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.

A Savonius wind turbine is one of the simplest vertical-axis turbines. Several researchers have been attracted to it because of its simple structure, low noise, appropriate torque, and independence from wind direction. SR3345 and SR5050 blade profiles will be investigated for their effects on the performance of Savonius wind turbines. First, the fabricated wind turbine is placed in front of an open circuit wind tunnel with a velocity of 6 m/s. Furthermore, governing relationships are used to calculate power and torque coefficients as well as tip speed. In this study, the power and torque coefficients of the turbine are compared with the two profiles considered based on overlap ratios between 0 and 0.3. Despite its increased stability, the central shaft reduced the power coefficient of the turbine. For blade SR3345, the best performance occurs at tip speed ratios of less than 1, while for blade SR5050, the best performance occurs at higher tip speed ratios. Both blades SR3345 and SR5050 achieve the highest power coefficients at overlap ratios of 0 and 0.18 when a central shaft is present.

Motivated by results on the location of zeros of a complex polynomial with monotonicity conditions on the coefficients (such as the classical Eneström-Kakeya Theorem, and its recent generalizations), we impose similar conditions and give bounds on the number of zeros in certain regions. We do so by introducing a reversal in monotonicity conditions on the real and imaginary parts of the coefficients, and also on their moduli. The results presented naturally apply to certain classes of lacunary polynomials.

This study presents an extensive collection of data on the aerodynamic behavior at a low Reynolds number and geometric coefficients for 2900 airfoils obtained through the class shape transformation (CST) method. By employing a verified OpenFOAM-based CFD simulation framework, lift and drag coefficients were determined at a Reynolds number of 10^5. Considering the limited availability of data on low Reynolds number airfoils, this dataset is invaluable for a wide range of applications, including unmanned aerial vehicles (UAVs) and wind turbines. Additionally, the study offers a method for automating CFD simulations that could be applied to obtain aerodynamic coefficients at higher Reynolds numbers. The breadth of this dataset also supports the enhancement and creation of machine learning (ML) models, further advancing research into the aerodynamics of airfoils and lifting surfaces.

This paper presents the experimental campaign conducted near the Condoroma dam at 4075 m a.s.l. in an experimental setup consisting of a series of standard profile spillways with a vertical upstream face of up to five different dimensionless heights (P/Hd). The experimental results indicate that for all P/Hd ratios studied, the discharge coefficients adjusted to the Condoroma altitude are lower than those reported by classical formulations used in conventional spillway design. As a result, a generalized equation is proposed to estimate the discharge coefficient for standard spillways located in dams at similar elevations above sea level.

The close proximity of different buildings heights can cause disturbances in the working of the smoke and ventilation ducts of lower buildings, threatening the health and even the lives of residents. To define the influence of high-rise building on the work of the ducts of the neighbouring double-storied building, experimental investigations in the wind tunnel were conducted. On this basis, empirical equations and graphs were developed leading to determining the aerodynamic coefficients considering different wind directions and the height of ducts. The direction of the wind reveals a greater influence than the height of the ducts. Properly using deflectors or increasing the height of the duct ensures maintaining static rarefaction in the area of smoke and ventilation ducts. The creation of rarefaction ensures the reliability of the natural ventilation system and the safety of the health of residents.

This work aims to investigate the effect of Pt concentration on crystal growth mechanism of Platinum-Palladium (Pt-Pd) binary alloy system during the annealing process starting from amorphous phase until some definite temperatures. The calculations have been performed by using molecular dynamic (MD) simulations. Interatomic interactions are described by on Sutton-Chen type Embedded Atom Potential Energy function. In order to understand the main structural properties at the stable and unstable phases, changes in RDF curves versus time have been analysed for different annealing temperatures. Crystalline type bonded pairs have been determined using MD calculations which is required for the computation of Avrami coefficients and for understanding crystal growth mechanism. The results demonstrate that the increase in concentration of Pt during annealing leads to migration of atoms in the crystal lattice points, elimination of dislocations and formation of perfect crystal structure.

