In the present paper, we introduced and study a new class of harmonic univalent functions on unit disc U. also we obtain coefficient conditions, extreme points, convolution condition for the above class of harmonic univalent functions.

Many natural signals exhibit a quasi-periodic behavior and are conveniently modeled as a combination of several harmonic sinusoids whose relative frequencies, magnitudes and phases vary with time. The waveform shape of those signals reflects important physical phenomena underlying their generation, which requires that those parameters be accurately estimated and modeled. In the literature, accurate phase estimation and modeling has received much less research effort than frequency estimation, or magnitude estimation. First, this paper addresses accurate DFT-based phase estimation of individual sinusoids in six scenarios involving two DFT-based filter banks and three different windows. It is shown that bias in phase estimation is less than 1E-3 radians when the SNR is equal to or larger than 2.5 dB. Taking as a reference the Cramér-Rao Lower Bound, it is shown that one particular window offers a performance of practical interest by approximating better the CRLB when signal conditions are favorable, and by minimizing the performance deviation when signal conditions are adverse. Second, this paper explains how a shift-invariant phase-related feature can be devised that characterizes harmonic phase structure, which motivates a signal processing paradigm that greatly simplifies parametric modeling, transformation and synthesis of harmonics signals, in addition to facilitating the understanding and reverse engineering of the phasegram. Theory and results are discussed in a reproducible perspective using dedicated experiments that are supported with code allowing not only to replicate figures and results in this paper, but also to expand research.

We discuss a formalism which allows for the calculation of a higher harmonic current response to an applied electric field for disordered superconducting systems described on the basis of tight-binding models. The theory is based on an expansion of the density matrix in powers of the field amplitudes where we solve the equation of motion for the individual components. This allows the evaluation of higher order response functions on significantly larger lattices than one can achieve with a previously used approach, which is based on a direct temporal integration of the equation of motion for the complete density matrix. In case of small lattices, where both methods can be applied by including also the contribution of collective modes, we demonstrate the agreement of the corresponding results.

Partial sums of analytic univalent functions and partial sums of starlike have been investigated extensively by several researchers. In this paper, we investigate a partial sums of convex harmonic functions that are univalent and sense preserving in the open unit disk.

Currently, one of the main focuses of attention in academia is microgrids (MGs) and their ability to maintain stable, resilient, reliable and high–power quality operations. A crucial component in MGs is power converters (PC), which facilitate the decentralization of power generation. This decentralization, however, poses challenges in terms of power quality. This paper presents a microgrid model based on the IEEE 14–bus distribution system and aims to investigate the power quality when the MG operates while connected to the conventional power grid. The MG model has been developed using MATLAB–Simulink®, a specialized tool for electrical engineering simulations. The results obtained are subjected to rigorous analysis and compared with the compatibility levels established by the IEEE–519 standard. This approach allows an accurate assessment of the MGs’ ability to maintain power quality at acceptable levels while interconnected to the conventional power grid. Finally, this study provides a valuable contribution to the MGs’ field of microgrids by providing a detailed and quantitative assessment of power quality, which will aid in the design and optimization of MGs’ for effective implementation in real electric power systems.

This study investigates the impact of narrow-band terahertz pulses on the ferroelectric order parameter in Ba0.8Sr0.2TiO3 films on various substrates. The 375 nm thick BST film on an MgO (001) substrate exhibits enhanced THz-induced second harmonic generation when excited by THz pulses with a central frequency of 1.6 THz, due to the resonant excitation of the soft phonon mode. Conversely, the BST film on a Si (001) substrate shows no enhancement, due to its polycrystalline state. The 800 nm thick BST film on an MgO (111) substrate demonstrates maximum of second harmonic generation signal when excited by THz pulses at 1.8 THz, that is also very close to it`s soft mode frequency (1.9 THz). Notably, the frequency spectrum of the BST/MgO (111) film reveals peaks at both the fundamental and doubled frequencies, highlighting the quadratic dependence of SHG intensity on the THz pulse's electric field strength.

In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

The signal processing technique is one of the principal tools for diagnosing power quality (PQ) issues in electrical power systems. The Discrete Fourier Transform (DFT) is a frequency analysis technique used to process power system signals and identify PQ problems. However, the DFT algorithm may lead to spectral leakage and picket-fence effect problems for asynchronously sampled signals that contain harmonic, inter-harmonic, and flicker components. To resolve this shortcoming, a hybrid method for frequency estimation based on a second-level DFT approach and a frequency-domain interpolation algorithm to obtain the accurate fundamental frequency of a power system is proposed in this paper. This method uses a second-level DFT to compute the cosine and sine parts for the fundamental frequency components of the acquired signals. Then, a frequency-domain interpolation approach is adopted to determine the amplitude ratio for the cosine and sine parts of the system's fundamental frequency. To demonstrate the performance of the proposed frequency estimation method, the observation window used by this paper to evaluate different estimation algorithms is 200 ms. According to the IEC standards, a 200 ms acquisition window is recommended for power system quality assessment. A set of mixed signals with harmonic, inter-harmonic, and flicker components with the fundamental frequency deviation is used. The evaluation results demonstrate the superiority of the new method over other approaches for assessing asynchronously sampled signals contaminated with noise, harmonic, inter-harmonic, and flicker components.

In this paper, we consider the relation of more than four harmonic points in a line. For this purpose, starting from the dependence of the harmonic points, Desargues’ theorems, and perspectivity, we note that it is necessary to conduct a generalization of the Desargues’ theorems for projective complete n-points, which are used to implement the definition of the generalization of harmonic points. We present new findings regarding the uniquely determined and constructed sets of H-points and their structure. The well-known fourth harmonic points represent the special case (n=4) of the sets of H-points of rank 2, which is indicated by P42.

The article is devoted to biological models using recurrence sequences, which are connected with the harmonic progression 1, 1/2, …, 1/n, and some cooperative properties of genomes. The harmonic progression is itself one of the recurrence sequences based on the harmonic mean. This progression appears in the hyperbolic rules of oligomer cooperative organization in eukaryotic and prokaryotic genomes. This allows thinking that the harmonic progression is also related to inherited physiological systems, which must be structurally consistent with the genetic coding system for their transmission to descendants and survival in evolution. The harmonic progression is one of historically known mathematical series, whose features were studied by Pythagoras, Leibniz, Newton, Euler, Fourier, Dirichlet, Riemann. It is widely used in many known algorithms and is closely related to some other important mathematical objects, for example, the function of the natural logarithm and harmonic numbers. Accordingly, the article describes the possibilities of using these interrelated mathematical objects to model biological structures, including logarithmic spirals and some other. Modeling inherited spiral configurations seems to be a particularly urgent task, since they are extremely common at all levels of organization of living bodies and, according to Goethe, are lines of life. The principle of a recurrence similarity, that is a special similarity of parts and transformations presented in recurrence sequences of numbers and matrix operators (the scale similarity and scale transformations are only particular cases of such similarity), is considered as one of the key principles of structural organization of living bodies.

Since the electro-hydraulic servo shaking table exists many nonlinear elements, such as, dead zone, friction and blacklash, its acceleration response has higher harmonics which result in acceleration harmonic distortion, when the electro-hydraulic system is excited by sinusoidal signal. For suppressing the harmonic distortion and precisely identify harmonics, a combination of the adaptive linear neural network and least mean M-estimate (ADALINE-LMM), is proposed to identify the amplitude and phase of each harmonic component. Namely, the Hampel’s three-part M-estimator is applied to provide thresholds for detecting and suppressing the error signal. Harmonic generators are used by this harmonic identification scheme to create input vectors and the value of the identified acceleration signal is subtracted from the true value of the system acceleration response to construct the criterion function. The weight vector of the ADALINE is updated iteratively by the LMM algorithm, and the amplitude and phase of each harmonic, even the results of harmonic components, can be computed directly online. The simulation and experiment are performed to validate the performance of the proposed algorithm. According to the experiment result, the above method of harmonic identification possesses great real-time performance and it has not only good convergence performance but also high identification precision.

This paper examines the energy efficiency of three variations of the two-degree-of-freedom transverse galloping energy harvester. These variants differ in the number and placement of electromechanical transducers. By utilizing the harmonic balance method, limit cycles of mathematical models of devices were determined. Analytical expressions derived from models were then used to formulate the efficiency of the systems. It was demonstrated that efficiency depends on flow speed and can be comprehensively characterized by four criteria parameters: peak efficiency, denoting the maximum efficiency of the system, and high efficiency bandwidth, which describes the range of flow velocities within which the efficiency remains at no less than 90% of peak efficiency. The values of these parameters are heavily reliant on the speed at which the system achieves peak efficiency—referred to as the nominal speed nominal speed, which in turn is related to the critical speed of the system. Comparative analysis revealed that only the two-degree-of-freedom device equipped with two electromechanical transducers can potentially outperform a simple one-degree-of-freedom system in terms of efficiency.

The Harmonic Graphs Conjecture states that there exists an asymptotic relation involving the Harmonic Index and the natural logarithm as the order of the graph increases. This conjecture, grounded in the novel context of Prime Graphs, draws upon the Prime Number Theorem and the sum of divisors function to unveil a compelling asymptotic connection. By carefully expanding the definitions of the harmonic index and the sum of divisors function, and leveraging the prime number theorem's approximations, we establish a formula that captures this intricate relationship. This work is an effort to contribute to the advancement of graph theory, introducing a fresh lens through which graph connectivity can be explored. The synthesis of prime numbers and graph properties not only deepens our understanding of structural complexity but also paves the way for innovative research directions.

