Differentiability and the Secant Slope Function

2021 ◽  
pp. 127-142
Author(s):  
Nicholas H. Wasserman ◽  
Timothy Fukawa-Connelly ◽  
Keith Weber ◽  
Juan Pablo Mejia-Ramos ◽  
Stephen Abbott
Keyword(s):  
Slope Function

Dependence of Diffusion Paths on Thermodynamic Factors in Ternary Systems

2008 ◽  
Vol 277 ◽  
pp. 119-124 ◽  
Author(s):  
Ü. Ugaste ◽  
J. Priimets ◽  
Tony Laas
Keyword(s):  
Approximate Equation ◽  
Ternary Systems ◽  
Diffusion Path ◽  
Tracer Diffusion ◽  
Diffusion Paths ◽  
Slope Function ◽  
Experimental Values ◽  
The Impact ◽  
Tracer Diffusion Coefficients ◽  
Thermodynamic Factors

The impact of thermodynamic factors on deviation from linearity of diffusion path in the ternary system Cu-Fe-Ni is analyzed. For that the slope function of the diffusion path for the diffusion couples 65Ni30Cu5Fe –29.5Ni16.5Cu54Fe, 49.5Ni50.5Fe – 51Ni49Cu and 84Cu16Ni – 50Ni50Fe, annealed at 1000°C for 196h, were calculated by an approximate equation using only thermodynamic data. Results of the calculation were compared with the values of the slope function obtained directly from experimental data. It is shown that despite of the fact that the tracer diffusion coefficients of the components in the system Cu-Fe-Ni are not equal the coincidence between the calculated and experimental values of the slope function is remarkable. This allows us to conclude that at least in this case the deviation of the diffusion path from linearity depends mainly on the thermodynamic properties of the system.

scholarly journals APLIKASI MINYAK CENGKEH SEBAGAI OBAT BIUS PADA KAKAP PUTIH (Lates calcarifer Bloch)

2006 ◽  
Vol 8 (1) ◽  
pp. 9
Author(s):  
Bambang Hanggono
Keyword(s):  
Survival Rate ◽  
Potential Application ◽  
Sea Water ◽  
Sea Bass ◽  
Abnormal Behavior ◽  
Clove Oil ◽  
Lates Calcarifer ◽  
Plastic Bag ◽  
Slope Function ◽  
External Stimuli

The objective of this study was to determine the safety and efficacy of clove oil as an anesthetic in sea bass (Lates calcarifer) and the potential application of clove oil as anesthetic to facilitate the sea bass fry transportation. Acute toxicity test indicated the 24-hr LC50 value of clove oil in sea bass fry as 30 ppm with slope function of 1.079 (1.05 to 1.107). In efficacy test, fish were exposed to 5, 10, 15, 20 and 25 ppm of clove oil for 15 minutes. At 5 ppm, clove oil caused only sedation effect (partial loss of reaction to external stimuli) while at 20 ppm, fish entered anesthesia stage (failure to respond to external stimuli) within about 3 minutes. Fish recovered from a 15-min period of exposure in 20 ppm clove oil within less than 10 minutes following removal from the anesthetic solution. There was neither mortality nor abnormal behavior of fish during 15-min exposure of clove oil as well as during 7 days post recovery from anesthesia. The potential application of clove oil as an aid in the transport of sea bass fry in plastic bag was also investigated. At 5 ppm, clove oil could reduce activities of the fish without loss of equilibrium (sedation stage) during the 4 hour simulated transport at 50 fish per 1,000 ml sea water (15 ppt). At 20 ppm, clove oil caused loss of equilibrium in fish resulting in the anesthesia stage throughout the 4 hour period. However, there was no improvement on survival rate and fish behavior with the use of clove oil during and after this 4 hour transport. Simulated transport at 50 fish per 500 ml sea water (15 ppt) for 8 hour did show better significant survival rate with additional of 5 and 20 ppm clove oil. In both short and long term transport study, clove oil did show the benefit by reducing the fish activities judging from the reduction of oxygen consumption, ammonia and carbon dioxide levels. Addition of appropriate concentration of clove oil in transport water ensured that the fish would stay calm by reducing fish activity and therefore, prevented any drastic changes of water qualities.

scholarly journals A Multi-Slope Sliding-Mode Control Approach for Single-Phase Inverters under Different Loads

2016 ◽  
Author(s):  
Ghazanfar Shahgholian ◽  
Babk Khajeh Shalaly
Keyword(s):  
Sliding Mode Control ◽  
Single Phase ◽  
Sliding Mode ◽  
Main Idea ◽  
Sliding Surface ◽  
Tracking Accuracy ◽  
Control Approach ◽  
Mode Control ◽  
Non Linear ◽  
Slope Function

In this paper, a new approach to the sliding-mode control of single-phase inverters under linear and non-linear loads is introduced. The main idea behind this approach is to utilize a non-linear, flexible and multi-slope function in controller structure. This non-linear function makes the controller possible to control the inverter by a non-linear multi-slope sliding surface. In general, this sliding surface has two parts with different slopes in each part and the flexibility of the sliding surface makes the multi-slope sliding-mode controller (MSSMC) possible to reduce the total harmonic distortion, to improve the tracking accuracy, and to prevent overshoots leading to undesirable transient-states in output voltage which are occurred when the load current sharply rises. In order to improve the tracking accuracy and to reduce the steady-state error, an integral term of the multi-slope function is also added to the sliding surface. The improved performance of the proposed controller is confirmed by simulations and finally, the results of the proposed approach are compared with a conventional SMC and a SRFPI controller.