This study focuses on the optimal deployment problem, and determines the optimal size of a military force to send to the battle field. The decision is optimized, based on an objective function, that considers the cost of deployment, the cost of the time it takes to win the battle, and the costs of killed and wounded soldiers with equipment. The cost of deployment is modeled as an explicit function of the number of deployed troops and the value of a victory with access to a free territory, is modeled as a function of the length of the time it takes to win the battle. The cost of lost troops and equipment, is a function of the size of the reduction of these lives and resources. An objective function, based on these values and costs, is optimized, under different parameter assumptions. The battle dynamics is modeled via the Lanchester differential equation system based on the principles of directed fire. First, the deterministic problem is solved analytically, via derivations and comparative statics analysis. General mathematical results are reported, including the directions of changes of the optimal deployment decisions, under the influence of alternative types of parameter changes. Then, the first order optimum condition from the analytical model, in combination with numerically specified parameter values, is used to determine optimal values of the levels of deployment in different situations. A concrete numerical case, based on documented facts from the Battle of Iwo Jima, during WW II, is analyzed, and the optimal US deployment decisions are determined under different assumptions. The known attrition coefficients of both armies, from USA and Japan, and the initial size of the Japanese force, are parameters. The analysis is also based on some parameters without empirical documentation, that are necessary to include to make optimization possible. These parameter values are motivated in the text. The optimal solutions are found via Newton- Raphson iteration. Finally, a stochastic version of the optimal deployment problem is defined. The attrition parameters are considered as stochastic, before the deployment decisions have been made. The attrition parameters of the two armies have the same expected values as in the deterministic analysis, are independent of each other, have correlation zero, and have relative standard deviations of 20%. All possible deployment decisions, with 5000 units intervals, from 0 to 150000 troops, are investigated, and the optimal decisions are selected. The analytical, and the two numerical, methods, all show that the optimal deployment level is a decreasing function of the marginal deployment cost, an increasing function of the marginal cost of the time to win the battle, an increasing function of the marginal cost of killed and wounded soldiers and lost equipment, an increasing function of the initial size of the opposing army, an increasing function of the efficiency of the soldiers in the opposing army and a decreasing function of the efficiency of the soldiers in the deployed army. With stochastic attrition parameters, the stochastic model also shows that the probability to win the battle is an increasing function of the size of the deployed army. When the optimal deployment level is selected, the probability of a victory is usually less than 100%, since it would be too expensive to guarantee a victory with 100% probability. Some of many results of relevance to the Battle of Iwo Jima, are the following: In the deterministic Case 0 analysis, the optimal US deployment level is 66200, the time to win the battle is 30 days and 14000 US soldiers are killed or wounded. If the marginal cost of the time it takes to win a victory doubles, the optimal deployment increases to 75400, the time to win a victory is reduced to 26 days, and less than 12000 soldiers are killed or wounded. In the stochastic Case 0 analysis, the optimal US deployment level is 65000, the expected time to win the battle is 46 days and almost 25000 US soldiers are expected to be killed or wounded. If the cost per killed or wounded soldier increases from 0 to 5 M $US, the optimal deployment level increases to 75000. Then, the victory is expected to appear after 35 days and 19900 US soldiers are expected to be killed or wounded.

The modeling of tilting-pad journal and thrust bearings presents a level of complexity beyond that of bearings of fixed-arc geometry, particularly with regard to dynamic influences. With tilting-pad bearings, the theory surrounding the fluid film must be complemented with representative modeling of the pad dynamics. What has been recognized in recent decades has been the significance of the pad support, in particular the flexibility of the pivot region of the pad. The typical model for including the stiffness of the pivot has been based on Hertzian contact theory. Some researchers have been noting that the Hertzian theory does not permit sufficient flexibility in the pivot region. It is suggested that the contact mechanics at the pivot would be better represented as a pairing of rough surfaces. The modeling used here is based on a statistical asperity micro-contact theory for rough-surface line contact that has been extended to include contact stiffness. This model has been applied to the determination of the effective dynamic properties of tilting-pad bearings. The results show that pivot stiffness can be as low as one-third the stiffness determined by Hertzian theory. Comparison to published experimental results confirms the significance of the rough-surface modeling, particularly for the line contacts associated with rocker-back tilting pads.

The work is devoted to the development of methods for constructing asymptotic formulas as x→∞ of a fundamental system of solutions of linear differential equations generated by a symmetric two-term differential expression of odd order. The coefficients of the differential expression belong to classes of functions that allow oscillation (for example, those that do not satisfy the classical Titchmarsh-Levitan regularity conditions). As a model equation, the 5th order equation i2p(x)y′′′′′+p(x)y′′′′′+q(x)y=λy, for which various cases of behavior of the coefficients p(x),q(x), is investigated. New asymptotic formulas are obtained for the case when the function h(x)=−1+p−1/2(x)∉L1[1,∞) significantly influences the asymptotics of solutions to the equation. The case when the equation contains a nontrivial bifurcation parameter is studied.

