The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In this paper, we propose and evaluate the theory of the 2D discrete Fourier Transform (DFT) in polar coordinates. This discrete theory is shown to arise from discretization schemes that have been previously employed with the 1D DFT and the discrete Hankel Transform (DHT). The proposed transform possesses orthogonality properties, which leads to invertibility of the transform. In the first part of this two-part paper, the theory of the actual manipulated quantities is shown, including the standard set of shift, modulation, multiplication, and convolution rules. Parseval and modified Parseval relationships are shown, depending on which choice of kernel is used. Similar to its continuous counterpart, the 2D DFT in polar coordinates is shown to consist of a 1D DFT, DHT and 1D inverse DFT.

The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In the first part of this two-paper series, we proposed and evaluated the theory of the 2D discrete Fourier Transform (DFT) in polar coordinates. The theory of the actual manipulated quantities was shown, including the standard set of shift, modulation, multiplication, and convolution rules. In this second part of the series, we address the computational aspects of the 2D DFT in polar coordinates. Specifically, we demonstrate how the decomposition of the 2D DFT as a DFT, Discrete Hankel Transform (DHT) and inverse DFT sequence can be exploited for efficient code. We also demonstrate how the proposed 2D DFT can be used to approximate the continuous forward and inverse Fourier transform in polar coordinates in the same manner that the 1D DFT can be used to approximate its continuous counterpart.

Despite the increasing popularity of liquid chromatography-mass spectrometry (LC-MS)-based lipidomics, there is a lack of accepted and validated method for lipid extract quality and quantity assessment prior to LC-MS. Fourier-Transform Infrared Spectroscopy (FTIR) has been reported for quantification of pure lipids, however, the sample complexity and purity complex lipid extract quantification in lipidomics experiments could be impact quantification accuracy. Here, we report comprehensive assessment of the sample matrix on the accuracy of lipid quantification using Attenuated Total Reflectance Fourier-Transform Infrared Spectroscopy (ATR-FTIR). Pure lipids are characterized by CH-and C=O-stretching vibrations on FTIR, with quantitative range of 40–3000 ng and a limit of detection of 12 ng. Sample extraction method and local baseline subtraction during FTIR spectral processing significantly impact lipid quantification by CH-stretching. To facilitate sample quality screening, we developed the Lipid Quality (LiQ) score from a spectral library of common contaminants, using a ratio of peak heights between CH-stretching vibrations maxima and the collective vibrations from amide/amine, CH-stretching minima and sugar moieties. We evaluated LiQ score as a rapid sample quality control method by comparing to total LC-MS intensity of targeted lipidomics of 107 human plasma lipid extracts. Exclusion of poor-quality samples based on LiQ score improved the correlation between FTIR and LC-MS quantification. Finally, the uncertainty of absolute quantification by FTIR was estimated using a 795 ng SPLASH LipidoMix standard to be <10%. In summary, this study identified key parameters for accurate FTIR-based quantification of complex lipid mixture, and developed a rapid workflow requiring only 1 µL of MS-ready sample and < 5 minutes for routine lipidomics sample quality and quantity assessment.

Ocean surface waves have been utilized as fundamental information in various fields of oceanic research. In this paper, we suggest a simulation and modelling technique for generating an ocean surface wave using an inverse Fast Fourier Transform (iFFT), and we subsequently verify the wave’s accuracy. The conventional method, linear superposition, requires recursive calculation because of the double summation and the time variable; to circumvent this issue, the new algorithm is presented. The Joint North Sea Wave Project (JONSWAP) spectrum is utilized for the ocean surface wave simulation example, and the parameters are the significant wave height (HS) and the zero-crossing wave period (TZ). A coordinate transform for the wavenumber domain was used to apply the inverse FFT algorithm. To verify the accuracy of the simulation result, the relative error between the input condition and the analysis result was calculated. The result for TZ is below 4% relative error, and the maximum relative error for HS is 7%. To avoid the Nyquist frequency for wave-field analysis and simulation, the minimum grid size was calculated by twice applying the maximum wavenumber.

Recognition, decoding and tracking of vortex patterns is of increasing importance in many fields reaching from astronomical observation of distant galaxies to turbulence phenomena in liquids or gases. Currently, coherent light beams with orbital angular momentum (OAM) are of particular interest for optical communication, metrology, micro-machining or particle manipulation. One common task is to identify characteristic spiral patterns in pixelated intensity maps at real-world signal-to-noise ratios. Recently, Fast Fourier Transform (FFT) was applied to the quantitative analysis of spiral interference patterns of OAM beams. Our study considers this approach in more detail. It is demonstrated that specific information can be extracted by combining conformal mapping by polar transform with determining one- or two-dimensional angular frequency spectra either in spatially fixed or scanning mode. Results of proof-of-principle experiments are presented.

Bacterial infections and resistance to antibiotic drugs represent the highest challenges to public health. The search for new and promising compounds with anti-bacterial activity is a very urgent matter. In order to promote the development of platforms enabling to the discovery of compounds with anti-bacterial activity, Fourier Transformed Mid-Infrared (FT-MIR) spectroscopy associated with the machine learning algorithms were used to predict the impact of compounds extracted from Cynara cardunculus against Escherichia coli cells. According to the plant tissue (seeds, dry and fresh leaves, and flowers) and the solvents (ethanol, methanol, acetone, ethyl acetate, and water), compounds with different compositions concerning, phenol content, antioxidant, and antimicrobial activity were obtained. Principal component analysis of spectra, allowed to discriminate compounds that inhibit the E. coli growth, according to the conventional assay. The supervised classification models enabled the prediction of the compound's impact on the E. coli growth, with the accuracy for the test data: Partial least squares-discriminant analysis of 94%; Support vector machines of 89%; k-Nearest neighbor of 72%; and a Backpropagation network of 100%. According to the promising results, the integration of FT-MIR spectroscopy with machine learning presents a high potential to promote the discovery of new compounds with antibacterial activity, thereby streamlining the drug exploratory process.

By utilizing the Fourier transform, we present a practical method for evaluating a function of a derivative applied to any other arbitrary function of a single complex variable. As an illustration of this approach, we compute the actions of the displacement and squeeze operators on an arbitrary function, as well as the propagation of paraxial fields, Airy and number states, without the need for algebraic quantum operator techniques or the Fresnel integral.

Polyhedral Oligomeric Silsesquioxanes (POSS) are one of the smallest silica nano particles. The presence of ordered ladder-like or cage conformation in their structure leads to remarkable thermal stability far greater than that for a linear polysiloxane. Reinforcement with nano particles is one of the recently favored strategy used to enhance the performance of polymers materials. The cyclic silica structure present in POSS ensures excellent thermal and mechanical stability. As a reinforcing filler, POSS can enhance the resistance of polymer matrix against pyrolysis and corrosion. In this paper, amine-terminated POSS with ladder like structure was synthesized by condensation of hydrolyzed aminosilane coupling agent. The ladder-like structure of POSS severely limits the motion of the chain backbone. The absence of phase transition for the synthesized POSS was confirmed by differential scanning calorimetry (DSC). Thermogravimetric analysis (TGA) was utilized to evaluate the thermal stability of POSS. TGA data show that the ladder-like POSS reported here has high char yield of about 75 % in nitrogen atmosphere and 54% in air atmosphere at 800℃. The TGA derivative curves show that the degradation of ladder-like POSS involves multiple stages and that the degradation rate is directly proportional to the heating rate. With the aid of Fourier Transform Infrared Spectroscopy (FT-IR), the cyclic structure of Si-O-Si bonding was determined to be the predominant structure. By analyzing the FTIR spectra of the cured POSS residue obtained at the specified temperatures, the detailed degradation mechanism of POSS was inferred. From the FTIR spectra of the low temperature cured samples, it was shown that the terminal silanol group was eliminated below 400℃. Some intermediate polymeric siloxane structures were observed by means of FT-IR and they eventually transitioned into silica which is the final product of pyrolysis of POSS. The presence of the FTIR transmission peaks at 1000 and 1100 cm-1, due to asymmetrical vertical and horizontal stretching of Si-O-Si, were the key evidence for the inferred ladder-like structure of POSS.

This algorithm is designed to perform Discrete Fourier Transforms (DFT) to convert temporal data into spectral data. This algorithm obtains the Fourier Transforms by studying the Coefficient of Determination of a series of artificial sinusoidal functions with the temporal data, and normalizing the variance data into a high-resolution spectral representation of the time-domain data with a finite sampling rate. What is especially beneficial about this DFT algorithm is that it can produce spectral data at any user-defined resolution.

In previous studies we used Laurent Schwartz’ theory of distributions to rigorously introduce discretizations and periodizations on tempered distributions. These results are now used in this study to derive a validity statement for four interlinking formulas. They are variants of Poisson’s Summation Formula and connect four commonly defined Fourier transforms to one another, the integral Fourier transform, the Discrete-Time Fourier Transform (DTFT), the Discrete Fourier Transform (DFT) and the Integral Fourier transform for periodic functions—used to analyze Fourier series. We prove that under certain conditions, these four Fourier transforms become particular cases of the Fourier transform in the tempered distributions sense. We first derive four interlinking formulas from four definitions of the Fourier transform pure symbolically. Then, using our previous results, we specify three conditions for the validity of these formulas in the tempered distributions sense.

We prove that the Legendre coefficients associated with a function f(x) can be represented as the Fourier coefficients of a suitable Abel-type transform of the function itself. Thus, the computation of N Legendre coefficients can be performed efficiently in O(NlogN) operations by means of a single Fast Fourier Transform of the Abel-type transform of f(x). We also show how the symmetries associated with the Abel-type transform can be exploited to further reduce the computational complexity. The dual problem of calculating the sum of Legendre expansions is also considered. We prove that a Legendre series can be written as the Abel transform of a suitable Fourier series. This fact allows us to state an efficient algorithm for the evaluation of Legendre expansions. Finally, numerical tests are presented to exemplify and confirm the theoretical results.

Recently Candida auris has emerged as a multi-resistant fungal pathogen, with a significant clinical impact, and has become a critical issue in WHO fungal priority list, due to its unique ability to persist for long time on human skin and hospital environments. It is therefore fundamental to reinforce hospital surveillance protocols to limit nosocomial outbreaks. The study purpose was the Fourier-Transform Infrared Spectroscopy (FT-IR) application to investigate the phylogenetic relationships between isolated strains within the C. auris outbreak at the university Intensive Care Unit of a Tertiary University hospital in Turin (Italy). In order to calculate a clustering cut-off, intra- and inter-isolates distance values were analysed. Data showed the presence of a major cluster Alfa and a minor cluster Beta with a defined C. auris clustering cut-off. The results were validated by an external C. auris strain and Principal Component and Linear Discriminant Analysis. The application of FT-IR technology had allowed to obtain important information about the phylogenetic relationships between the analysed strains, defining for the first time a “not WGS-based” clustering cut-off with a statistical-mathematical approach. FT-IR could represent a valid alternative to molecular methods for rapid and cost saving typing of C. auris strains with important clinical implications.

