A Comprehensive Study of Mass Accretion and Atmospheric Effect of Raindrop

The mass accretion of a raindrop in different layers of the atmosphere is not dealt with so far. A comprehensive brief study of the motion of raindrops through the atmosphere (i) without mass accretion, (ii) with mass accretion and (iii) finally pressure variation in the atmosphere with altitude using Bernoulli’s equation is illustrated. Acquirement of mass from moist air is mass accretion and mass accretion during the motion of raindrop through resistive medium holds an arbitrary power-law equation. Bernoulli’s equation when applied to it, the generalized first-order differential equation is reduced to a polynomial equation. Results show a single intersecting point of approximate terminal velocity 1 m/s and mass 10-06 mg as illustrated. Terminal velocity is achieved within 25 sec. There is the approximate exponential growth of terminal velocity. An increase in momentum is due to mass accretion during motion. Various conditions of no mass accretion and mass accretion show the same result while for atmospheric effect using Bernoulli’s equation the first-order differential equation reduces to a polynomial equation.

Combined Surfactant and Enzyme-Assisted Extraction of Pectin from Hawthorn (Crataegus monogyna Jacq.) Fruits

Introduction. Commercial pectin is usually obtained from apples or citrus fruits. However, some wild fruits, such as hawthorn, are also rich in pectin with valuable nutritional and medical properties. The research objective was to study and improve the process of combined surfactant and enzyme-assisted extraction of pectin from hawthorn fruits. Study objects and methods. The study involved a 1% solution of Polysorbate-20 surfactant and a mix of two enzymes, namely cellulase and xylanase, in a ratio of 4:1. The response surface methodology with the Box-Behnken experimental design improved the extraction parameters. The experiment featured three independent variables – temperature, time, and solvent-to-material ratio. They varied at three levels: 20, 40, and 60°C; 120, 180, and 240 min; 15, 30, and 45 mL per g. Their effect on the parameters on the pectin yield was assessed using a quadratic mathematical model based on a second order polynomial equation. Results and discussion. The response surface methodology made it possible to derive a second order polynomial regression equation that illustrated the effect of extraction parameters on the yield of polyphenols. The regression coefficient (R2 = 98.14%) and the lack-of-fit test (P > 0.05) showed a good accuracy of the model. The optimal extraction conditions were found as follows: temperature = 41°C, time = 160 min, solvent-to-material ratio = 32 mL per 1 g. Under the optimal conditions, the predicted pectin yield was 14.9%, while the experimental yield was 15.2 ± 0.4%. The content of galacturonic acid in the obtained pectin was 58.5%, while the degree of esterification was 51.5%. The hawthorn pectin demonstrated a good complex-building ability in relation to ions of copper (564 mg Cu2+/g), lead (254 mg Pb2+/g), and cobalt (120 mg Co2+/g). Conclusion. Combined surfactant and enzyme-assisted extraction made improved the extraction of pectin from hawthorn fruits. The hawthorn pectin can be used to develop new functional products.

Experimental Study on Phase Conjecture Based on Two-dimensional Image and Carrying Three-dimensional Image With Mist in Electro-holographic Reconstruction *

A method is proposed for phase conjecture based on the intensity curve of a two-dimensional(2D) image by computing a polynomial equation. The intensity values of the 2D image, which represents the distance between the image detectors and the three-dimensional(3D) scene is converted to phase information by our method. The results of numerical calculation with phase conjecture are analyzed. And what’s more, the numerical reconstruction results with phase information obtained as initial phase factors of a complex object for Fresnel kinoform and dynamic pseudorandom-phase tomographic computer holography(DPP-TCH) are compared. The peak signal-to-noise ratio(PSNR) and correlation coefficient (CC) between the reconstructed images and original object are analyzed. An experimental system is designed for photoelectric holographic reconstruction based on phase-only liquid crystal spatial light modulator(LC-SLM) and mist screen. The electro-optical experimental results indicate that suppressed the speckle noise 3D images that can be observed with naked eye have been obtained.

Exact solutions of sixth and fifth degree equations

The real problematic with algebraic polynomial equations is how to exactly solve any sixth and fifth degree polynomial equations. In this study, we give a new absolute method that presents a new decomposition to exactly solve a sixth degree polynomial equation, while the corresponding fifth degree equation can be easily transformed into a sixth degree equation of this kind (sixth degree equation solvable by this method), then the sextic equation (sixth degree equation) obtained will be solved by applying the principles of this method; moreover, the solutions of the quintic equation (fifth degree equation) will be easily deduced.

Investigating the Effect of Tic Coating Layer on the Surface Roughness of Tungsten Carbide Cutting Tools Using Taguchi Design

In this study, external longitudinal turning operation was performed on (AISI 1020) steel to examine the influences of coating of the cutting tool on the machined surface roughness. The cutting tools used were coated and uncoated cemented carbide inserts. The tests are performed at four spindle speeds (80, 315, 500, and 800) rpm, at each of which two feed rates (0.2 and 0.5mm/rev) and two depth of cut (0.5 and 0.7mm) were used. Taguchi design of experiments (DOE) with a designed mathematical predictive model was used to investigate the effect of the coating layer and determine the machining conditions for minimum surface roughness. Accordingly, a suitable mixed orthogonal array L16 (3*4) was selected. The results showed that the surface roughness produced by using TiC coated inserts for identical machining conditions was lower than that produced due to uncoated tool by 41% to 53%. Regression analysis showed that the non-linear quadratic polynomial equation appears to be more suitable for representing the relation of spindle speed, feed rate, and depth of cut with the surface roughness. Taguchi method and the designed mathematical model had been used to predict the optimal cutting conditions. A confirmation test for the obtained results verified that the designed Taguchi experiments and the designed model successfully investigated the effect of the coating on the surface roughness. Data fit ver.9 and Mtb14 software had been employed to achieve the object of the presented work.