Building situated in the flow path of wind is subjected to differential velocity and pressure distribution around the building envelope. Wind effects are influenced and vary for each individual shape of the tall building. Tall building structures are considered as cantilever structures with fixed ends at the ground. Wind exponential velocity acting along the height of the building makes velocity and pressure distribution more complex as the height of the building structure increases. This study discussed the effect of wind on an irregular cross-section shape. The study was conducted numerically with a building model placed in a virtual wind tunnel using the ANSYS (CFX) software tool. Wind effects are investigated on building model situated in a terrain category - II defined in IS: 875 (Part 3): 2015 wind scale model of 1:100 and turbulence intensity is 5 % and power law index α is considered as 0.143. Validation and verification of the study were made by comparing pressure coefficients on faces of a rectangular model of similar floor area and height as taken for a C-plan diamond-shaped model under similar boundary conditions, wind environment, and solver setting of numerical setup. The values of surface pressures generated on the recessed faces of the model and wind flow patterns within the recessed cavity were studied at wind incident angles 0°, 300, 60°, 1050, 1350 & 1800. The critical suction on all the recessed faces was observed to be at a 105° angle of wind attack.

This study entailed the design and analysis of a 400 m-class underwater glider operated by a bladder-type buoyancy engine. The underwater glider was designed for high-speed movement with a maximum velocity of 2 knots. The shape of the hull was designed to reduce water resistance using the Myring hull profile equation. The reliability was verified by performing simulations using resistance coefficients. The relationship between the control value of the ballast discharged from the buoyancy engine and the glider's speed according to the path angle was analyzed. Further, the relationship between the optimal glide angle and the design control value of the ballast was derived, and the optimal glider speed was estimated accordingly. Based on the analysis results, a bladder-type buoyancy engine was developed, and the maximum speed of the tested underwater glider was measured via sea trials.

Road intersections are made of asphalt pavement, a popular road surface material used worldwide. The pavement may suffer deformities and deterioration, resulting in higher maintenance expenses and an elevated likelihood of road accidents, due to factors such as heavy vehicles and environmental variables like temperature and rainfall. To tackle these obstacles, researchers have devised several machine-learning algorithms and optimization techniques. These tools aim to forecast and scrutinize pavement deformation, with the goal of refining pavement design and maintenance approaches, as well as obtaining a more comprehensive comprehension of the factors that impact pavement effectiveness. This paper shows that heavy vehicles contribute significantly more to road erosion, and the retention and braking of vehicles greatly impact roadways. We also emphasize the statistical errors computed on the actual data range and demonstrate the results of the multilayer perceptron (MLP) model. The MLP model used the lath erosion standard to simulate future impact. Even though the model given is based on a small sample of data from one intersection, its estimates for road erosion in a year were found to be accurate when contrasted to real data. Controlling traffic flow can significantly improve road conditions, reducing erosion decay by reducing the time spent at intersections and other parameters. We conclude that machine learning can help control traffic flow, which can significantly improve road conditions, reducing vehicle time stretches at intersections.

Boundary behavior of a given important function or its limit values are essential in the whole spectrum of mathematics and science. We consider some tractable cases of limit values in which either a difference of two ingredients or a difference equation is used coupled with the relevant functional equations to give rise to unexpected results. This involves the expression for the Laurent coefficients including the residue, the Kronecker limit formulas and higher order coefficients as well as the difference formed to cancel the inaccessible part, typically the Clausen functions. We also state Abelian results which yield asymptotic formulas for weighted summatory function from that for the original summatory function

Ziyuan-3 (ZY-3) satellite is the first civilian stereo mapping satellite in China and was designed to achieve the 1: 50000 scale mapping for land and ocean. Rigorous sensor model (RSM) is required to build the relationship between the three-dimensional (3D) object space and two-dimensional (2D) image space of ZY-3 satellite imagery. However, each satellite sensor has its own imaging system with different physical sensor models, which increase the difficulty of geometric integration of multi-source images with different sensor models. Therefore, it is critical to generate generic model， especially rational polynomial coefficients (RPCs) of optical imagery. Recently, relatively a few researches have been conducted on RPCs generation to ZY-3 satellite. This paper proposes an approach to evaluate the performance of RPCs generation from RSM of ZY-3 imagery. Three scenarios experiments with different terrain features (such as ocean, city and grassland) are designed and conducted to comprehensively evaluate the replacement accuracies of this approach and analyze the RPCs fitting error. All the experimental results demonstrate that the proposed method achieved the encouraging accuracy of better than 1.946E-04 pixel in both x-axis direction and y-axis direction, and it indicates that the RPCs is suitable for ZY-3 imagery and can be used as a replacement for the RSM of ZY-3 imagery.

