scholarly journals Non-abelian analogs of lattice rounding

2015 ◽  
Vol 7 (2) ◽  
Author(s):  
Evgeni Begelfor ◽  
Stephen D. Miller ◽  
Ramarathnam Venkatesan
Keyword(s):  
Euclidean Space ◽  
Word Problem ◽  
Discrete Group ◽  
Point Of View ◽  
Ambient Space ◽  
Basis Set ◽  
Theoretical Justification ◽  
Matrix Groups ◽  
Nearest Point ◽  
Random Products

AbstractLattice rounding in Euclidean space can be viewed as finding the nearest point in the orbit of an action by a discrete group, relative to the norm inherited from the ambient space. Using this point of view, we initiate the study of non-abelian analogs of lattice rounding involving matrix groups. In one direction, we consider an algorithm for solving a normed word problem when the inputs are random products over a basis set, and give theoretical justification for its success. In another direction, we prove a general inapproximability result which essentially rules out

scholarly journals Photochemistry of 1-Phenyl-4-Allyl-Tetrazol-5-One: A Theoretical Study Contribution towards Mechanism Elucidation

2021 ◽  
Vol 11 (9) ◽  
pp. 4045
Author(s):  
Amilcar Duque-Prata ◽  
Carlos Serpa ◽  
Pedro J. S. B. Caridade
Keyword(s):  
Density Functional ◽  
Reaction Pathway ◽  
Intramolecular Proton Transfer ◽  
Polarizable Continuum Model ◽  
Uv Spectra ◽  
Point Of View ◽  
Basis Set ◽  
Pathway Evolution ◽  
Photodegradation Mechanism ◽  
Energetic Point

The photodegradation mechanism of 1-phenyl-4-allyl-tetrazol-5-one has been studied using (time-dependent) density functional theory with the M06-HF, B3LYP, and PBE0 functionals and the VDZ basis set. All calculations have been carried out using the polarizable continuum model to simulate the solvent effects of methanol. The reaction pathway evolution on the triplet state has been characterised to validate a previously postulated experimental-based mechanism. The transition states and minimums have been initially located by local scanning in partial constrained optimisation, followed by a fully relaxed search procedure. The UV spectra has shown to be better described with PBE0 functional when compared with the experimental results, having the M06-HF a shift of 40 nm. From the energetic point of view, the postulated mechanism has been validated in this work showing a concerted photoextrusion of the N2 molecule. The intramolecular proton transfer occurs at a later stage of the mechanism after cyclization of the allyl group on a triplet biradical intermediate. The photoproduct observed experimentally, a pyrimidinone, has been characterised. The infrared spectroscopic reaction profile has also been proposed.

SMOLYANOV–WEIZSÄCKER SURFACE MEASURES GENERATED BY DIFFUSIONS ON THE SET OF TRAJECTORIES IN RIEMANNIAN MANIFOLDS

2008 ◽  
Vol 11 (01) ◽  
pp. 21-31 ◽  
Author(s):  
ILYA V. TELYATNIKOV
Keyword(s):  
Brownian Motion ◽  
Euclidean Space ◽  
Diffusion Process ◽  
Riemannian Manifolds ◽  
Marginal Distribution ◽  
Diffusion Processes ◽  
Ambient Space ◽  
Time Interval ◽  
Standard Brownian Motion ◽  
Limit Surface

We consider surface measures on the set of trajectories in a smooth compact Riemannian submanifold of Euclidean space generated by diffusion processes in the ambient space. A construction of surface measures on the path space of a smooth compact Riemannian submanifold of Euclidean space was introduced by Smolyanov and Weizsäcker for the case of the standard Brownian motion. The result presented in this paper extends the result of Smolyanov and Weizsäcker to the case when we consider measures generated by diffusion processes in the ambient space with nonidentical correlation operators. For every partition of the time interval, we consider the marginal distribution of the diffusion process in the ambient space under the condition that it visits the manifold at all times of the partition, when the mesh of the partition tends to zero. We prove the existence of some limit surface measures and the equivalence of the above measures to the distribution of some diffusion process on the manifold.

scholarly journals DFT Visualization and Experimental Evidence of BHT-Mg-Catalyzed Copolymerization of Lactides, Lactones and Ethylene Phosphates

