Order Polynomial Research Articles

Rheological effects in peristaltic flow of Prandtl fluid through elliptical duct: A comprehensive analysis

AbstractThis research venture comprehends a theoretical examination of non‐Newtonian fluid flowing peristaltic via an elliptical channel. Furthermore, the Prandtl fluid method for this elliptic duct problem is thoroughly considered. This mathematical inquiry adopts a non‐Newtonian Prandtl fluid model. A polynomial methodology is used to analyze partial differential equations that appear in nondimensional form and deliver an exact analytical solution for the temperature and velocity profile. This study is the first to utilize a novel order polynomial of degree eight having eleven constants to precisely solve the temperature equation for Prandtl fluid flow via an elliptic domain. A comprehensive graphical analysis is also provided to understand the mathematical conclusions fully. The graphs of the velocity profiles clearly show that the non‐Newtonian effects are more potent along the minor axis of the elliptical duct. The streamlined graphs accentuating the trapping phenomenon show specific closed contours close to the boundary wall of the peristaltic duct.

Optimization Strategy for Process Design in Rubber Injection Molding: A Simulation-Based Approach Allowing for the Prediction of Mechanical Properties of Vulcanizates.

Selecting the optimal settings for the production of rubber goods can be a very time-consuming and resource-intensive process. A promising method for optimizing rubber processing in a short period of time is the use of simulation routines. However, process simulations have only recently enabled meaningful predictions of not only the part's state of cure but also its mechanical characteristics. As a first approach, second-order polynomials were considered suitable for describing the properties of compression-molded parts. However, more precision is required for injection molding due to the narrower distribution of mechanical characteristics of parts produced at different vulcanization temperatures. This became evident when the approximation of mechanical data with second order models partly revealed significant failures of part behavior prediction. To tackle this issue, a combined approach for approximation is proposed in this contribution by means of logistic growth function in addition to second order polynomials. To feed the model, an experimental plan was designed for producing injection-molded parts from an SBR compound at various temperatures and to different degrees of cure. The parts obtained were then characterized mechanically, and the results were opposed to varying degrees of cure and extents of reaction to calculate the model coefficients. Once available, a simulation-based calculation of the mechanical part quality is possible. The comparison of test results from the simulation and the real process has shown a reliable prediction, as simulation results were found within the natural deviation of the real measurements.

Estimates of Genetic Parameters, Growth Curve, and Environmental Effects for Nellore Cattle in the Pantanal.

The objective was to estimate the growth curves and genetic parameters using random regression methodology for Nellore cattle raised in Pantanal, MS, Brazil (6974 calves; n = 53,233 weights), with at least four weighings per individual. The model considered direct and maternal genetic additives and maternal permanent environmental effects at random. Orthogonal Legendre polynomials of cubic order were used to fit the growth curve. Analyses of variance were performed using the GLM procedure. The model used contained the fixed effects of sex, year of birth, farm, and the covariates calf birth month (linear and quadratic) and cow age at calving (linear and quadratic). The adjusted mean weight at 120 days of age was 93.43 ± 19.78 kg, and for 205 days of age, it was 180.42 ± 26.58 kg. Animals born in the dry season had a higher average weight [kg] (219.57 vs. 211.78, 3.7% higher) and, consequently, had higher weights at 646 days of age. Estimates of direct heritabilities (h2a) ranged from 0.35 to 0.75 (high magnitudes), and maternal heritabilities (h2m) along the trajectory of low magnitudes ranged from 0.03 to 0.08, respectively. The use of random regression to evaluate beef animals allows for adjusting the growth curve and selecting the best animals to be the parents of future generations.

