Fourth-order Polynomial Equation Research Articles

The digital aqueous humor outflow meter: an alternative tool for screening of the human eye outflow facility

To develop, characterize, and validate a prototype digital aqueous humor outflow tonographer (DAHOM). The DAHOM was developed, characterized, and validated in three phases. Phase 1 involved construction of the sensor. This was broadly based on the fundamental design of a typical Schiotz tonographer with a series of improvements, including corneal indentation, which was converted to an electrical signal via a linear variable differential transducer, an analog signal which was converted to digital via ADC circuitry, and digital data acquisition and processing which was made possible by a serial port interface. Phase 2 comprised development of software for automated assessment of the outflow facility. Automated outflow facility assessment incorporated a series of fundamental improvements in comparison with traditional techniques, including software-based filtering of ripple noise and extreme variations, rigidity impact analysis, and evaluation of the impact of patient age, central corneal thickness, and ocular axial length. Phase 3 comprised characterization and validation of DAHOM, for which we developed an experimental setup using porcine cadaver eyes. DAHOM's repeatability was evaluated by means of Cronbach's alpha and intraclass correlation coefficient. The level of agreement with a standard Schiotz tonographer was evaluated by means of paired t-tests and Bland-Altman analysis in human eyes. The experimental setup provided the necessary data for the characterization of DAHOM. A fourth order polynomial equation provided excellent fit (R square >0.999). DAHOM demonstrated high repeatability (Cronbach's alpha ≥0.997; intraclass correlation coefficient ≥0.987) and an adequate level of agreement with a standard Schiotz tonographer. This study presents the development, characterization, and validation of a prototype digital tonographer. DAHOM demonstrates high repeatability and a sufficient level of agreement with a typical Schiotz tonographer, while its digital design remedies known vulnerabilities of conventional tonographers.

New fat free mass - fat mass model for use in physiological energy balance equations

BackgroundThe Forbes equation relating fat-free mass (FFM) to fat mass (FM) has been used to predict longitudinal changes in FFM during weight change but has important limitations when paired with a one dimensional energy balance differential equation. Direct use of the Forbes model within a one dimensional energy balance differential equation requires calibration of a translate parameter for the specific population under study. Comparison of translates to a representative sample of the US population indicate that this parameter is a reflection of age, height, race and gender effects.ResultsWe developed a class of fourth order polynomial equations relating FFM to FM that consider age, height, race and gender as covariates eliminating the need to calibrate a parameter to baseline subject data while providing meaningful individual estimates of FFM. Moreover, the intercepts of these polynomial equations are nonnegative and are consistent with observations of very low FM measured during a severe Somali famine. The models preserve the predictive power of the Forbes model for changes in body composition when compared to results from several longitudinal weight change studies.ConclusionsThe newly developed FFM-FM models provide new opportunities to compare individuals undergoing weight change to subjects in energy balance, analyze body composition for individual parameters, and predict body composition during weight change when pairing with energy balance differential equations.

Measurement of thermodynamic properties of some hydrogen absorbing alloys

In this paper, the effect of hydrogen concentration on the reaction enthalpies of some metal hydride alloys during hydriding and dehydring is presented. Pressure–concentration–temperature characteristics of the metal hydride alloys are measured under nearly isothermal condition during both absorption and desorption. Reaction enthalpies and entropies of LaNi 5, LaNi 4.7Al 0.3, LmNi 4.91Sn 0.15, Ti 0.99Zr 0.01V 0.43Fe 0.09Cr 0.05Mn 1.5 and MmCo 0.72Al 0.87Fe 0.04Ni 3.91 are estimated by constructing van't Hoff plots at different hydrogen concentrations. It is observed that the effect of hydrogen concentration on reaction enthalpies is more significant for the alloys having larger plateau slopes. At the initial stage of hydrogenation, metal hydrides are found to have larger reaction enthalpies which decrease gradually by about 5–15% at the end of the hydrogen absorption. At any given temperature, desorption enthalpies of LaNi 5, LmNi 4.91Sn 0.15, MmCo 0.72Al 0.87Fe 0.04Ni 3.91, LaNi 4.7Al 0.3 and Ti 0.99Zr 0.01V 0.43Fe 0.09Cr 0.05Mn 1.5 are found to be higher by about 5, 8, 10, 28 and 32% than their respective absorption enthalpies. Reaction enthalpies of the selected metal hydride alloys are expressed as a function of hydrogen concentration by a fourth order polynomial equation obtained from fitting with the experimental data.