Polymers ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1641 ◽  
Author(s):  
Ilya Nifant’ev ◽  
Andrey Shlyakhtin ◽  
Maxim Kosarev ◽  
Dmitry Gavrilov ◽  
Stanislav Karchevsky ◽  
...  
Keyword(s):  
Ring Opening ◽  
Density Functional ◽  
Point Of View ◽  
Basis Set ◽  
Random Copolymers ◽  
Key Factors ◽  
Functional Theory ◽  
Cyclic Esters ◽  
Dft Modeling ◽  
Derivatives Of

Catalytic ring-opening polymerization (ROP) of cyclic esters (lactides, lactones) and cyclic ethylene phosphates is an effective way to process materials with regulated hydrophilicity and controlled biodegradability. Random copolymers of cyclic monomers of different chemical nature are highly attractive due to their high variability of characteristics. Aryloxy-alkoxy complexes of non-toxic metals such as derivatives of 2,6-di-tert-butyl-4-methylphenoxy magnesium (BHT-Mg) complexes are effective coordination catalysts for homopolymerization of all types of traditional ROP monomers. In the present paper, we report the results of density functional theory (DFT) modeling of BHT-Mg-catalyzed copolymerization for lactone/lactide, lactone/ethylene phosphate and lactide/ethylene phosphate mixtures. ε-Caprolactone (ε-CL), l-lactide (l-LA) and methyl ethylene phosphate (MeOEP) were used as examples of monomers in DFT simulations by the Gaussian-09 program package with the B3PW91/DGTZVP basis set. Both binuclear and mononuclear reaction mechanistic concepts have been applied for the calculations of the reaction profiles. The results of calculations predict the possibility of the formation of random copolymers based on l-LA/MeOEP, and substantial hindrance of copolymerization for ε-CL/l-LA and ε-CL/MeOEP pairs. From the mechanistic point of view, the formation of highly stable five-membered chelate by the products of l-LA ring-opening and high donor properties of phosphates are the key factors that rule the reactions. The results of DFT modeling have been confirmed by copolymerization experiments.

scholarly journals Point vortex equilibria and optimal packings of circles on a sphere

2010 ◽  
Vol 467 (2129) ◽  
pp. 1468-1490 ◽  
Author(s):  
Paul K. Newton ◽  
Takashi Sakajo
Keyword(s):  
Particle Interaction ◽  
Point Vortex ◽  
Packing Problem ◽  
Point Of View ◽  
Basis Set ◽  
Equilibrium Solutions ◽  
Optimal Packing ◽  
Packing Process ◽  
Point Vortex Equilibria ◽  
The One

We answer the question of whether optimal packings of circles on a sphere are equilibrium solutions to the logarithmic particle interaction problem for values of N =3–12 and 24, the only values of N for which the optimal packing problem (also known as the Tammes problem) has rigorously known solutions. We also address the cases N =13–23 where optimal packing solutions have been computed, but not proven analytically. As in Jamaloodeen & Newton (Jamaloodeen & Newton 2006 Proc. R. Soc. Lond. Ser. A 462 , 3277–3299. ( doi:10.1098/rspa.2006.1731 )), a logarithmic, or point vortex equilibrium is determined by formulating the problem as the one in linear algebra, , where A is a N ( N −1)/2× N non-normal configuration matrix obtained by requiring that all interparticle distances remain constant. If A has a kernel, the strength vector is then determined as a right-singular vector associated with the zero singular value, or a vector that lies in the nullspace of A where the kernel is multi-dimensional. First we determine if the known optimal packing solution for a given value of N has a configuration matrix A with a non-empty nullspace. The answer is yes for N =3–9, 11–14, 16 and no for N =10, 15, 17–24. We then determine a basis set for the nullspace of A associated with the optimally packed state, answer the question of whether N -equal strength particles, , form an equilibrium for this configuration, and describe what is special about the icosahedral configuration from this point of view. We also find new equilibria by implementing two versions of a random walk algorithm. First, we cluster sub-groups of particles into patterns during the packing process, and ‘grow’ a packed state using a version of the ‘yin-yang’ algorithm of Longuet-Higgins (Longuet-Higgins 2008 Proc. R. Soc. A (doi:10.1098/rspa.2008.0219)). We also implement a version of our ‘Brownian ratchet’ algorithm to find new equilibria near the optimally packed state for N =10, 15, 17–24.

