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Search for "polynomial" in Full Text gives 54 result(s) in Beilstein Journal of Nanotechnology.

Preparation and morphology-dependent wettability of porous alumina membranes

  • Dmitry L. Shimanovich,
  • Alla I. Vorobjova,
  • Daria I. Tishkevich,
  • Alex V. Trukhanov,
  • Maxim V. Zdorovets and
  • Artem L. Kozlovskiy

Beilstein J. Nanotechnol. 2018, 9, 1423–1436, doi:10.3762/bjnano.9.135

Graphical Abstract
  • triangles) – 65 µm; 4 (purple circles) – 75 µm. The inset shows an SEM image of the outer surface. The black dotted line is a polynomial fit shown as a guide to the eye for all data sets. Contact angle measurements for the back side of the PAM as a function of pore diameter for various membrane thicknesses
  • . The black dotted lines are polynomial fits shown as a guide to the eye for selected data sets. Physical characteristics (average values) of the experimental samples (before etching, as-produced amorphous membrane). Contact angle values for as-made PAMs obtained in 0.3 M oxalic acid (type I and type II
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Published 15 May 2018

Formation and development of nanometer-sized cybotactic clusters in bent-core nematic liquid crystalline compounds

  • Yuri P. Panarin,
  • Sithara P. Sreenilayam,
  • Jagdish K. Vij,
  • Anne Lehmann and
  • Carsten Tschierske

Beilstein J. Nanotechnol. 2018, 9, 1288–1296, doi:10.3762/bjnano.9.121

Graphical Abstract
  • director n. The order parameters S′ and S″ represent the degree of molecular orderings within clusters and the degree of ordering of clusters in the macroscopic sample, respectively. These are obtained from the following equations: Here P2 is the second order Legendre polynomial in angles θ and Θ in
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Published 25 Apr 2018

Atomistic modeling of tribological properties of Pd and Al nanoparticles on a graphene surface

  • Alexei Khomenko,
  • Miroslav Zakharov,
  • Denis Boyko and
  • Bo N. J. Persson

Beilstein J. Nanotechnol. 2018, 9, 1239–1246, doi:10.3762/bjnano.9.115

Graphical Abstract
  • temperature with confidence intervals of the second-degree polynomial approximation. Radial distribution function for the Al and Pd nanoparticles containing 20000 atoms for the bulk crystal at a temperature of 300 K and after cooling, and at 1150 K for palladium before cooling, and at 750 K for aluminum
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Published 19 Apr 2018

Electrostatic force spectroscopy revealing the degree of reduction of individual graphene oxide sheets

  • Yue Shen,
  • Ying Wang,
  • Yuan Zhou,
  • Chunxi Hai,
  • Jun Hu and
  • Yi Zhang

Beilstein J. Nanotechnol. 2018, 9, 1146–1155, doi:10.3762/bjnano.9.106

Graphical Abstract
  • images with tip biases of (b) 0 V, (c) 5 V and (d) −5 V of sample 0; EFM images of (e, f) sample 1, (g, h) sample 2, (i, j) sample 3, (k, l) sample 4, and (m, n) sample 5; (o) EFM spectra and the corresponding polynomial fits of samples 0–5 (the dashed vertical lines show the position of the biases at
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Published 11 Apr 2018

Automated image segmentation-assisted flattening of atomic force microscopy images

  • Yuliang Wang,
  • Tongda Lu,
  • Xiaolai Li and
  • Huimin Wang

Beilstein J. Nanotechnol. 2018, 9, 975–985, doi:10.3762/bjnano.9.91

Graphical Abstract
  • automatically segmented with accurate boundary detection. The extracted foreground features were taken as exclusion masks. In the second step, data points in the background were fitted as polynomial curves/surfaces, which were then subtracted from raw images to get the flattened images. Moreover, sliding-window
  • -based polynomial fitting was proposed to process images with complex background trends. The working principle of the two-step image flattening scheme were presented, followed by the investigation of the influence of a sliding-window size and polynomial fitting direction on the flattened images
  • . Additionally, the role of image flattening on the morphological characterization and segmentation of AFM images were verified with the proposed method. Keywords: atomic force microscopy; contour expansion; image flattening; polynomial fitting; sliding window; Introduction Since its invention, the atomic
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Published 26 Mar 2018

