New applications to invariant matrix norms and combinatorics of an integral representation of natural powers of the numerical values

2021 ◽  
Vol 15 (4) ◽  
Author(s):  
Hassan A. Issa ◽  
Bassam Mourad ◽  
Hassane Abbas
Keyword(s):  
Integral Representation ◽  
New Applications ◽  
Matrix Norms

Representation by Quadratic Forms

1949 ◽  
Vol 1 (4) ◽  
pp. 344-364 ◽  
Author(s):  
Gordon Pall
Keyword(s):  
Integral Representation ◽  
Quadratic Forms ◽  
Binary Quadratic Forms ◽  
Ternary Quadratic Forms ◽  
Large Numbers ◽  
New Applications ◽  
Correct Estimate

1. Introduction. The elementary portions of the theory of integral representation of numbers or forms by quadratic forms will be somewhat simplified and generalized in this article. This indicates certain directions in which new applications can be made. The applications made here will be largely to the representation of numbers or binary quadratic forms by ternary quadratic forms. Particularly, we shall obtain the correct estimate (Theorem 10) needed to fill a lacuna in certain work of U. V. Linnik [1] on the representation of large numbers by ternary quadratic forms. Since Linnik applied his theorem on ternaries to prove [9] that every large number is a sum of at most seven positive cubes, a lacuna in this proof can now be regarded as filled.

1250-kilovolt scanning transmission electron microscope

1984 ◽  
Vol 42 ◽  
pp. 624-625
Author(s):  
T. Imura ◽  
S. Maruse ◽  
K. Mihama ◽  
M. Iseki ◽  
M. Hibino ◽  
...  
Keyword(s):  
High Voltage ◽  
Electron Probe ◽  
Scanning Transmission Electron Microscope ◽  
Pressure Vessels ◽  
Practical Applications ◽  
Voltage Generator ◽  
Transmission Electron ◽  
Scanning Transmission ◽  
New Applications ◽  
High Voltage Generator

Ultra high voltage STEM has many inherent technical advantages over CTEM. These advantages include better signal detectability and signal processing capability. It is hoped that it will explore some new applications which were previously not possible. Conventional STEM (including CTEM with STEM attachment), however, has been unable to provide these inherent advantages due to insufficient performance and engineering problems. Recently we have developed a new 1250 kV STEM and completed installation at Nagoya University in Japan. It has been designed to break through conventional engineering limitations and bring about theoretical advantage in practical applications.In the design of this instrument, we exercised maximum care in providing a stable electron probe. A high voltage generator and an accelerator are housed in two separate pressure vessels and they are connected with a high voltage resistor cable.(Fig. 1) This design minimized induction generated from the high voltage generator, which is a high frequency Cockcroft-Walton type, being transmitted to the electron probe.

IN-BEAM NUCLEAR MAGNETIC RESONANCE OF β-ACTIVE NUCLEI PRODUCED BY CAPTURE OF POLARIZED NEUTRONS - SOME NEW APPLICATIONS

1982 ◽  
Vol 43 (C7) ◽  
pp. C7-305-C7-308
Author(s):  
H. Ackermann ◽  
B. Bader ◽  
P. Freiländer ◽  
P. Heitjans ◽  
G. Kiese ◽  
...  
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Polarized Neutrons ◽  
New Applications ◽  
Nuclear Magnetic

WHO WHO'S STRATEGY IN THE NATIONAL MEDICINE SECTOR FOR 2013-2023 AND NEW APPLICATIONS OF PHYTOTIC PRODUCTION IN THE CARPATHIANS

Fitoterapia ◽  
2019 ◽  
Vol 4 (4) ◽  
pp. 74-75
Author(s):  
O. I. Voloshуn ◽  
◽  
M. M. Stovpyuk ◽  
O. V. Hyndych ◽  
L. O. Voloshina ◽  
...  
Keyword(s):  
The Carpathians ◽  
New Applications

Extending the Applicability of the ANI Deep Learning Molecular Potential to Sulfur and Halogens

2020 ◽  
Author(s):  
Christian Devereux ◽  
Justin Smith ◽  
Kate Davis ◽  
Kipton Barros ◽  
Roman Zubatyuk ◽  
...  
Keyword(s):  
Drug Development ◽  
Autonomous Vehicles ◽  
Potential Energy Surfaces ◽  
Organic Molecules ◽  
Chemical Elements ◽  
Molecular Potential ◽  
Wide Range ◽  
Energy Surfaces ◽  
New Applications ◽  
Physical Phenomena

<p>Machine learning (ML) methods have become powerful, predictive tools in a wide range of applications, such as facial recognition and autonomous vehicles. In the sciences, computational chemists and physicists have been using ML for the prediction of physical phenomena, such as atomistic potential energy surfaces and reaction pathways. Transferable ML potentials, such as ANI-1x, have been developed with the goal of accurately simulating organic molecules containing the chemical elements H, C, N, and O. Here we provide an extension of the ANI-1x model. The new model, dubbed ANI-2x, is trained to three additional chemical elements: S, F, and Cl. Additionally, ANI-2x underwent torsional refinement training to better predict molecular torsion profiles. These new features open a wide range of new applications within organic chemistry and drug development. These seven elements (H, C, N, O, F, Cl, S) make up ~90% of drug like molecules. To show that these additions do not sacrifice accuracy, we have tested this model across a range of organic molecules and applications, including the COMP6 benchmark, dihedral rotations, conformer scoring, and non-bonded interactions. ANI-2x is shown to accurately predict molecular energies compared to DFT with a ~10<sup>6</sup> factor speedup and a negligible slowdown compared to ANI-1x. The resulting model is a valuable tool for drug development that can potentially replace both quantum calculations and classical force fields for myriad applications.</p>

Nickel-Catalyzed Inter- and Intramolecular Carbon-Sulfur Bond Metathesis by Reversible Arylation

2019 ◽  
Author(s):  
Tristan Delcaillau ◽  
Alessandro Bismuto ◽  
Zhong Lian ◽  
Bill Morandi
Keyword(s):  
Good Yield ◽  
Functional Group ◽  
Product Formation ◽  
Single Bond ◽  
Ring Closing Metathesis ◽  
Catalytic Systems ◽  
Metathesis Reactions ◽  
New Applications ◽  
Further Development ◽  
Sulfur Bond

A nickel-catalyzed carbon-sulfur bond metathesis has been developed to access high-value thioethers. 1,2-bis(dicyclohexylphosphino)ethane (dcype) is essential to promote this highly functional group tolerant reaction. Further, synthetically challenging macrocycles could be obtained in good yield in an unusual example of ring-closing metathesis which does not involve alkene bonds. In-depth organometallic studies support a reversible Ni(0)-Ni(II) pathway to product formation. Overall, this work does not only disclose a more sustainable and more functional group tolerant alternative to previous catalytic systems based on Pd, but also presents new applications and mechanistic information which are highly relevant to the further development and application of unusual single bond metathesis reactions.

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