Analytical method for locating the secondary instant centres of indeterminate planar linkages

This article presents a new analytical method for locating secondary instant centres (SICs) of indeterminate planar linkages. In this method the SICs are first discriminated into three classes according to their level of geometric dependencies. The concepts of instant-centre digraph, instant-centre walk, and instant-centre circuit are then introduced to establish the recursive relationships between the classified instant centres. It is shown that the location of the instant centres within an instant-centre circuit can be evaluated recursively by first solving a second-order polynomial equation. In addition, by combining the recurrence conditions of several related instant-centre walks, the locations of SICs that are not within an instant-centre circuit can be solved analytically from a fourth-order polynomial equation. The proposed method does not rely on any velocity information or graphical techniques; therefore, it can be applied systematically to all types of indeterminate linkages. It can also be implemented on digital computers for automated analysis. Three numerical examples are presented to demonstrate the usage of this method.

Bifurcation and post-buckling analysis of bimodal optimum columns

A mathematical formulation of column optimization problems allowing for bimodal optimum buckling loads is developed in this paper. The columns are continuous and linearly elastic, and assumed to have no geometrical imperfections. It is first shown that bimodal solutions exist for columns that rest on a linearly elastic (Winkler) foundation and have clamped-clamped and clamped-simply supported ends. The equilibrium equation for a non-extensible, geometrically nonlinear elastic column is then derived, and the initial post-buckling behaviour of a bimodal optimum column near the bifurcation point is studied using a perturbation method. It is shown that in the general case the post-buckling behaviour is governed by a fourth order polynomial equation, i.e., near the bifurcation point there may be up to four post-buckling equilibrium states emanating from the trivial equilibrium state. Each of these equilibrium states may be either supercritical or subcritical in the vicinity of the bifurcation point. The conditions for stability of these non-trivial post-buckling states are established based on verification of positive semi-definiteness of a two-by-two matrix whose coefficients are integrals of the buckling modes and their derivatives. In the end of the paper we present and discuss numerical results for the post-buckling behaviour of several columns with bimodal optimum buckling loads.

Thermoelastic composites with columnar microstructure and cylindrically anisotropic phases. Part II: One-parameter generalized self-consistent estimates

The effective transverse shear modulus of a transversely isotropic composite with columnar microstructure and with two cylindrically orthotropic phases is estimated by a one-parameter generalized self-consistent model. The equation characterizing the effective transverse shear modulus is a fourth-order polynomial equation instead of the quadratic one determined by the classical generalized self-consistent model. The result obtained in Part II of this work extends the relevant one of Hashin [Z. Hashin, Thermoelastic properties and conductivity of carbon/carbon fiber composites, Mech. Mater. 8 (1990) 293–308].

Numerical modelling of biopotential field for detection of breast tumour

Breast cancer is a disease characterised by the uncontrolled growth of abnormal cells. These cancer cells can travel through the body by way of blood or lymph nodes. Previous studies have indicated that, changes in the electrical properties of abnormal breast are more significant compared to the breast normal tissues. In the present study, a simple 2D models of breast (close to realistic), with and without artificially inserted malignant cancer were simulated, based upon electrical activity within the breast. We developed an inhomogeneous female breast model, closer to the actual, by considering a breast as a hemisphere with various layers of unequal thickness in supine condition. In order to determine the potential distribution developed due to a dipole source, isotropic homogeneous conductivity was assigned to each of these compartments and the volume conductor problem was solved using finite element method. Significant changes in the potential distribution were recoded in the malignant and normal breast regions. The surface potential decreases about 0.5%, for the small malignant region of surface area 13 mm 2 (spherical diameter = 2 mm ). And it (surface potential) decreases about 16.4% for large malignant surface area of 615 mm 2 (spherical diameter = 14 mm ). Hence, the results show that, the sizes of tumours result in the reduction of surface potential and follows a fourth order polynomial equation. Thus, biofield analysis yields promising results in the detection of the breast cancer of various sizes.