Background: During pregnancy, major physiological changes occur in every system. Understanding the hemodynamic changes in different stages of pregnancy can help to identify abnormal states during pregnancy. Harmonic analysis could be a useful tool in monitoring the state of the ventricular-arterial system during pregnancy. The aim of this study was to investigate the specific statistical relationships between changes in harmonic indices during different stages of pregnancy. Methods: A Total of 380 women (190 pregnant women and 190 age-matched non-pregnant women), with ages ranging from 20 to 45, were enrolled in the study. The visit measured the subject’s hemodynamic parameters including heart rate, systolic blood pressure (SBP), diastolic blood pressure (DBP) and photoplethysmography (PPG). SBP and DBP were evaluated by an automatic blood pressure monitor. PPG signal were continuously recorded for 12-seconds using a PPG sensor. Spectrum analysis of the PPG signal was performed to evaluate the first five harmonic components (C1 – C5) and harmonic phases (P1 – P5). Result: A comparison between pregnant women and non-pregnant women showed that the non-pregnant women had lower DBP, C3, C5 and P5 (p<0.05). Waist Circumference, Heart rate, C2, C4 and P2 were higher in pregnant women. Logistic regression analysis was used to determine the associations between pregnancy and harmonics indices. C2, C4 and P3 were positively and P1 and P4 were negatively associated with pregnancy after controlling age, BMI, waist circumference, heart rate, SBP and DBP. Conclusion: The results of this study provide information on the changes in the harmonic frequency components during various stages of pregnancy. The harmonic components of the PPG signal have independent predictive value for changes in a woman's physiology during pregnancy. Since non-invasive PPG measurements can be performed frequently and easily, in the future, it is possible that the hemodynamic changes from some pregnancy-related disorders could be studied by harmonic analysis.

We design an asymmetric nonlinear optical nanoantenna composed of a dielectric nanodisk and an adjacent nanobar. The proposed composite structure made of AlGaAs exhibits resonant response at both the fundamental and doubled frequencies. Being driven by the strong magnetic dipole resonance at the pump wavelength and a high-quality mode at the harmonic wavelength, the efficient second-harmonic radiation is generated predominantly along the vertical directions under the normally incident plane-wave excitation.

This paper addresses the analysis for the nonlinear vibration response of a rectangular tube with a flexible end and non-rigid acoustic boundaries. This is a further work of the linear structural acoustic problem in a well-known acoustic book. In fact, the acoustic boundaries of an enclosed space sometimes are non-rigid and the structural vibration responses are nonlinear. These two points are the focuses of this paper. The multi-level residue harmonic balance method is applied to this nonlinear structural acoustic problem. The results obtained from the multi-level residue harmonic balance method and numerical method are generally in good agreement. The effects of excitation magnitude, tube length, and phase shift parameter etc. are examined.

A prime gap is the difference between consecutive prime numbers. The $n^{\text{th}}$ prime gap, denoted $g_{n}$, is calculated by subtracting the $n^{\text{th}}$ prime from the $(n+1)^{\text{th}}$ prime: $g_{n}=p_{n+1}-p_{n}$. Oppermann's conjecture is a prominent unsolved problem in pure mathematics concerning prime gaps. Despite verification for numerous primes, a general proof remains elusive. If true, the conjecture implies that prime gaps grow at a rate bounded by $g_{n}<{\sqrt {p_{n}}}$. This note presents a proof of Oppermann's conjecture using the Euler-Maclaurin formula on harmonic numbers. This proof simultaneously establishes Andrica's, Legendre's, and Brocard's conjectures.

To study the coupling mechanism and dynamic response of the end-face movable gear trans-mission system under complex excitation, a specific configuration of end-meshing movable gear reduction mechanism was used to achieve predetermined rigid thrust transmission and mis-matched gear meshing functions, which solved the inherent defects of traditional harmonic gear mechanism thin-wall flexible wheel easy to be damaged by fatigue. Considering the phenomenon of elastic deformation of live teeth accompanied by significant changes in meshing characteristics in the transmission process of end-meshing harmonic reducer, the influence of dynamic meshing parameters, live tooth deformation, time-varying stiffness of tooth meshing, and time-varying backlash on nonlinear dynamic performance was explored, as well as the mechanism of mul-ti-parameter coupling on transmission performance. The nonlinear dynamics model of the end-meshing harmonic reducer is established to solve the chattering prediction problem. Finally, a comprehensive test bed for the transmission system of harmonic reducer with meshing type with adjustable characteristic end was built to verify the correctness of the theoretical model and provide the theoretical and technical basis for exploring the optimal parameter selection of pas-sive vibration suppression problem.

In this contribution a new configuration of a DC-DC Boost and Buck-Boost converters is proposed to track sinusoidal signals exactly, with zero tracking error. The stage is conformed by two DC-DC converters connected to the same load, this is, they are not connected in cascade. To track exactly the sinusoidal reference the control scheme is base on the indirect control algorithm and the harmonic balance method. The proposed algorithm considers a second control input with the end of cancel out the second harmonic, this second harmonic is produced by the non linearity of the model and must be cancelled since there must be a single frequency in the output. The result is such that the converters can track sinusoidal signals with exactly zero error, some numerical results are presented to corroborate the proposal.

The fault diagnosis of the gearbox is primarily based on the analysis of the harmonic response. However, the generation mechanism of the harmonic response of the gear pair is still not distinctly explained in a healthy gearbox. Therefore, this paper is dedicated to establishing a dynamic model of the gearbox for this issue. In this model, the contact force of the bearing and the meshing stiffness of the gear pair are determined by the Hertz theory and the potential energy method, then the shaft motion is used as the connection to establish the coupling relationship between the gear pair and the bearing. After this dynamic model is confirmed by experiments and existing models, the coupling relationship inside the gearbox and the harmonic response of the gear pair are studied using this model. The result demonstrates that a closed control loop is formed due to the vibration transmission between the gear pair, the bearing and the shaft, and there is a strong coupled vibration between the gear pair and the bearing in the gearbox. Due to the generation of the center distance error, misalignment angle and disorganized meshing process of the gear pair, the meshing stiffness is altered, which excites the harmonic response of the gear pair. When the speed of the gearbox is increased, although the vibration amplitude of the gearbox is increased, the system predominantly vibrates at the fundamental frequency, and the harmonic of the gear pair is also shifted to the low frequency band.

The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.

The valley pseudospin properties of electrons in two–dimensional hexagonal materials result in lots of fascinating physical phenomena, which opens up the new field of valleytronics. The valley-contrasting physics aims at distinguishing the valley degree of freedom based on valley–dependent effects. Here, we theoretically demonstrate that both of the valley–selective high harmonic generation and valley–selective electronic excitation can be achieved by using an orthogonal two–color (OTC) laser field in gapped graphene. It is shown that the asymmetry degrees of harmonic yields in the plateaus, cutoff energies of generated harmonics and electron populations from two different valleys can be precisely controlled by the relative phase of the OTC laser field. Thus the selectivity of the dominant valley for the harmonic radiation and electronic polarization can be switched by adjusting the relative phase of the OTC laser field. Our work offers an all–optical route to produce the valley–resolved high harmonic emissions and manipulate the ultrafast valley polarization on a femtosecond timescale in condensed matter.

This study aimed to discuss the combined theoretical and experimental results of elastic properties of the tungsten trioxide films supported on Quartz (YX)/45°/10° resonator, as surface acoustic wave (SAW) device. The SAW system with different thicknesses of WO3 thin films were imaged and structurally characterized by X-Ray diffraction, atomic force and transmission electron microscopy. The deposited WO3 films (100 nm, 200 nm and 300 nm) were crystallized in a single monoclinic phase. The acoustoelectric properties of the SAW system were obtained by combining theoretical simulations with experimental measurements. The modeling of the SAW devices has been performed by the finite element and boundary element methods (FEM/BEM). The theoretical and experimental electrical admittances responses obtained at room temperature gave access to elastic constants. The gravimetric effect of the deposited layers is observed by a resonance frequencies shift to lower values with thicknesses film. Moreover, the acoustic losses are affected by the dielectric losses of the WO3 films, while the resonant frequency decreases almost linearly. SAW devices revealed strong displacement fields with low acoustic losses as a function of WO3 thicknesses. For all the deposited layers, the Young's modulus and the Poisson coefficient obtained are respectively of 8 GPa and 0.5.

Metasurfaces of gold (Au) nanoparticles on a SiO2-Si substrate were fabricated for the enhancement of second harmonic generation (SHG) using electron beam lithography and lift-off. Triangular Au nanoprisms which are non-centro-symmetric and support the second- order non-linearity were examined for SHG. The thickness of the SiO2 spacer is shown to be an efficient parameter to spectrally tune to maximise SHG. Electrical field enhancement at the fundamental wavelength was shown to define the intensity of the second harmonics. Numerical modeling of light enhancement was verified by experimental measurements of SHG and reflectivity spectra at the normal incidence. At the plasmonic resonance, SHG is enhanced up to ∼3.5×103 times for the optimised conditions.