Exploring wear at the nanoscale with circular mode atomic force microscopy

  • Olivier Noel,
  • Aleksandar Vencl and
  • Pierre-Emmanuel Mazeran

Beilstein J. Nanotechnol. 2017, 8, 2662–2668, doi:10.3762/bjnano.8.266

Graphical Abstract
  • track (Figure 3D); 5) the baseline (red line) is determined by fitting the portion of the profile excluding the wear track with polynomial algorithms of order 1 to 4. The difference in height between the experimental and the four different fitted curves is integrated to compute the volume of the wear
  • previously determined; the bottom image D is the average height as a function of the distance from the center of the wear track circle. The baseline (dotted red line) in this example is obtained by a polynomial fit of order 4 of the profile without considering the wear track. The wear volume is calculated by
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Published 11 Dec 2017

Fabrication of gold-coated PDMS surfaces with arrayed triangular micro/nanopyramids for use as SERS substrates

  • Jingran Zhang,
  • Yongda Yan,
  • Peng Miao and
  • Jianxiong Cai

Beilstein J. Nanotechnol. 2017, 8, 2271–2282, doi:10.3762/bjnano.8.227

Graphical Abstract
  • smoothed using a Savitzky–Golay filter with a third-order polynomial and a smooth window size of 13. Second, the baseline of the Raman spectra was adjusted by subtracting a spline interpolation using WiRE 3.4 software. Figure 6 shows the Raman spectra of R6G molecules on a PDMS substrate coated with a 10
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Published 01 Nov 2017

Evaluating the toxicity of TiO2-based nanoparticles to Chinese hamster ovary cells and Escherichia coli: a complementary experimental and computational approach

  • Alicja Mikolajczyk,
  • Natalia Sizochenko,
  • Ewa Mulkiewicz,
  • Anna Malankowska,
  • Michal Nischk,
  • Przemyslaw Jurczak,
  • Seishiro Hirano,
  • Grzegorz Nowaczyk,
  • Adriana Zaleska-Medynska,
  • Jerzy Leszczynski,
  • Agnieszka Gajewicz and
  • Tomasz Puzyn

Beilstein J. Nanotechnol. 2017, 8, 2171–2180, doi:10.3762/bjnano.8.216

Graphical Abstract
  • linear modeling. On the other hand, as we set a polynomial kernel for nano-QSAR modeling, it became possible to investigate set of polynomials separately. For this purpose, separate equations were obtained directly from the experimental data. As summarized in Table 4 and Figure 5, linear modeling failed
  • highlighted, that in the case of core–shell systems, polynomial relationships were observed between cytotoxicity and average size of nanoparticles, whereas in the case of alloys, a polynomial relationship was observed between cytotoxicity and BET surface. Using Equations 1–3 we calculated RMSE values for each
  • covers ca. 80% of the initial dataset; the test set covers the remaining ca. 20%. Descriptors from training set were standardized and then the Gaussian process using normalized polynomial kernel was applied. The statistical quality of the QSAR model and its predictive ability were assessed using
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Published 17 Oct 2017

A review of demodulation techniques for amplitude-modulation atomic force microscopy

  • Michael G. Ruppert,
  • David M. Harcombe,
  • Michael R. P. Ragazzon,
  • S. O. Reza Moheimani and
  • Andrew J. Fleming

Beilstein J. Nanotechnol. 2017, 8, 1407–1426, doi:10.3762/bjnano.8.142

Graphical Abstract
  • sine and cosine signals, two multipliers, two low-pass filters, and an output block with square-root functionality and an arctan calculation method such as polynomial approximation or the CORDIC algorithm [55] to calculate the phase [43]. Such an implementation is schematically shown in the block
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Published 10 Jul 2017