Forward Kinematics of Casing Oscillator

This paper presents the forward kinematics of the casing oscillator, which is a heavy construction machine. This machine has a four-degrees-of-freedom (DoF) parallel mechanism with one redundancy. By using the geometric approach, the forward position kinematics for the casing oscillator is derived as a fourth-order polynomial equation in square form of one output variable

Activity coefficients of the species in the methanol solutions of acetaminophen and two silylated derivatives at 298.15 K

An isopiestic method was used to measure the solvent osmotic coefficients in solutions of acetaminophen, triethylsilylacetaminophen and tertiarybuthyldimethylsilylacetaminophen in methanol at 298.15 K. The experimental data for osmotic coefficients have been correlated and solute unsymmetric convention activity coefficients have been calculated using the nonrandom factor (NRF) model, the nonrandom, two-liquid (NRTL) model, a three-parameter Margules equation, and a fourth-order polynomial equation in terms of molality. Standard deviations are least for the models with more parameters, but all models describe the data within experimental uncertainty. The solute activity coefficients are greater than unity, increasing with molecular size.

Spatial variability in crop response under contour hedgerow systems in the Andes region of Ecuador

Land management practices on tropical soils have been studied extensively during the past decades. However, assessments of their impact on field-scale spatial variability in crop performance are rare. A case of practices affecting spatial crop response at field level in a systematic way is the contour hedgerow system, a widespread soil conservation technique on steep lands in the tropics. The objectives of this study were to assess: (i) spatial variability in crop response under contour hedgerow systems in the Andes and (ii) implications for management of steep land alley farming. In order to measure spatial variability in crop response, Triticum aestivum was sown in rows following the contours, placed every 25 cm along the slope direction. Grain yield was monitored on eight alleys, having slopes from 15 to 30%, a length of 4–8 m and soils ranging from Dystri-Vertic Cambisols to Haplic Phaeozem, in the Andes region of Ecuador. In order to relate crop response with soil fertility, soil sampling was carried out in bands following the contour. Top soil properties, such as organic carbon, N Total, NO 3 −, P, exchangeable Aluminium, P fixation, exchangeable bases, CEC and texture, were analysed. The barrier strips of the contour hedgerow systems were composed of: (i) Pennisetum clandestinum and Lolium multiflorum or (ii) Phalaris tuberosa. Spatial variability in crop response was described by fourth-order polynomial equations, where position in the alley was the independent variable and plant characteristics were the dependent variables. Grain yield ranged from 0.8 to 4.0 t ha −1 (net area). Clear and significant patterns of spatial variability in crop response were found in all alleys, with R 2 varying from 0.55 to 0.90. Crop response was strongly and positively correlated with NO 3 −, P, exchangeable bases or organic carbon, dependent on the management, age and soil conditions of the alleys. Tillage erosion and soil accumulation on respectively the upper and lower elevations of the alleys were the main causes for a tendency to a significantly increased crop response along the slope direction. However, according the type of grass used in the barrier strip, competition for soil fertility and soil moisture occurred and influenced in negative way crop productivity in the lower elevations of the alleys. An index is proposed to assess the effect of contour hedgerows on crop response. The present study shows that contour hedgerow systems cannot always be evaluated as completely positive. Soil fertility improvement on the upper part of the alleys and a better management of the barrier strip are suggested to enhance crop productivity of contour hedgerow systems.