According to the growing concern of various focus groups, in regard to the mitigation of the negative impacts generated because of the tourism, has born the interest of proposing sustainable tourism projects derivatives of the feeling within the communities (1) Background: the aim is to propose a differentiated diagnosis of the Subsystems (biophysical and anthropic) and their relationship with traditional-rational knowledge; (2) Methods: from the Theory of Complex Systems was propose the Harmonic Tourism Methodology, that try to correlation the subsystem and knowledge in the community of San Juan Tlahuica Atzingo, State of Mexico (4) Conclusions: Among the most outstanding results that are on the one hand, we must work through tourism projects to the rescue and preservation of natural and cultural resources, reassessing them through the strengthening of social cohesion. On the other hand, the application of this case allowed us to visualize that it is necessary to consolidate the elements and steps of the methodology in order to apply it to different communities that are beginning their journey in the field of the tourism and that can improve and potentiate their resources, seeking harmony between them.

Background: This research presents the use of photoplethsmography combined with Traditional Tibetan Pulse reading for the estimation of the three energies of a person: Activity, Transformation and Stability. The growing interest to revive traditional finger pulse reading attests of the need to find alternative ways to approach complex multi-source diseases as well as individualised diagnostic wearable or portable cost effective systems. Method: Our work is presented in two studies. The first study presents the development of the technique of photoplethsmography to classify the three energies. The second study presents a validation of this methodology on mental stress and relaxation. Results: Energies classification achieved a sensitivity above 85% and specificity above 72%. Mental stress and relaxation could be significantly discriminated from baseline condition. Harmonic analysis gave further insights into the dynamic of the pulse wave under stress/relaxation. Conclusion: The photoplethsmogram contains information pertaining to the mental and physiological state of a person as interpreted with the Eastern energies concepts. The implication of this work points towards a holistic understanding and impact of human activities, health and its environment.

The interaction between the grid network and the offshore wind power plant (WPP) network can lead to the amplification of certain harmonics and potentially resonant conditions. Offshore WPP should limit the increment of harmonic voltage distortion at the point of connection to the grid network as well as within their internal network. The harmonic distortion should be limited within the planning level limits using harmonic compensation, which is usually achieved by using static filters. In this paper an active damping compensation strategy with a STATCOM using emulation of resistance at the harmonic frequencies of concern is analysed. Such a compensation is effective for the local bus, though the performance is not guaranteed at the remote bus. This paper investigates the challenges associated with remote harmonic compensation in the offshore WPP, which is connected to the onshore grid through long high-voltage cables and transformers. First, the harmonic distortion and the compensating effects of the filter are theoretically assessed. Afterwards, they are demonstrated using harmonic propagation studies and time domain simulations in PSCAD.

The concept of neutrosophic number is a significant mathematical tool to deal with real scientific problems because it can tackle indeterminate and incomplete information which exists generally in real problems. In this article, we use neutrosophic numbers (a + bI), where a and bI denote determinate component and indeterminate component respectively. We explore the situations in which the input information is needed to express in terms of neutrosophic numbers. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine unknown criteria weights. We define neutrosophic number harmonic mean operators and proved their basic properties. Then, we develop two novel MCGDM strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility and effectiveness of the proposed two strategies. Sensitivity analysis with variation of “I” on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of “I”. The efficiency of the developed strategies is ascertained by comparing the obtained results from the proposed strategies with the existing strategies in the literature.

The World Health Organization (WHO) cancer agency predicts that more than 35 mil-lion cases of will be experienced in 2050, a 77 % increase over the 2022 estimate. Cur-rently, the leading cancer diagnosed cancer are breast, lung and colorectal. There is no standardized tool for cancer diagnosis; initially clinical procedures are guided by the patient´s symptoms and generally involve biochemical blood tests, imaging and biopsy. Label-free nonlinear optical approaches are promising tool for tumor imaging, due to their inherent non-invasive biosafe contrast mechanisms and the ability to monitor collagen-related disorders and metabolic changes during cancer progression. Last ad-vances in nonlinear modalities for tumor imaging are reviewed here. In addition, an application of a blind deconvolution procedure to improve the quality of two-photon images of breast tumor tissues is shown.

Chitosan is a biodegradable polymer derived from chitin, that is a versatile material for various biological applications for its attractive properties such as biocompatibility, biodegradability, and non-toxicity. Furthermore, chitosan possesses Second Harmonic Generation properties, that are useful for bio-sensing applications. In this work we explored the possibility to exploit chitosan-based nanospheres as SHG-based bio-sensors, and also as carriers of 89Sr radionuclide, an Active Pharmaceutical Ingredient for radiopharmaceutical treatments in cancer therapy. To load opportunely the Sr ion on the nanospheres, we used a fructose-based Metal Organic Framework, of formula [Sr(C6H12O6)2(H2O)2]Cl2·H2O, because the sugar was able to drive the Sr ions on the chitosan matrix. The Sr-loaded chitosan nanospheres were synthetized, characterized, and their SHG response was measured. The results encouraged us to propose the nanospheres for theranostic purposes, i.e. at the same time valuable for both therapy and diagnostic applications.

The potential use of nanostructured dipeptide self-assemblies in materials science for energy harvesting devices is a highly sought-after area of research. Specifically, aromatic cyclo-dipeptides containing tryptophan have garnered attention due to their wide-bandgap semiconductor properties, high mechanical rigidity, photoluminescence, and nonlinear optical behavior. In this study, we present the development of a hybrid system comprising biopolymer electrospun fibers incorporated with the chiral cyclo-dipeptide L-Tryptophan-L-Tyrosine. The resulting nanofibers are wide-bandgap semiconductors (bandgap energy 4.0 eV) and consist of self-assembled nanotubes embedded within a polymer matrix, exhibiting intense blue photoluminescence. Moreover, the cyclo-dipeptide L-Tryptophan-L-Tyrosine incorporated into polycaprolactone nanofibers displays a strong effective second harmonic generation signal of 0.36 pm/V and also shows notable piezoelectric properties with a high effective coefficient of 22 pCN−1. These hybrid systems hold great promise for applications in the field of nanoenergy harvesting and nanophotonics.

In this paper, the stabilization and high efficiency of an unstable Second Harmonic Generation (SHG) of a Nd : YVO4 laser with a KTP intracavity is carried out by using a passive Q-switching crystal and a parametric modulation method (harmonic modulation) is shown. The harmonic modulation was defined as um(t) = Amsin(2π fmt), with modulation amplitude as Am(Vpp), and modulation frequency as fm(Hz), applied to the pumping of the Nd : YVO4 -KTP laser to control the amplitude and frequency of the emission, thus stabilizing the dynamic states of this laser. The promising application of this green light source is materialized when such light is necessary for high-density optics, such as in the treatment materials industry or in some aesthetic applications.

We use a recently proposed formulation of quantum mechanics based, not on potential functions but rather, on orthogonal energy polynomials. In this context, the most important building block of a quantum mechanical system, which is the wavefunction at a given energy, is expressed as pointwise convergent series of square integrable functions in configuration space. The expansion coefficients of the series are orthogonal polynomials in the energy; they contain all physical information about the system. No reference is made at all to the usual potential function. We consider, in this new formulation, few representative problems at the level of undergraduate students who took at least two courses in quantum mechanics and are familiar with the basics of orthogonal polynomials. The objective is to demonstrate the viability of this formulation of quantum mechanics and its power in generating rich energy spectra illustrating the physical significance of these energy polynomials in the description of a quantum system. To assist students, partial solutions are given in an appendix as tables and figures.

In this paper we develop from first principles a unique law pertaining to the flow of fluids through closed conduits. This law, which we call “Quinn’s Law”, may be described as follows: When fluids are forced to flow through closed conduits under the driving force of a pressure gradient, there is a linear relationship between the normalized dimensionless pressure gradient, P_Q, and the normalized dimensionless fluid current, C_Q. The relationship is expressed mathematically as: P_Q = k₁ +k₂C_Q. This linear relationship remains the same whether the conduit is filled with or devoid of solid obstacles. The law differentiates, however, between a packed and an empty conduit by virtue of the tortuosity of the fluid path, which is seamlessly accommodated within the normalization framework of the law itself. When movement of the fluid is very close to being at rest, i.e., very slow, this relationship has the unique minimum constant value of k₁, and as the fluid acceleration increases, it varies with a slope of k₂ as a function of normalized fluid current. Quinn’s Law is validated herein by applying it to the data from published classical studies of measured permeability in both packed and empty conduits, as well as to the data generated by home grown experiments performed in the author’s own laboratory.

Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In this paper, bounds for the Randić, general Randić, sum-connectivity, the general sum-connectivity and harmonic indices for tensor product of graphs are determined by using the combinatorial inequalities and combinatorial computing.

This paper investigates the influence of magnetic field for a two dimensional deformations on a two temperature problem at the free surface of a semi-infinite semiconducting medium under the effect of mechanical force during a photothermal theory and the effect of hydrostatic initial stress on the medium. The Harmonic Wave Method (Normal Mode Analysis) has been used to obtain the equations of elastic waves, heat conduction equation, quasi-static electric field, carrier density, two temperature coefficient, ratios, and constitutive relationships for the thermo-magnetic-electric medium. The effects of several parameters as thermoelastic and thermoelectric coupling parameters and two temperature parameter of this force on the displacement component, force stress, carrier density and temperature distribution has been depicted graphically.