scholarly journals ON THE GRAPH EDIT DISTANCE COST: PROPERTIES AND APPLICATIONS

2012 ◽  
Vol 26 (05) ◽  
pp. 1260004 ◽  
Author(s):  
ALBERT SOLÉ-RIBALTA ◽  
FRANCESC SERRATOSA ◽  
ALBERTO SANFELIU
Keyword(s):  
Euclidean Space ◽  
Edit Distance ◽  
Point Of View ◽  
Graph Edit Distance

We model the edit distance as a function in a labeling space. A labeling space is an Euclidean space where coordinates are the edit costs. Through this model, we define a class of cost. A class of cost is a region in the labeling space that all the edit costs have the same optimal labeling. Moreover, we characterize the distance value through the labeling space. This new point of view of the edit distance gives us the opportunity of defining some interesting properties that are useful for a better understanding of the edit distance. Finally, we show the usefulness of these properties through some applications.

Feasibility study of hydrogen-bonded nucleic acid base pairs in gas and water phases — A theoretical study

2011 ◽  
Vol 89 (11) ◽  
pp. 1403-1409 ◽  
Author(s):  
S. Arshadi ◽  
A.R. Bekhradnia ◽  
A. Ebrahimnejad
Keyword(s):  
Hydrogen Bonding ◽  
Nucleic Acid ◽  
Hydrogen Bonds ◽  
Density Functional ◽  
Biological Properties ◽  
Point Of View ◽  
Basis Set ◽  
Base Pairs ◽  
Bonding Properties ◽  
Energetic Point

To investigate the base pair binding probabilities for nucleic acid bases, numerous models were studied for contacts between adenine, thymine, guanine, cytosine, and uracil using density functional theory (DFT) in combination with the 6–311G* basis set. We obtained an assessment for the energy given by our calculations in gas and aqueous phases, which showed that it should be incorporated into hydrogen bonding and propeller rotational energies. The 42 complexes of base pairs (5 regular and 37 irregular base pairs) were proposed and their hydrogen-bonding (H-bonding) properties were verified. The hydrogen bonds in some irregular base pairs, including CC, UU, and TT (series 1), were stronger than in regular GC and AT base pairs. Also, the strength of the hydrogen bonds in the proposed base pairs, including CU, GG, GU, and TU (series 2), were similar to regular base pairs from an energetic point of view. The propeller rotations revealed a higher rotational barrier energy (6–7.5 kcal/mol; 1 cal = 4.184 J) for irregular base pairs (series 1 and 2) than regular GC and AT ones (1–3 kcal/mol). Nevertheless, the trend in these affinities of the complex contact probabilities and their biological properties were confirmed by our calculations.

scholarly journals Theoretical justification of the influence of change of dilaton and compression bonds of atoms of materials of machine parts on their tribological effect

2021 ◽  
Vol 100 (2) ◽  
pp. 71-78
Author(s):  
V. Aulin ◽  
◽  
S. Lysenko ◽  
A. Hrinkiv ◽  
О. Derkach ◽  
...  
Keyword(s):  
Composite Materials ◽  
Friction And Wear ◽  
Composite Coatings ◽  
Point Of View ◽  
Solid State Physics ◽  
Surface Layers ◽  
Theoretical Justification ◽  
Friction Zone ◽  
Machine Parts ◽  
Bulk Content

The course of friction and wear processes in the surface layers of conjugations of machine parts is clarified on the basis of the idea of dilaton and compression bonds of atoms in the materials of parts. Dilaton-compression connections are random in nature, and therefore in this work the theory of destruction of parts by S.M. Zhurkov, thermodynamic and quantum physical approaches. The entropy at the macro-, meso- and microscopic levels and the local regions of the materials of conjugation of the parts subject to friction loading are considered. In the diagram of the state of atomic-molecular bonds the dependence curve Fi(ri) or Ti(ri) is considered and the analysis of transformations of bonds according to the specified diagram is carried out. From the point of view of solid state physics and tribophysics, the manifestation, evolution and consequences of the influence on the characteristics and properties of the friction zone of dilaton and compression bonds of material atoms are considered. Composite materials (composite coatings) are substantiated in more detail. This takes into account the assessment of the concept of material stresses in the friction zone, the ability to relax it, as well as the presence of the SD effect. The fracture process is associated with the modulus of elasticity of the components of the composite material and the bulk content of the filler. An appropriate condition is proposed, which determines the tribological efficiency of composite materials and coatings.