The ordered Ca3TaGa3Si2O14 and disordered La3Ga5SiO14 crystals of the lantangallium silicate family were grown by the Czochralski method. The independent coefficients of thermal expansion of crystals αc and αa were determined by X-ray powder diffraction based on the analysis of X-ray diffraction spectra measured in the temperature range of 25÷1000°C. It is shown that in the temperature range of 25÷800°C the thermal expansion coefficients are linear. At temperatures above 800°C there is a nonlinear character of the thermal expansion coefficients associated with a decrease in the Ga content in the crystal lattice of the lantangallium silicate family crystals.

Rice varieties such as Mahsuri Mutan and Basmati 370 are categorized as specialty rice with kernel elongation ratio exceeding 1.6 and 2.0, respectively. Ageing treatment in rice could affect the physical and chemical properties of rice such as grain size and shape, quality and taste of the cooked rice. The main objective of this study was to determine the effects of ageing treatment on the physicochemical properties of Mahsuri Mutan, Basmati 370 and MR219 rice varieties. The three rice varieties were subjected to heat treatment at 90ºC using the oven for 3 hours. After the heat treatment, the samples were cooled at room temperature (25ºC) for 1 hour. Physicochemical properties such as alkali digestion value, water uptake ratio (WUR), solids in cooking water (SCW), high kernel elongation (HKE) ratio and amylose contents were determined. Data collected on physicochemical traits and ageing vs non-ageing treatments were subjected to analysis of variance (ANOVA) using SAS software version 9.4. Phenotypic correlation coefficient indicated that there was a high positive correlation between HKE and water uptake ratio. The ageing treatment also showed significant difference in all the physicochemical traits of the varieties studied. Observation under electron microscope showed that the ageing samples had more cracks on the tissue structure compared to normal rice samples. The hexagon structure in Mahsuri Mutan gave more elongation effect on its kernel. The findings from this study could be useful to breeders in selection and development of new high kernel elongation rice variety.

The conceptual and theoretical backbones of symmetry/asymmetry detections or similarity/dissimilarity, and identity/unidentity study are automorphism or isomorphism respectively. However, the development of equations and methods for symmetry/asymmetry detections, similarity/dissimilarity, and identity/unidentity measures deviates from these backbones. In this article, an equation was proposed for symmetry/asymmetry detections, similarity/dissimilarity, and identity/unidentity measures, and proved that its isoreflective pairs-points are functionally bijective and inverse. The proposal, called Kabirian-based optinalysis, is based on the conceptual and theoretical frameworks of automorphism and isomorphism. The Kabirian-based optinalysis is also proven and characterized as invariant (robust) under translation (i.e., scaling and location shift), and rotation or reflection. Computing codes were written in python language for Kabirian-based optinalysis to serve as working codes for application and verification.

The World Health Organization(WHO) in 2016 considered mHealth as: “the use of mobile wireless technologies including smart devices such as smartphones and smartwatches for public health” as an important resource for health services delivery and public health given their ease of use, broad reach and acceptance. WHO emphasizes the potential of this technology to increase access to health information, services and skills as well as promoting positive changes in health behaviors and management of diseases. In this regard, the capability of smartphones and smartwatches for m-health monitoring as well as verification of the patient the signal has become an important component of mHealth system. Most of the smartwatches could extract more than one bioelectrical signal therefore, therefore they provide suitable platform for extracting health data for e-monitoring. The existing approaches have not considered the integrity of data obtained from these smart devices. Therefore, it is important that the integrity of the collected data be verified continuously through user authentication. This could be done using any of the bioelectrical signals extracted and transmitted for e-monitoring. In this article, a smartwatch is used for extracting bioelectrical signal before decomposing the signal into sub-bands of Detail and Approximation Coefficient for user authentication. To select suitable features using biorthogonal wavelet decomposition of signal from a non-intrusive extraction, a detailed experiment is conducted extracting suitable statistical features from the bioelectrical signal from 30 subjects using different biorthogonal wavelet family. Ten features are extracted using Biorthogonal wavelet to decompose the signal into three levels of sub-band Detail and Approximation Coefficient and features extracted from each level the decomposed Detail and Approximation Coefficients. Comparison analysis is done after the classification of the extracted features based on the Equal Error Rate (EER). Using Neural Network (NN) classifier, Biorthogonal Wavelet Detail Coefficient Sub-band level 3 of bior1.1 achieved the best result of EER 13.80% with the fusion of the best sub-band three levels of bior1.1 achieving a better result of 12.42% EER.

