On Generating Elements of Orders Dividing p 2k ±p k  + 1

Grześkowiak, Maciej

doi:10.1007/978-3-540-89598-5_1

Cited by 3 publications

(4 citation statements)

References 15 publications

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“…17 It should be pointed out that NPT simulations of crytsals are difficult to set up for the reason that packing solvent is a tedious process of trial and error, causing most crystal simulations to be performed in the NVT ensemble. Each system is solvent equilibrated in a multistage fashion through a cycle of minimization, NVT heating, and NPT equilibration where the constraint weight on the solute is approximately halved at each turn [50,25,10,5,2 kcal/ (mol•Å 2 )], yielding in a total of ~100 ns solvent equilibration with fixed solute. Supercells are then constructed by propagating the solvent equilibrated unit cells and are further solvent equilibrated through the same cycle.…”

Section: Methodsmentioning

confidence: 99%

“…All studied systems except for the A-DNA (137D 48 ) have some form of coaxial stacking of the helices, which is common in nucleic acid crystals. Z-DNA (1LJX 49 ) and the two decamer B-DNAs (5DNB 43 and 1D23 50 ) form uniform columns and behave like "infinite" DNA helices, where the only coaxial interaction between molecules is base stacking. The dodecamer B-DNA (119D 51 and 1BNA 52 ) have zig-zag coaxial stacking induced by the special inter-molecular interactions denoted as Dickerson Interactions (DI) 55 where sets of three base pairs at both ends hydrogen bond with the consecutive molecules.…”

Section: Torsional Angle Distributionsmentioning

confidence: 99%

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Framework for Conducting and Analyzing Crystal Simulations of Nucleic Acids to Aid in Modern Force Field Evaluation

Ekesan

York

2019

J. Phys. Chem. B

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Crystal simulations provide useful tools, along with solution simulations, to test nucleic acid force fields, but should be interpreted with care owing to the difficulty of establishing the environmental conditions needed to reproduce experimental crystal packing. These challenges underscore the need to construct proper protocols for carrying out crystal simulations and analyzing results to identify the origin of deviations from crystallographic data. Toward this end, we introduce a novel framework for B-factor decomposition into additive intramolecular, rotational, and translational atomic fluctuation components, and partitioning of each of these components into individual asymmetric unit and lattice contributions. We apply the framework to a benchmark set of A-DNA, Z-DNA and B-DNA double helix systems of various chain lengths. Overall the intramolecular deviations from the crystal were quite small (≤ 1.0 Å), suggesting high accuracy of the force field, whereas crystal packing was not well reproduced. The present work establishes a framework to conduct and analyze crystal simulations that ultimately take on issues of crystal packing, and can provide insight into nucleic acid force fields.

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Section: Methodsmentioning

confidence: 99%

Section: Torsional Angle Distributionsmentioning

confidence: 99%

Framework for Conducting and Analyzing Crystal Simulations of Nucleic Acids to Aid in Modern Force Field Evaluation

Ekesan

York

2019

J. Phys. Chem. B

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“…32 A person must act for the benefit of another person or a collective entity. 33 That is why the regulation is criticised for unjust differentiation within the protection of a person acting in necessary defence, since as a result a person repelling an attack on someone else's good protected by law is granted stronger protection than the one defending their personal property. 34 It is also emphasised that this distinction is difficult to justify.…”

Section: Repelling An Attack On Someone Else's Good Protected By Lawmentioning

confidence: 99%

Intervention-related self-defence

Stefańska

2023

Ius Novum

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The scholarly and research-focused article examines the content of Article 25 §§ 4 and 5 CC, which was transferred to the new Article 231b §§ 1 and 2 CC of Chapter XXIX of the Criminal Code by means of Act of 20 February 2015 amending the Criminal Code Act and Certain Other Acts. The regulation concerns the intervention-related self-defence, wherein a person acting in self-defence and repelling an attack on another’s good protected by law, while simultaneously protecting public security or order, is granted the same legal protection as public officials. The article analyses the genesis and development of this defence, its legal nature, objectives, conditions for application, the scope of criminal law protection for a person acting within the intervention-related self-defence, the exclusion of this protection, and the relationship between Article 231b § 1 and Article 217a CC. The primary scientific objective is to evaluate the legitimacy of its introduction to the Criminal Code and the correctness of defining the premises for its application and its scope. The aim of the considerations is to demonstrate that this measure, despite the negative assessment of its introduction to the Criminal Code in the doctrine, can play a vital role in ensuring security and public order.

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“…The third approach for generating required primes was introduced by the author in [13][14][15][16][17]. For n = 5, the algorithm works as follows [17].…”

Section: A Formulation Of the Problem And Historical Commentsmentioning

confidence: 99%