scholarly journals Cu-Doped KCl Unfolded Band Structure and Optical Properties Studied by DFT Calculations

2020 ◽  
Author(s):  
Cesar Castillo-Quevedo ◽  
Jose Luis Cabellos ◽  
Raul Aceves ◽  
Roberto Núñez-González ◽  
Alvaro Posada-Amarillas
Keyword(s):  
Optical Properties ◽  
Band Structure ◽  
Density Functional ◽  
Copper Ions ◽  
Point Of View ◽  
Basis Set ◽  
Theoretical Point ◽  
Conduction Bands ◽  
Cu Substitution ◽  
Effect Of Copper

The unfolded band structure and optical properties of Cu-doped KCl crystals were computed by first principles within the framework of density functional theory, implemented in the ABINIT electronic structure package utilizing pseudopotential approximation and a plane-wave basis set. From a theoretical point of view, Cu substitution into pristine KCl crystals requires calculation by the supercell (SC) method. This procedure shrinks the Brillouin zone, resulting in a folded band structure that is difficult to interpret. To solve this problem and gain insight into the effect of copper ions (Cu+) on electronic properties, the band structure of SC KCl:Cu was unfolded to make a direct comparison with the band structure of the primitive cell (PC) of pristine KCl. To understand the effect of Cu substitution on optical absorption, we calculated the imaginary part of the dielectric function of KCl:Cu through a sum-over-states formalism and broke it down into different band contributions by partially making an iterated cumulative sum (ICS) of selected valence and conduction bands. Consequently, we identified those interband transitions that give rise to the absorption peaks due to the Cu+ ion. These transitions involve valence and conduction bands formed by the Cu-3d and Cu-4s electronic states

scholarly journals On one relator groups and HNN extensions

1973 ◽  
Vol 16 (2) ◽  
pp. 249-256 ◽  
Author(s):  
James McCool ◽  
Paul E. Schupp
Keyword(s):  
Finite Order ◽  
Word Problem ◽  
Point Of View ◽  
Hnn Extensions ◽  
One Relator Groups

In his work [5] on subgroups of one relator groups, Moldavanski observed that if G is a one relator group whose defining relator R is cyclically reduced and has exponent sum zero on some generator occurring in it, then G is an HNN extension of a one relator group H whose defining relator is shorter than R. This observation, together with Britton's Lemma, can be used to give rather easy proofs of the basic results on one relator groups. To exposit this point of view, we give here a proof of the Freiheitssatz, the solvability of the word problem for one relator groups, and the theorem classifying elements of finite order in one relator groups. In particular, the solution obtained for the word problem is often easy to apply. We also give a proof of the “Spelling Theorem” of Newman [6].

scholarly journals On Certain Mappings of Riemannian Manifolds

1965 ◽  
Vol 25 ◽  
pp. 121-142
Author(s):  
Minoru Kurita
Keyword(s):  
Differential Geometry ◽  
Euclidean Space ◽  
Conformal Mapping ◽  
Riemannian Manifolds ◽  
Stereographic Projection ◽  
Point Of View ◽  
The Other ◽  
Central Projection ◽  
Special Cases ◽  
Special Case

In this paper we consider certain tensors associated with differentiable mappings of Riemannian manifolds and apply the results to a p-mapping, which is a special case of a subprojective one in affinely connected manifolds (cf. [1], [7]). The p-mapping in Riemannian manifolds is a generalization of a conformal mapping and a projective one. From a point of view of differential geometry an analogy between these mappings is well known. On the other hand it is interesting that a stereographic projection of a sphere onto a plane is conformal, while a central projection is projectve, namely geodesic-preserving. This situation was clarified partly in [6]. A p-mapping defined in this paper gives a precise explanation of this and also affords a certain mapping in the euclidean space which includes a similar mapping and an inversion as special cases.

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