A2GCN: Graph Convolutional Networks with Adaptive Frequency and Arbitrary Order

Graph Neural Networks (GNNs) gain remarkable success in various graph learning tasks under homophily graph assumption. This assumption is extremely fragile since real-world graphs with heterophily are ubiquitous. Under this circumstance, existing GNNs attempt to design or learn graph spectral filters for observed graphs. The representation ability of them, however, is limited due to: (1) Constant frequency response is incapable of simulating complicated filters that real-world applications require. (2) Fixed polynomial order fails to effectively uncover the node label patterns concealing different order neighborhoods. To this end, we propose a novel Graph Convolutional Networks with Adaptive Frequency and Arbitrary Order (A2GCN) to learn various graph spectral filters suitable for distinct networks. Specifically, a simple but elegant filter with adaptive frequency response is designed to span across multiple layers for capturing different frequency components hiding in varying orders, producing A2GCN filter bases. Afterward, the coefficients of the A2GCN basis for each node are learned to achieve A2GCN filters with arbitrary polynomial order. The resulting A2GCN filters possess flexible frequency response that can automatically adapt to the node label pattern, as such, it empowers A2GCN with stronger expressiveness and naturally alleviates the over-smoothing problem. Theoretical analysis is provided to show the superiority of the proposed A2GCN. Additionally, extensive experiments on both node-level and graph-level tasks validate that the proposed A2GCN accomplishes highly competitive performance and improves classification accuracy. Codes are available at https://github.com/AIG22/A2GCN.

Field validation of NDVI to identify crop phenological signatures

Purpose and MethodsCrop identification using remotely sensed imagery provides useful information to make management decisions about land use and crop health. This research used phonecams to acquire the Normalized Difference Vegetation Index (NDVI) of various crops for three crop seasons. NDVI time series from Sentinel (L121-L192) images was also acquired using Google Earth Engine (GEE) for the same period. The resolution of satellite data is low therefore gap filling and smoothening filters were applied to the time series data. The comparison of data from satellite images and phenocam provides useful insight into crop phenology. The results show that NDVI is generally underestimated when compared to phenocam data. The Savitzky-Golay (SG) and some other gap filling and smoothening methods are applied to NDVI time series based on satellite images. The smoothened NDVI curves are statistically compared with daily NDVI series based on phenocam images as a reference.ResultsThe SG method has performed better than other methods like moving average. Furthermore, polynomial order has been found to be the most sensitive parameter in applying SG filter in GEE. Sentinel (L121-L192) image was used to identify wheat during the year 2022–2023 in Sargodha district where experimental fields were located. The Random Forest Machine Leaning algorithm was used in GEE as a classifier.ConclusionThe classification accuracy has been found 97% using this algorithm which suggests its usefulness in applying to other areas with similar agro-climatic characteristics.

Prediction of building settlement amount based on the ARIMA-LSTM-GXBoost combined model

Accurate prediction of building settlement amounts is crucial for ensuring the safety of building structures and human lives. Addressing issues such as the scarcity of building settlement measurement data and the lack of weighting in combined prediction model results, which have not yet led to further improvements in prediction accuracy, this study first selected building CJ06 in Yizheng City, Yangzhou, as the research subject. Polynomial fitting was applied to the obtained non-equidistant time series data, and the fitting data with a preferable polynomial order was chosen to replace the original numerical data. Then, using the first 140 days of data as the training set and the subsequent 63 days of data as the test set, an ARIMA (AutoRegressive Integrated Moving Average) model was initially established for the building settlement, to address the linear features in the fitted sequence. This was followed by using LSTM (Long Short-Term Memory) to correct the ARIMA model's prediction residuals, and combining the results with the XGBoost (Extreme Gradient Boosting) prediction model. Weights were determined using the reciprocal error method for combined prediction, and the results of the combined prediction model were compared with those of the ARIMA-LSTM, ARIMA, LSTM, and GXBoost models. The comparison periods were chosen as follows: 143d, 158d, 173d, 188d, and 203d; ultimately, the maximum absolute relative error and mean square error (MSE) were used as the evaluation metrics for model prediction accuracy. The results showed that the ARIMA-LSTM-GXBoost prediction model's results were more closely aligned with actual values, with a maximum absolute relative error and mean square error of 1.68% and 0.03, respectively. The prediction accuracy was higher than the other four comparison models, achieving high-precision prediction of building settlement amounts.

Probabilistic Degenerate Fubini Polynomials Associated with Random Variables

Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and the degenerate Fubini polynomials of order r, namely the probabilisitc degenerate Fubini polynomials associated with Y and the probabilistic degenerate Fubini polynomials of order r associated with Y. We derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials. As special cases of Y, we treat the gamma random variable with parameters α,β>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha ,\\beta > 0$$\\end{document}, the Poisson random variable with parameter α>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha > 0$$\\end{document}, and the Bernoulli random variable with probability of success p.

An Optimized Strain-Compensated Arrhenius Constitutive Model of GH4169 Superalloy Based on Hot Compression.