The use of entropy concepts in the field of stochastic electrodynamics is briefly reviewed here. Entropy calculations to date that have been fully carried out are discussed in two main situations: first, where electric dipole oscillators interact with zero-point, or zero-point plus Planckian, or Rayleigh-Jeans radiation, and second where only these radiation fields exist within a cavity. The emphasis here will be on the first more difficult situation where both charged particles and radiation fields are present and interacting. Unlike the usual exposition on entropy in clasical statistical mechanics involving probabilistic notions of phase space occupation, the calculations to date for both particles and fields or for fields alone, follow the caloric entropy method where the notions of heat flow, adiabatic surfaces, and isothermal conditions, are utilized. Probability notions certainly still enter into the calculations, as the fields and charged particles interact stochastically together, following Maxwellian electrodynamics. Examples of phase-space calculations for harmonic oscillators and classical hydrogen atoms are carried out, emphasizing how much farther caloric entropy calculations have been successfully utilized.

This research presents a novel algorithmic implementation to improve the analysis of visually controlled interception and accompanying motor action through the computational application of harmonic ratios and stimulation invariants. Unlike traditional models that focus mainly on psychological aspects, our approach integrates the relevant constructs into a practical mathematical framework. This allows for dynamic prediction of interception points with improved accuracy and real-time perception-action capabilities, essential for applications in neurorehabilitation and virtual reality. Our methodology uses stimulation invariants as key parameters within a mathematical model to quantitatively predict and improve interception outcomes. The results demonstrate the superior performance of our algorithms over conventional methods, confirming their potential for ad-vancing robotic vision systems and adaptive virtual environments. By translating complex theo-ries of visual perception into algorithmic solutions, this study provides innovative ways to im-prove motion perception and interactive systems. This study aims to articulate the complex inter-play of geometry, perception, and technology in understanding and utilizing cross-ratios at infin-ity, emphasizing their practical applications in virtual and augmented reality settings.

We have investigated the canine of olive flounder in terms of the nonlinear optical signals of two-photon excitation autofluorescence (2PEF) and second harmonic generation (SHG), whereby two kinds of nonlinear microscope images of the canine were obtained using ~140 femtosecond pulses. For increasing excitation power of laser pulses, a photobleaching effect was found to be significant in the red and green ranges of autofluorescence, where a double-exponential decay of the intensity occurs within hundreds of second due to collagen fluorophores in the canine. In the blue range of autofluorescence, the photobleaching is suppressed due to an energy conversion of the incident laser pulse to SHG signal. As a result, the signal in blue range remains constant for long term exposure to laser. We have also found that the SHG intensity depends on the orienta-tion of linearly polarized excitation, and the optical anisotropy of SHG can be attributed to the collagen alignment of canines.

Harmonic resonances are part of the Power Quality (PQ) problems of electrified railways and have serious consequences for the continuity of service and integrity of components in terms of overvoltage stress. The interaction between Traction Power Stations (TPSs) and trains that causes line resonances is briefly reviewed showing the dependence on infrastructure conditions. The objective is real-time monitoring of resonance conditions seen first of all from the onboard panto-graph interface, but it is equally applicable at TPS terminals. Voltage and current spectra, and de-rived impedance and power spectra, are analyzed proposing compact and efficient methods based on Short-Time Fourier Transform, suitable for real-time implementation with the hardware avail-able for energy metering and harmonic interference monitoring. The methods are tested by sweeping long recordings taken at some European railways, covering cases of longer and shorter supply sections, with a range of resonance frequencies of about one decade. They give insight into the spectral behavior of resonances, their dependency on position and change over time, and criteria to recognize genuine infrastructure resonances from rolling stock emissions.

This paper deals with the design, simulation and implementation of shunt hybrid compensator to maintain the power quality in 3-phase distribution networks feeding different types balanced and unbalanced nonlinear loads. The configuration of the compensator consists of a selective harmonic elimination passive filter, a series connected conventional 6-pulse IGBT inverter, acting as the active filter terminated with a dc link capacitor. The theory and modelling of the compensator based on current harmonic components at the load end and their decomposition in d-q axis frame of reference are utilized in the reference current generation algorithm. Accordingly, the source current waveform is made to follow the reference current waveform using a high frequency carrier based controller. Further, this inner current control loop is supported by a slower outer voltage control loop for sustaining desirable dc link voltage. Performance of the compensator is evaluated through MATLAB simulation covering different types of loads and reduction of harmonic currents and THD at the supply side along with excellent regulation of dc link voltage are confirmed. The performance of a hybrid compensator designed and fabricated using the above principles is evaluated and corroborated with the simulation results.

In reservoir engineering, one of the main sources of information for the characterization of reservoir and well parameters is well testing. Among the unconventional well testing methodologies, Harmonic Well Testing (HPT) is appealing from an economic standpoint because it could provide well performance and reservoir behavior monitoring without having to interrupt field production. Recorded pressure analysis is performed in the frequency domain by adopting a derivative approach similar to conventional well testing. To this end, pressure and rate data must be decomposed into harmonic components. Test interpretability can be significantly improved if pressure data are detrended prior to interpretation, filtering out non periodic events such as discontinuous production from neighboring wells and flow regime variations which did not respect the designed test periodicity. Therefore, detrending offers the possibility of overcoming the limitation of HPT applicability due to the difficulty of imposing a regularly pulsing rate for the whole test duration (typically lasting several days). This makes HPT attractive for well performance monitoring, especially in gas storage fields. In this paper, the application of different detrending methodologies to synthetic HPT pressure data generated in different reservoir and operational scenarios is presented and discussed. Moreover, a real case application is also presented.

In this paper, a method is developed for presenting a novel virtual torque sensor based on precise model and position measurements avoids the need of traditional strain gauges and amplifiers. More specifically, the harmonic drive compliance model and the Gaussian process regression (GPR) technique are used together to achieve virtual torque sensor measurement. While the harmonic drive compliance model provides the analytic part, the Gaussian process regression method is used to reconstruct the unmolded part based on motor-side and link-side joint angles as well as motor current. After an automatic offline calibration, the method allows for a lean online implementation. The virtual torque sensor measurement is compared with measurements of a commercial torque sensor, and the results have attested the effectiveness of the proposed method.

The bulk LiNa5Mo9O30 (LNM) crystals were successfully grown in the [010] and [001] directions without internal inclusions and cracks by the Czochralskii method with low temperature gradient. The crystal grown in the [010] direction showed a tendency to twinning. The crystal grown in the [001] direction demonstrated high structural perfection (FWHM=13'') for the (001) plane and high optical quality Δn≈210-5. The laser induced damage threshold was measured along a, b and c axes and was 15.7, 27.0 and 27.5 J/cm2 respectively. The thermo-optical coefficient dn/dT was measured for the main crystallographic axes, which was -5.7510-6, -2.0210-5 and 3.6510-6 K-1 along the a, b and c axes, respectively. The second harmonic generation (SHG) is conducted in crystalline LNM sample. The maximum efficiency value of 3.5% at pump power of 12 W had been achieved.

Gravity forward modeling as a basic tool has been wildly used to topography correction and 3D density inversion. The source region is usually discretized into tesseroid (i.e., spherical prism) to consider the influence of the curvature of planets in global or large-scale problems. Traditional gravity forward modeling methods in spherical coordinates, including the Taylor expansion and Gaussian-Legendre quadrature, are all based on spatial domain, which are mostly low computational efficiency. This study proposes a high-efficient forward modeling method of gravitational fields in spherical harmonic domain, in which the gravity anomalies and gradient tensors can be expressed as spherical harmonic synthesis form of spherical harmonic coefficients of 3D density distribution. A homogeneous spherical shell model has been used to test its effectiveness compared with traditional spatial domain methods. It demonstrates that the computational efficiency of the proposed spherical harmonic domain method has improved by four orders of magnitude and with a similar level of computational accuracy compared with the optimized 3D GLQ method. Finally, the proposed forward method is applied to topography correction of the Moon. The results show that the gravity response of the topography by our method is close to that of the optimized 3D GLQ method, and is also consistent with previous results.

Adjustable frequency converters are widely used in modern automated asynchronous drives due to their high efficiency and high responsiveness control strategies. Control algorithms for frequency converters are divided into two main groups: constant frequency commutation and random frequency commutation. Research results on various commutation frequencies, conducted using Matlab/Simulink software, show that the use of random frequency commutation provides better efficiency by significantly reducing the amplitude of harmonic oscillations at different frequencies, with a reduction in switching losses in transistors. Currently, a converter with random frequency commutation is being researched and applied in the direct torque control system. The traditional direct control system, based on a two-level inverter, is widely used due to its simplicity and ease of implementation. However, this method results in the output current of the two-level converter, supplied to the motor stator, having many harmonic distortions, leading to strong torque fluctuations regardless of the rotation speed and ultimately causing additional losses in the stator windings and reducing the motor's lifespan. To enhance the efficiency of automated asynchronous drives, this article presents an algorithm for a direct control system based on a three-level NPC inverter using a PI speed regulator. The proposed algorithm's research is validated in the Matlab/Simulink environment. The research results show that in the absence of harmonic filtering, the stator current harmonic distortion coefficient is approximately 11%, and torque fluctuations are less than 5% of the resistive torque. The fluctuations between the two capacitors remain almost unchanged throughout the entire process.