This paper is devoted to the study of multi-dimensional integral transform with Fox H-function in the kernel in weighted spaces integrable functions in the domain R+n with positive coordinates. Mapping properties such as the boundedness, the range, the representations of the considered transformation are established.

After proposing a natural metric for the space in which particles spin which implements the principle of maximum frequency, E=hf is generalised and its inverse Fourier transform is calculated. As a necessary result, a metric is found for the space in which quantum particles spin, hence the possibility of explanation of correlation of spacelike-separated particles is opened up.

A PLS-based quality prediction method is proposed for batch processes using two-dimensional extended windows. To realize the adoption of information in the direction of sampling time and batch, a new definition region of support (ROS), k-i-back-extended region of support (KIBROS), is proposed to establish the extended window, which including the data of the previous sampling times in the same batch, the data of the same sampling time in the historical batches, the data of the previous sampling times in the historical batches and the data of the later sampling times in the historical batches. According to these regions of support, extended windows are established, and different models are proposed based on the extended windows for batch processes quality prediction. Further, using a typical batch process as an example, the injection molding process, the proposed quality prediction method is experimentally verified, proving that the proposed methods have higher prediction accuracy than the traditional method and the prediction stability is also improved.

We study the application of Optimal Control Theory to Ion Cyclotron Resonance. We test the validity and the efficiency of this approach for the robust excitation of an ensemble of ions with a wide range of cyclotron frequencies. Optimal analytical solutions are derived in the case without any pulse constraint. A gradient-based numerical optimization algorithm is proposed to take into account limitation in the control intensity. The efficiency of optimal pulses is investigated as a function of control time, maximum amplitude and range of excited frequencies. A comparison with adiabatic and SWIFT pulses is done. On the basis of recent results in Nuclear Magnetic Resonance, this study highlights the potential usefulness of optimal control in Ion Cyclotron Resonance.

In this paper, the Fourier-based synchrosqueezing transform (FSST) method is introduced into the power system to realize low frequency oscillation identification. Firstly, the modal components of low frequency oscillation signal are separated by FSST, and calculating the instantaneous parameters including magnitude, frequency and phase of every mode component with Hilbert transform. Then , calculating the damping ration of every modal component based on above parameters and derived the formulas. Thus, it realized effective identification of of modal parameters of low frequency oscillation signal. The experimental results of simulated data and 16-generator system demonstrate the validity and correctness of the FSST method. Comparing with the classical Prony method shows that the FSST method is better in the identification accuracy when the low frequency oscillation signal is polluted by noise. Finally, the effectiveness of the FSST in Actual power grid is verified based on the real data from Sichuan power grid.

Crystalline silver thin layers were obtained by high-energy pulsed laser ablation without heating of the deposition substrate. The fluid Plateau-Rayleigh (PRI), Rayleigh – Taylor (RTI) and Richtmyer – Meshkov (RMI) instabilities, as well as crown splash induced during pulsed laser deposition (PLD) in high energy regime, resulting in ring and pearl shaped structures, offer the benefit of increased sorption surface. These morphological structures obtained for the silver thin layers make them of interest for catalytic applications. The study presented with this work addresses both the fundamental and applied issues on the morphological structures obtained for the silver thin layer and their catalytic function in organic processes. In this sense, the catalytic action of the thin silver layer was highlighted by modifications of the Reactive Blue 21 dye (C.I.) in aqueous solution with sodium bicarbonate. Specific investigations and analyzes were carried out by electron microscopy and elemental analysis (SEM-EDX), atomic force microscopy (AFM) and profilometry, mass spectrometry, ablation plasma diagnosis, diffractograms (XRD), as well as IR spectroscopy (FTIR). In addition to the experimental investigation and analyzes, simulation of the ionization energy threshold was conducted in COMSOL for complementary evaluation on the involved processes and phenomena.

Medical image segmentation is a critical step in various healthcare applications, aiding in diagnosis, treatment planning, and disease monitoring. In this study, we investigate the efficacy of a segmentation approach based on the 2D wavelet transform. Leveraging a dataset comprising 10 diverse medical images, we evaluate the performance of our segmentation method using three key metrics: accuracy, precision, and recall. Our findings demonstrate that the proposed approach enhances segmentation accuracy, offering promising results compared to existing methods. By harnessing the multi-resolution feature extraction capabilities of the 2D wavelet transform, our method achieves improved delineation of medical image structures, paving the way for more accurate and efficient healthcare interventions.

The goal of the current study is to analyse several nonlinear two-dimensional time-fractional Rosenau Hymanequations. The two-dimensional fractional Rosenau-Hyman equation has extensive use in engineering and applied sciences. The fractional view analysis of two-dimensional time-fractional Rosenau-Hyman equations is discussed using the homotopy perturbation approach, adomian decomposition method, and Yang transformation. Some examples involving two-dimensional time-fractional Rosenau-Hyman equations are provided in order to better understand the suggested approaches. The solutions appear as infinite series. We offer a comparison between the accurate solutions and those that are generated employing the proposed approaches in order to demonstrate the effectiveness and applicability of the proposed techniques. The results are graphically illustrated using 2D and 3D graphs. It has been noted that the obtained results and the targeted problems real solutions are quite similar. Calculated solutions at various fractional levels describe some of the problems useful dynamics. Other fractional problems that arise in other fields of science and engineering can be solved using a modified version of the current techniques.

The special affine Fourier transform (SAFT) is a useful and powerful analyzing tool in signal processing, optics and communications. In this paper, we mainly discuss the randomized nonuniform sampling and reconstruction for random signals bandlimited in the SAFT domain. First, we show that the nonuniform sampling is identical to the uniform sampling after a pre-filter in the sense of second order statistic characters. Then, we propose an approximate reconstruction based on sinc interpolation for the nonuniform sampling of random signals bandlimited in the SAFT domain. Finally, we give the mean square error estimate for the proposed approximate recovery approach.

Texture is essential information for image representation, capturing patterns, and structures. Consequently, texture plays a crucial role in the manufacturing industry and has been extensively studied in the fields of computer vision and pattern recognition. However, real-world textures are susceptible to defects, which can degrade the image quality and cause various issues. Therefore, there is a need for accurate and effective methods to detect texture defects. In this study, a simple autoencoder and Fourier transform were employed for texture defect detection. The proposed method combines Fourier transform analysis with the reconstructed template obtained from the simple autoencoder. Fourier transform is a powerful tool for analyzing the frequency domain of images and signals. Moreover, analyzing the frequency domain enables effective defect detection because texture defects often exhibit characteristic changes in specific frequency ranges. The proposed method demonstrates effectiveness and accuracy in detecting texture defects. Experimental results are presented to evaluate its performance and compare it with those of existing approaches.

Fokker-Planck PDEs (incl. diffusions) for stable Lévy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image analysis, directional statistics and probability theory. Exact analytic designs and solutions are known in the 2D case, where they have been obtained using Fourier transform on $SE(2)$. Here we extend these approaches to 3D using Fourier transform on the Lie group $SE(3)$ of rigid body motions. More precisely, we define the homogeneous space of 3D positions and orientations $\mathbb{R}^{3}\rtimes S^{2}:=SE(3)/(\{\mathbf{0}\} \times SO(2))$ as the quotient in $SE(3)$. In our construction, two group elements are equivalent if they are equal up to a rotation around the reference axis. On this quotient we design a specific Fourier transform. We apply this Fourier transform to derive new exact solutions to Fokker-Planck PDEs of $\alpha$-stable Lévy processes on $\mathbb{R}^{3}\rtimes S^{2}$. This reduces classical analysis computations and provides an explicit algebraic spectral decomposition of the solutions. We compare the exact probability kernel for $\alpha = 1$ (the diffusion kernel) to the kernel for $\alpha=\frac12$ (the Poisson kernel). We set up SDEs for the Lévy processes on the quotient and derive corresponding Monte-Carlo methods. We verify that the exact probability kernels arise as the limit of the Monte-Carlo approximations.

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

Covid-19 is a lung disease caused by a Coronavirus family virus. Due to its extraordinary prevalence and death rates, it has spread quickly to every country in the world. Thus, achieving peaks and outlines and curing different types of relapses is extremely important. Given the worldwide prevalence of Coronavirus and the participation of physicians in all countries, Information has been gathered regarding the properties of the virus, its diverse types, and the means of analyzing it. Numerous approaches have been used to identify this evolving virus. It is generally considered the most accurate and acceptable method of examining the patient's lungs and chest through a CT scan. As part of the feature extraction process, a method known as fractional Fourier transform (FrFT) has been applied as one of the time-frequency domain transformations. The proposed method was applied to a database consisting of 2481 CT images. Following the transformation of all images into equal sizes and the removal of non-lung areas, multiple combination windows are used to reduce the number of features extracted from the images. In this paper, the results obtained for KNN and SVM classification have been obtained with accuracy values of 99.84% and 99.90%, respectively.

Incorporating linear-scanning MEMS micromirrors into Fourier transform spectral acquisition systems can greatly reduce the size of the spectrometer equipment, making portable Fourier transform spectrometers (FTS) possible. How to minimize the tilting of the MEMS mirror plate during its large linear scan is a major problem in this application. In this work, an FTS system has been constructed based on a biaxial MEMS micromirror with a large piston displacement of 180 μm, and a biaxial H∞ robust controller is designed. Compared with open-loop control and PID closed-loop control, H∞ robust control has good stability and robustness. The experimental results show that the stable scanning displacement reaches 110.9 μm under the H∞ robust control, and the tilting angle of the MEMS mirror plate in that full scanning range falls within ±0.0014°. Without control, the FTS system cannot generate meaningful spectra. In contrast, the FTS yields a clean spectrum with an FWHM spectral linewidth of 96 cm-1 under the H∞ robust control. Moreover, the FTS system can maintain good stability and robustness under various driving conditions.

The interfacial polymerization (IP) of piperazine (PIP) and trimesoyl chloride (TMC) has been extensively utilized to synthesize nanofiltration (NF) membranes. However, it is still a huge challenge to monitor the IP reaction, because of the fast reaction rate and the formed ultra-thin film. Herein, two effective strategies were applied to reduce the IP reaction rate: (1) the introduction of hydrophilic interlayers between the porous substrate and the formed polyamide layer, and (2) the addition of macromolecular additives in the aqueous solution of PIP. As a result, in situ Fourier transform infrared (FT-IR) spectroscopy was firstly used to monitor the IP reaction of PIP/TMC with hydrophilic interlayers or macromolecular additives in the aqueous solution of PIP. Moreover, the formed polyamide layer growth on the substrate was studied in a real-time manner. The in situ FTIR experimental results confirmed that the IP reaction rates were effectively suppressed and that the formed polyamide thickness was reduced from 138 ± 24 nm to 46 ± 2 nm according to TEM observation. Furthermore, an optimized NF membrane with excellent performance was consequently obtained, which included boosted water permeation of about 141–238 (L/m²·h·MPa) and superior salt rejection of Na₂SO₄ > 98.4%.