Optimization and validation of polyherbal formulation by applying Box-Behnken design for the treatment of Inflammatory bowel disease in experimental animals.

Background: The use of herbal medicine in inflammatory bowel disease (IBD) had been increased significantly. Allopathic treatment of IBD leads too many side effects therefore use of the herbal formulation is promising. Aegle Marmelos, Bombax malabericum, and Hollarrhena antidysentrica plants have been used to treat IBD. Objective: To evaluate a designed polyherbal formulation in experimentally induced inflammatory bowel disease in rats and To validate mathematical model derived by Box-Behnken experimental design for optimized polyherbal formulation for the treatment of IBD in experimental rats by checkpoint analysis. Method: Three-level Box-Behnken design was selected to optimize the dose. Polyherbal formulation consist of plant extract of Aegle Marmelos (X1), Bombax malabericum (X2), and Hollarrhena antidysentrica (X3) in different ratios were selected as independent variable. Polynomial equations were established based on Analysis of variance (ANOVA). To validate the chosen polynomial equation checkpoint analysis were performed. The percentage of predictive error is presented. Results: ANOVA reveals that X2 plant does not have any significant impact on the response surface. The checkpoint batch showed the experimental value of CMDI and Disease activity index (DAI) as 1.33 and 0.66 respectively. It is worthwhile to note that the observed values were quite close to the calculated values of CMDI. A little difference in the value of DAI may be attributed to the inherent variation observed in animal studies. Conclusion: From this study, it was concluded that a dose of Aegle marmelos 100 mg/kg, a dose of Bombax malabericum 300 mg/kg, and a dose of Holarrhena antidysentrica 200 mg/kg will always be effective in IBD patients.

Derivation of an Enhanced Pressure Differential Expression, for a Penetration Injection with Back Pressure

In real-world water injection applications, an in-line injection facilitates a pressure differential that boosts the current flow. A pressure differential created by the injection of a pressurized flow into the mainline of flow is derived from the momentum transfer equation. Heat loss is disregarded, and such empirical equations provide a ballpark value to these pressure differentials during the injection. In industrial applications, injection of the fluid is done on the surface, due to weld and other constraints where losses due to friction and eddy current formation are imminent. On the other hand, penetration injection provides a far more augmented pressure differential that has a polynomial impact based on the mainline flow rate and the injection flow rate. This paper aims to derive an accurate representation of the pressure differential values obtained from a penetration injection through experimentation and compare it against a surface injection or empirical calculation. The paper concludes by indicating that the penetration injection augments the pressure differential with a new empirical formula for the derived pressure differential as a polynomial equation for this apparatus and can be extended across different sizes of the mainline and injection line diameters. This work provides a precise formula that can be used to derive pressure differential and estimate the flow and pressure rates. The formula also provides a platform for further utility in the fracturing operations where fracture flow from the well upstream presents multiple injection fractures to the mainline through fracture pores.

Kinematic analysis of an augmented 3-RPSP tripod mechanism with six degrees of freedom for bone reduction surgery

Robotic-assisted bone reduction surgery consists in using robots to reconnect patients’ bone fragments prior to fracture healing. The goal of this study is to propose a novel augmented 3-RPSP tripod mechanism with six degree of freedom for longitudinal bone reduction surgery. Its inverse kinematic model is studied and its forward kinematic model is solved by establishing the constraint equations, applying Sylvester’s dialytic method and finding the solutions of the resulting polynomial equation. The velocity model is calculated and its Jacobian matrix is used to identify its singular configurations. In comparison to the Stewart–Gough platform that is a typical mechanism used in this application, the proposed mechanism offers larger reachable workspace which is an important aspect in the femoral shaft bone reduction. A Physiguide and Msc Adams software are used to carry out a simulation of a real femur fracture reduction using the proposed mechanism to validate its suitability. A robotic prototype has been designed and manufactured in order to test its capability of performing diaphyseal femur reduction surgery.

Removal of Ag remanence and improvement in structural attributes of silicon nanowires array via sintering

Metal-assisted chemical etching (MACE) is popular due to the large-area fabrication of silicon nanowires (SiNWs) exhibiting a high aspect ratio at a low cost. The remanence of metal, i.e., silver nanoparticles (AgNPs) used in the MACE, deteriorates the device (especially solar cell) performance by acting as a defect center. The superhydrophobic behavior of nanowires (NWs) array prohibits any liquid-based solution (i.e., thorough cleaning with HNO3 solution) from removing the AgNPs. Thermal treatment of NWs is an alternative approach to reduce the Ag remanence. Sintering temperature variation is chosen between the melting temperature of bulk-Ag (962 °C) and bulk-Si (1412 °C) to reduce the Ag particles and improve the crystallinity of the NWs. The melting point of NWs decreases due to surface melting that restricts the sintering temperature to 1200 °C. The minimum sintering temperature is set to 1000 °C to eradicate the Ag remanence. The SEM–EDS analysis is carried out to quantify the reduction in Ag remanence in the sintered NWs array. The XRD analysis is performed to study the oxides (SiO and Ag2O) formed in the NWs array due to the trace oxygen level in the furnace. The TG-DSC characterization is carried out to know the critical sintering temperature at which remanence of AgNPs removes without forming any oxides. The Raman analysis is studied to determine the crystallinity, strain, and size of Si nanocrystals (SiNCs) formed on the NWs surface due to sidewalls etching. An optimized polynomial equation is derived to find the SiNCs size for various sintering temperatures.