The optimal regime of three-photon resonant excitation of a helium atom by a femtosecond ul-traviolet (UV) pulse was discovered and numerically studied, at which the maximum power of the third harmonic of the UV field is achieved in the spectrum of dipole acceleration (the second time derivative of the induced dipole moment) of the atom. It is shown that the optimal frequency of the UV field nearly coincides with the frequency of the three-photon transition 1s2 – 1s2p, taking into account its shift as a result of the dynamic Stark effect, and the intensity of the UV field is dictated by the condition of maximizing the product of the populations of the 1s2 and 1s2p states, averaged over the time interval during which the UV field is non-zero. For the considered UV field durations, from 10 to 100 cycles of the carrier frequency (from units to tens of femtoseconds), the optimal intensity lies in the range from 10^14 W/cm^2 to several units of 10^14 W/cm^2. It is shown that with an optimal choice of the frequency and intensity of the UV field, the dynamics of excitation of bound and continuum states, as well as the shape of the time envelope of the dipole acceleration of the atom, weakly depend on the duration of the UV field envelope; only their time scale changes significantly. In addition, under the optimal conditions the average power of the third harmonic signal in the dipole acceleration spectrum is practically independent of the duration of the UV field envelope.

In this review, our goal is to design and test quantum-like algorithms for Artificial Intelligence (AI) in open systems to structure a human-machine team to be able to reach its maximum performance. Unlike the laboratory, in open systems, teams face complexity, uncertainty and conflict. All task domains have complexity levels, some have low, and others high levels. Complexity in this new domain is affected by the environment and the task, which are both affected by uncertainty and conflict. We contrast the individual and interdependence approaches to teams. The traditional and individual approach focuses on building teams and systems by aggregating the best available information for individuals, their thoughts, behaviors and skills. Its concepts are characterized chiefly by one-to-one relations between mind and body, a summation of disembodied individual mental and physical attributes, and degrees of freedom corresponding to the number of members in a team; however, this approach is characterized by the many researchers who have invested in it for almost a century with few effects that can be generalized to human-machine interactions; by the replication crisis of today (e.g., the invalid scales for self-esteem, implicit racism, and honesty); and by its many disembodied concepts. In contrast, our approach is based on the quantum-like nature of interdependence. It allows us to theorize about the bistability of mind and body, but it proposes a measurement problem and a non-factorable nature. Bistability addresses team structure and performance; the measurement problem solves the replication crisis; and the non-factorable aspect of teams reduces the degrees of freedom and the information derivable from teammates to match findings by the National Academies of Science. We begin with a review of the science of teams and a focus on human-machine team research in the laboratory versus the open; justifications for rejecting traditional social science while supporting our approach; a full understand of the complexity of the domain, tasks in the domain, and how teams address both; the mathematics involved; a review of results from our model versus the open field; a discussion of the results; conclusions; and the path forward to successfully advance the science of interdependence and autonomy.

In this work we present the results obtained with an artificial neural network (ANN) which we trained to predict the expected output of high-order harmonic generation (HHG) process, while exploring a multi-dimensional parameter space. We argue on the utility and efficiency of the ANN model and demonstrate its ability to predict the outcome of HHG simulations. In this case study we present the results for a loose focusing HHG beamline, where the changing parameters are: the laser pulse energy, gas pressure, gas cell position relative to focus and gas cell length. The physical quantity which we predict here using ANN is directly related to the total harmonic yield in a specified spectral domain (20-40 eV). We discuss the versatility and adaptability of the presented method.

Owing to the nondiffracting, self-accelerating, and self-healing properties, Airy beams of different nature have become a subject of immense interest in the past decade. Their interesting properties have opened doors to many diverse applications. Consequently, the questions of how to properly design spatial manipulation of Airy beams or how to implement them in different setups have become important and timely in the development of various optical devices. Here, based on our previous work, we present a short review on the spatial control of Airy beams, including the interactions of Airy beams in nonlinear media, beam propagation in harmonic potential, and the dynamics of abruptly autofocusing Airy beams in the presence of a dynamic linear potential. We demonstrate that under the guidance of nonlinearity and external potential, the trajectory, acceleration, structure, and even the basic properties of Airy beams can be adjusted to suit specific needs. We describe other fascinating phenomena observed with Airy beams, such as self-Fourier transformation, periodic inversion of Airy beams, and the appearance of spatial solitons in the presence of nonlinearity. These results have promoted the development of Airy beams, and have been utilized in various applications, including particle manipulation, self-trapping, and electronic matter waves.

In this short communication, following a brief introduction, we undertake a comprehensive analytical study of the weighted Simpson index. Our primary emphasis concerns the precise determination of the optimal point (minimizer) coordinates and of the minimum value of the index, a differentiable convex function, which is related to the harmonic mean concept. Furthermore, we address and solve the inversion problem and show the tight connection between both approaches. Last, we give some insights and final remarks on this subject.

The crystal structure of a polymorph of Glycyl-L-alanine HI.H2O was synthesized from chiral cyclic Glycyl-L-alanine dipeptide, known to show molecular flexibility in different environments. The space group is polar (P21) and therefore pyroelectricity and optical second harmonic generation properties are allowed by symmetry. We report a pyroelectric coefficient as high as 45 µC/m2K occurring at 345 K, one order of magnitude smaller than the semi-organic ferroelectric Triglycine Sulphate (TGS) crystal. Furthermore, the polymorph displays a nonlinear optical effective coefficient of 0.14 pm/V, around 14 times smaller than the value from a phase-matched inorganic Barium Borate (BBO) single crystal.

Mechanical power and motion are often transmitted by the gear-rotor-bearing system. When there are fitting clearances between the housing and outer ring in bearings, complex vibration responses will be generated, which makes the operating status difficult to identify. Therefore, for analyzing dynamic responses, a dynamic model of gear-rotor-bearing systems with bearing fitting clearances is proposed. In the model, the bearing system with fitting clearances and gear pair system are combined, and the coupling relationship is determined by the gyroscopic mo-tion of the shaft. The friction force and collision force caused by fitting clearances are also con-sidered, which are simulated by the Coulomb friction model and Hertz theory. The result shows that the meshing stiffness will also be excited by the bearing displacement. When there are fit-ting clearances on the bearing, the amplitude modulation of the bearing outer raceway to the system time-domain response is intensified, and the multiple harmonic frequency of bearings and gear pairs are generated on the spectrum, as well as defect frequencies of gear pairs. As the fitting clearance is increased, the higher multiple harmonic responses will be caused. Although the response amplitude of the gearbox is increased by raising the input speed, multiple harmon-ic responses are suppressed, which makes the system mainly vibrate at the fundamental fre-quency. Then, the dynamic model and the vibration analysis are experimentally verified.

We report on the application of femtosecond laser micromachining to the fabrication of complex glass microdevices, for high-order harmonic generation in gas. The three-dimensional capabilities and extreme flexibility of femtosecond laser micromachining allow us to achieve accurate control of gas density inside the micrometer interaction channel. This device gives a considerable increase in harmonics generation efficiency if compared with traditional harmonic generation in gas jets. We propose different chip geometries that allow to control the gas density and driving field intensity inside the interaction channel to achieve quasi-phase matching conditions in the harmonic generation process. We believe that these glass micro-devices will pave the way to future downscaling of High-order Harmonic Generation beamlines.

The increase in the emission of greenhouse gases (GHG) is one of the most important world problems. Decreasing of GHG emission is a big challenge in the future. Transportation sector uses a significant part of petroleum production in the world and it leads to an increase in the emission of GHG. The result of this issue is that population of the world befoul environment of transportation system automatically. Electric Vehicles (EV) have a potentiality to solve a big part of the GHG emission and energy efficiency issues such as stability and reality of energy. The energy actors and their research team determine some targets for 2050; hence, they hope to decrease the world temperature to 6 °C in the best and 2 °C in the normal condition. Fulfillment of these scenarios needs suitable grid infrastructure but in most of the countries, the grid does not have a suitable background to apply those scenarios. In this paper, some problems about energy scenarios, energy storage systems, grid infrastructure and communication systems in supply and demand side of the grid and its solutions have been investigated.

In the transition from traditional electrical energy generation with mainly linear sources to increasing inverter-based distributed generation, electrical power systems’ power quality requires new monitoring methods. Integrating a high penetration of distributed generation, which is typically located in medium- or low-voltage grids, shifts the monitoring tasks from the transmission to distribution layers. Compared to high-voltage grids, distribution grids feature a higher level of complexity. Monitoring all relevant buses is operationally infeasible and costly. State estimation methods provide knowledge about unmeasured locations by learning a physical system’s non-linear relationships. This article examines a new flexible, close-to-real-time concept of harmonic state estimation using synchronized measurements processed in a neural network. A physics-aware approach enhances a data-driven model, taking into account the structure of the electrical network. An OpenDSS simulation generates data for model training and validation. Different load profiles for both training and testing were utilized to increase the variance in the data. The results of the presented concept demonstrate high accuracy compared to other methods for harmonic orders 1 to 20.