The emergence of the semiconductor industry in the early 1960s resulted in a significant stage in the evolution of computing when large computational problems, as typified by the application of the discrete Fourier transform (DFT) to the task of spectrum estimation, could suddenly, with the availability of suitable algorithms, be solved in close to real time fashion. This paper provides a brief and meandering account of the history of the DFT’s various solutions, referred to generically as the fast Fourier transform (FFT), the algorithm being chosen for its mathematical elegance, practical significance and ever‑increasing range of applications. We touch upon a few of the most striking personalities, places and events that were encountered along the way and look, in particular, at the recent British contribution to the journey.

The object of this paper is the bending analysis of isotropic rectangular Kirchhoff plates subjected to non-uniform heating (NUH) using the Fourier transform method. The bottom and top surfaces of the plate are assumed to have different changes in temperature, whereas the change in temperature of the mid-surface is zero. According to classical plate theory, the governing equation of the plate contains second derivatives of the NUH; these derivatives are zero by constant value of the NUH, which leads to its absence in the governing equation. This paper presented an approach by which Fourier sine transform was utilized to describe the NUH, while the double trigonometric series of Navier and the simple trigonometric series of Lévy were utilized to describe the deflection curve. Thus, the NUH appeared in the governing equation, which simplified the analysis. Rectangular plates simply supported along all edges were analyzed, bending moments, twisting moments, and deflections being determined. In addition, rectangular plates simply supported along two opposite edges were analyzed; the other edges having various support conditions (free, simply supported, and fixed).

The Stepped Frequency Waveform (SFW) is commonly employed in radar technology to synthesize wideband signals through the aggregation of narrow-band pulses, thereby achieving high-resolution range profiles without the need to increase the radar's instantaneous bandwidth. However, the inherent large time-bandwidth product of SFW introduces substantial ranging errors and energy dispersion, which significantly hinders its efficacy in detecting high-speed objects. This paper introduces a pioneering velocity estimation technique utilizing the fractional Fourier transform (FrFT) to address these limitations. Leveraging the characteristic of the Doppler signal from a moving target, which manifests as a chirp signal with a rate proportional to the target's velocity, the FrFT is utilized for precise velocity estimation. Subsequent to this, velocity compensation is applied using the deduced metrics, followed by the application of the inverse fast Fourier transform (iFFT) to pinpoint the target's exact location. To optimize the computational efficiency of determining the FrFT's optimal order, we propose an iterative algorithm founded on the golden section search method. The effectiveness of the proposed approach is verified by simulation data, and the results demonstrate that the proposed approach can accurately estimate the velocity and the range of the high-speed targets with a relatively low computational complexity.

The electroencephalogram (EEG) is a record of brain activity. Brain Computer Interface (BCI) technology formed by the EEG signal has become one of the hotspots at present. How to extract the feature signal of EEG is the most basic research of BCI technology. In this paper, A new method of recognizing fatigue, conscious, concentrated state of human brain is proposed by the combination of discrete wavelet transform and the neural network based on EEG signal. First of all, the law signal is preprocessed by the wavelet denoising method because the law EEG signal contains a large number of high frequency noise, which is decomposed into multi-layer high frequency signal and low frequency signal. thus, δ wave, θ wave, α wave, β wave are obtained by the wavelet transform. And then, frequency band energy of the different wave is regards as the feature signal of EEG. In the experiment, the feature signal is classified by radial basic function (RBF) and annealed chaotic competitive learning network (ACCLN). RBF and ACCLN networks are trained with 500 sets of sample data and are tested by 100 sets of samples in different mental states. The experimental results show that the average accuracy of RBF network under three conditions are 88.75%, 88.25%, 88.5%, respectively, and the correct rate of ACCLN network is 97%, 98%, 98%, respectively.

Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.

The interaction between single or a fixed number of photons with a single absorber is of fundamental interest in quantum technology. The harnessing of light matter interactions at the single particle limit has several potential applications ranging from quantum communication and quantum metrology to quantum imaging. In this letter, a setup for heralded two-photon absorption at the single absorber level is proposed. The setup is based on a heralded two-photon source utilizing spontaneous parametric down-conversion, entanglement swapping and sum frequency generation for joint detection. The feasibility of the scheme is discussed by reviewing recent achievements in utilizing entangled and correlated photons for two-photon absorption as well as single photon absorption experiments at the limit of single absorbers in the context of applications in imaging (here mainly microscopy) and spectroscopy.

The Doppler band compensated by the keystone transform (KT) is limited. Therefore, it needs to be used in conjunction with the Doppler ambiguity compensation function to correct the range migration (RM) caused by maneuvering targets with Doppler ambiguity. However, the KT implemented by sinc interpolation suffers from significant performance loss at boundaries of compensation Doppler bands. Additionally, in a multi-target scenario, KT implementation methods occupy high complexity when the Doppler range of targets spans over two compensation Doppler bands. To address aforementioned issues, this study presents a variable Doppler starting point keystone transform (VDSPKT) method, where a new form of ambiguity compensation function is constructed, turning the Doppler starting point of the compensation band in KT variable. Firstly, the position of the compensation Doppler band is changed from fixed to adjustable as needed, enhancing the flexibility of KT. Crucially, the connection points of the compensation Doppler bands in sinc interpolation are reset, avoiding the performance loss at their boundaries. Also, the compensation band is adjusted to cover the narrow Doppler frequency range caused by targets, significantly improving the computational efficiency. Finally, the simulation results demonstrate that the proposed approach effectively addresses the performance degradation and high computational complexity of KT in the aforementioned scenarios, resulting in a computational load reduced by approximately 50% compared to traditional methods.

As one of the representatives of emerging metallic transition metal dichalcogenides, niobium ditelluride (NbTe₂) has attracted intensive interest recently due to its distorted lattice structure and unique physical properties. Here, we report on the ultrafast carrier dynamics in NbTe₂ measured using time-resolved pump-probe transient reflection spectroscopy. A thickness-dependent carrier relaxation time is observed, exhibiting a clear increase in the fast and slow carrier decay rates for thin NbTe₂ flakes. In addition, pump power dependent measurements indicate that the carrier relaxation rates are power-independent, with the peak amplitude of the transient reflectivity increasing linearly with pump power. Isotropic relaxation dynamics in NbTe₂ is also verified by performing polarization-resolved pump-probe measurements. These results provide an insight into the light-matter interactions and charge carrier dynamics in NbTe₂ and will pave the way for its applications to photonic and optoelectronic devices.

The exact similarity solutions (also called as special exact solutions) of two dimensional laminar boundary layer were obtained by Blasius in 1908, however, no similarity solutions for two dimensional turbulent boundary layers have been reported in the literature. With the help of dimensional analysis and invariance principle, Prandtl mixing length $\ell=\kappa y$ for one dimensional turbulent boundary layer is extended to $\ell(x,y)=\kappa y (1-\frac{y}{\delta})\sqrt{\frac{\nu}{U\delta}} $ for the two dimensional turbulent boundary layers, furthermore, with a similarity transformation, we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation $f'''+ ff''+\beta(1-f'^2)+\kappa^2[\eta^2(1-\eta)^2f''|f''|]'=0$. As an application, similarity solutions of the two dimensional turbulent boundary layer on a flat plate at zero incidence have been studied in detail. To solve the ordinary differential equation numerically, a complete Maple code is provided.

This contribution is an attempt to reconstruct the favorable atmosphere that prevailed in Lau-sanne in 1986-87 and provided the backdrop of our invention of two-dimensional ion cyclotron resonance mass spectroscopy (2D ICR-MS). To avoid a self-centered histoire d’ancien combattant, we shall try to emphasize the context, the contributions of key players within our nascent research group at UNIL and the established group of Tino Gäumann at EPFL, the role of external speakers, and the open atmosphere that was not yet polluted by bibliometrics, obsessive concern with im-pact factors, and top-down management of research. We shall also explain why the idea of 2D ICR-MS has been ignored for many years and still has a limited impact: different scientific cul-tures in the ICR and NMR communities, different concerns with fundamental vs. applied research, different status of theory and numerical simulations, different levels of commitment of instrument manufacturers, not to mention many theoretical problems that appear to be at least as challenging in ICR as in NMR.

The ability of 2D hybrid structures formed by boron, nitrogen and carbon atoms (h-BNCs) as potential substrates for surface enhanced Raman spectroscopy (SERS) detection of dioxin-like pollutants is theoretically analyzed. The strong confinement and high tunability of the electromagnetic response of the carbon nanostructures embedded within the h-BNC sheets point out that these hybrid structures could be promising for applications in optical spectroscopies, such as SERS. In this work, two model dioxin-like pollutants, TCDD and TCDF, and a model h-BNC surface composed by a carbon nanodisk of ninety-six atoms surrounded by a string of borazine rings, BNC96, are employed for the simulation of the adsorption complexes and the static and pre-resonance Raman spectra of the adsorbed molecules. A large affinity of BNC96 by these pollutants is reflected on the large interaction energies obtained for the most stable stacking complexes, with dispersion being the most important contribution to their stability. The large vibrational coupling of some active modes of TCDF and, specially, of TCDD makes the Raman static spectra display a ‘pure’ chemical enhancement of one order of magnitude. On the other hand, due to the strong electromagnetic response of BNC96, confined within the carbon nanodisk, pre-resonance Raman spectra obtained for TCDD and TCDF display large enhancement factors of 108 and 107, respectively. Promisingly, laser excitation wavelengths frequently used in SERS experiments also provoke significant Raman enhancements, around 104, for the TCDD and TCDF signals. Both the strong confinement of the electromagnetic response within the carbon domains and the high modulation of the resonance wavelengths within the visible and/or UV ranges in h-BNCs should lead to a higher sensitivity than graphene and white graphene parent structures, solving one of the main disadvantages of using 2D substrates for SERS applications.

Two-dimensional (2D) bismuth oxyhalides (BiOX) have attracted much attention as potential optoelectronic materials. Expecting for their application diversity, we herewith systematically investigate the tunable properties of 2D BiOX by using first principles calculations. Their electronic and optical properties can be modulated by changing the number of monolayers, applying strain, and/or varying the halogen composition. The bandgap shrinks monotonically and approaches the bulk value, the optical absorption coefficient increases, and the absorption spectrum redshifts, as the layer number of 2D BiOX increases. Carrier transport property can be improved by applying tensile strain, and the ability of photocatalytic hydrogen evolution can be obtained by applying compressive strain. General strain engineering will be effective in linearly tune the bandgap of BiOX in a wide strain range. Strain together with halogen composition variation can tune the optical absorption spectrum to be on demand in the range from visible to ultraviolet. It suggests that that 2D BiOX materials have potential serving as tunable novel photodetectors, can be used to improve clean energy techniques, and are prospective in the field of flexible optoelectronics.

