scholarly journals THREE-VARIABLE ALTERNATING TRIGONOMETRIC FUNCTIONS AND CORRESPONDING FOURIER TRANSFORMS

2016 ◽  
Vol 56 (3) ◽  
pp. 156
Author(s):  
Agata Bezubik ◽  
Severin Pošta
Keyword(s):  
Fourier Transforms ◽  
Special Functions ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Trigonometric Functions ◽  
New Class ◽  
The Common

The common trigonometric functions admit generalizations to any higher dimension, the symmetric, antisymmetric and alternating ones. In this paper, we restrict ourselves to three dimensional generalization only, focusing on alternating case in detail. Many specific properties of this new class of special functions useful in applications are studied. Such are the orthogonalities, both the continuous one and the discrete one on the 3D lattice of any density, corresponding discrete and continuous Fourier transforms, and others. Rapidly increasing precision of the interpolation with increasing density of the 3<em>D</em> lattice is shown in an example.

Radon transforms, alignment, and 3d-reconstruction from random projections

1996 ◽  
Vol 54 ◽  
pp. 588-589
Author(s):  
Michael Radermacher
Keyword(s):  
Radon Transform ◽  
Fourier Transforms ◽  
Three Dimensional ◽  
Radon Transforms ◽  
One Dimensional ◽  
Dimensional Reconstruction ◽  
Section Theorem ◽  
Common Lines ◽  
The Common ◽  
Polar Grid

Since their inception three-dimensional reconstruction techniques have been based on the theory of Radon transforms. Only much later have Radon transforms been recognized as powerful tools for image processing and pattern recognition. Techniques like the “common lines ” technique for finding the orientation of projections of highly symmetrical particles, which had been developed using Fourier transforms, can easily be translated into a technique that uses Radon transforms. In contrast to Fourier transforms Radon transforms have the advantage of being real valued which simplifies many interpolation steps. The central section theorem known for Fourier transforms also applies to Radon transforms. The two- or three-dimensional Fourier transform on a polar grid can be obtained from the two- or three-dimensional Radon transform by a one-dimensional (radial) Fourier transforms and vice versa. Fourier transforms obtained by a one-dimensional transformation of the Radon transform will be referred to a Fourier/Radon transforms.

A Peptoid with Extended Shape in Water

2019 ◽  
Author(s):  
Jumpei Morimoto ◽  
Yasuhiro Fukuda ◽  
Takumu Watanabe ◽  
Daisuke Kuroda ◽  
Kouhei Tsumoto ◽  
...  
Keyword(s):  
Spectroscopic Analysis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Biomolecular Recognition ◽  
Biological Application ◽  
New Class ◽  
Proteolytic Resistance ◽  
Pharmacokinetic Properties ◽  
Optically Pure ◽  
Three Dimensional Space

<div> <div> <div> <p>“Peptoids” was proposed, over decades ago, as a term describing analogs of peptides that exhibit better physicochemical and pharmacokinetic properties than peptides. Oligo-(N-substituted glycines) (oligo-NSG) was previously proposed as a peptoid due to its high proteolytic resistance and membrane permeability. However, oligo-NSG is conformationally flexible and is difficult to achieve a defined shape in water. This conformational flexibility is severely limiting biological application of oligo-NSG. Here, we propose oligo-(N-substituted alanines) (oligo-NSA) as a new peptoid that forms a defined shape in water. A synthetic method established in this study enabled the first isolation and conformational study of optically pure oligo-NSA. Computational simulations, crystallographic studies and spectroscopic analysis demonstrated the well-defined extended shape of oligo-NSA realized by backbone steric effects. The new class of peptoid achieves the constrained conformation without any assistance of N-substituents and serves as an ideal scaffold for displaying functional groups in well-defined three-dimensional space, which leads to effective biomolecular recognition. </p> </div> </div> </div>

Synthetic Strategies to Access Heteroatomic Spirocentres Embedded in Natural Products