A precise constitutive model is essential for capturing the deformation characteristics of the GH4169 superalloy in numerical simulations of thermal plastic forming processes. Hence, the aim of this study was to develop a precise modified constitutive model to describe the hot deformation behavior exhibited by the GH4169 superalloy. The isothermal cylindrical uniaxial compression tests of the GH4169 superalloy were carried out at temperatures of 950~1100 °C and strain rates of 0.01~10 s-1 using a Thermecmastor-200KN thermal-mechanical simulator. The original strain-stress curves were corrected by minimizing the effects of plastic heat and interfacial friction. Based on the true stress-strain curves, the original strain-compensated Arrhenius constitutive model was constructed using polynomial orders of 3, 5, and 10, respectively. The results showed that once the polynomial order exceeds the 5th, further increasing the order has little contribution to the accuracy of the model. To improve prediction ability, a higher precision Arrhenius constitutive model was established by extending a series of material parameters as functions that depend on temperature, strain, and strain rate, in which the error can be reduced from 4.767% to 0.901% compared with the classic strain-compensated Arrhenius constitutive model.

Third Order Polynomial Bundle Adjustment For Optical Calibration Refinement

We propose a refinement and validity region expansion process of a 3rd order polynomial calibration based on bundle adjustment. The present methodology can be expanded to any model as long as the mapping is a smooth function. Both methods are tested with a tomographic Particle Tracking Velocimetry measurement whose results are compared in terms of the smoothness and length of the retrieved tracks. The refinement method shows a significant improvement in both the associated PDFs. Similarly, the expansion shows a corresponding behaviour to the original calibration even though a higher degree of smoothness of the tracks is achieved.

Hilbert's tenth problem for lacunary entire functions of finite order

AbstractIn the context of Hilbert's tenth problem, an outstanding open case is that of complex entire functions in one variable. A negative solution is known for polynomials (by Denef) and for exponential polynomials of finite order (by Chompitaki, Garcia‐Fritz, Pasten, Pheidas, and Vidaux), but no other case is known for rings of complex entire functions in one variable. We prove a negative solution to the analogue of Hilbert's tenth problem for rings of complex entire functions of finite order having lacunary power series expansion at the origin.

The impact of diffusion tensor imaging tractography settings on muscle fascicle architecture and diffusion parameter estimates: Tract length, completion, and curvature are most sensitive to tractography settings.

Diffusion-tensor (DT)-MRI tractography provides information about properties relevant to muscle health and function, including estimates of architectural properties such as fascicle length, pennation angle, and curvature and diffusion properties such as mean diffusivity (MD) and fractional anisotropy (FA). Tractography settings, including integration algorithms, thresholds for early tract termination, and tract smoothing approaches, impact the accuracy of the muscle property estimates. However, muscle DT-MRI tractography is performed using a variety of these settings, complicating comparisons between different studies. The effects of different tractography settings on muscle architecture estimates have not been fully explored, and optimized settings for muscle tractography have not yet been determined. We examined the influence of integration algorithm and termination check settings combined with a range of step sizes, termination criteria, and smoothing polynomial orders on tract characteristics, completion/reason for termination, and goodness of fit between fiber tracts and smoothing polynomials using 3-T DT-MR images of the lower leg muscles of seven healthy adults. We found that tract length and completion were highly sensitive to strict FA and intersegment angle thresholds (25%-69% reduction in complete fiber tracts from lowest to highest minimum FA threshold and 11%-36% reduction from highest to lowest intersegment angle threshold). Higher order polynomials (third and fourth order vs. second order) better fit the muscle fiber trajectories, but curvature estimates were highly sensitive to smoothing polynomial order (3.9-6.6 m-1 increase for second- vs. fourth-order fitting polynomials). Step size impacted curvature estimates, albeit to a lesser degree. Integration algorithm had little impact, and mean pennation angle, and tract-based FA and MD, were relatively insensitive to all parameters. The results demonstrate which muscle diffusion measures and architectural estimates are most sensitive to varying tractography settings and support the need for consistent reporting of tractography details to aid interpretation and comparison of results between studies.

NfL concentration in CSF is a quantitative marker of the rate of neurodegeneration in aging and Huntington's disease: a semi-mechanistic model-based analysis.