In this short communication, we conducted first-principles calculations to explore the stability of boron monochalcogenides (BX, X=S, Se or Te), as a new class of two-dimensional (2D) materials. We predicted BX monolayers with two different atomic stacking sequences of ABBA and ABBC, referred in this work to 2H and 1T, respectively. Analysis of phonon dispersions confirm the dynamical stability of BX nanosheets with the both 2H and 1T atomic lattices. Ab-initio molecular dynamics simulations reveal the outstanding thermal stability of all predicted monolayers at high temperatures over 1500 K. BX structures were found to exhibit high elastic modulus and tensile strengths. It was found that BS and BTe nanosheets can show high stretchability, comparable to that of the graphene. It was found that all predicted monolayers exhibit semiconducting electronic character, in which 2H structures present lower band-gaps as compared with 1T lattices. The band-gap values were found to decrease from BS to BTe. According to the HSE06 results, 1T-BS and 2H-BTe show respectively, the maximum (4.0 eV) and minimum (2.06 eV) electronic band-gaps. This investigation introduces boron monochalcogenides as a novel class of 2D semiconductors with remarkable thermal, dynamical and mechanical stability.

Two-dimensional mass spectrometry (2D MS) is a method for tandem mass spectrometry that relies on manipulating ion motions to correlate precursor and fragment ion signals. 2D mass spectra are obtained by performing a Fourier transform in both the precursor ion mass-to-charge ratio (m/z) dimension and the fragment ion m/z dimension. The phase of the ion signals evolves linearly in the precursor m/z dimension and quadratically in the fragment m/z dimension. This study demonstrates that phase-corrected absorption mode 2D mass spectrometry improves signal-to-noise ratios by a factor of 2 and resolving power by a factor of 2 in each dimension compared to magnitude mode. Furthermore, phase correction leads to an easier differentiation between ion signals and artefacts, and therefore easier data interpretation.

The paper presents an error model of a measurement chain containing link performing discrete wavelet transform algorithm which is most often the last stage of measurement signal processing. The goal is to determine the uncertainty budget of the input quantities of the wavelet transform algorithm. The error model takes into account parts of analog, analog-to-digital and digital processing, describing the properties of subsequent fragments of the chain using their transmittance and processing functions. The proposed model enables the description of both deterministic and non-deterministic properties of signal errors. The proposed model was validated using an example measurement chain created for this purpose.

Edible mushrooms have been recognized as highly nutritional food for a long time, due to their specific flavor, texture and also for therapeutic effects. This study proposes a new simple approach, based on FT-IR analysis, followed by statistical methods, in order to differentiate three wild mushrooms species from Romanian spontaneous flora, namely Armillaria mellea, Boletus edulis and Cantharellus cibarius. The preliminary data treatment consisted of data set reduction with principal component analysis (PCA), which provided scores for the next methods. Linear discriminant analysis (LDA) manage to 100% classify the three species and the cross validation step of the method returned 97.4% of correctly classified samples. Only one A. mellea sample overlapped on B. edulis group. When kNN was used in the same manner as LDA, the overall percent of correctly classified samples from the training step was 86.21%, while for holdout set the percent raised at 94.74%. The lowered values obtained for the training set was due to one C. cibarius sample, two B. edulis and five A. mellea, which were placed to other species. Anyway, for holdout sample set, only one sample from B. edulis was misclassified. The fuzzy c-means clustering (FCM) analysis successfully classified investigated mushroom samples according to their species, meaning that in every partition the predominant specie had the biggest DOMs, while samples belonging to other specie had lower DOMs.

To make wind power more competitive, it is necessary to reduce turbine downtime and reduce costs associated with wind turbine Operation and Maintenance (O&M). Incorporating machine learning in developing condition-based predictive maintenance methodologies for wind turbines can enhance their efficiency and reliability. This paper presents a monitoring method that utilizes Base Density for the Support Vector Machine (BDSVM) and the evolutionary Fourier spectra of vibrations. This method allows smart monitoring of the function evolution of the turbine. A complex optimal function (FO) for 5-degree order has been developed that will be the boundary function of the BDSVM to timely determine the magnitude, frequency, and place of the failure occurring in wind turbine drive.

In the book “Everyhing Is A Circle: A New Model For Orbits Of Bodies In The Universe”, and further in the Article “Distance Between Two Circles in Any Number of Dimensions is a Vector Ellipse”, it has been mathematically demonstrated that “distance between points on any two different circles in any number of multiple dimensions” is equivalent to “distance of points on a vector ellipse from another fixed or moving point”. Using this mathematical methodology, a method is provided in this Article as a measure for the amount of interaction between two international economies, which are two countries or economic zones, by modelling each economy in terms of a “circle in four dimensions”. Based on this method, the proximity of the two economies at the end of each fiscal period, which is generally a fiscal year, is then measured by the distance between points at the end of the given period on the two circles in four dimensions, associated with these two economies in our model.

In two dimensional disordered lattices, presence of interaction makes particles less localized than the non-interacting ones within the range of disorder strength W ≤ 4 and interaction strength V ≤ 4. If the interaction strength is higher, then particles localize more. Although, a localization-delocalization transition is not found, a transition with changes in the dominant correlations is observed. The nature of correlations between the particles as nearest neighbors become dominant beyond certain disorder strengths.

Carotid atherosclerotic lesions are a major cause of cerebrovascular disease (CVD). Identification and quantification of carotid plaques are important for categorizing the vulnerability of plaques for rupture and assessing the impact of treatments. The irregularity of plaque surface is associated with previous plaque rupture and plays an important role in the risk of stroke. Thus, the aim of this study is to develop and validate novel vulnerability biomarkers from three-dimensional ultrasound (3DUS) images by analyzing the surface morphological characterization of carotid plaque using fractal geometry features. 3D box-counting and 3D blanket are the two types of 3D fractal dimension that were employed to describe the smoothness of plaques. This fractal dimension analysis tool was used to evaluate the effect of atorvastatin using 3DUS carotid images, which were acquired from 6 patients treated with atorvastatin with 80 mg daily and 5 patients with placebo. The Student's T Test results showed that those two fractal features were effective for detecting the statin-related changes in carotid atherosclerosis with p<0.0068 and p<0.015 respectively, suggesting that 3D fractal dimension measurements can be used effectively to analyze the surface characteristics of carotid plaques, especially for evaluating the impact of the treatment.

Two-dimensional heat diffusion problem with heat source which is quasilinear parabolic problem is examined analytically and numerically. Periodic boundary conditions are used as a boundary conditions. Since the problem is not linear, Picard’s successive approximation theorem is used. Under certain conditions of natural regularity and consistency imposed on the input data, establish the existence, uniqueness and constant dependence of the solution on the data using the generalized Fourier method. As a numerical solution, implicit finite difference scheme is used. The results ob-tained from analytical and the numerical solutions are so close to each other.

Issues of fairness and consistency in Taekwondo poomsae evaluation have emerged owing to the lack of an objective evaluation method. This study proposes a three-dimensional (3D) convolutional neural network (CNN)-based action recognition model for the objective evaluation of Taekwondo poomsae. The model exhibits robust recognition performance regardless of variation in perspective by reducing the discrepancies between training and test images. The model uses 3D skeletons of the poomsae unit action collected using a full-body motion-capture suit to generate synthesized two-dimensional (2D) skeletons from the desired perspective. This approach aids in obtaining 2D skeletons from diverse perspectives as part of the training dataset and ensures consistent recognition performance regardless of the viewpoint. The model was trained using 2D skeletons projected from diverse viewpoints, and its performance was evaluated using various test datasets, including projected 2D skeletons and RGB images captured from various viewpoints. Comparison of the performance of the proposed model with that of previously reported action recognition models demonstrated the superiority of the model, underscoring its effectiveness in recognizing and classifying Taekwondo poomsae actions.

This study extends the CGAN-based MODIS cloud vertical-profile (64×64-scene, about 70km width×15km height) retrieval technique developed by Leinonen et al. (2019) [1] to construct seamless 3D cloud fields for the MODIS granules [2]. Firstly, the accuracy and spatial continuity of the Leinonen et al. [1] retrievals are statistically evaluated. Then, according to the characteristics of the retrieval error, a spatially overlapping-scene ensemble generation method and a bi-directional Ensemble Binning Probability Fusion (CGAN-BEBPF) technique are developed, which improves the CGAN retrieval accuracy and support to construct seamless 3D clouds. The CGAN-BEBPF technique involves three steps: cloud masking, intensity scaling, and optimal value selection. It ensures adequate coverage of the low reflectivity areas while preserving the high reflectivity cloud cores. The technique is applied to retrieve the 3D cloud fields of Typhoon Chaba and a multi-cell convective system. The cloud structures of the CGAN-BEBPF results are highly consistent with the ground-based radar observations. It can retrieve weak clouds at the top levels of convective storms and hurricanes that were missed by ground-based radars and fill the gaps of the ground-based radar lower-level PPI scan. Overall, CGAN-BEBPF can be automated to retrieve the rich informative 3D structures of typhoons and severe convective systems over the oceans along the MODIS swath, which certainly presents great value for improving maritime and near-shore typhoons and convection prediction and other cloud-sensitive applications.

The chiral optical Tamm state (COTS) is a special localized state at the interface of a handedness-preserving mirror and a structurally chiral medium such as a cholesteric liquid crystal or a chiral sculptured thin film. The spectral behavior of COTS, observed as reflection resonances, is described by the temporal coupled-mode theory. Mode coupling is different for two circular light polarizations because COTS has a helix structure replicating that of the cholesteric. The mode coupling for co-handed circularly polarized light exponentially attenuates with the cholesteric layer thickness since the COTS frequency falls into the stop band. Cross-handed circularly polarized light freely goes through the cholesteric layer and can excite COTS when reflected from the handedness-preserving mirror. The coupling in this case is proportional to anisotropy of the cholesteric and theoretically it is only anisotropy of magnetic permittivity that can ultimately cancel this coupling. These two couplings being equal results in a polarization crossover (the Kopp--Genack effect) for which a linear polarization is optimal to excite COTS. The corresponding cholesteric thickness and scattering matrix for COTS are generally described by simple expressions.