The objective of this study is to clarify the effect of restoring the lowered masticatory muscle functional pressure and correcting the imbalance of bilateral masticatory muscle functional pressure on jawbone growth during growth and development with quantitative evaluation of the changes in micro/nanostructural characteristics of entheses. Male Wistar rats aged 4 weeks were divided into an experimental group injected with a botulinum toxin serotype A (BoNT/A) formulation to reduce muscle function (BTX group) and a control group (CTRL group). They were euthanized after 6, 8, 10, 12, and 16 weeks after measuring the difference between the midline of the upper and lower incisors. The mandibles were harvested for histological examination, second harmonic generation imaging, and quantitative evaluation of biological apatite (BAp) crystal alignment. The midline difference decreased with age in weeks. In rats from 6 weeks after BoNT/A administration to 12 weeks after administration, collagen fibre bundle diameter was significantly smaller in the BTX group; the difference between the two groups decreased with increasing age. BAp crystal alignment was significantly different on the X-axis and the Y-axis on the BTX group from 6 weeks after BoNT/A administration to 10 weeks after administration. Asymmetry of mandibular bone formation caused by load imbalance during growth could be corrected by adjustment of the function of the masseter muscle on either side.

This research will examine the computational methods to calculate the nonlinear optical process of second harmonic generation (SHG) that will be hypothesized to be present during lithium ion insertion into silicon nanowires. First it will be determined whether the medium in which SHG is conveyed is non-centrosymmetric or whether the medium is inversion symmetric where SHG as a part of the second-order nonlinear optical phenomenon does not exist. It will be demonstrated that the main interaction that determines SHG is multiphoton absorption on lithium ions. The quantum harmonic oscillator (QHO) is used as the background that generates coherent states for electrons and photons that transverse the length of the silicon nanowire. The matrix elements of the Hamiltonian which represents the energy of the system will be used to calculate the probability density of second-order nonlinear optical interactions which includes collectively SHG, sum-frequency generation (SFG) and difference-frequency generation (DFG). As a result it will be seen that at varies concentrations of lithium ions (Li+) within the crystallized silicon (c-Si) matrix the second-order nonlinear optical process has probabilities substantial enough to create second harmonic generation that could possibly be used for such applications as second harmonic imaging microscopy.

Power quality is a major concern in electrical power systems. The power quality disturbances such as sags, swells, harmonic distortion and other interruptions have impact on the electrical devices and machines and in severe cases can cause serious damages. Therefore it is required to recognize and compensate all types of disturbances at an earliest to ensure normal and efficient operation of the power system. To solve these problems, many types of power devices are used. At the present time, one of those devices, Dynamic Voltage Restorer (DVR) is the most efficient and effective device used in power distribution system. In this paper, design and modeling of a new structure of multifunctional DVR for voltage correction is presented. The performance of the device under different conditions such as voltage swell, voltage sag due to symmetrical and unsymmetrical short circuit, starting of motors, and voltage distortion are described. Simulation result shows the superior capability of proposed DVR to improve power quality under different operating conditions. The proposed new DVR controller is able to detect the voltage disturbances and control the converter to inject appropriate voltages independently for each phase and compensate to load voltage through three single- phase transformers.

Mode locked pulse generation has been reported using both active and passive mode locking schemes. Active mode locking technique has been proven to be an effective way to generate high-repetition-rate pulses by incorporating a modulator inside the laser cavity. Compared to actively mode locked lasers, passively mode locked lasers can generate pulse train at ultrashort pulse width but with relatively lower repetition rate. Thus, it is a brilliant idea to build a hybrid mode locked system combining both active and passive mode lockers. In this review, several hybrid mode locked fiber ring laser systems are discussed and summarized. Hybrid mode locking is a promising method to generate high speed ultrashort optical pulses for fiber-optic telecommunication system.

Classical k-ratio models, e.g. ZAF and phi(rho z), used in electron probe microanalysis (EPMA) assume a homogeneous or multi-layered material structure, which essentially limits the spatial resolution of EPMA to the size of the interaction volume where characteristic x-rays are produced. We present a new model for characteristic x-ray emission that avoids assumptions on the material structure to not restrict the resolution of EPMA a-priori. Our model bases on the spherical harmonic (PN) approximation of the Boltzmann equation for electron transport in continuous slowing down approximation. PN models have a simple structure, are hierarchical in accuracy and well-suited for efficient adjoint-based gradient computation, which makes our model a promising alternative to classical models in terms of improving the resolution of EPMA in the future. We present results of various test cases including a comparison of the PN model to a minimum entropy moment model as well as Monte-Carlo (MC) trajectory sampling, a comparison of PN-based k-ratios to k-ratios obtained with MC, a comparison with experimental data of electron backscattering yields as well as a comparison of PN and Monte-Carlo based on characteristic X-ray generation in a three-dimensional material probe with fine structures.

In this article we study the presence of chaos in supersymmetric(SUSY) quantum mechanics. For that purpose we present a form of 4-point out of time order correlator(OTOC) for SUSY quantum mechanical systems using tensor product formalism. We calculate the 4-point OTOC for SUSY 1D harmonic oscillator and find that the OTOC is exactly equal to that of 1D bosonic harmonic oscillator system. In similar manner using the eigenstate representation of supersymmetric systems we calculate the generalized higher order out of time order correlator. The higher order OTOC is a more sensitive measure of chaos than the usual 4-point correlator used in literature. Finally, we calculate the generalized 2N-point OTOC for SUSY 1D harmonic oscillator.

During flux weakening operation time (FWOT), the total iron loss rises and affects the accuracy of loss prediction and efficiency especially if a large range of FWOT exists. Iron loss prediction is widely employed in investigations for a fast electrical machine analysis using 2-D FEA. This paper studies harmonic loss analytically by a steady-state equivalent circuit. Consideration of skin effects and iron saturation are utilized in order to examine the accuracy through the relative error distribution in the frequency domain of each model from 50 to 700 Hz. Additionally, this comparative study presents a torque-frequency-flux density calculation over each single term of the modified IEM-formula. The analytical calculation is performed using 2-D FEA for a classic and modified IEM-formula along with experimental verifications on a surface-mounted PMSG for a wind generation application.

We explores the hydrodynamical limit of a homogeneous electron gas, considering the interplay between the infrared limit and phenomenological hydrodynamics. Our study involves interactions generated by non-linear coordinate transformations. The focus begins with an analysis of non-linear coordinate transformations and their impact on normal modes in a harmonic system. The Lagrangian for a harmonic oscillator is used as an illustrative example, highlighting the role of position-dependent effective mass in preventing certain coordinate values. Moving beyond single degrees of freedom, we extend the discussion to a system with several harmonic degrees of freedom, introducing a collective variable. The effective dynamics of this collective variable are defined through a Lagrange multiplier term, emphasizing linearity in the description. Our study extends to the Current Two-Point function (CTP) formalism, introducing matrices and their inverses, such as $\hD$ and $\hD^{-1}$. Further, we delve into the dynamics of current in a homogeneous electron gas at finite density and zero temperature. Green's functions are generated using a functional integral approach, and the effective action is constructed via functional Legendre transformation. The quadratic part of the generator functional is expanded to derive the effective action, leading to the Maxwell equation and the subsequent elimination of the photon field. The resulting effective action for current dynamics is expressed in terms of the Current Two-Point function, paving the way for further exploration of the hydrodynamical aspects of the electron gas. Our study combines theoretical developments and mathematical formalism to provide insights into the hydrodynamical behavior of homogeneous electron gases.

This work is divided into two parts. In the first one the combinatorics of a new class of randomly generated objects, exhibiting the same properties as the distribution of prime numbers, is solved and the probability distribution of the combinatorial counterpart of the n-th prime number is derived, together with an estimate of the prime-counting function π(x). A proposition equivalent to the Prime Number Theorem (PNT) is proved to hold, while the equivalent of the Riemann Hypothesis (RH) is proved to be false with probability 1 (w.p. 1) for this model. Many identities involving Stirling numbers of the second kind and harmonic numbers are found, some of which appear to be new. The second part is dedicated to generalizing the model to investigate the conditions enabling both PNT and RH. A model representing a general class of random integer sequences is found, for which RH holds w.p. 1. The prediction of the number of consecutive prime pairs, as a function of the gap d, is derived from this class of models and the results are in agreement with empirical data for large gaps. A heuristic version of the model, directly related to the sequence of primes, is discussed and new integral lower and upper bounds of π(x) are found.

The author's method of oligomer sums for analysis of oligomer compositions of eukaryotic and prokaryotic genomes is described. The use of this method revealed the existence of general rules for cooperative oligomeric organization of a wide list of genomes. These rules are called hyperbolic because they are associated with hyperbolic sequences including the harmonic progression 1, 1/2, 1/3, .., 1/n. These rules are demonstrated by examples of quantitative analysis of many genomes from the human genome to the genomes of archaea and bacteria. The hyperbolic (harmonic) rules, speaking about the existence of algebraic invariants in full genomic sequences, are considered as candidates for the role of universal rules for the cooperative organization of genomes. The described phenomenological results were obtained as consequences of the previously published author's quantum-information model of long DNA sequences. The oligomer sums method was also applied to the analysis of long genes and viruses including the COVID-19 virus; this revealed, in characteristics of many of them, the phenomenon of such rhythmically repeating deviations from model hyperbolic sequences, which are associated with DNA triplets. In addition, an application of the oligomer sums method are shown to the analysis of the following long sequences: 1) amino acid sequences in long proteins like the protein Titin; 2) phonetic sequences of long Russan literary texts (for checking of thoughts of many authors that phonetic organization of human languages is deeply connected with the genetic language). The topics of the algebraic harmony in living bodies and of the quantum-information approach in biology are discussed.

