial on Some Graph Operations

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1074 ◽  
Author(s):  
Walter Carballosa ◽  
José Manuel Rodríguez ◽  
José María Sigarreta ◽  
Nodari Vakhania
Keyword(s):  
Large Family ◽  
Topological Indices ◽  
Graph Operations ◽  
Inverse Degree ◽  
Corona Product ◽  
Mathematical Relations

Given any function f : Z + → R + , let us define the f-index I f ( G ) = ∑ u ∈ V ( G ) f ( d u ) and the f-polynomial P f ( G , x ) = ∑ u ∈ V ( G ) x 1 / f ( d u ) − 1 , for x > 0 . In addition, we define P f ( G , 0 ) = lim x → 0 + P f ( G , x ) . We use the f-polynomial of a large family of topological indices in order to study mathematical relations of the inverse degree, the generalized first Zagreb, and the sum lordeg indices, among others. In this paper, using this f-polynomial, we obtain several properties of these indices of some classical graph operations that include corona product and join, line, and Mycielskian, among others.

A Bayesian View on the Hilbert Transform and the Kramers-Kronig Transform of Electrochemical Impedance Data: Probabilistic Estimates and Quality Scores

2020 ◽  
Author(s):  
Jiapeng Liu ◽  
Ting Hei Wan ◽  
Francesco Ciucci
Keyword(s):  
Power Generation ◽  
Electrochemical Impedance Spectroscopy ◽  
Hilbert Transform ◽  
Electrochemical Impedance ◽  
The Self ◽  
Impedance Data ◽  
The Hilbert Transform ◽  
Validation Tests ◽  
Self Consistency ◽  
Mathematical Relations

<p>Electrochemical impedance spectroscopy (EIS) is one of the most widely used experimental tools in electrochemistry and has applications ranging from energy storage and power generation to medicine. Considering the broad applicability of the EIS technique, it is critical to validate the EIS data against the Hilbert transform (HT) or, equivalently, the Kramers–Kronig relations. These mathematical relations allow one to assess the self-consistency of obtained spectra. However, the use of validation tests is still uncommon. In the present article, we aim at bridging this gap by reformulating the HT under a Bayesian framework. In particular, we developed the Bayesian Hilbert transform (BHT) method that interprets the HT probabilistic. Leveraging the BHT, we proposed several scores that provide quick metrics for the evaluation of the EIS data quality.<br></p>

On the Radial Symmetry Property for Harmonic Functions

2020 ◽  
Vol 64 (10) ◽  
pp. 9-19
Author(s):  
V. V. Volchkov ◽  
Vit. V. Volchkov
Keyword(s):  
Harmonic Functions ◽  
Symmetry Property ◽  
Radial Symmetry

Semiconductors

2018 ◽  
Author(s):  
L. Solymar ◽  
D. Walsh ◽  
R. R. A. Syms
Keyword(s):  
Crystal Growth ◽  
Molecular Beam ◽  
Vapour Deposition ◽  
Energy Levels ◽  
Chemical Vapour ◽  
Optical Excitation ◽  
Organic Chemical ◽  
Metal Organic ◽  
Mathematical Relations ◽  
Semiconductor Properties

Both intrinsic and extrinsic semiconductors are discussed in terms of their band structure. The acceptor and donor energy levels are introduced. Scattering is discussed, from which the conductivity of semiconductors is derived. Some mathematical relations between electron and hole densities are derived. The mobilities of III–V and II–VI compounds and their dependence on impurity concentrations are discussed. Band structures of real and idealized semiconductors are contrasted. Measurements of semiconductor properties are reviewed. Various possibilities for optical excitation of electrons are discussed. The technology of crystal growth and purification are reviewed, in particular, molecular beam epitaxy and metal-organic chemical vapour deposition.

scholarly journals Simulation Tests of a Cow Milking Machine—Analysis of Design Parameters

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1358
Author(s):  
Ewa Golisz ◽  
Adam Kupczyk ◽  
Maria Majkowska ◽  
Jędrzej Trajer
Keyword(s):  
Mathematical Model ◽  
Simplified Model ◽  
Design Parameters ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Local Loss ◽  
Linear Drag ◽  
Milking Machine ◽  
Machine Analysis ◽  
The Impact

The objective of this paper was to create a mathematical model of vacuum drops in a form that enables the testing of the impact of design parameters of a milking cluster on the values of vacuum drops in the claw. Simulation tests of the milking cluster were conducted, with the use of a simplified model of vacuum drops in the form of a fourth-degree polynomial. Sensitivity analysis and a simulation of a model with a simplified structure of vacuum drops in the claw were carried out. As a result, the impact of the milking machine’s design parameters on the milking process could be analysed. The results showed that a change in the local loss and linear drag coefficient in the long milk duct will have a lower impact on vacuum drops if a smaller flux of inlet air, a higher head of the air/liquid mix, and a higher diameter of the long milk tube are used.

Optimization of performance in multi-cell beams with different surface slopes for use in vehicle structure using a multi-objective evolutionary algorithm based on decomposition

2021 ◽  
pp. 146442072199784
Author(s):  
S Chahardoli ◽  
Mohammad Sheikh Ahmadi ◽  
TN Tran ◽  
Afrasyab Khan
Keyword(s):  
Decomposition Method ◽  
Experimental Tests ◽  
Surface Slope ◽  
Optimal Model ◽  
Degree Polynomial ◽  
Numerical Tests ◽  
Numerical Studies ◽  
Surface Slopes ◽  
Vehicle Structure ◽  
Number Of Cells

This study examined the effect of the upper surface slope and the number of cells in the side beams on the collapse properties using experimental and numerical tests. The numerical studies were conducted with LS-DYNA software, and the accuracy of numerical results was investigated by experimental tests. Using MATLAB software, the second-degree polynomial functions were obtained for the collapse properties of the specimens. Also, after the optimization by the decomposition method, the best mode was introduced for the specimens. The studies on collapse properties showed that increasing the number of cells leads to a decrease in all collapse properties, and increasing the upper surface slope leads to an increase in the collapse properties. Moreover, the optimization results by decomposition method showed that this method could suggest the most optimal model for multi-cell and sloping beams.

scholarly journals MATHEMATICAL RELATIONS OF CERTAIN CHEST MEASUREMENTS.

JAMA ◽  
1904 ◽  
Vol XLIII (12) ◽  
pp. 787
Author(s):  
WINFIELD S. HALL
Keyword(s):  
Mathematical Relations

Kinematics of a New High-Precision Three-Degree-of-Freedom Parallel Manipulator

2006 ◽  
Vol 129 (3) ◽  
pp. 320-325 ◽  
Author(s):  
Farhad Tahmasebi
Keyword(s):  
Power Dissipation ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Base Plane ◽  
Degree Polynomial ◽  
Payload Capacity ◽  
Half Angle ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

Closed-form direct and inverse kinematics of a new three-degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three-DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base mounted, higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of the tangent of the half-angle between one of the limbs and the base plane. Hence, there are at most 16 assembly configurations for the manipulator. In addition, it is shown that the 16 solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

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