Post-harvest physico-mechanical properties of orange peel and fruit

The post-harvest physico-mechanical properties data of fruits and vegetables are important in adoption and design of various handling, packaging, storage and transportation systems. Physico-mechanical properties namely, orange peel tensile strength and cutting energy and fruit color, weight loss, bioyield point, firmness, puncture force and cutting energy were determined with respect to storage period under ambient and refrigerated conditions. Peel tensile strength, modulus of elasticity and cutting energy decreased with storage period in both ambient and refrigerated conditions. The color index of orange followed a fourth-order polynomial equation during storage. At the end of 17 days storage, the fruit cumulative weight losses in ambient and refrigerated conditions were 19.4% and 7.3%, respectively. Bioyield point, firmness, puncture force and cutting energy of orange fruits decreased with respect to number of days of storage. The firmness of orange fruit was significantly higher in stem-calyx axis in vertical position than that in horizontal position.

Prediction of the Layer Longitudinal Compression Strength

This paper presents a new approach to the prediction of the layer longitudinal compression strength of continuous fibre polymer matrix composites. It is known that failure is caused by fibre microbuckling and that the initial fibre waviness and the matrix non-linear behaviour play a major role. A previous model compared very well with experimental results, but required a relatively complex numerical solution procedure. In the present model, the compression strength is obtained by solving a fourth-order polynomial equation. Although based on several simplifying assumptions, the model is in good agreement with the numerical model predictions and with experimental data. Further model simplifications lead to a closed-form expression that seems to be valid for carbon and boron fibre composites.

Improved Inherent Flaw Model for Tensile Fracture of Cracked Composite Laminates

Modifications are made in the inherent flaw model to predict the tensile fracture strength of cracked composite laminates. A simple relation is used for the inherent flaw length to improve the accuracy while evaluating the fracture strength of laminates. A quartic (fourth-order polynomial) equation is developed for the fracture strength of an infinite width plate containing a crack. This model is successfully applied to centre crack tensile specimens of graphite/epoxy and nylon/glass polyamide.

A Genetic Study of Dentin Growth in the Mandibular Second and Third Molars of Male Mice(雄マウスの下顎第2および第3臼歯の象牙質成長発育の遺伝学的研究)

Although the influence of genetic and environmental factors on the completed crown size of mandibular molars in mice is well known, such influence on the growth process of the mandibular second and third molars of mice has not yet been clarified. The purpose of the present study is to examine the growth pattern of the dentinal formation and evaluate the relative contributions of both genetic and environmental factors to longitudinal dentin formation by the use of the partial diallel cross-genetic approach, the time-marking method and a computerized image measurement system. The following results were obtained: 1) the onset of dentinal formation in the second molar was on the 6-9th day after birth, while that of the third molar was on the 9-12th day after birth; 2) the best fitted growth curve of the dentinal formation for the first molar was the fifth order polynomial equation, while for the second molar the fourth order polynomial equation was best, and for the third molar the third order polynomial equation was best; 3) maternal effect strongly influenced the second and the third molar dentin growth at an early stage of postnatal growth. Thus, it could be concluded that the dentinal formation growth pattern differed among the three kinds of mouse molars while maternal environmental factors, in addition to genetic factors, played an important role in the mouse second and third molar dentin growth during the early stage of postnatal growth.

Calculation of pH in fresh and sea water aquaculture systems

A procedure for the calculation of pH in fresh and salt waters has been developed. The method is based on a fourth-order polynomial relationship between hydrogen ion concentration and other (conservative) water quality parameters. The method avoids trial and error estimations and results in a direct calculation procedure that can be implemented in models developed in various modeling environments, such as spreadsheets, conventional programming languages (BASIC, C, FORTRAN, PASCAL, etc.) or specialized modeling languages (Extend ™, Stella ™). The method developed is based on the solution of the full alkalinity-pH equation. Because of the need for simplification of the equations to yield explicitly solvable polynomial equations, the accuracy of the solutions depends on the simplification made and varies with water properties. Three simplifications are tested based on a second-, a third-and a fourth-order polynomial equation for hydrogen ion concentrations. the equations have been tested for salinities ranging from 0 to 35‰ (fresh to sea water), for temperatures ranging from 0 to 35°C, for total carbonate carbon concentrations of 0·1 and 5·0 mmol/liter, and for total ammonia nitrogen concentrations of 0 and 10 mg/liter. Approximations are most accurate in waters of high total carbonate carbon and low ammonia concentrations, where the fourth-order approximation yields results that are within 0.05 pH units for the full range of pH values tested (5–10).