Exercising surds to represent figures is a common practice in scientific and Engineering fields, especially in scripts where calculators are banned or unapproachable. Peter Chew Theorem make result becomes simple when dealing with converting Quadratic Surds. The substance of the Peter Chew Theorem lies in enabling the forthcoming generation to simple break problems related to Quadratic Surds more effectively, easing a direct comparison with contemporary results. By employing the Peter Chew Theorem, one can streamline the tutoring and literacy of math, particularly concerning second- order direct equations with constant portions. This theorem's objective aligns with Albert Einstein's famed quotation Everything should be made as simple as possible, but not simpler.

Tomato is exposure to diverse abiotic stresses. Cold stress is one of harsh environmental stresses and abnormal low temperature affects tomato growth and development including physio- logical disorders, flower drops, and abnormal fruit morphology, causing the decrease of tomato yield and a fruit quality. It is important to identify low temperature-(LT) tolerant tomato (Solanum lycopersicum L.) cultivars relying on different fruit types. This study focused on analyzing physiological traits of 35 tomato accessions with three different fruit types (cherry, medium, and large sizes) under night temperature set-points of 15°C for normal temperature (NT) and 10°C for LT, respectively. Plant heights (PH) of most tomato accessions in LT were remarkably decreased compared to those in NT. The growth of leaf length (LL) and leaf width (LW) was reduced depending on the genotypes under LT. In addition, the number of fruits (NFR), fruit set (FS), fruit yield (FY), and marketable yield (MY) were negatively affected in LT. The variation was further investigated by the correlation analysis, the principal component (PCA), and the cluster analysis. Interestingly, positive correlations between different vegetative and reproductive traits were uncovered. Multivariate analysis including the PCA and hierarchical clustering classified LT-treated 35 tomato accessions into four major groups. The identified accessions were associated with vegetative and reproductive parameters on positive directions and might be utilized for breeding programs on selecting LT-tolerant cultivars.

In this paper, we mainly show that generalized hyperharmonic number sums with reciprocal binomial coefficients can be expressed in terms of classical (alternating) Euler sums, zeta values and generalized (alternating) harmonic numbers.

The only cases where exact distributions of estimates are known is for samples from exponential families, and then only for special functions of the parameters. So statistical inference was traditionally based on the asymptotic normality of estimates. To improve on this we need the {\it Edgeworth expansion} for the distribution of the standardized estimate. This is an expansion in $n^{-1/2}$ about the normal distribution, where $n$ is typically the sample size. The 1st few terms of this expansion were originally given for the special case of a sample mean. In earlier work we derived it for {\it any } standard estimate, hugely expanding its application. We call an estimate $\hat{w}$ of an unknown vector $w\in R^p$, a {\it standard estimate}, if $E\ \hat{w}\rightarrow w$ as $n\rightarrow \infty$, and for $r\geq 1$ the $r$th order cumulants of $\hat{w}$ have magnitude $n^{1-r}$ and can be expanded in $n^{-1}.$ Here we give another huge extension. We give the expansion of the distribution of {\it any smooth function} of $\hat{w}$, say $t(\hat{w})\in R^q,$ giving its distribution to $n^{-5/2}$. We do this by showing that $t(\hat{w})$, is a standard estimate of $t(w)$. This provides far more accurate approximations for the distribution of $t(\hat{w})$ than its asymptotic normality. %NOT USED: The building blocks of the Edgeworth expansions are the {\it cumulant coefficients } of the estimate. These cumulant coefficients are also needed for bias reduction, Bayes estimates and confidence regions. We give {\it chain rules} for the cumulant coefficients of $t(\hat{w})$ in terms of those of $\hat{w}$ and the derivatives of $t(w)$, up to those needed for 5th order Edgeworth expansions for $t(\hat{w})$ and its {\it tilted expansion}, useful for the tail of the distribution.