Surface-enhanced Raman spectroscopy of cell lysates mixed with silver nanoparticles for tumor classification

  • Mohamed Hassoun,
  • Iwan W.Schie,
  • Tatiana Tolstik,
  • Sarmiza E. Stanca,
  • Christoph Krafft and
  • Juergen Popp

Beilstein J. Nanotechnol. 2017, 8, 1183–1190, doi:10.3762/bjnano.8.120

Graphical Abstract
  • current and the constant voltage bias by subtracting a smoothed dark spectrum. The resulting spectra were corrected for the polynomial background arising from residual excitation light using the penalized least squares-based Whittaker smoother algorithm outlined by Eilers [32]. The background corrected
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Published 01 Jun 2017

Preparation of thick silica coatings on carbon fibers with fine-structured silica nanotubes induced by a self-assembly process

  • Benjamin Baumgärtner,
  • Hendrik Möller,
  • Thomas Neumann and
  • Dirk Volkmer

Beilstein J. Nanotechnol. 2017, 8, 1145–1155, doi:10.3762/bjnano.8.116

Graphical Abstract
  • equipped with a Gatan image filter. Holey carbon-coated copper grids were used for sample preparation. Atomic force topographic images were sampled by means of an Agilent 5500 AFM with MAC III controller operating in tapping mode. A polynomial background subtraction was applied for image processing
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Published 26 May 2017

Fiber optic sensors based on hybrid phenyl-silica xerogel films to detect n-hexane: determination of the isosteric enthalpy of adsorption

  • Jesús C. Echeverría,
  • Ignacio Calleja,
  • Paula Moriones and
  • Julián J. Garrido

Beilstein J. Nanotechnol. 2017, 8, 475–484, doi:10.3762/bjnano.8.51

Graphical Abstract
  • the calibration curves for the Ph40 sensing element in the presence of n-hexane at 288, 298, 308, and 323 K. The curves depict the variation of the reflectance on a logarithmic scale as a function of concentration. The experimental data were fitted to a second-degree polynomial function using Excel
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Published 21 Feb 2017

Prediction of the mechanical properties of zeolite pellets for aerospace molecular decontamination applications

  • Guillaume Rioland,
  • Patrick Dutournié,
  • Delphine Faye,
  • T. Jean Daou and
  • Joël Patarin

Beilstein J. Nanotechnol. 2016, 7, 1761–1771, doi:10.3762/bjnano.7.169

Graphical Abstract
  • describes a mathematical model to predict the mechanical properties (uniaxial and diametric compression) of these pellets for arbitrary dimensions (height and diameter) using a design of experiments (DOE) methodology. A second-degree polynomial equation including interactions was used to approximate the
  • surface response methodology was used. A second-degree polynomial equation including interactions was used to approximate experimental results. A set of 105 equations (corresponding to the experimental trials) with 10 coefficients was statically solved by minimizing a quadratic criterion. Results and
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Published 18 Nov 2016

Polystyrene-block-poly(ethylene oxide) copolymers as templates for stacked, spherical large-mesopore silica coatings: dependence of silica pore size on the PS/PEO ratio

  • Roberto Nisticò,
  • Giuliana Magnacca,
  • Sushilkumar A. Jadhav and
  • Dominique Scalarone

Beilstein J. Nanotechnol. 2016, 7, 1454–1460, doi:10.3762/bjnano.7.137

Graphical Abstract
  • block copolymer composition on the pore dimensions of the silica coatings was investigated. In detail, trying to rationalize the dependence of the pore size from the length of each block (both PS and/or PEO), no experimental trends were evidenced. Surprisingly, a second-order polynomial trend, with good
  • data accuracy (Figure 4A), was achieved by plotting the average pore size as a function of the PS/PEO ratio. Both the investigated formulations (namely 95TEOS/5PS-b-PEO and 93TEOS/7PS-b-PEO) showed this polynomial trend. In particular, the lower the PS/PEO ratio (PS/PEO < 0.5), the smaller the pore
  • (Figure 4B). In order to validate this behavior, the theoretical pore size of the validation sample with a PS/PEO ratio of 0.89 was calculated by substituting this value in the four equations reported in Figure 4A,B. The calculated values are 25 nm (polynomial curve) and 24 nm (linear curve) for the 95/5
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Published 14 Oct 2016

Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout

  • Mostafa Mirzaei and
  • Yaser Kiani

Beilstein J. Nanotechnol. 2016, 7, 511–523, doi:10.3762/bjnano.7.45

Graphical Abstract
  • this study, the approximation of the displacement field is carried out using the Ritz method whose shape functions are written in terms of the Chebyshev polynomials. As a result, the essential variables may be written as In Equation 15, the i-th Chebyshev polynomial of the first kind is denoted by Pi
  • ] and Mundkur et al. [46]. Malekzadeh et al. [45] obtained the frequencies according to a three dimensional elasticity formulation and using the Chebyshev–Ritz formulation, whereas boundary characteristics of orthogonal polynomial functions are invoked into the Ritz formulation by Mundkur et al. [46] to
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Published 07 Apr 2016

Simulation of thermal stress and buckling instability in Si/Ge and Ge/Si core/shell nanowires

  • Suvankar Das,
  • Amitava Moitra,
  • Mishreyee Bhattacharya and
  • Amlan Dutta

Beilstein J. Nanotechnol. 2015, 6, 1970–1977, doi:10.3762/bjnano.6.201

Graphical Abstract
  • ). The length of the simulation cell in the axial direction fluctuates during the MD simulation (Figure 1b). A derivative of the third-order polynomial fit to the thermal strain vs temperature results is used to obtain the coefficient of thermal expansion, α. The open source MD codes LAMMPS [27] and MD
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Published 02 Oct 2015

Using natural language processing techniques to inform research on nanotechnology

  • Nastassja A. Lewinski and
  • Bridget T. McInnes

Beilstein J. Nanotechnol. 2015, 6, 1439–1449, doi:10.3762/bjnano.6.149

Graphical Abstract
  • learning algorithms implemented in the package: (1) multinomial naive Bayes classifier, (2) decision trees, (3) stochastic gradient descent (SGD) logistic regression, (4) L-1 regularized logistic regression, (5) L-2 regularized logistic regression, (6) linear support vector machine and (7) polynomial
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Published 01 Jul 2015

Accurate, explicit formulae for higher harmonic force spectroscopy by frequency modulation-AFM

  • Kfir Kuchuk and
  • Uri Sivan

Beilstein J. Nanotechnol. 2015, 6, 149–156, doi:10.3762/bjnano.6.14

Graphical Abstract
  • Chebyshev polynomial of the first kind. As expected, by setting γ = 0 in (7), we recover the result obtained by Dürig [17]. To invert the integral in Equation 6 and express the force in terms of the measured amplitudes μn and νn, we generalize the derivation of the Sader–Jarvis formula [12] to an arbitrary
  • upon tip–sample separation. It then follows from Equation 3 that where is the nth order Chebyshev polynomial of the second kind and Integrating by parts and using the identity , Equation 17 assumes the form where . Comparing Equation 19 with Equation 6, we see that these expressions are identical and
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Published 13 Jan 2015

Dynamic calibration of higher eigenmode parameters of a cantilever in atomic force microscopy by using tip–surface interactions

  • Stanislav S. Borysov,
  • Daniel Forchheimer and
  • David B. Haviland

Beilstein J. Nanotechnol. 2014, 5, 1899–1904, doi:10.3762/bjnano.5.200

Graphical Abstract
  • regimes of the tip motion has only one global minimum lying in the deep valley defined by the curve . Moreover, increasing the reconstructed polynomial power, Pz, makes this valley deeper and hence more resistant to noise. This method allows for the estimation of the product α2k2 with higher accuracy than
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Published 29 Oct 2014

Near-infrared dye loaded polymeric nanoparticles for cancer imaging and therapy and cellular response after laser-induced heating