As known all physical properties of solids are described well by the system of quantum linear harmonic oscillators. It is shown in the present paper that the system consisting of classical linear harmonic oscillators having temperature dependent masses or (and) frequencies has the same partition function as the system consisting of quantum linear harmonic oscillators having temperature independent masses and frequencies while the means of the square displacements of the positions of the oscillators from their mean positions for the system consisting of classical linear harmonic oscillators having: the temperature dependent masses; temperature dependent frequencies; and temperature dependent masses and frequencies differ from each other and from that of the system consisting of quantum linear harmonic oscillators, and hence, the system consisting of classical linear harmonic oscillators describes well the thermodynamic properties of the system consisting of quantum linear harmonic oscillators and solids.

The superharmonic imaging of tissue has the potential for high spatial and contrast resolutions, compared to the fundamental and second harmonic imaging. For this technique, the spectral bandwidth of an ultrasound transducer is divided for transmission of ultrasound and reception of its superharmonics (i.e., higher than the second harmonic). Due to the spectral division for the transmission and reception, transmitted ultrasound energy is not sufficient to induce superharmonics in media without using contrast agents, and it is difficult that a transducer has a -6-dB fractional bandwidth of higher than 100%. For the superharmonic imaging of tissue, thus, multi-frequency array transducers are the best choice if available; transmit and receive elements are separate and have different center frequencies. However, the construction of a multi-frequency transducer for intravascular ultrasound (IVUS) imaging is particularly demanding because of its small size of less than 1 mm. Here, we report a recently developed dual-element focused IVUS transducer for the third harmonic imaging of tissue, which consists of a 35-MHz element for ultrasound transmission and a 105-MHz element for third harmonic reception. For high quality third harmonic imaging, both elements were fabricated to have the same focus at 2.5 mm. The results of tissue mimicking phantom tests demonstrated that the third harmonic images produced by the developed transducer had higher spatial resolution and deeper imaging depth than the fundamental images.

Recent US Congressional hearings on UAPs have made the study of exotic propulsion systems a matter of serious academic study and indeed, military necessity. This speculative paper looks at the possibility that microscopic sources could produce gravitational radiation with minimal energy requirements, whilst trapping the electromagnetic radiation stress-energy from being emitted. It may be possible to form an array of these micro-emitters of sufficient strength, acting with collective phenomenon, to allow non-linearities and the formation of soliton waves suitable for a putative warp field. Interestingly we find no need for exotic matter or negative energy. Moving onto the Alcubierre metric we ponder if the field could actually be made to travel superluminally by a repetitive stepped process of, expanding space just ahead of the craft initially to speed-up the propagation of the field, via the Shapiro Delay, so that a second field propagates that contracts space aggressively; the net effect being space contracting ahead of the craft faster than light.

Multiphoton microscopy (MPM) is a cutting-edge nonlinear microscopy technique known for its exceptional capabilities in imaging dense tissues, making it an ideal tool for exploring human kidney tissue. This study delves into the application of MPM in evaluating renal cell tumors and characterizing tumor capsules. MPM encompasses two core methods: two-photon excitation fluorescence (TPEF) and second harmonic generation (SHG). It leverages femtosecond lasers to provide deep tissue imaging while minimizing phototoxicity, making it well-suited for live tissue analysis. The study analyzed 100 formalin-fixed paraffin-embedded (FFPE) kidney tissue samples, ensuring compliance with ethical standards. Using a Ti:Sapphire laser for femtosecond pulses and a variety of optical components and filters, the researchers captured TPEF and SHG signals, facilitating image analysis. Normal kidney tissue exhibited distinctive structures like glomeruli and tubules under MPM. Renal cell carcinoma (ccRCC) displayed unique TPEF patterns with eccentrically located nuclei and indistinct cytoplasmic membranes. Papillary RCC (pRCC) exhibited a papillary pattern with dark nuclei, while chromophobe RCC (chRCC) showcased distinct features like thick cell membranes, strong TPEF signal in nuclei, and granular cytoplasm. Renal oncocytoma (RO) presented strong TPEF signals in cuboidal cells with microcyst-like arrangements. Overall, MPM proved invaluable in assessing human kidney tissue, offering distinct TPEF patterns for different renal cell tumor types. This non-invasive technique has the potential to enhance pathological examinations and advance our understanding of complex biological processes, ultimately contributing to improved diagnostics and treatment strategies for renal diseases.

In the permanent magnet synchronous motor (PMSM) drive system, the unwilling and ear-piercing vibro-acoustics caused by high-frequency sideband harmonics becomes unacceptable in the electric vehicle application. In this paper, a modified space vector pulse-width modulation (SVPWM) technique implemented with hybrid carrier frequency modulation (HCFM) is provided to reduce the sideband current harmonic components and vibro-acoustic responses. The principle and implementation of the proposed HCFM technique are firstly presented, in which the fixed carrier frequency is improved with the sawtooth and random signal-based coupling modulation based on the rotor position. For verification, the experiment tests are carried out on a prototype 12/10 PMSM and microcontroller unit. The effectiveness of the HCFM technique can hence be confirmed, in which the sideband vibro-acoustics reduction shows more effectively than that in conventional random PWM. The proposed approach may provide a new route in noise-cancelling and electromagnetic compatibility for the electric drive powertrain.

The zinc oxide (ZnO) arrester is positioned on locomotive roof preventing other onboard electrical equipment from the harm caused by external and internal overvoltages. A number of locomotive arrester burnout and explosion accidents occur during traction supply network harmonic resonance causing train stoppages and power outages in the network. This study firstly carries out high-frequency tests to investigate the wide frequency band electrical characteristics of the locomotive arrester, explaining that the arrester is prone to fault during resonance. Consequently, a prognostics and health management (PHM) for locomotive arrester is proposed providing on online monitoring, fault warning and health assessment solutions, which is beneficial to the operation and maintenance of arresters in the future. The testing method and PHM scheme presented in this paper can be not only applied to the arrester, also readily expanded to other high-voltage electrical equipment on the electric locomotive.

Thermally-assisted-occupation density functional theory (TAO-DFT) has been an efficient electronic structure method for studying the ground-state properties of large electronic systems with multi-reference character over the past few years. To explore the time-dependent (TD) properties of electronic systems (e.g., subject to an intense laser pulse), in this work, we propose a real-time (RT) extension of TAO-DFT, denoted as RT-TAO-DFT. Besides, we employ RT-TAO-DFT to study the high-order harmonic generation (HHG) spectra and related TD properties of molecular hydrogen H2 at the equilibrium and stretched geometries, aligned along the polarization of an intense linearly polarized laser pulse. The TD properties obtained with RT-TAO-DFT are compared with those obtained with the widely used time-dependent Kohn-Sham (TDKS) method. In addition, issues related to the possible spin-symmetry breaking effects in the TD properties are discussed.

As the penetration of renewable energies increases, their acceptance of the power grid system is becoming an important issue. In the case of South Korea, a 22.9kV transformer is frequently utilized to reduce the power loss of the generated renewable energy transmission, so the power quality at the point of common connection (PCC) is inevitably influenced by the nonlinearity of the transformer and the uncertainty of the inductance and resistance of the transmission line. In this paper, we present a point of common connection voltage-modulated direct power control (PCCVM-DPC) system that enhances power quality at the PCC. First, we present the mathematical dynamics of active and reactive power at the PCC side, which contains the step-up transformer’s nonlinearity, the grid voltage harmonics, and the parameter uncertainties. By analyzing the disturbance terms of the PCCVM-DPC system, we present the disturbance observer (DOB) for the PCCVM-DPC system. To assess the efficacy of our approach, we perform comparative studies of the PCCVM-DPC without DOB and PCCVM-DPC with DOB by constructing the simulation environment based on the commercial step-up transformer and ESS inverter datasheet. We have validated that the active and reactive power control performance of the PCCVM-DPC with DOB outperforms the PCCVM-DPC without DOB from the observation that the current total harmonic distortion reduced by more than 40% compared to the PCCVM-DPC without the DOB.

Non-Linear Simulation by Harmonic Balance Techniques of Load Modulated Power Amplifier Driven by Random Modulated Signals. Comparison with measured results.

This paper presents an optimal design for the inner current control loop of the continuous current conduction mode (CCM) power factor correction (PFC) stage, which it can be used as the front stage of the two stages alternating current-direct current (AC-DC) telecom power supply. Conventional single-phase CCM-PFC boost converter usually implemented with using of the proportional-integral (PI) controllers in both of the voltage and current control loops, to regulate the output DC voltage to the specified value, moreover to maintains the input current follows the input voltage which offers converter with high power factor (P.F) and low current total harmonic distortion (THD). However, due to the slow dynamic response of the PI controller at the zero-crossing point of the input supply current, input current can’t fully follow the input voltage which leads to high THD. Digitally controlled PFC converter with an optimal design of the inner current control loop using doubly control loops IP controller to reduce the THD and to offer input current with unity P.F was performed in this paper. Furthermore, for the economic design of the digitally control PFC converter, two isolated AC and DC voltage sensors are proposed and designed for the interfacing with the microcontroller unit (MCU). PSIM software was used to test the converter performance with using the proposed designed current controllers and isolated voltage sensors. High power density digitally controlled telecom PFC stage with P.F of about 99.93%, full load efficiency of about 98.70% and THD less 5.50% is achieved in this work.