This paper propose an original approach of achieving a Cymatics based visual perception of isolated speech commands. The idea is to smartly combine the effective speech processing and analysis methods with the phenomena of Cymatics. In this context, an effective approach for automatic isolated speech based message recognition is proposed. The incoming speech segment is enhanced by applying the appropriate pre-emphasis filtering, noise thresholding and zero alignment operations. The Mel-Frequency Cepstral coefficients (MFCCs), Delta coefficients and Delta-Delta coefficients are extracted from the enhanced speech segment. Later on, the Dynamic Time Warping (DTW) technique is employed to compare these extracted features with the reference templates. The comparison outcomes are used to make the classification decision. The classification decision is transformed into a methodical excitation. Finally, this excitation is converted into the systematic visual perceptions via the phenomenon of Cymatics. The system functionality is tested with an experimental setup and results are presented. The approach is novel and can be employed in various applications like visual art, encryption, education, archeology, architecture, integration of impaired people, etc.

The occurrence rate of occupational accidents caused by slipping and falling is 50% worldwide. Determining the slip safety risk is necessary to minimize the accidents caused by slipping in pedestrian walking areas. By on-site testing, this study aims to determine the slip risks of floor coverings used in walking areas with many pedestrians in public service buildings (PSB). For this purpose, on-site measurements were performed in two environments and six locations in PSB using portable GMG 200 and pendulum testers operating according to DIN 51131 and TS EN 14231 standards. These tests were performed on four-floor coverings with polished surface treatment in PSB. Since the floor coverings measured have a polished surface, it can be seen that the dynamic friction coefficients (DCOF) values are very low, and the slip risks are high. By statistically analyzing the slip test data using the K-means method, a new safety classification was made according to the usage areas of floor coverings. To minimize the risk of slip safety, especially for students, patients, and employees in PSB, it is recommended to use floor coverings with high DCOF values and low slip risk.

Intraband energy transitions of an electron in GaAs/AlGaAs hexagonal quantum well wires in the presence of external electric and magnetic fields are presented. We consider the effects of the revolve of the quantum well wires via a geometric factor that converts the quantum wires straight and symmetric with respect to the z−axis, into a curved wires that no longer has this symmetry. In addition, the influence of having a shallow donor impurity on (off) is calculated. The shape of this quantum string corresponds to the core/shell structure. The energy levels and wave functions of the electron in the heterostructure with a finite potential between the shells are calculated using the effective mass approximation and the finite element method. The calculations of the optical properties are obtained from the compact density matrix and an iterative method. The direction of the applied external fields is parallel (anti-parallel) to the z−direction. The results reveal a significant dependence of the physical properties calculated with the deformation parameter, the dimensions of the quantum well wires and the presence or not of the impurity. The electronic transitions are in a range between 4.90 meV to 41.50 meV under the effect of the electric field, this corresponds to a range of frequencies of optical responses between 1.20 to 10 THz, that is, the mid-infrared. For the magnetic field the range is between 1.24 meV to 14 meV, that is, in frequencies from 0.36 to 3.38 THz, that is, in the far-infrared.

Based on the Generalized bracket, or Beris-Edwards, formalism of non-equilibrium thermodynamics, we have recently proposed [Stephanou et al. Materials, 13, 2867 (2020)] a new differential constitutive model for the rheology of entangled polymer melts and solutions. It has amended the shortcomings of a previous model that was too strict in the values of the convective constraint release parameter for the model not to violate the second law of thermodynamics and has been shown capable of predicting a transient stress undershoot (following the overshoot) at high shear rates. In this work, we wish to further examine this model’s capability of predicting the rheological response of industrial polymer systems by extending it to its multiple-mode version. The comparison against industrial rheological data (High-Density Polyethylene resins), as compared against available experimental data in (a) Small Amplitude Oscillatory shear, (b) start-up shear, and (c) start-up uniaxial elongation, is noted to be good.

