On a special case of the two-variable Newton interpolation polynomial

CCCA12 ◽  
2012 ◽  
Author(s):  
Dimitris N. Varsamis ◽  
Nicholas P. Karampetakis
Keyword(s):  
Interpolation Polynomial ◽  
Newton Interpolation ◽  
Special Case

scholarly journals A generalization of Hermite's interpolation formula in two variables

1974 ◽  
Vol 18 (4) ◽  
pp. 402-410 ◽  
Author(s):  
M. M. Chawla ◽  
N. Jayarajan
Keyword(s):  
Interpolation Problem ◽  
Cartesian Product ◽  
Interpolation Formula ◽  
Interpolation Polynomial ◽  
Cartesian Grid ◽  
Rectangular Grid ◽  
Partial Derivatives ◽  
Fixed Order ◽  
Derivatives Of ◽  
Special Case

Spitzbart [1] has considered a generalization of Hermite's interpolation formula in one variable and has obtained a polynomial p(x) of degree n + Σnj=0 = rj in x which interpolates to the values of a function and its derivatives up to order rj at xj, j = 0, 1,···n. Ahlin [2] has considered a bivariate generalization of Hermite's interpolation formula. He has developed a bivariate osculatory interpolation polynomial which agrees with f(x, y) and its partial and mixed partial derivatives up to a specified order at each of the nodes of a Cartesian grid. However, the above interpolation problem considered by Ahlin assumes that the values of partial and mixed partial derivatives of the same fixed order k – 1 are available at every point of the rectangular grid. It may also be observed that Ahlin's formula is essentially a Cartesian product of a special case of Spitzbart's formula in one variable.

A Simple Model for Solvent Evaporation in Electrospinning Process

NANO ◽  
2017 ◽  
Vol 12 (03) ◽  
pp. 1750028 ◽  
Author(s):  
Sh. Maghsoodlou ◽  
B. Noroozi ◽  
A. K. Haghi
Keyword(s):  
Critical Role ◽  
Three Dimensional ◽  
Forecast Accuracy ◽  
Polynomial Equation ◽  
Interpolation Polynomial ◽  
Electrospinning Process ◽  
Solvent Evaporation ◽  
Newton Interpolation ◽  
Modified Model ◽  
Viscoelastic Element

One of the most important issues in electrospinning process is whipping instability and solvent evaporation that plays a critical role in nanofiber formation. This report simulates whipping process using numerical methods for a bead-viscoelastic element fiber model combined with a polynomial equation for adding solvent evaporation influence on the three-dimensional path. The suggested equation has been obtained by applying Newton interpolation polynomial operation. Then the results of nanofiber diameters for experimental data, original model and modified model are compared with different statistical methods. ANOVA analysis shows the prediction of diameters could be more accurate and meaningful. Meanwhile, a calculation forecast accuracy chart is presented in detail. It is observed that our suggested model shows more accuracy and is more reliable than the bead-spring model.

Research on Lower Muscle Strength Feature for Elite Speed Skaters in High Speed Gliding

2011 ◽  
Vol 117-119 ◽  
pp. 67-70
Author(s):  
Xin Wang
Keyword(s):  
Muscle Strength ◽  
Video Analysis ◽  
Power Output ◽  
High Speed ◽  
Interpolation Polynomial ◽  
Experimental Results ◽  
Testing Methods ◽  
Newton Interpolation ◽  
Isokinetic Testing

In order to obtain the Lower Muscle Strength Feature for Elite Speed Skaters in High Speed Gliding, this paper applied video analysis and isokinetic testing methods to conduct kinematic and kinetics dates. Contrasting to the kinematics dates, torques were computed by the Newton interpolation polynomial, which are simulated as the actual moments during gliding. According to the experimental results, the sLower Muscle Strength Feature is unique and correct.The larger of the velocity, the less moments produced from the hip, knee and ankle muscular, which will do harm to the power output.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

Determination of the phase structure of polymerblends by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 492-493
Author(s):  
Dr. G. Kaemof
Keyword(s):  
Screw Extruder ◽  
Electron Microscopic ◽  
Thin Sections ◽  
Single Screw Extruder ◽  
Transmission Electron ◽  
The Matrix ◽  
Twin Screw ◽  
Special Case ◽  
Microscopic Investigations

A mixture of polycarbonate (PC) and styrene-acrylonitrile-copolymer (SAN) represents a very good example for the efficiency of electron microscopic investigations concerning the determination of optimum production procedures for high grade product properties.The following parameters have been varied:components of charge (PC : SAN 50 : 50, 60 : 40, 70 : 30), kind of compounding machine (single screw extruder, twin screw extruder, discontinuous kneader), mass-temperature (lowest and highest possible temperature).The transmission electron microscopic investigations (TEM) were carried out on ultra thin sections, the PC-phase of which was selectively etched by triethylamine.The phase transition (matrix to disperse phase) does not occur - as might be expected - at a PC to SAN ratio of 50 : 50, but at a ratio of 65 : 35. Our results show that the matrix is preferably formed by the components with the lower melting viscosity (in this special case SAN), even at concentrations of less than 50 %.

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