A large amount of accurate river cross-section data is indispensable for predicting river stages. However, the measured river cross-section data are usually sparse in the transverse direction at each cross-section as well as in the longitudinal direction along the river channel. This study presents three algorithms to resample the river cross-section data points in both the transverse and longitudinal directions from the original data. The resampled cross-section data based on the linear interpolation satisfactorily maintains the topographic and morphological features of the river channel, especially in the meandering river segment. A two-dimensional (2D) high-resolution unstructured-grid hydrodynamic model was used to assess the performance of the original and resampled cross-section data on a simulated river stage under low flow and high flow conditions. The simulated river stages are significantly improved using the resampled cross-section data based on the linear interpolation in the tidal river and non-tidal river segments. Furthermore, the performance of the 2D and three-dimensional (3D) models on the simulated river stage was also evaluated using the resampled cross-section data. The results indicate that the 2D and 3D models reproduce similar river stages in both tidal and non-tidal river segments under the low flow condition. However, the 2D model overestimates the river stages in both the tidal and non-tidal river segments compared to the 3D model under the high flow condition. The model sensitivity was implemented to investigate the influence of bottom drag coefficient and vertical eddy viscosity on river stage. The results reveal that bottom drag coefficient has a minor impact on river stage, but the vertical eddy viscosity is insensitive to river stage.

The advent of graphene opens up the research into two-dimensional (2D) material, which is considered as a revolutionary material in the future. Due to its unique geometric structure, graphene exhibits a series of exotic physical and chemical properties. Besides, single-element-based 2D materials (Xenes) have garnered tremendous interest. At present, 16 kinds of Xenes (silicene, borophene, germanene, phosphorene, tellurene, etc.) have been explored, mainly distributed in the third, fourth, fifth and sixth main groups. The current methods to prepare monolayer or few-layer 2D materials include epitaxy growth, mechanical exfoliation, and liquid phase exfoliation. Although two Xenes (aluminene and indiene) have not been synthesized due to the limitations of synthetic methods or stability of Xenes, other Xenes have been successfully realized by elaborately artificial design and synthesis. Focusing on elemental 2D materials, this review mainly summarizes the recently reported work about tuning the electronic, optical, mechanical, or chemical properties of Xenes via surface modifications achieved by controllable approaches (doping, adsorption, strain, intercalation, phase transition, etc.) to broaden the applications in various fields, including spintronics, electronics, optoelectronics, superconducting, photovoltaics, sensors, catalysis, and biomedicines. These advances in surface modification of Xenes have laid a theoretical and experimental foundation for the development of 2D materials and their practical applications in diverse fields.

We extended the usage of the expansion method based on Sine-Gordon equation to the two dimensional Fisher equation. The relation between the trigonometric and hyperbolic functions are derived from the Sine-Gordon equation de ned in two space dimension. The complex-valued traveling wave solutions to the two dimensional Fisher and Nagumo equations are set in forms a nite series of multiplications of powers of sech(.) and tanh(.) functions.

Meshfree particle method, which is always regarded as a pure Lagrangian approach, is easily represented complicated domain topologies, moving boundaries, and multiphase media. Solving acoustic problems with the mesfree particle method forms a branch of the acoustic wave modeling field, namely, particle-based computational acoustics (PCA). The aim of this paper is to improve the accuracy of using the PCA method to solve two-dimensional acoustic problems, and realize the particle representation with a hybrid meshfree and finite-difference time-domain (FDTD) method for acoustic boundary conditions at both the plane and curved surface. As a widely used Lagrangian meshfree method, the smoothed particle hydrodynamics (SPH) based on the support domain and the kernel function has developed rapidly in recent years. The traditional SPH method is easily implements parallel processing and has been applied in sound wave simulation. As a corrective method with higher accuracy than SPH, the acoustic propagation and scattering in the time domain is simulated with the corrective smoothed particle method (CSPM). Moreover, a hybrid meshfree-FDTD boundary treatment technique is utilized to represent different acoustic boundaries in the Lagrangian approach. In this boundary treatment technique, the parameter value of virtual particles is obtained with the FDTD method, which concerns truncation errors based on the Tayler series expansion. Soft, rigid, and Mur’s absorbing boundary conditions are developed to simulate sound waves in finite and infinite domain. Results of modeling acoustic propagation and scattering show that CSPM is accurate and convergence with exact solutions, and different acoustic boundaries are validated to be effective in the computation.

Quantum Computation, in the gate array version, uses logical gates adopting convenient forms for computational algorithms based on those of classical computation. There, two-level quantum systems are the basic elements connecting the binary nature of classical computation with the settlement of quantum processing. Despite, their design depends on specific quantum systems and physical interactions involved, exacerbating the dynamics analysis. Predictable and controllable manipulation should be addressed to control the quantum states, but resources are restricted to limitations imposed by the physical settlement. This work presents a formalism to decompose the quantum information dynamics in SU(2^2d) for 2d-partite two-level systems into 2^2d-1 SU(2) quantum subsystems. Decomposition lets to set control procedures, to generate large entangled states and to design specialized dedicated quantum gates. There, easy and traditional operations proposed by quantum computation are recovered for more complex and large systems. Alternating the parameters of local and non-local interactions, the procedure states a universal exchange semantics on the generalized Bell states basis. It could be understood as a momentary splitting of the 2d information channels into 2^2d-1 pairs of 2 level quantum information subsystems and a settlement of the quantum information manipulation free of the imposed restrictions by the underlying physical system.

The Double Random Phase Encoding (DRPE) image encryption method has garnered significant attention in color image processing and optical encryption, thanks to its parallel encryption of R, G, B. However, DRPE-based color image encryption faces two challenges. Firstly, it disregards the correlation of R, G, and B, compromising the encrypted image's robustness. Secondly, DRPE schemes relying on Discrete Fourier Transform (DFT) and Discrete Fractional Fourier Transform (DFRFT) are vulnerable to linear attacks, such as Known Plaintext Attack (KPA) and Chosen Plaintext Attack (CPA). Quantum walk stands out as a remarkable tool for designing modern cryptographic mechanisms, offering resistance to potential attacks from both classical and quantum computers.Therefore, this study presents an optical color image encryption algorithm that combines two-dimensional quantum walk with 24-bit plane permutation, dubbed OCT. This approach employs pseudo-random numbers generated by Two-Dimensional Quantum Walking (TDQW) for phase modulation in DRPE and scrambles the encrypted image's real and imaginary parts using the Generalized Arnold Transform. The 24-bit plane permutation helps reduce correlation of the R, G, B, while the Generalized Arnold Transform bolsters DRPE's resistance to linear attacks. By incorporating TDQW, the key space is significantly expanded. Experimental results validate the effectiveness and security of proposed method.

Two-dimensional (2D) ice I is an atomic-level ice that is composed of two interlocked atom-ic layers saturated with hydrogen bonds. It has recently been experimentally observed but its properties have yet to be clarified. Accordingly, we theoretically studied the hydrophobic properties of 2D ice I. On the contrary, simulation of a hydrogen fluoride molecule on a 2D ice surface manifested that it destroyed the 2d ice structure and connected new hydrogen bonds with water molecules. Investigations of the interfacial effect between 2D and three-dimensional (3D) ice films indicated that the network structure of 2D ice was not de-stroyed by a 3D ice surface, as the former was saturated with hydrogen bonds. However, the surface of 3D ice reorganized to form as many hydrogen bonds as possible. Thus, the 2D ice film was hydrophobic and inhibited the growth of 3D ice. This shows that if 2D ice can be produced on an industrial scale, it could be used as an anti-3D-icing agent under low tem-perature.

Keywords: olfactory rehabilitation; chronic pain; fMRI;

We consider a specific holographic model in the limit where the gauge field does not couple to the rest of of the holographic fields (gravity and scalar sector) and investigate a phase of matter at zero charge density, a realistic feature that may have implications for disordered strange metals. We then pick a specific form of the gauge coupling $Z(\alpha)$ with a certain disorder realization and argue that this provides a hard-gapped insulator with exponentially-suppressed conductivity by holographic methods. The limit is non-trivial: as there is backreaction at zero density amount, surviving in the coupled case.

A lead zirconate titanate [PZT;Pb(Zr_0.52Ti_0.48)O₃] layer embedded infrared (IR) detector decorated with wavelength-selective plasmonic crystals has been investigated for high-performance non-dispersive infrared (NDIR) spectroscopy. A plasmonic IR detector with an enhanced IR absorption band has been designed based on numerical simulations, fabricated by conventional microfabrication techniques, and characterized with a broadly tunable quantum cascade laser. The enhanced responsivity of the plasmonic IR detector at specific wavelength band has improved the performance of NDIR spectroscopy and pushed the limit of detection (LOD) by an order of magnitude. In this paper, a 13 fold enhancement in the LOD of a methane gas sensing using NDIR spectroscopy is demonstrated with the plasmonic IR detector.

Diesel is consistently a very popular fuel for internal combustion engines. Its consumption in the European Union has been rising over recent years, as has the number of engines increasingly sensitive to fuel contamination. One of the most important parameters affecting diesel quality is water content. Although its exceedances of the standard’s permissible amount are not common, they carry the risk of serious damage to expensive, modern fuel injection systems. Current methods of measuring water content require both specialised personnel and equipment, as well as transporting the sample to a suitable laboratory. The research presented in this paper was aimed at verifying whether it would be possible to test the moisture content of diesel using impedance spectroscopy. Once refined, such measurement method could be used in situ. Analysing the properties of diesel is challenging, mainly because many types of the fuel are sold, the chemical composition of which is always a well-guarded manufacturer’s secret. The experimental results obtained on many types of commercially available diesel show that it is possible to use impedance spectroscopy to estimate the water content of different types of diesel fuel. The measurement accuracy achieved makes it possible to detect approaching or exceeding the permissible water content.

In this study, we present a numerical method for solving two--dimensional space--time fractional partial differential equations (FPDEs), where the solutions of the FPDEs are expanded in terms of the shifted Chebyshev polynomials. The numerical approximations are evaluated at the Chebyshev-Gauss-Lobatto points. In the case when the FPDE is nonlinear, we employ a Newton-Raphson approach to linearize the equation. Both the linear and nonlinear cases lead to a consistent system of linear algebraic equations. The scheme is tested on selected FPDEs and the numerical results show that the proposed numerical scheme is accurate and computationally efficient in terms of CPU times. To establish the accuracy of the method, we also present an error analysis which shows the convergence of the numerical method. These positive attributes make the proposed method a good approach for solving two--dimensional fractional partial differential equations with both space and time fractional orders.