Synthesis ◽  
2021 ◽  
Author(s):  
Michael P. Badart ◽  
Bill C. Hawkins
Keyword(s):  
Natural Products ◽  
Heterocyclic Compound ◽  
Chemical Space ◽  
Three Dimensional ◽  
Coupling Reactions ◽  
Conjugate Additions ◽  
Biological Targets ◽  
Compound Libraries ◽  
The Common ◽  
Significant Attention

AbstractThe spirocyclic motif is abundant in natural products and provides an ideal three-dimensional template to interact with biological targets. With significant attention historically expended on the synthesis of flat-heterocyclic compound libraries, methods to access the less-explored three-dimensional medicinal-chemical space will continue to increase in demand. Herein, we highlight by reaction class the common strategies used to construct the spirocyclic centres embedded in a series of well-studied natural products.1 Introduction2 Cycloadditions3 Palladium-Catalysed Coupling Reactions4 Conjugate Additions5 Imines, Aminals, and Hemiaminal Ethers6 Mannich-Type Reactions7 Oxidative Dearomatisation8 Alkylation9 Organometallic Additions10 Conclusions

scholarly journals Crystal structure of a new monoclinic polymorph ofN-(4-methylphenyl)-3-nitropyridin-2-amine

2014 ◽  
Vol 70 (8) ◽  
pp. 58-61
Author(s):  
Aina Mardia Akhmad Aznan ◽  
Zanariah Abdullah ◽  
Vannajan Sanghiran Lee ◽  
Edward R. T. Tiekink
Keyword(s):  
Three Dimensional ◽  
Basis Set ◽  
Dihedral Angles ◽  
Asymmetric Unit ◽  
Acta Cryst ◽  
Common Features ◽  
Compound C ◽  
B3lyp Level ◽  
The Common ◽  
Independent Molecules

The title compound, C12H11N3O2, is a second monoclinic polymorph (P21, withZ′ = 4) of the previously reported monoclinic (P21/c, withZ′ = 2) form [Akhmad Aznanet al.(2010).Acta Cryst.E66, o2400]. Four independent molecules comprise the asymmetric unit, which have the common features of asyndisposition of the pyridine N atom and the toluene ring, and an intramolecular amine–nitro N—H...O hydrogen bond. The differences between molecules relate to the dihedral angles between the rings which range from 2.92 (19) to 26.24 (19)°. The geometry-optimized structure [B3LYP level of theory and 6–311 g+(d,p) basis set] has the same features except that the entire molecule is planar. In the crystal, the three-dimensional architecture is consolidated by a combination of C—H...O, C—H...π, nitro-N—O...π and π–π interactions [inter-centroid distances = 3.649 (2)–3.916 (2) Å].

The crystal structure of myoglobin. VI. Seal myoglobin

1960 ◽  
Vol 258 (1293) ◽  
pp. 181-201 ◽  
Keyword(s):  
Tertiary Structure ◽  
Heavy Atom ◽  
Three Dimensional ◽  
Sperm Whale ◽  
Fourier Synthesis ◽  
Heavy Atoms ◽  
Isomorphous Replacement ◽  
Unit Cells ◽  
The Common ◽  
Sperm Whale Myoglobin

Myoglobin from the common seal ( Phoca vitulina ) when crystallized from ammonium sulphate forms monoclinic crystals with space group the unit cell, a = 57·9Å, b = 29·6Å, c = 106·4Å, β = 102°15', contains four molecules. The method of isomorphous replacement has been used in an investigation of the centrosymmetric b -axis projection in which it has been possible to determine signs for nearly all the h0l reflexions having spacings greater than 4Å. Three independent heavy-atom derivatives were employed and the signs so determined have been used to compute a map of the electron density projected on the (010) plane. This projection has been interpreted in terms of the molecule of sperm-whale myoglobin, as deduced by Bodo, Dintzis, Kendrew & Wyckoff (1959) from a three-dimensional Fourier synthesis to 6Å resolution. The results of the interpretation show that the two myoglobin molecules are very similar in form (tertiary structure) in spite of the differences in their amino-acid composition. The relative orientation of the two unit cells with respect to the myoglobin molecule is given and a comparison is made of the positions of the heavy atoms in each molecule.