In this paper, precise examination of multi-port antennas with large mutual coupling between the ports is studied. For this purpose, some vital parameters such as active reflection coefficients and realised gain are emphasized. The main motivation of this research is the ignorance of this issue in several recently published papers. Hence, corrections and criticisms to some recently reported results are presented. At first, a microstrip patch consisting of two inverted U-slots is re-examined, which has been proposed in a recently published paper for wideband applications. However, the authors did not present satisfactory results to indicate the performance of the proposed structure. In reverse, some important parameters such as the antenna gain appear to be incorrectly reported. In this paper, the characteristics of the antenna are compared with a simple 50 Ω microstrip line excited by two probes, indicating no significant differences. In the remainder of this paper, some corrections are provided on two examples of wide-beam circularly polarised multi-fed antennas for satellite applications. The first example is the multi-fed spiral antennas with folded arms, which have been proposed as the widebeam antennas at 435 MHz. It is indicated that the antenna height should be increased for better performance. The second example is the quadrifilar square helical antennas with folded arms, which have been proposed as the widebeam antennas for 435 MHz with minor responses at 145 MHz. Some corrections are presented on the previously reported minor responses at 145 MHz.

A formulation of nonequilibrium thermo field dynamics has been performed using the nonequilibrium statistical operator method by D.N. Zubarev. Generalized transfer equations for a consistent description of kinetics and hydrodynamics of the dense quantum-field system with strongly coupled states are derived.

Classification of electromyographic signals has a wide range of applications, from clinical diagnosis of different muscular diseases to biomedical engineering, where their use as input control of prosthetic devices has become a hot topic of research. Challenge of classifying this signals relies on the accuracy of the proposed algorithm and the possibility of its implementation on hardware. This paper consider the problem of electromyography signal classification, solved with the proposed signal processing and feature extraction stages, with focus lying on the signal model and time domain characteristics for better classification accuracy. The proposal considers a simple preprocessing technique that produces signals suitable for feature extraction, and the Burg reflection coefficients to form learning and classification patterns. These coefficients yield a competitive classification rate compared to used time domain features. Sometimes, the feature extraction from electromyographic signals showed that procedure can omit less useful traits for machine learning models. Using feature selection algorithms provides a higher classification performance with as fewer traits as possible. Algorithms achieved a high classification rate up to 100% with low pattern dimensionality, with other kinds of uncorrelated attributes for hand movement identification.

In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence A287326 in OEIS. The main property of A287326 that it returns a perfect cube n as sum of n-th row terms over k; 0 ≤ k ≤ n−1 or 1 ≤ k ≤ n, by means of its symmetry. In this paper we have derived a similar triangles in order to receive powers m = 5; 7 as row items sum and generalized obtained results in order to receive every odd-powered monomial n^2m+1; m ≥ 0 as sum of row terms of corresponding triangle. In other words, in this manuscript are found and discussed the polynomials D_m(n,k) and U_m(n,k), such that, when being summed up over k in some range with respect to m and n returns the monomial n^2m+1.

In this article, the usual factorials and binomial coefficients have been generalized and extended to the negative integers. Basing on this generalization and extension, a new kind of polynomials has been proposed, which led directly to the non-classical hypergeometric orthogonal polynomials and the non-classical second-order hypergeometric linear DEs. The resulting polynomials can be used in non-relativistic and relativistic QM, particularly, in the case of the Schrödinger equation, and Dirac equations for an electron in a Coulomb potential field.

Recent astronomical observations with respect to measurements in distant supernovas, cosmic microwave background and weak gravitational lensing confirm that the Universe is undergoing a phase of accelerated expansion and it has been proposed that this cosmological behavior is caused by a hypothetical dark energy which has a strong negative pressure that allows explain the expanding universe. Several theoretical ideas and models related dark the energy includes the cosmological constant, quintessence, Chaplygin gas, braneworld and tachyonic scalar fields. In this paper, we have obtained new relativistic stellar configurations considering an anisotropic fluid distribution with a charge distribution which could represents a potential model of a dark energy star. In order to investigate the effect of a quadratic equation of state in this anisotropic model we specify particular forms for the gravitational potential that allow solving the Einstein-Maxwell field equations. For these new solutions we checked that the radial pressure, metric coefficients, energy density, anisotropy factor, charge density , mass function are well defined and are regular in the interior of the star. The solutions found can be used in the development of dark energy stars models satisfying all physical acceptability conditions but the causality condition and strong energy condition are violated. We expect that these models have multiple applications in astrophysics and cosmology.