This paper presents an approach to the two-dimensional analysis of elastic isotropic deep beams using the finite difference method (FDM). Deep beams are subjected to in-plane loading and present a shear span to height ratio of less than 2.50; consequently, Euler-Bernoulli beam theory and Timoshenko beam theory do not apply. Deep beams analysis is generally conducted using numerical methods such as the finite element method and to a lesser extent the FDM; the strut-and-tie model and the stress field method are also widely utilized. Analytical approaches usually make use of the Airy stress function, where stresses are formulated in terms of the stress function; however, the exact solution of this function satisfying all of the boundary conditions can hardly be found, even for simple cases. In this paper, deep beams were analyzed using the FDM. The FDM is an approximate method for solving problems described with differential equations. The FDM does not involve solving differential equations; equations are formulated with values at selected nodes of the structure. Therefore, the deep beam was discretized with a two-dimensional grid, and additional nodes were introduced at the boundaries and at positions of discontinuity (openings, brutal change of material properties, non-uniform grid spacing), the number of additional nodes corresponding to the number of boundary conditions at the node of interest. The introduction of additional nodes allowed us to apply the governing equations at boundary nodes and satisfy the boundary and continuity conditions. An Airy stress function approach and a displacement potential function approach were considered in this study whereby strong formulations of equations (equilibrium, kinematic, and constitutive) were set. Stress and stability analyses were carried out with this model; furthermore, deep beams of varying stiffness, layered beams, and beams having openings were analyzed. For slender beams, the results obtained with the Airy stress function approach showed good agreement with those of the Euler-Bernoulli beam theory, and for deep beams, the shapes of stress distributions were in good agreement with a proper understanding of the behavior of structures. On the other hand, the displacement potential function approach delivered unsatisfactory results, probably due to the use of an inefficient equation solver; a more powerful tool will be needed in future research for this purpose.

The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908, however, for two dimensional turbulent boundary layers, no similarity solutions (special exact solutions) have ever been found. In the light of Blasius' pioneer works, we extend Blasius similarity transformation to the two dimensional turbulent boundary layers, and successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation. By author's Maple code, we numerically solve the ordinary differential equation and produce some useful quantities.

Surface passivation, which has been intensively studied recently, is essential for the perovskite solar cells (PSCs), due to the intrinsic defects in perovskite crystal. A series of chemical or physical methods have been published for passivating the defects of perovskite, which effectively suppressed the charge recombination and enhanced the photovoltaic performance. In this study, the n-type semiconductor of [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) is dissolved in chlorobenzene (CB) for the surface passivation during the spin-coating process for depositing the two-dimensional (2D) perovskite film. This approach simplifies the fabrication process of 2D PSCs and benefits the film quality. As a result, the defects of perovskite film are effectively passivated by this method. A better perovskite/PCBM heterojunction is generated, exhibiting an increased film coverage and improved film morphology of PCBM. It is found that this technology results in an improved electron transporting performance as well as suppressed charge recombination for electron transport layer. As a result, PSCs based on the one-step formed perovskite/PCBM heterojunctions exhibit the optimized power conversion efficiency of 15.69% which is about 37% higher than that of regular perovskite devices. The device environmental stability is also enhanced due to the quality-improved electron transport layer.

In this work, we report the fabrication of the new heterojunction of two 2D hybrid layered semiconductors, ZnO(stearic acid)/V₂O₅(hexadecylamine), and its behavior in the degradation of aqueous methylene blue under visible light irradiation. The optimal photocatalyst efficiency, reached at a ZnO(stearic acid)/ V₂O₅(hexadecylamine) ratio of 1:0.25, results to be about six times higher than that of pristine zinc oxide. Reusability test shows that after three photocatalysis cycles no significant changes in neither the dye degradation efficiency loss nor photocatalyst structure occur. Visible light photocatalytic performance observed indicates there is synergetic effect between both 2D nanocomposites used in the heterojunction. The visible light absorption enhancement promoted by the narrower bandgap V₂O₅ based components; an increased photo generated charge separation favored by extensive interface area; and abundance of hydrophobic sites for dye adsorption appear as probable causes of the improved photocatalytic efficiency in this hybrid semiconductors heterojunction. Estimated band-edge positions for both conduction and valence band of semiconductors together with experiments using specific radical scavengers allow a plausible photodegradation mechanism.

In this research, we utilize density functional theory (DFT) to study and investigate the adsorption process of methanol on three unique two-dimensional nanomaterials, namely BN, Graphene, and AlN. Eight sites for BN, AlN, and six sites for graphene were considered to reach full structural optimization. By conducting comprehensive simulations and analyses, we discovered diverse adsorption configurations and energy levels, which indicate different interaction strengths between methanol and the three 2D nanomaterials. Remarkably, AlN exhibits superior adsorption capabilities when compared to Graphene and BN which can be explained by attributable to the nature of charge transfer between the adsorbate and the adsorbent. For methanol adsorption on AlN, the strongest adsorption energy was (-0.5532 eV), and the amount of charge transferred from methanol to AlN was found to be (+0.075). For BN, the strongest adsorption energy was (-0.1351 eV), and the amount of charge transferred from methanol to BN was (+0.022). The density of states results indicated that the bandgap decreased, with a shift to the right. In contrast, for methanol adsorption on graphene, the strongest adsorption energy was found to be (-0.073 eV), and the amount of charge transferred from methanol to graphene was (+0.004). The density of states results showed no change in the bandgap. Our findings underscore the superiority of AlN’s potential over BN and Graphene for applications requiring efficient methanol adsorption, such as gas separation and storage technologies. This study emphasizes the superiority of AlN over Graphene and BN for tasks that necessitate effective methanol adsorption.

In this study, cotton fabric reinforced phenolic resin (CPF) composites were modified by adding four two-dimensional fillers: graphitic carbon nitride (g-C3N4), graphite (Gr), molybdenum disulfide (MoS2), and hexagonal boron nitride (h-BN). The tribological properties of these modified materials were investigated under dry friction and water lubrication conditions. CPF/ Gr composite exhibits significantly better tribological performance than the other three fillers modified CPF composites under dry friction, with a 24% reduction in friction coefficient and a 78% reduction in wear rate compared to unmodified CPF composite. Under water lubrication conditions, all four fillers did not significantly alter the friction coefficient of the CPF composite. However, except for an excessive amount of Gr, the other three fillers can reduce the wear rate. Particularly, in the case of 10% MoS2 content, the wear rate decreased by 56%. Scanning electron microscopy (SEM) and X-ray photoelectron spectroscopy (XPS) were employed for the analysis of the morphology and composition of the transfer films. Additionally, molecular dynamics (MD) simulations were conducted to investigate the adsorption effects of Gr, MoS2, and PF on the counterpart surface under both dry friction and water lubrication conditions. The difference in the adsorption capacity of Gr and MoS2 on the counterpart, as well as the resulting formation of transfer films, accounts for the variation in tribological behavior between CPF/Gr and CPF/MoS2 composites. By combining the lubrication properties of MoS2 and Gr under dry friction and water lubrication conditions, using them as co-fillers can achieve a synergistic lubrication effect.

The research community has shown significant interest in the aqueous synthesis of nanomaterials due to its ability to eliminate the need for complex organic solvents. This synthesis approach aligns with the principles of green chemistry, attracting considerable attention. Aqueous solution technology in fabricating nanostructures has gained recognition for its potential to create ultrasensitive, low-energy, and ultrafast optoelectronic devices. This report focuses on synthesizing lead iodide (PbI2) nanoplates using a water-based solution technique and fabricating a planar photodetector. The photodetectors with a planar type of device structure (ITO/PbI2 NPs/Au) demonstrated a remarkable photosensitivity of 3.9×103 and a photoresponsivity of 0.51 mA/W at a wavelength of 405 nm. Notably, the asymmetrical output properties of ITO/PbI2 NPs/Au detector deliver additional evidence of the effective creation of a Schottky contact. Thus, the photodetector exhibited a photoresponse even at 0 V bias, leading to the realization of self-powered photodetectors. Additionally, the device exhibited a rapid photoresponse of 0.21/0.38 s (−5 V) in the visible range. This study has expanded the horizons for the aqueous-phase synthesis of nanoplate nanostructures, enabling the large-area fabrication of high-performance photodetectors.

Optimization of Magnetohydrodynamics parameters on the velocity profile and temperature distribution of incompressible fluid flow on a porous channel was evaluated. The fluid flow was considered to be unsteady, incompressible and flowing in 2-D in porous channel. The effects of magnetic parameter, Darcy’s number and fluid pressure on velocity profiles, and the effect of variable viscosity and Eckert number on temperature distribution in incompressible fluid flow were determined. The flow was considered to be in a channel running along the x-axis on which the magnetic field exist and finally along the y-axis on the porous part of the channel. The resulting model equations were solved by Finite Difference Method (FDM) in MATLAB software. Analysis of results indicated that increasing Darcy’s number and fluid pressure leads to increase in fluid velocity profile, while increasing magnetic parameter decreases fluid velocity profile. Also, it was observed that increase in both Eckert number and fluid viscosity lead to increase in temperature distribution. Optimization in temperature was achieved by increasing the magnetic field while viscosity was optimized by increasing the length of the porous part of the channel. This study will helpful to contribute alternative equations and methodology to engineering and in factories where getting the MHD parameters optimally is the main objective, particularly on temperature, velocity and pressure.

The purpose of this paper is to present advanced techniques in optical biodevices. Moreover different configurations involving the generation of fiber optical biosensors are described. To overcome some limitations of fiber optical biosensors, plasmonic phenomena proposed. In addition novel plasmonic phenomena have broaden researcher’s horizons in new discovering in terms of technology and application. As regards there are many challenges to detect ultra-low concentration samples with high sensitivity in real time. Researchers have always made great efforts to discover more effective methods. Throughout the paper SPR and LSPR as a powerful analysis instrument are introduced. Finally surveys the current practical performances of plasmonic sensors in detection of bio target are provided. As a result these devices demonstrate great potential in identifying target analytic due to their unique optical biosensors.

This research focuses on the Hopf bifurcation occurring at a singular point with high-order degeneracy in a class of three-dimensional systems. Based on center manifold theorem, by expanding the technique for determining singular point values of degenerate singularities in two-dimensional systems, the formal series method to determine the singular point values at the high-order degenerate critical point is discussed. Furthermore, a class of specific three-dimensional differential systems with high-order degenerate singularities is explored. By computing the singular point values and determining center conditions, we proved that a minimum of 5 small-amplitude limit cycles in the vicinity of the origin. This research provides new perspectives on the center problem and limit cycle bifurcation in high-dimensional systems with high-order degenerate singular points.

This paper concentrates on the general birth-death processes with two different types of catastrophes. The Laplace transform of transition probability function for birth-death processes with two-type catastrophes are is successfully expressed with the Laplace transform of transition probability function of the birth-death processes without catastrophe. The first effective catastrophe occurrence time is considered. The Laplace transform of its probability density function, expectation and variance are obtained.