The concentrations of neurofilament light chain (NfL) in cerebrospinal fluid (CSF) and plasma have become key biomarkers of many neurodegenerative diseases, including Huntington's Disease (HD). However, the relationship between the dynamics of NfL concentrations in CSF and the time-course of neurodegeneration (whole brain atrophy) has not yet been described in a quantitative and mechanistic manner. Here, we present a novel semi-mechanistic model, which postulates that the amount of NfL entering the CSF corresponds to the amount of NfL released from damaged neurons, whose degeneration results in a decrease in brain volume. In mathematical terms, the model expresses the NfL concentration in CSF in terms of the NfL concentration in brain tissue, the rate of change of whole brain volume and the CSF flow rate. To test our model, we used a non-linear mixed effects approach to analyze NfL and brain volume data from the HD-CSF study, a 24-month prospective study of individuals with premanifest HD, manifest HD and healthy controls. The time-course of whole brain volume, obtained from MRI, was represented empirically by a 2nd order polynomial, from which its rate of change was computed. CSF flow rates in healthy and HD populations were taken from recent literature data. By estimating the NfL concentration in brain tissue, the model successfully described the time-course of the NfL concentration in CSF in both HD subjects and healthy controls. Furthermore, the model-derived estimate of NfL concentration in brain agreed well with recent direct experimental measurements. The consistency of our model with the NfL and brain volume data suggests that the NfL concentration in CSF reflects the rate, rather than the extent, of neurodegeneration and that the increase in NfL concentration over time is a measure of the accelerating rate of neurodegeneration associated with aging and HD. For HD subjects, the degree of acceleration was found to increase markedly with the number of CAG repeats on their HTT gene. The application of our semi-mechanistic NfL model to other neurodegenerative diseases is discussed.

Improvement for modeling the damping of the wake oscillator based on the Van der Pol scheme

Given the importance of risers and umbilical cables in the exploitation of deep-sea resources, the vortex induced vibration (VIV) of long flexible cylinders has been systematically studied, and it is acknowledged that the wake oscillator is a satisfactory tool in practically predicting the VIV for offshore engineering applications. Based on the conventional wake oscillator with different damping term formulations, the present study systematically explores the influences of the coefficients and the maximum order of a polynomial damping term within the Van der Pol type wake oscillator. More specifically, the coefficients of the second-order polynomial are adjusted to vary inside a reasonable range, and the polynomial order is increased from the conventional specification of 2–4, 6, and 8. The vibrations of the flexible cylinder predicted by the revised wake oscillator are compared to the measurements taken from an experiment reported in the literature. The comparison indicates that increasing polynomial coefficients generally reduce VIV dominant mode numbers. In addition, increasing the polynomial order aligns the dominant mode more closely with experimental data, although this effect diminishes when the polynomial order exceeds 4. It is argued that the gradual change in phase differences along the cylinder induced by increasing either polynomial coefficient or maximum order could be the reason. The present study sheds light into the mechanism for the damping effect observed in hydrodynamic forces observed in VIVs and lays the foundation for suggesting an optimal formulation of the damping terms as 0.45q2+0.6q−0.3 compared to the conventional formulation of 0.3q2−0.3.

An exactly divergence-free hybridized discontinuous Galerkin method for the generalized Boussinesq equations with singular heat source

The purpose of this work is to propose and analyze a hybridized discontinuous Galerkin (HDG) method for the generalized Boussinesq equations with singular heat source. We use polynomials of order k, k − 1 and k to approximate the velocity, the pressure and the temperature. By introducing Lagrange multipliers for the pressure, the approximate velocity field obtained by the HDG method is shown to be exactly divergence-free and H(div)-conforming. Under a smallness assumption on the problem data and solutions, we prove by Brouwer’s fixed point theorem that the discrete system has a solution in two dimensions. If the viscosity and thermal conductivity are further assumed to be positive constants, a priori error estimates with convergence rate O(h) and efficient and reliable a posteriori error estimates are derived. Finally numerical examples illustrate the theoretical analysis and show the performance of the obtained a posteriori error estimator.