In this study, deep neural network (DNN) and transfer learning (TL) techniques were employed to predict the viscous resistance and wake distribution based on the positions of flow control fins (FCFs) applied to containerships of various sizes. Both methods utilized data collected through Computational Fluid Dynamics (CFD) analysis. The position of the flow control fin (FCF) and hull-form information were utilized as input data, and the output data included viscous resistance coefficients and components of propeller axial velocity. The base DNN model was trained and validated using a source dataset from a 1000 TEU containership. Grid search cross-validation technique was employed to optimize the hyperparameters of the base DNN model. Then, transfer learning was applied to predict the viscous resistance and wake distribution for containerships of varying sizes. To enhance the accuracy of feature prediction with a limited amount of dataset, learning rate optimization was conducted. Transfer learning involves retraining and reconfiguring the base DNN model, and the accuracy was verified based on the fine-tuning method of the learning model. The results of this study can provide hull designers for containerships with performance evaluation information by predicting wake distribution, without relying on CFD analysis.

Dynamic variables in the non-equilibrium systems of life are determined by catalytic activities. These relate to the expression of the genome. The extent to which such a variable depends on the catalytic activity defined by a gene has become more and more important in view of the possibilities to modulate gene expression or intervene with enzyme function through the use of medicinal drugs. With all the complexity of cellular systems biology, there are still some very simple principles that guide the control of variables such as fluxes, concentrations, and half-times. Using time-unit invariance we here derive a multitude of laws governing the sums of the control coefficients that quantify the control of multiple variables by all the catalytic activities. We show that the sum of the control coefficients of any dynamic variable over all catalytic activities is determined by the control of the same property by time. When the variable is at a maximum, minimum or steady, this limits the sums to simple integers like 0, -1, 1, and -2, depending on the variable under consideration. Some of the implications for biological control are discussed as is the dependence of these results on the precise definition of control.

In this work we looked for a stable and accurate procedure to perform feature selection in datasets with a much higher number of predictors than individuals, as in Genome-Wide Association Studies. Due to the instability in feature selection when many potential predictors are measured, a variable selection procedure is proposed that combines several replications of shrinkage regression models. A weighted formulation is used to define the final predictors. The procedure is applied to investigate Single Nucleotide Polymorphisms (SNPs) predictors associated to Alzheimer’s disease in the Alzheimer’s disease Neuroimaging Initiative (ADNI) dataset. Two data scenarios are investigated: one considering only the set of SNPs and another with the covariates age, sex, educational level and APOE4 genotype. The SNP rs2075650 and the APOE4 genotype are given as risk factors for AD, which is in line with the literature, and other four new SNPs are pointed, opening new hypotheses for in vivo analyses. These experiments demonstrate the potential of the new method for stable feature selection.

We report recent enhancements of the online atomic database at the Ohio State University, NORAD-Atomic-Data, that provides various parameters for radiative and collisional atomic processes dominant in astrophysical plasma. NORAD stands for Nahar Osu RADiative. The database belongs to the data sources, especially for the latest works, of the international collaborations of the Opacity Project and the Iron Project. The contents of the database are calculated values for energies, oscillator strengths, radiative decay rates, lifetimes, cross sections for photoionization, electron-ion recombination cross sections and recombination rate coefficients. We have recently expanded NORAD-Atomic-Data with several enhancements over those reported earlier. They are as follows. i) We continue to add energy levels, transition parameters, cross sections for atoms and ions with their publications. ii) Recently added radiative atomic data contains significant amount of transition data for photo-absorption spectral features corresponding to x-ray resonance fluorescence effect, prominent wavelength regions of bio-signature elements, such as phosphorus ions, and emission bumps of heavy elements, such as of lanthanides, that may be created in a kilonova event. We are including iii) collisional data for electron-impact-excitation, iv) experimental data for energies and oscillator strengths for line formation, v) experimental cross sections for photoionization that can be applied for benchmarking and other applications, and vi) introduction of a web-based interactive feature to calculate spectral line ratios at various plasma temperature and density diagnostics, starting with our recently published data for P II. We presented summary description of theoretical backgrounds for the computed data in the earlier paper. With introduction of experimental results, we present summary description of measurement of high resolution photoionization cross sections at Advanced Light Source of LBNL synchrotron set-up and briefly discuss other set-ups. These additions should make NORAD-Atomic-Data more versatile for various applications. For brevity, we provide information on the extensions and avoid repetition of data description of the original paper.