Kim-Kim (Russ. J. Math. Phys. 2017, 24, 241-248) defined the degenerate Laplace transform and investigated some of their certain properties. Motivated by this study, in this paper, we introduce the degenerate Sumudu transform and establish some properties and relations. We derive degenerate Sumudu transforms of power functions, degenerate sine, degenerate cosine, degenerate hyperbolic sine, degenerate hyperbolic cosine, degenerate exponential function, and function derivatives. We also acquire a relationship between degenerate Sumudu transform and degenerate gamma function. Moreover, we investigate a scale preserving theorem for the degenerate Sumudu transform. Furthermore, we show that the degenerate Sumudu transform is the theoretical dual transform to the degenerate Laplace transform.

Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu transform and investigate many properties and relations including modified Sumudu transforms of the power function, sine, cosine, hyperbolic sine, hyperbolic cosine, exponential function, and function derivatives. Moreover, we attain two shifting properties and a scale preserving theorem for the modified Sumudu transform. We give modified inverse Sumudu transform and investigate some relations and examples. Furthermore, we show that the modified Sumudu transform is the theoretical dual transform to the modified Laplace transform.

Fingerprints are essential for human identification and are valuable tools in criminal investigations. The pursuit of new materials for digital printing is expanding, with increasing interest in natural compounds such as bixin, sourced from annatto seeds. Despite its traditional use as a natural dye with medicinal properties, the potential of bixin in papilloscopy remains largely untapped. In this study, we meticulously extracted bixin from annatto seeds and meticulously developed composites incorporating zinc carbonate (bixin/ZnCO3) and kaolinite (bixin/kaolinite). UV-visible spectroscopy was used for characterization, and the extracted bixin showed absorption peaks at 429, 453, and 481 nm, which were very similar to standard peaks at 429, 457, and 487 nm. The two samples also had the same retention times (7.07 min) according to further liquid chromatography analysis. Sweat pores were easier to detect thanks to the effectiveness of the bixin/ZnCO3 and bixin/kaolinite composites in creating high contrast sebaceous and natural latent fingerprints. These results highlight the composites’ potential as novel and fascinating instruments for papilloscopy applications, which might also improve forensic investigations.

Earth observation satellites can capture images of specific areas in Earth's orbit based on user requirements. Despite the high demand for satellite imagery, satellites remain a scarce resource. When there are many observation tasks that are large and dense, they may interfere with each other due to satellite mobility. To address this issue, a multi-satellite scheduling algorithm based on a task merging mechanism has been proposed. This paper proposes a two-stage approach to the problem: task merging phase and merging task scheduling phase. The task merging phase introduces two methods based on Mean Shift and Complete Graph to generate the merging task set. In the merging task scheduling phase, a multi-satellite scheduling algorithm based on merging tasks is employed to solve the problem. Finally, certain measurement experiments suggest the effectiveness of the algorithm.

In this research, a computation algorithm is established for a fractional order 2D fuzzy heat equation. In this study, Elzaki transform and HPM fusion is produced. Computing the desired outcome in series yields a fast convergence on an appropriate response. Examples are provided to support the conclusions, which are then compared with a particular approach to show the effectiveness and potential of the suggested approach. Two crisp equations—one for the lower bound solution and one for the upper bound solution are constructed from the input fuzzy fractional heat equation. The contour and surface representations of the approximate and exact results are offered for the lower and upper-bound solutions. The l∞-error norm is used in this study to validate the numerical convergence aspect. Together with the absolute inaccuracy, the approximate and exact solutions are matched. It has been demonstrated that the proposed regime will make it feasible to work with fuzzy fractional partial differential equations in a wide range of dimensions.

Two-dimensional (2D) materials have been a research hot topic in the passed decades due to their unique and fascinating properties. Among them, mechanical properties plays an important role for their application. However, there lacks an effective tool for high-throughput calculating, analysing and visualizing the mechanical properties of 2D materials. In this work, we present, mech2d package, a highly automated toolkit for calculating and analysing second-order elastic constants (SOECs) tensor and relevant properties of 2D materials with considering their symmetry. In the mech2d, the SOECs can be fitted by both strain-energy and stress-strain approach, where the energy or strain can be calculated by first-principles engine, such as VASP. As a key feature, the mech2d package can automatically submit and collect the tasks from local or remote machine with robust fault-tolerant ability, make it suitable for high-throughput calculation. The present code has been validated by several common 2D materials, including graphene, black phosphorene, GeSe2 and so on.

Due to increasing concerns about global warming and energy crisis, intensive efforts have been made to explore renewable and clean energy sources. Single-atom metals and two-dimensional (2D) nanomaterials have attracted extensive attention in the fields of energy and environment because of their unique electronic structures and excellent properties. In this review, we sum-marize the state-of-art progress on the single-atom metal supported at 2D MoS2 (single-atom metal/2D MoS2) for electrochemical CO2 reduction and water splitting. First, we introduce the advantages of single-atom metal/2D MoS2 catalysts in the fields of electrocatalytic CO2 reduction and water splitting, followed by the strategies for improving electrocatalytic performances of single-atom metal/2D MoS2 hybrid nanomaterials and the typical preparation methods. Further, we discuss the important applications of the nanocomposites in electrocatalytic CO2 reduction and water splitting via some typical examples, particularly focusing on their synthesis routes, modification approaches, and physiochemical mechanisms for improving their electrocatalytic performances. Finally, our perspectives on the key challenges and future directions of exploring high-performance metal single-atom catalysts are presented based on recent achievements in the development of single-atom metal/2D MoS2 hybrid nanomaterials.

Motivated by diffraction experiments on the $\left(2\sqrt{3}\times \sqrt{3}\right)\mathrm{R}{30}^{\circ }$ reconstructed Si(111) due to deposition of rare earth elements (Dy, Tb) and silicide formation we analyse the splitting and non-splitting of superstructure spots. For this purpose, we model diffraction patterns for one dimensional structures generated by the binary surface technique and use supercell models to keep the analysis simple. Diffraction pattern are calculated in the framework of the kinematical diffraction theory and they are analyzed as a function of the domains and domain boundaries. Basic properties of the diffraction pattern are analyzed for model systems of a two-fold and a three-fold periodicity. The rules derived from these calculations are applied to the "real-world" system of Si(111)-($\left(2\sqrt{3}\times \sqrt{3}\right)\mathrm{R}{30}^{\circ }$)-RESi$2_{}$ (RE = Dy or Tb). Depending on the combination of domains and domain boundaries of different types a plethora of different features are observed in the diffraction patterns. These are analyzed to determine the sizes of both domain boundaries and domains from experimentally observed splitting of specific superstructure spots.

The twisted Wang transform distribution family, defined as the composition of parameter shifted inverse CDF function with an original CDF function, is found to be most suitable for matching low shape factor distributions, characterizing hard to fit or to simulate reinsurance portfolio losses for some perils from our previous study. Among them, the best form for matching a hard-to-fit empirical loss distribution for a specific peril, is the Exponential Fractional Extra Power 0 Distribution in (0,1) with CDF:.The simplest yet still a good form of this family is the Transformed Hyperbolic Tangent Distribution with CDF:,which has analytical formulas for the moments. The twisted Wang transform distribution family is compared and confirmed to be superior to all other well-known distribution families through extensive numerical optimization practice, distribution forms guesses, and computer-aided exploration experiments.

The interest in lipid composition profiling is significantly increasing as research reveals the immense importance of lipids in medicine, plant science, food and agriculture. However, lipidomic analysis requires high-end specialty equipment. We used two-dimensional thin-layer chromatography (2D TLC) as a readily available, low-cost tool for basic lipidomic profiling of lipid classes in algal samples as model: Chlamydomonas reinhardtii, Auxenochlorella protothecoides, and Euglena gracilis. Algal lipid extracts were separated on a 2D-TLC plate, and TLC analysis was followed by scraping individual TLC spots off the plate, and a subsequent liquid chromatography separation and tandem mass spectrometry (LC-MS/MS) analysis. For comparison, crude lipid extracts were also injected directly to the LC-MS/MS system. Lipid class annotation was achieved by a combination of accurate mass, retention time information, neutral loss and fragment ion analysis by MS2Analyzer, and by matching spectra to LipidBlast MS/MS library. Overall, we were able to identify 15 lipid classes, and to adequately profile the lipid classes in all three organisms. This TLC method is thus suggested as an accessible tool for lipid class profiling of algal, plant, and food lipids, alike, when a rapid and simple analysis is required, e.g., for screening purposes.

In this paper, we investigate a financial market in which asset prices evolve based on a multi-dimensional Brownian motion process and a multi-dimensional Poisson process with different credit and deposit rates We proceed to evaluate European options by establishing upper and lower hedging prices through a transition to a suitable auxiliary market. Additionally, we address the minimization of shortfall risk and no-arbitrage price bounds in incomplete markets within this framework.

Due to the intermittency and fluctuation of photovoltaic (PV) output power, a high proportion of grid-connected PV power generation systems has a significant impact on power systems. Accurate PV power forecasting can alleviate the uncertainty of the PV power and is of great significance for the stable operation and scheduling of the power systems. Therefore, in this study, a feature rise-dimensional (FRD) two-layer ensemble learning (TLEL) model for short-term PV power deterministic forecasting and probability forecasting is proposed. First， based on the eXtreme Gradient Boosting (XGBoost), Random Forest (RF), CatBoost, and Long-short-term memory (LSTM) models, a TLEL model is constructed utilizing the ensemble learning algorithm. Meanwhile, the FRD method is introduced to construct the FRD-XGBoost-LSTM (R-XGBL), FRD-RF-LSTM(R-RFL), and FRD- CatBoost - LSTM (R-CatBL) models. Subsequently, the above models are combined to construct the FRD-TLEL model for deterministic forecasting, and perform probability interval forecasting based on quantile regression(QR). Finally, the performance of the proposed model is demonstrated with a real-world dataset. By comparing with other models, the proposed model displays better forecasting accuracy for deterministic forecasting and reliable forecasting intervals for probability forecasting, and good generalization ability in the datasets of different seasons and weather types.

: Two-dimensional instability of a horizontal layer of boiling liquid with a finite height is experimentally studied. In this layer, “vapor columns” rose at the corners of a square rectangular grid. The symmetry of “vapor column” location on the heating surface is considered. The model considers the approach to the boiling crisis in terms of both developed nucleate boiling and transitional boiling (the Zuber problem). When dealing with developed nucleate boiling, the layer of boiling liquid is considered in calculations as an isotropic homogeneous system (foam). It is shown how the conditions on the heating surface (capillary-porous coating) affect external hydrodynamics of the liquid layer and, ultimately, the value of the critical heat flux. The calculation ratio obtained by approaching the boiling crisis with regard to developed nucleate boiling takes into account the dependence of the critical heat flux on the void fraction of the boiling liquid layer. A new solution to the boiling crisis problem is proposed when approaching the crisis from the point of transitional boiling (the Zuber problem). This new solution eliminates some shortcomings of the classical problem (in particular, the void fraction of the layer corresponds to the experiments).