Examining across year genotype by environment interactions for production and reproduction traits in Merino sheep

Variation in feed resource availability within production systems can cause genotype by environment interactions that change the ranking of the best animals to select between environments. Mediterranean environments have high variation in pasture growth between years that could cause genetic by environment interactions for sheep production traits. Therefore, we estimated heritabilities for live weight, fleece weight, fibre diameter and number of lambs weaned in six years from 2000 to 2005 and correlations between years comparing multivariate analysis and random regression analysis. We compared 3 methods: 1 multivariate analysis estimating (co)variances for traits in each year, 2 Random regression estimated (co)variances for intercept and slope for traits as repeated measurements fitted against average pasture growth in each year and 3. Random regression fitted against corrected average performance of animals in each year. Random regression was estimated with an order of polynomial of one for additive genetic variance and zero for permanent environmental effects. This combination of polynomials was the best fit based on Bayesian information criterion. We estimated heritabilities for each year and correlations between years using records from 3299 pedigreed Merino ewes managed at Katanning in Western Australia. There were 4651 records for adult live weight, 6750 for adult clean fleece weight, 6965 for adult fibre diameter, and 7774 for number of lambs weaned across all 6 years. Number of lambs weaned had more genotype by environment interactions than other traits, with fibre diameter and fleece weight having genotype by environment interactions between only a few years. Based on Bayesian information criterion values, multivariate analysis fit the data better for live weight, fleece weight and fibre diameter. Additionally, random regression estimated higher genetic correlations between years than multivariate analysis suggesting there was not enough flexibility in the random regression analysis, which used only first order polynomials, to fit differences between years. Pasture growth across years did not explain differences in performance for traits across years. Therefore, for number of lambs weaned, random regression using corrected average performance was a better fit than average pasture growth. For other traits, more years or a better indicator of variation in performance within and between years are required to use random regression for genotype by environment interactions.

A block-spectral adaptive H-/p-refinement strategy for shock-dominated problems

An adaptive H-/p-refinement strategy using a novel sensor is devised and tested in a block-spectral compressible Euler code equipped with adaptive-mesh refinement (AMR) and high-order flux-reconstruction numerics. At each Gauss quadrature point (or solution point) within each spectral block (or mesh element) the discrete velocity jump ΔU = ∂U/∂y1Δy1+∂V/∂y2Δy2+∂W/∂y3Δy3 is calculated and normalized by the local speed of sound, a. The grid spacing, Δxi, is calculated in each direction as the distance between auxiliary Gauss-Lobatto points, staggered relative to the solution points. The polynomial order is increased from p=0 to p=pmax in regions of weak compression, (ΔU/a)crit<ΔU/a<0 and kept at p=pmax in regions of flow expansion ΔU/a≥0, while staying at the H=0 base mesh level. Regions experiencing strong compressions, i.e. ΔU/a<(ΔU/a)crit, are H-refined up to H=Hmax where Hmax is applied at the location of maximum compression, ΔU/a=min(ΔU/a) in the domain, while keeping p=0 to guarantee robustness and monotonicity of the solution in the H refined region. The critical value of (ΔU/a)crit= -0.06 is found to effectively separate smooth and non-smooth solution regions, supported by a 1D detonation initiation test case in ideal gas and a shock-to-detonation transition in high explosives. Using this value, the Sod shock tube, Shu-Osher problem, double Mach reflection and a 2D detonation in a high-explosive are simulated with the proposed adaptive H-/p-refinement. In the Sod shock tube case, p-refinement resolves the (weak) contact discontinuity while H-refinement enhances the grid resolution in the shock exploiting the monotonicity of the p=0 reconstruction. For the Shu-Osher problem, p-refinement captures the small-scale oscillations trailing the shock that would be otherwise attenuated, while H-refinement triggered by the ΔU-sensor appropriately tracks the shock. In the double Mach reflection problem, H-refinement confines the numerical diffusion around the reflected shock while p-refinement recaptures many physical features trailing the shock. Finally, in the 2D high-explosive detonation case, H-refinement follows the leading shock and resolves the curvature of the detonation wave, while p-refinement adds resolution to the trailing reaction zone. Finally, the proposed methodology is tested in a detonation-wave propagation test case in high-explosives with numerical predictions comparing favorably against experiments.

An advanced Polynomial Chaos Expansion method for sensitivity analysis of aero-engine fuel gear pumps

Global sensitivity analysis plays an important role in robustness optimization design of aero-engine fuel gear pumps to investigate how input parameters uncertainties contribute to performances uncertainties. In this paper, inspired by the Leave-One-Out method, an advanced Polynomial Chaos Expansion (PCE) method equipped with Adaptive design of both training Points and polynomial Order, denoted as APO-PCE, is proposed to efficiently estimate the variance-based sensitivity indices. A novel active learning strategy is developed for identifying the optimal candidate sample point to adaptively design training points and simultaneously update the polynomial order. Input parameters, including rotational speed, inlet pressure, outlet pressure, and gear tip clearance, are reasonably characterized as nine convenient sampling Gaussian variables by probabilistic modeling and Karhuben–Loève expansion. The results show that the proposed APO-PCE method is superior to the classical PCE method, and the uncertainties of rotational speed, inlet pressure, and outlet pressure are the main factors for the uncertainties of supply performances and flow field characteristics, while the gear tip clearance uncertainty only affects the flow loss at lower rotational speed.