Mechanism Design and Kinematics Simulation of Massage Mechanical Arm

2011 ◽  
Vol 101-102 ◽  
pp. 279-282 ◽  
Author(s):  
Jun Xie ◽  
Jun Zhang ◽  
Jie Li
Keyword(s):  
Mechanism Design ◽  
Three Dimensional ◽  
Forward Kinematics ◽  
Kinematics Analysis ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Kinematics Model ◽  
Kinematics Simulation ◽  
The Common ◽  
Executive Mechanism

Based on the characteristics and the common massage manipulations of Chinese medical massage, a practical series mechanical arm was presented to act the manipulations with the parallel executive mechanism. Forward kinematics was solved by the Denavit-Hartenberg transformation after the kinematics model of the arm was established. And the three-dimensional model of the arm was created by Pro/E and was imported into ADAMS for the kinematics analysis. The results indicated that the common massage manipulations could be simulated by the arm correctly and flexibly, and it verified the accuracy of the mechanism design of the arm.

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

1996 ◽  
Vol 126 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Anne de Bouard
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Ion Acoustic Waves ◽  
Stability And Instability ◽  
Ion Acoustic ◽  
De Vries ◽  
The Stability

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

A three-dimensional hierarchical Fe2O3@NiO core/shell nanorod array on carbon cloth: a new class of anode for high-performance lithium-ion batteries

Nanoscale ◽  
2013 ◽  
Vol 5 (17) ◽  
pp. 7906 ◽  
Author(s):  
Qin-qin Xiong ◽  
Jiang-ping Tu ◽  
Xin-hui Xia ◽  
Xu-yang Zhao ◽  
Chang-dong Gu ◽  
...  
Keyword(s):  
Lithium Ion Batteries ◽  
High Performance ◽  
Three Dimensional ◽  
Lithium Ion ◽  
Nanorod Array ◽  
Core Shell ◽  
Carbon Cloth ◽  
New Class

Trajectory planning for coordinately operating robots

1990 ◽  
Vol 4 (3) ◽  
pp. 165-177 ◽  
Author(s):  
Y. P. Chien ◽  
Qing Xue
Keyword(s):  
Trajectory Planning ◽  
Three Dimensional ◽  
Initial Position ◽  
Minimum Time ◽  
Future Research ◽  
Rigid Object ◽  
Redundant Robots ◽  
Planning Algorithm ◽  
The Common ◽  
Joint Velocity

An efficient locally minimum-time trajectory planning algorithm for coordinately operating multiple robots is introduced. The task of the robots is to carry a common rigid object from an initial position to a final position along a given path in three-dimensional workspace in minimum time. The number of robots in the system is arbitrary. In the proposed algorithm, the desired motion of the common object carried by the robots is used as the key to planning of the trajectories of all the non-redundant robots involved. The search method is used in the trajectory planning. The planned robot trajectories satisfy the joint velocity, acceleration and torque constraints as well as the path constraints. The other constraints such as collision-free constraints, can be easily incorporated into the trajectory planning in future research.

scholarly journals Fast and Robust Orientation of Cryo-Electron Microscopy Images

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Guoliang Xu ◽  
Xia Wang ◽  
Ming Li ◽  
Zhucui Jing
Keyword(s):  
Sparse Matrix ◽  
Three Dimensional ◽  
Image Plane ◽  
Real Space ◽  
Computation Method ◽  
Common Line ◽  
The Matrix ◽  
Common Lines ◽  
The Common ◽  
Dimensional Object

AbstractWe present an efficient and reliable algorithm for determining the orientations of noisy images obtained fromprojections of a three-dimensional object. Based on the linear relationship among the common line vectors in one image plane, we construct a sparse matrix, and show that the coordinates of the common line vectors are the eigenvectors of the matrix with respect to the eigenvalue 1. The projection directions and in-plane rotation angles can be determined fromthese coordinates. A robust computation method of common lines in the real space using aweighted cross-correlation function is proposed to increase the robustness of the algorithm against the noise. A small number of good leading images, which have the maximal dissimilarity, are used to increase the reliability of orientations and improve the efficiency for determining the orientations of all the images. Numerical experiments show that the proposed algorithm is effective and efficient.

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