  • Tingjun Lei,
  • Alicia Fernandez-Fernandez,
  • Romila Manchanda,
  • Yen-Chih Huang and
  • Anthony J. McGoron

Beilstein J. Nanotechnol. 2014, 5, 313–322, doi:10.3762/bjnano.5.35

Graphical Abstract
  • Zetasizer (Malvern Instruments, Worcestershire, United Kingdom). The size of the particles was measured by determining a correlation function and fitting a polynomial to the correlation function. We used the cumulant analysis as a fitting model for the correlation function in our study. The average particle
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Published 18 Mar 2014

3D nano-structures for laser nano-manipulation

  • Gediminas Seniutinas,
  • Lorenzo Rosa,
  • Gediminas Gervinskas,
  • Etienne Brasselet and
  • Saulius Juodkazis

Beilstein J. Nanotechnol. 2013, 4, 534–541, doi:10.3762/bjnano.4.62

Graphical Abstract
  • were fitted from the experimental values obtained in literature, by means of a built-in polynomial model. The finite-difference time-domain (FDTD) included a section of the substrate, enclosed in all directions by perfectly matched layers (PML) to avoid spurious reflections. The central area of 5×5
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Published 17 Sep 2013

Topological edge properties of C60+12n fullerenes

  • A. Mottaghi and
  • Ali R. Ashrafi

Beilstein J. Nanotechnol. 2013, 4, 400–405, doi:10.3762/bjnano.4.47

Graphical Abstract
  • graph. In this work, the topological properties of a class of fullerenes were given by edge contributions of its molecular graph. Our calculations with this and other classes of fullerenes suggest that the edge PI index can be computed by a polynomial of degree 2, whereas edge Szeged and edge revised
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Published 26 Jun 2013

Polynomial force approximations and multifrequency atomic force microscopy

  • Daniel Platz,
  • Daniel Forchheimer,
  • Erik A. Tholén and
  • David B. Haviland

Beilstein J. Nanotechnol. 2013, 4, 352–360, doi:10.3762/bjnano.4.41

Graphical Abstract
  • polynomial force reconstruction from experimental intermodulation atomic force microscopy (ImAFM) data. We study the tip–surface force during a slow surface approach and compare the results with amplitude-dependence force spectroscopy (ADFS). Based on polynomial force reconstruction we generate high
  • -resolution surface-property maps of polymer blend samples. The polynomial method is described as a special example of a more general approximative force reconstruction, where the aim is to determine model parameters that best approximate the measured force spectrum. This approximative approach is not limited
  • to spectral data, and we demonstrate how it can be adapted to a force quadrature picture. Keywords: AFM; atomic force microscopy; force spectroscopy; multifrequency; intermodulation; polynomial; Introduction The combination of high-resolution imaging [1][2][3][4] and high-accuracy force
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Published 10 Jun 2013

Guided immobilisation of single gold nanoparticles by chemical electron beam lithography

  • Patrick A. Schaal and
  • Ulrich Simon

Beilstein J. Nanotechnol. 2013, 4, 336–344, doi:10.3762/bjnano.4.39

Graphical Abstract
  • ” and “Correct horizontal scars (strokes)”. In addition, measurements with an edge length greater than 5 µm or distinct curvature were also corrected with “Remove polynomial background (degree: 2)”. Calculation of primary electron paths Paths of primary electrons in solid substrates were calculated with
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Published 31 May 2013

Interpreting motion and force for narrow-band intermodulation atomic force microscopy

  • Daniel Platz,
  • Daniel Forchheimer,
  • Erik A. Tholén and
  • David B. Haviland

Beilstein J. Nanotechnol. 2013, 4, 45–56, doi:10.3762/bjnano.4.5

Graphical Abstract
  • possible. We have previously shown how the individual amplitudes [26] and phases [30] of the IMPs in the narrow band around the first flexural resonance can be used for imaging. Furthermore, a polynomial reconstruction of the tip–surface force [31][32] and a numerical fit of the parameters of a force model
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Published 21 Jan 2013
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