Towards Wall-Resolved Large-Eddy Simulation of the High-Lift Common Research Model

In the present study, we performed a sixth-order wall-resolved large-eddy simulation (WRLES) of the high-lift Common Research Model (CRM-HL) on the Leadership Class Computing Cluster Summit. During the 4th High-Lift Prediction Workshop (HLPW-4), wall-modeled LES (WMLES) and hybrid Reynolds-averaged Navier–Stokes (RANS)/LES approaches showed promise in predicting the maximum lift and large flow separations near stall. In those simulations, however, laminar and transition regions were not resolved since the flow was assumed to be fully turbulent. If one wants to resolve these regions, the only viable approach is WRLES. The main purpose of the present study is to demonstrate the feasibility of WRLES for a complex real-world configuration at the wind tunnel Reynolds number. A high-order unstructured mesh LES solver called hpMusic was employed in the study. The simulation at solution polynomial order P=5 has more than 14 billion degrees of freedom per equation. Computational results are compared to experimental data in the form of surface oil flows and pressure coefficient profiles. We highlight lessons learned from attempting a grand-challenge type large-scale simulation: 1) such a simulation is feasible but very expensive, estimated to be at least three orders more expensive than WMLES, 2) oil flows produced with WRLES agree very well with experimental oil flows in fine detail, not observed in those produced with WMLES, and 3) flow visualization is a severe bottleneck, and parallel postprocessing capability is needed.

Multiplier-less Broadband and Linear Phase Digital Hilbert Transformers

The Hilbert transformation for generating the analytic signal or signal envelope is widely used in modern communication receivers, in radar and sonar systems. It introduces a 90∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$90^{\\circ }$$\\end{document} phase shift of the input signal. Since the impulse response of the ideal Hilbert transformer is non-causal, it must be approximated by an FIR or IIR filter. This paper shows results of novel algorithms for designing broadband digital IIR Hilbert transformers and its implementation. The designs employ Galerkin or collocation techniques. The transfer function of the Hilbert transformer is a rational polynomial of low order and exhibits approximately linear phase. The filters match the 90∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$90^{\\circ }$$\\end{document} phase shift requirement of Hilbert transformers almost perfectly and exhibit approximately constant group delay in the passband. The achieved image rejection ratio is typically larger than 50 dB. The quantization of the filter coefficients is realized by a Canonical Signed Digit (CSD) representation, reducing the hardware resources compared with two’s complement. The resulting filters are multiplier-less, which is crucial for high-speed signal processing and low power consumption. The design techniques and the CSD representation are realized in a MATLAB toolbox. The filters were moreover implemented in VHDL and SystemC. Additionally, a MATLAB tool for automatically generating a VHDL package containing the filter parameters has been implemented.

Efficacy of Okra Leaf [Abelmoschus esculentus L.] Extract for Removal of Egg Adhesiveness During Artificial Propagation of African Catfish [Clarias gariepinus, Burchel 1822

This study evaluated the most effective immersion duration and concentration of okra leaf extract for removing the adhesive properties of Clarias gariepinus eggs. For the breeding experiment, a male and a female C. gariepinus broodstock, weighing 1.3 kg and 1.4 kg respectively, were used. The okra leaf extract was tested at three different concentrations: 1%, 3%, and 5%. Tannic acid at a concentration of 0.75 g per liter of water served as the reference de-adhesion agent, while plain water (without tannic acid or plant extract) was used as the control. The fish eggs were rinsed with the solutions for one, three, and five minutes. Each concentration and rinsing time were recorded in triplicate. The generated data was subjected to an Analysis of Variance Test, followed by a third order polynomial regression analysis to determine the best concentration and immersion period for removing C. gariepinus egg adhesiveness. The results of the study showed that the use of okra leaf extract at 1% lowest concentration and 1 minute immersion period was not significantly different (p&gt;0.05) from the use of tannic acid solution. Therefore, this study found that okra leaf extract at 1% concentration with a one-minute immersion period can effectively remove egg adhesiveness and increase hatching in C. gariepinus.