Effects of thuringiensin on European red mite (Acarina: Tetranychidae) mortality, oviposition rate and feeding

Effects of two formulations of thuringiensin (ABG-6162A and ABG-6266) on mortality, oviposition rate, and feeding of European red mite, Panonychus ulmi (Koch) were evaluated. Mite toxicities of the formulations were not significantly different. Immature instars were significantly more susceptible than adults. Low mortality of all instars was recorded after 3 d, indicating slow activity. The relationship between log (concentration + 1) of ABG-6162A and ABG-6266 and P. ulmi oviposition rate was best described by fourth-order polynomial equations, suggesting that thuringiensin both inhibits and stimulates P. ulmi oviposition. ABG-6162A affected oviposition at lower concentrations than ABG-6266. A quadratic relationship was observed between log (concentration + 1) of thuringiensin and P. ulmi adult female feeding. ABG-6162A reduced feeding more than ABG-6266 at concentrations ⩾ 1 mg liter−1. Toxicity to immatures and the sublethal effects described suggest that thuringiensin may control field populations of P. ulmi despite low initial mortality.

The curvilinear motion of coarse particles: New thoughts on theory and applications

Investigations of the aerodynamic behavior of coarse particles require the inclusion of inertial terms of the Navier-Stokes equation. Theoretical investigation of the motion of coarse particles in a uniform and a non-uniform flow field reported in this paper uses the modification of Stokes solution as a function of Reynolds number. This modification is achieved by development of a fourth order polynomial equation which is a semi-empirical correction for the drag force. The trajectories of particles of sizes from 25 to 200 μm are calculated in a constant velocity and a spatially defined velocity field using equation of motion of particles. It is found out that the coarse particles up to 200 μm can stay airborne for substantial times and distances in the environment where such particles are generated.

Blood oxygen transport in the house sparrow,Passer domesticus

Oxygen equilibrium curves (O2EC's) were generated for the adult house sparrowPasser domesticus at temperatures from 35 to 45 °C using a thin blood film technique (Fig. 1). At in vivo pH (7.47±0.02) and 41 °C, the half-saturationP O 2 was 43.4±0.5 Torr. Cooling the blood from normal body temperature to 35 °C had a greater, effect on O2 affinity (ΔH=−12.3 kcal/mol O2) than warming the blood to 45 °C (−6.2 kcal/mol O2). The CO2 Bohr coefficients (Δlog $$P_{{\text{O}}_{\text{2}} } $$ /Δ pH) atP 50 were similar at 35, 41, and 45 °C (range −0.48 to −0.49). Furthermore, the CO2 Bohr slopes were reasonably saturation independent between 10 and 90% S. Hill plots forPasser blood were nonlinear at each temperature; Hill coefficients (n H ) increased from the 2.5–2.7 range below 40% S to values of 3.3–3.6 above 60% S (Fig. 2). The sparrow equilibrium data at each temperature were accurately fitted by fourth order polynomial equations (Figs. 3, 4). The mean absolute errors in $$P_{{\text{O}}_{\text{2}} } $$ for these empiric expressions were 0.14, 0.09 and 0.33 Torr for O2EC's at 35,41 and 45 °C, respectively. These complex equilibrium curve shapes observed withPasser blood may reflect the presence of multiple hemoglobins; isoelectric focusing techniques revealed two structurally distinct isohemoglobins with a molar ratio of 3.7 (Table 2). The combined effects of the sparrow O2EC, shape (steep upper limb), (Fig. 5), the large ΔH, with blood cooling, and the influence of respiratory alkalosis on oxygen affinity may promote blood-O2 transport at altitude.