This study presents a synthesizer topology based on a DLL and programmable frequency multiplier for 5G+ communication systems. The proposed synthesizer comprises a 512-phase DLL, an intermediate frequency generator (IFG), and an RF frequency multiplier (RFFM). The 512-phase DLL provides 512 delayed pulses through a chain of 256 delay units and single-to-differential complementary converters (S2DCs). The IFG comprises I/Q-multiplexers, I/Q-accumulators, an XOR, and an S2DC. The I/Q-multiplexer outputs switch to the phase lag or lead waveforms at every rising or falling edge of the outputs, which makes the I/Q-multiplexer output frequency, fMX, programmable. The IF, fIF, is two times fMX, and fIF is up-converted to RF, fRF, through the RFFM. When reference clock frequency, fref is 156.25 MHz, the fIF range is 156.863–312.5 MHz and the fRF dynamic range is approximately 1.89–9.96 GHz. The channel resolution range is 3.698–38.609 MHz. Consequently, the proposed synthesizer provides a wide 134 % output frequency bandwidth and a finer channel resolution smaller than fref. The presented synthesizer is fabricated in a 65-nm CMOS process. The total power consumption is 15 mW, and the rms jitter integrated from 12 kHz to 20 MHz measured as 83 fs.

Spherical harmonic (SH) interpolation is a commonly used method to spatially up-sample sparse Head Related Transfer Function (HRTF) datasets to denser HRTF datasets. However, depending on the number of sparse HRTF measurements and SH order, this process can introduce distortions in high frequency representation of the HRTFs. This paper investigates whether it is possible to restore some of the distorted high frequency HRTF components using machine learning algorithms. A combination of Convolutional Auto-Encoder (CAE) and Denoising Auto-Encoder (DAE) models is proposed to restore the high frequency distortion in SH interpolated HRTFs. Results are evaluated using both Perceptual Spectral Difference (PSD) and localisation prediction models, both of which demonstrate significant improvement after the restoration process.

We try to solve three decades-old physics challenges. List all elementary particles. Describe dark matter. Describe mechanisms that govern the rate of expansion of the universe. We propose new modeling. The modeling uses extensions to harmonic oscillator mathematics. The modeling points to all known elementary particles. The modeling suggests new particles. Based on those results, we do the following. We explain observed ratios of dark matter amounts to ordinary matter amounts. We suggest details about galaxy formation. We suggest details about inflation. We suggest aspects regarding changes in the rate of expansion of the universe. We interrelate the masses of some elementary particles. We interrelate the strengths of electromagnetism and gravity. Our work seems to offer new insight regarding applications of harmonic oscillator mathematics. Our work seems to offer new insight regarding three branches of physics. The branches are elementary particles, astrophysics, and cosmology.

We develop and apply new physics theory. The theory suggests specific unfound elementary particles. The theory suggests specific constituents of dark matter. We apply those results. We explain ratios of dark matter amounts to ordinary matter amounts. We suggest details about galaxy formation. We suggest details about inflation. We suggest aspects regarding changes in the rate of expansion of the universe. The theory points to relationships between masses of elementary particles. We show a relationship between the strength of electromagnetism and the strength of gravity. The mathematics basis for matching known and suggesting new elementary particles extends mathematics for harmonic oscillators.

With the unceasing advancement in wide-bandgap (WBG) semiconductor technology, the minimal reverse-recovery charge Qrr and other more powerful natures of WBG transistors enable totem-pole bridgeless PFC to become a dominant solution for energy storage systems (ESS). This paper focuses on design and implementation of a control structure for a totem-pole boost PFC with newfangled enhancement-mode Gallium Nitride (eGaN) FETs, not only to simplify the control implementation, but also to achieve high power quality and efficiency. The converter is designed to convert a 90-264-VAC input to a 385-VDC output for a 2.6-kW output power. Lastly, to validate the methodology, an experimental prototype is characterized and fabricated. The uttermost efficiency at 230 VAC attains 99.14%. The lowest total harmonic distortion in the current (ITHD) at high line condition (230 V) reaches 1.52% while the power factor gains 0.9985.

Motivated by assumptions that Quantum Mechanics (QM) is not the basement of reality and that additional dimensionality (XD) is required to complete and extend the Standard Models (SM) of Particle Physics and Cosmology, experimental protocols utilizing putative properties of Kaluza-Klein-like (KK) cyclicality embedded within Dirac’s electron hypertube model in conjunction with a Dirac covariant polarized vacuum is developed to produce a new type of low-energy tabletop cross section based on topological phase transitions rather than high energy collision sprays as in the LHC. The model is presented in a highly theoretical axiomatic manner utilizing off-the-shelf parameters generally marginalized by the mainstream physics community. When successful the protocol leads to obsolescence of the highly efficacious 100-year supercollider run producing a paradigm shift with an inherent new set of Unified Field (UF) transformations beyond the Galilean Lorentz-Poincaré transformations of the SM to 3rd regime natural science: Classical – Quantum - UF.

Physics theory has yet to settle on specific descriptions for new elementary particles, for dark matter, and for dark energy forces. Our work extrapolates from the known elementary particles. The work suggests well-specified candidate descriptions for new elementary particles, dark matter, and dark energy forces. This part of the work does not depend on theories of motion. This work embraces symmetries that correlate with motion-centric conservation laws. The candidate descriptions seem to explain data that prior physics theory seems not to explain. Some of that data pertains to elementary particles. Our theory suggests relationships between masses of elementary particles. Our theory suggests a relationship between the strengths of electromagnetism and gravity. Some of that data pertains to astrophysics. Our theory seems to explain ratios of dark matter effects to ordinary matter effects. Our theory seems to explain aspects of galaxy formation. Some of that data pertains to cosmology. Our theory suggests bases for inflation and for changes in the rate of expansion of the universe. Generally, our work proposes extensions to theory in three fields. The fields are elementary particles, astrophysics, and cosmology. Our work suggests new elementary particles and seems to explain otherwise unexplained data.

DC-connected parallel inverter systems are gaining popularity in industrial applications. However, such parallel systems generate excess current ripple (harmonics) at the DC-link due to harmonic interactions between the inverters in addition to the harmonics from the PWM switching. These DC-link harmonics cause the failure of fragile components such as DC-link capacitors. This paper proposes an interleaving scheme to minimize the current harmonics induced in the DC-link of such a system. The results show that when the carrier waves of the two inverters are phase-shifted by 90° angle, the maximum high-frequency harmonic ripple cancellation occurs, which reduces the overall RMS value of the DC-capacitor current.The outcome of this proposed solution is a cost-effective DC-harmonics mitigating strategy for the industrial designers to practically configuring multi-inverter systems, even when most of the drives are not operating at rated power levels. Experimental and simulation results presented in this paper verify the effectiveness of the proposed carrier-based phase-shifting scheme for two different configurations of common DC connected multi-converter systems.

Microarray gene expression-based detection and classification of medical conditions have been prominent in research studies over the past few decades. However, extracting relevant data from the high-volume microarray gene expression with inherent nonlinearity and inseparable noise components raises significant challenges during data classification and disease detection. So, this paper proposes a two-level strategy involving feature extraction and selection methods before the classification step. The feature extraction step utilizes Short Term Fourier Transform (STFT), and the feature selection step employs Particle Swarm Optimization (PSO) and Harmonic Search (HS) metaheuristic methods. The classifiers employed are Non-Linear Regression, Gaussian Mixture Model, Softmax Discriminant, Naive Bayes, SVM (Linear), SVM (Polynomial), and SVM (RBF). The two-level extracted relevant features are compared with raw data classification results, including Convolutional Neural Network (CNN) Methodology. Among the methods, STFT with PSO feature selection and SVM (RBF) classifier produced the highest accuracy of 94.47%.

Short-range Internet of Things (IoT) sensor nodes operating at 2.4 GHz need to provide ubiquitous wireless sensor networks (WSNs) with energy-efficient, wide-range output power (POUT) and fully integrated on a single chip for wireless body area networks (WBANs) and wireless personal area networks (WPANs) using low-power Bluetooth (BLE) and Zigbee standards. The proposed fully integrated transmitter (TX) utilizes a digitally controllable current-mode class-D (CMCD) power amplifier (PA) with a second harmonic distortion (HD2) suppression to reduce VCO pulling in an integrated system while meeting harmonic limit regulations. The CMCD PA is divided into 7-bit slices that can be reconfigured between differential and single-ended topologies. Duty cycle distortion compensation is performed for HD2 suppression, and an HD2 rejection filter and a modified C-L-C low-pass filter (LPF) reduce HD2 further. Implemented in a 28 nm CMOS process, the TX achieves a wide POUT range of from 12.1 to -31 dBm and provides a maximum efficiency of 39.8% while consuming 41.1 mW at 12.1 dBm POUT. The calibrated HD2 level is -82.2 dBc at 9.93 dBm POUT, resulting in a transmitter figure of merit (TX_FoM) of -97.52 dB. Higher order harmonic levels remain below -41.2 dBm even at 12.1 dBm POUT, meeting regulatory requirements.