II. A solution of the integro-differential equation for the slope of the jet

1961 ◽  
Vol 261 (1304) ◽  
pp. 97-118 ◽  
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Coordinate Transformation ◽  
Present Author ◽  
Numerical Solutions ◽  
Two Dimensional ◽  
Integro Differential Equation ◽  
Mellin Transforms ◽  
Momentum Coefficient ◽  
Slope Function

In an earlier paper with the same general title (Spence 1956, referred to as I), a mathematical model was developed to discuss the flow past a two-dimensional wing at incidence a in a steady incompressible stream, with a jet of momentum coefficient C j emerging from the trailing edge at an angular deflexion r to the chordline. In linearized approximation it was shown that the slope of the jet is given by a certain singular integro-differential equation, and numerical solutions for the equation were obtained by a pivotal points method. A coordinate transformation has now been found (Spence 1959) which makes the equation independent of the jet strength for small values of 14 C j = u, say, yielding a simpler equation solved by Lighthill (1959) using Mellin transforms (and by Stewartson (1959) and the present author by other methods). In this paper the expansion of the slope function is continued in ascending powers of u and In u multiplied by functions of x found by solving, by Lighthill’s method, a series of closely-related inhomogeneous equations. From these, expansions of the lift derivatives with respect to a and r are found as To this order the expressions agree closely with the numerical results found earlier, the discrepancy at u = 1 being less than 4 %.

scholarly journals An Improved Dynamic Friction Model Using a Data-Based Approach

2017 ◽  
Author(s):  
Nathan A. Weir ◽  
Andrew G. Alleyne
Keyword(s):  
Control Systems ◽  
Friction Model ◽  
Model Parameters ◽  
Model Accuracy ◽  
Precision Motion Control ◽  
Frequency Domains ◽  
Slope Function ◽  
The Time Domain ◽  
Precision Motion ◽  
Fitting Model

A significant challenge associated with the development of precision motion control systems is the identification and modeling of friction. In particular, dynamic (presliding) friction is often difficult to accurately model in both the time domain and frequency domain simultaneously. We present a data-based modification to an existing friction model, known as the Dahl Dynamic Hysteresis Model (DHM), which incorporates an empirical friction slope function to provide a more accurate representation of arbitrarily shaped hysteresis curves. This data-based approach avoids the added complexity of identifying or fitting model parameters, and can be implemented with a simple look up table. Simulation results are validated with measured friction data collected from an experimental testbed. We show that the data-based approach significantly improves the friction model accuracy in both the time and frequency domains.

Generation of partial orders for intervals by means of the slope function

2015 ◽  
Vol 266 ◽  
pp. 67-83
Author(s):  
Jun Han ◽  
Bao Qing Hu
Keyword(s):  
Partial Orders ◽  
Slope Function

scholarly journals Genetic control of transition from juvenile to mature wood with respect to microfibril angle (MFA) in Norway spruce (Picea abies) and lodgepole pine (Pinus contorta)

2018 ◽  
Author(s):  
Haleh Hayatgheibi ◽  
Nils Forsberg ◽  
Sven-Olof Lundqvist ◽  
Tommy Mörling ◽  
Ewa J. Mellerowicz ◽  
...  
Keyword(s):  
Genetic Control ◽  
Norway Spruce ◽  
Pinus Contorta ◽  
Lodgepole Pine ◽  
Microfibril Angle ◽  
Threshold Level ◽  
Logistic Function ◽  
Direct Selection ◽  
Narrow Sense Heritability ◽  
Slope Function

AbstractGenetic control of microfibril angle (MFA) transition from juvenile to mature was evaluated in Norway spruce and lodgepole pine. Increment cores were collected at breast height from 5,618 trees in two 21-year-old Norway spruce progeny trials in southern Sweden, and from 823 trees in two 34-35 – year-old lodgepole pine progeny trials in northern Sweden. Radial variations in MFA from pith to bark were measured for each core using SilviScan. To estimate MFA transition from juvenile to mature, a threshold level of MFA 20° was considered and six different regression functions were fitted to the MFA profile of each tree after exclusion of outliers, following three steps. The narrow-sense heritability estimates (h2) obtained for MFA transition were highest based on the slope function, ranging from 0.21 to 0.23 for Norway spruce and from 0.34 to 0.53 for lodgepole pine, while h2 were mostly non-significant based on the logistic function, under all exclusion methods. Results of this study indicate that it is possible to select for an earlier MFA transition from juvenile to mature in Norway spruce and lodgepole pine selective breeding programs, as the genetic gains (∆G) obtained in direct selection of this trait were very high in both species.

Sharing Teaching Ideas: Guessing The Slope Function

1989 ◽  
Vol 82 (8) ◽  
pp. 621-622
Author(s):  
Joseph A. Gallian
Keyword(s):  
Correct Solution ◽  
Geometry Problem ◽  
Slope Function ◽  
Teaching Ideas

In the excellent film “Let Us Teach Guessing,” Pólya (1966) poses a geometry problem to a class and asks the students to guess the solution. Without saying whether these guesses are right, he proceeds to lead the class step by step to the point where they can guess the correct solution of the problem. As Poly a has said, “Everything is just a guess—concerning your job, your home, your family, even the laws of physics.”

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