This work presents a multi-start algorithm for solving the capacitated vehicle routing problem with two-dimensional loading constraints (2L-CVRP) allowing for the rotation of goods. Researches dedicated to graph theory and symmetry considered the vehicle routing problem as a classical application. This problem has complex aspects that stimulate the use of advanced algorithms and symmetry in graphs. The use of graph modeling of the 2L-CVRP problem by undirected graph allowed the high performance of the algorithm. The developed algorithm is based on metaheuristics such as the Constructive Genetic Algorithm (CGA), to construct promising initial solutions; a Tabu Search (TS), to improve the initial solutions on the routing problem; and a Large Neighborhood Search (LNS), for the loading subproblem. Although each one of these algorithms allowed to solve parts of the 2L-CVRP, the combination of these three algorithms to solve this problem was unprecedented in the scientific literature. In our approach, a parallel mechanism for checking the loading feasibility of routes was implemented using multi-threading programming to improve the performance. Additionally, memory structures, like hash-tables, were implemented to save time by storing and querying previously evaluated results for the loading feasibility of routes. For benchmarks, tests were done on well-known instances available in the literature. The results proved that the framework matched or outperformed most of the previous approaches. As the main contribution, this work brings higher quality solutions for large-size instances of the pure CVRP. This paper involves themes related to the symmetry journal, mainly complex algorithms, graphs, search strategies, complexity, graph modeling, and genetic algorithms. In addition, the paper especially focuses on topic-related aspects of special interest of the community involved in symmetry studies, such as, graph algorithms and graph theory.

In this paper, we study the global asymptotically stability of following system of difference equations with quadratic terms: x_{n+1}=A+B((y_{n})/(y_{n-1}²)),y_{n+1}=A+B((x_{n})/(x_{n-1}²)) where A and B are positive numbers and the initial values are positive numbers. We also investigate the rate of convergence and oscillation behaviour of the solutions of related system.

Sentiment analysis to characterize properties of Bitcoin prices and their forecasting is here developed thanks to the capability of the Fuzzy transform to capture stylized facts and mutual connections between time series having different nature. Six years of daily Bitcoin Prices and Google Trends are analyzed in order to establish new perspectives in the management of their dynamics.

In this paper, a multi-patch weakly singular isogeometric boundary element method (WSIGABEM) for two-dimensional elastostatics is proposed. Since the method based on the weakly singular boundary integral equation, the quadrature techniques, dedicated for the weakly singular and regular integrals, are applied in the method. A new formula for the generation of collocation points is suggested to take the full advantage of the multi-patch technique. The generated collo-cation points are essentially inside the patches without any correction. If the boundary conditions are assumed to be continuous in every patch, no collocation point lies on the discontinuous boundaries, thus simplifying the implementation. The multi-patch WSIGABEM is verified by the simple examples with analytical solutions. The feature of the present multi-patch WSIGABEM is investigated by the comparison with the traditional IGABEM. Furthermore, the combination of the present multi-patch WSIGABEM and the particle swarm optimization algorithm results in a shape optimization method in two-dimensional elastostatics. By changing some specific control points and their weights, the shape optimizations of the fillet corner, the spanner and the arch bridge are verified to be effective.

Quantification of bone loss for follow-up comparisons has not been routinely performed in patients with parietal thinning so far. This study compares different methodological approaches including both 2- and 3-dimensional methods in computerized tomographies of a single patient. The 2-dimensional method provides accurate measurements of bone thickness, while the 3-dimensional method allows for a more comprehensive view of the bone's structure, including parameters like shape, size, and thickness. The techniques provided valuable data for the treating physician and suggest a possible effect of corticosteroids in this individual patient. The study concludes that 3-dimensional reconstruction of computerized tomographies with subsequent 2-dimensional analyses appears justified for routine radiological practice to increase clinical awareness of the size of the parietal bone defects and allow for quantification of bone loss during long-term follow-ups. Further validation of the proposed analytical approaches is warranted in larger studies to investigate patterns of bone thinning across the skull and changes in bone volumes over time, with specialized software to be approved for such analyses.

Antimony (Sb) has gained significance as a critical raw material (CRM) within the European Union (EU) due to its strategic importance in various industrial sectors, particularly in the textile industry for flame retardants and as a component of Sb-based semiconductor materials. Moreover, Sb is emerging as a potential alternative for anodes used in lithium-ion batteries, a key element in the Energy transition. This study focused on exploring the feasibility of identifying and quantifying Sb mineralizations through the spectral signature of soils using reflectance spectroscopy, a non-invasive remote sensing technique, and by employing deep learning algorithms such as Convolutional Neural Networks (CNNs). Common signal preprocessing techniques were applied to the spectral data, and the soils were analyzed by Inductively Coupled Plasma Mass Spectrometry (ICP-MS). Despite achieving high R-squared values, the study faces a significant challenge of generalization of the model to new data. Despite the limitations, this study provides valuable insights into potential strategies for future research in this field.

In this work, a mixture of Elzaki transform and projected differential transform method is applied to solve a nonlinear wave-like equations with variable coefficients. Nonlinear terms can be easily manipulated by using the projected differential transformation method. The method gives the results show that the proposed method is very efficient, simple and can be applied to other applications.

Bacteriophages (phages) are potential alternatives to chemical antimicrobials against pathogens of public health significance. Understanding the diversity and host specificity of phages is important for developing effective phage biocontrol approaches. Here, we assessed the host range, morphology, and genetic diversity of eight Salmonella enterica phages isolated from a wastewater treatment plant. The host range analysis revealed that six out of eight phages lysed more than 81% of the 43 Salmonella enterica isolates tested. The genomic sequences of all phages were determined. Whole genome sequencing data (WGS) data revealed that phage genome sizes ranged from 41 to 114 kb with GC contents be-tween 39.9 and 50.0 %. Two of the phages SB13 and SB28 represent new species Epsep-timavirus SB13 and genera Macdonaldcampvirus, respectively as designated by the In-ternational Committee for the Taxonomy of Viruses (ICTV) as per genome based taxonomic classification. One phage (SB18) belonged to the Myoviridae morphotype while the re-maining phages belonged to the Siphoviridae morphotype. The gene content analyses showed that none of the phages possessed virulence, toxin, antibiotic resistance, type I-VI toxin-antitoxin modules or lysogeny genes. Three (SB3, SB15 and SB18) out of the eight phages possessed tailspike proteins. Whole genome-based phylogeny of the eight phages with their 113 homologs revealed three clusters A, B, C and seven subclusters (A1, A2, A3, B1, B2, C1 and C2). While cluster C1 phages were predominantly isolated from animal sources, cluster B contained phages from both wastewater and animal sources. The broad host range of these phages highlights their potential use to control the presence of S. enterica in foods.

We address the dynamics of two-dimensional Navier-Stokes models with infinite delay and hereditary memory, whose kernels are a much larger class of functions than the one considered in the literature, on a bounded domain. We prove the existence and uniqueness of weak solutions by means of Faedo-Galerkin method. Moreover, we establish the existence of global attractor for the system with the existence of a bounded absorbing set and asymptotic compact property.

An investigation of compressible flow over two-dimensional obstacles is presented in this paper. When shock waves are formed on surfaces due to compressibility and these shocks interfere with the boundary layer, undesirable effects such as friction, separation, and flow instability occur. To weaken the shock and reduce its effects, various methods have been employed in the past, including surface suction, surface blowing, and vortex generators. Using numerical solutions, the present work attempts to reduce the negative effects of the shock generated by the obstacle by creating porosity on its surface. Numerical methods such as the finite volume method and the Navier-Stokes equations as well as the Spalart-Allmaras model are used. By creating suction and blowing and increasing the cross-sectional area of the flow, porous surfaces reduce the effects of shock. Achieving around 50% porosity on the obstacle weakened the shock and reduced the Mach number after it, according to this paper's results. Also, the area under the skin friction diagram has decreased by about 38% as a result of less interference between the shock and the boundary layer and blowing caused by the porous surface.

Background and Objectives: Mechanical and biological complications can lead to system fracture or screw loss on dental implants. Narrow and regular platforms have been used without a consensus about the effect of distance the abutment from the prosthetic platform margin. The aim of this study is to evaluate different insertion torques in the deformation of tri-channel platform connections through two- and three-dimensional measurements with micro-CT. Materials and Methods: 164 implants were divided into groups (platform diameter and type): 3.5, 3.75, and 4.3 mm NP (Narrow Platform), and 4.3 mm RP (Regular Platform). Each implant-platform group was then divided into four subgroups (n = 10) with different torques: T45 (45 Ncm), T80 (80 Ncm), T120 (120 Ncm) and T150 (150 Ncm). The implant-abutment-screw assemblies were scanned and the images obtained were analyzed. Results: A significant difference was observed for the linear and volume measures between the different platforms (p &lt;0.01) and the different implant insertion torques (p &lt;0.01). Qualitative analysis suggested higher deformation resistance for the 3.75 NP compared to the 3.5 NP, and RP was more resistant compared to the NP. Conclusions: The 0.25-mm increment in the implant platform did not increase the resistance to the applied insertion torques; the 4.3-mm implant was significantly stronger compared to the 3.5-mm implant and the proposed micro-CT analysis was considered valid for both 2D and 3D analyses of micro gaps, qualitatively and quantitatively.

We discuss the electrodeposition of two-dimensional (2D) Pt-nanostructures on HOPG achieved under constant applied potential versus a Pt counter electrode (Eappl = ca. - 2.2 V vs RHE). The deposition conditions are discussed in terms of the electrochemical behavior of the electrodeposition precursor (H2PtCl6). We performed cyclic voltammetry (CV) of the electrochemical Pt deposit on HOPG and on Pt substrates to study the relevant phenomena that affect the morphology of Pt deposition. Under conditions where the Pt deposition occurs and H2 evolution is occurring at the diffusion-limited rate (- 0.3 V vs RHE), Pt forms larger structures on the surface of HOPG, and the electrodeposition of Pt is not limited by diffusion. This indicates the need for large overpotentials to direct the 2D growth of Pt. Investigation of the possible effect of Cl- showed that Cl- deposits on the surface of Pt at low overpotentials, but strips from the surface at potentials more positive than the electrodeposition potential. The CV of Pt on HOPG is a strong function of the nature of the surface. We propose that during immersion of HOPG in the electrodeposition solution (3 mM H2PtCl6, 0.5 M NaCl, pH 2.3) Pt islands are formed spontaneously, and these islands drive the growth of the 2D nanostructures.

This paper reviews the unilateral and bilateral, one- and two-dimensional Laplace transforms. The unilateral and bilateral Laplace transforms are compared in the one-dimensional case, leading to the formulation of the initial-condition theorem. This problem is solved with all generality in the one- and two-dimensional cases with the bilateral Laplace transform. General two-dimensional linear systems are introduced and the corresponding transfer function defined.