symmetry relations
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2021 ◽  
Vol 29 ◽  
Author(s):  
Ahmed Hameed Abdulmajeed Abeer Hussein Abid

This research work is part of a project to get an M.A. degree. Some of the linguistic sciences specialized in the search for meaning in the text, such as semantics, pragmatics, cognitive linguistics and etc. will be clarified. Besides, we shed light on the elements of semantic analysis with examples according to the basic scheme theory of reference, which indicates that the language is of a fictional nature. As it is a variety of similarity and symmetry relations between the form of the word and its meaning, whether it is phonetic or written or related to metaphor, metonymy or analogy, and it is not a random relationship. In all these genres, a very important role is played by imaginative comprehension, which subsequently acquires a traditional character and spreads due to the common collective understanding of the word among speakers of the speech community.


2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Marcel Algueró ◽  
Paula Alvarez Cartelle ◽  
Alexander Mclean Marshall ◽  
Pere Masjuan ◽  
Joaquim Matias ◽  
...  

Abstract In this paper we present a detailed study of the four-body decay B0 → K+π−ℓ+ℓ−, where tensions with the Standard Model predictions have been observed. Our analysis of the decay with P- and S-wave contributions to the K+π− system develops a complete understanding of the symmetries of the distribution, in the case of massless and massive leptons. In both cases, the symmetries determine relations between the observables in the B0 → K+π−ℓ+ℓ− decay distribution. This enables us to define the complete set of observables accessible to experiments, including several that have not previously been identified. The new observables arise when the decay rate is written differentially with respect to $$ {m}_{K_{\pi }} $$ m K π . We demonstrate that experiments will be able to fit this full decay distribution with currently available data sets and investigate the sensitivity to new physics scenarios given the experimental precision that is expected in the future.The symmetry relations provide a unique handle to explore the behaviour of S-wave observables by expressing them in terms of P-wave observables, therefore minimising the dependence on poorly-known S-wave form factors. Using this approach, we construct two theoretically optimized S-wave observables and explore their sensitivity to new physics. By further exploiting the symmetry relations, we obtain the first bounds on the S-wave observables using two different methods and highlight how these relations may be used as cross-checks of the experimental methodology and the parametrization of the B0 → K+π−ℓ+ℓ− differential decay rate. We identify a zero-crossing point that would be at a common dilepton invariant mass for a subset of P- and S-wave observables, and explore the information on new physics and hadronic effects that this zero point can provide.


IUCrJ ◽  
2021 ◽  
Vol 9 (1) ◽  
Author(s):  
Anna Olejniczak ◽  
Anna Katrusiak ◽  
Marcin Podsiadło ◽  
Andrzej Katrusiak

Partial hydration of organic compounds can be achieved by high-pressure crystallization. This has been demonstrated for the high-nitrogen-content compound 6-chloro-1,2,3,4-tetrazolo[1,5-b]pyridazine (C4H2N5Cl), which becomes partly hydrated by isochoric crystallizations below 0.15 GPa. This hydrate, C4H2N5Cl·xH2O, is isostructural with the ambient-pressure phase α of C4H2N5Cl, but the crystal volume is somewhat larger than that of the anhydrate. At 0.20 GPa, the α-C4H2N5Cl anhydrate phase transforms abruptly into a new higher-symmetry phase, α′; the transformation is clearly visible due to a strong contraction of the crystals. The hydrate α-C4H2N5Cl·xH2O can also be isothermally compressed up to 0.30 GPa before transforming to the α′-C4H2N5Cl·xH2O phase. The isochoric recrystallization of C4H2N5Cl above 0.18 GPa yields a new anhydrous phase β, which, on releasing pressure, transforms back to the α phase below 0.15 GPa. The structural transition from the α to the β phase is destructive for the single crystal and involves a large volume drop and significant elongation of all the shortest intermolecular distances which are the CH...N and CH...Cl hydrogen bonds, as well as the N...N contacts. The α-to-α′ phase transition increases the crystal symmetry in the subgroup relation; however, there are no structural nor symmetry relations between phases α and β.


Author(s):  
Marcos Barp ◽  
Felipe Arretche

The Fourier transform of Cartesian Gaussian functions product is presented in the light of positron scattering. The calculation of this class of integrals is crucial in order to obtain the scattering amplitude in the first Born approximation framework for an ab initio method recently proposed. A general solution to the scattering amplitude is given to a molecular target with no restriction due to symmetry. Moreover, symmetry relations are presented with the purpose of identifying terms that do not contribute to the calculation for the molecules in the D∞h point group optimizing the computational effort. Keywords — Positron and electron scattering, Fourier transform of the Gaussian product theorem, McMurchie-Davidson procedure, Obara-Saika procedure, linear molecules .


Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1756
Author(s):  
Abdelmejid Bayad ◽  
Yilmaz Simsek

The main purpose of this paper is to define p-adic and q-Dedekind type sums. Using the Volkenborn integral and the Teichmüller character representations of the Bernoulli polynomials, we give reciprocity law of these sums. These sums and their reciprocity law generalized some of the classical p-adic Dedekind sums and their reciprocity law. It is to be noted that the Dedekind reciprocity laws, is a fine study of the existing symmetry relations between the finite sums, considered in our study, and their symmetries through permutations of initial parameters.


Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1162
Author(s):  
Khaled A. AL-Utaibi ◽  
Sadiq H. Abdulhussain ◽  
Basheera M. Mahmmod ◽  
Marwah Abdulrazzaq Naser ◽  
Muntadher Alsabah ◽  
...  

Krawtchouk polynomials (KPs) and their moments are promising techniques for applications of information theory, coding theory, and signal processing. This is due to the special capabilities of KPs in feature extraction and classification processes. The main challenge in existing KPs recurrence algorithms is that of numerical errors, which occur during the computation of the coefficients in large polynomial sizes, particularly when the KP parameter (p) values deviate away from 0.5 to 0 and 1. To this end, this paper proposes a new recurrence relation in order to compute the coefficients of KPs in high orders. In particular, this paper discusses the development of a new algorithm and presents a new mathematical model for computing the initial value of the KP parameter. In addition, a new diagonal recurrence relation is introduced and used in the proposed algorithm. The diagonal recurrence algorithm was derived from the existing n direction and x direction recurrence algorithms. The diagonal and existing recurrence algorithms were subsequently exploited to compute the KP coefficients. First, the KP coefficients were computed for one partition after dividing the KP plane into four. To compute the KP coefficients in the other partitions, the symmetry relations were exploited. The performance evaluation of the proposed recurrence algorithm was determined through different comparisons which were carried out in state-of-the-art works in terms of reconstruction error, polynomial size, and computation cost. The obtained results indicate that the proposed algorithm is reliable and computes lesser coefficients when compared to the existing algorithms across wide ranges of parameter values of p and polynomial sizes N. The results also show that the improvement ratio of the computed coefficients ranges from 18.64% to 81.55% in comparison to the existing algorithms. Besides this, the proposed algorithm can generate polynomials of an order ∼8.5 times larger than those generated using state-of-the-art algorithms.


2021 ◽  
pp. e00932
Author(s):  
Prosper K. Doh ◽  
Kondo H. Adjallah ◽  
Babiga Birregah

Author(s):  
Joachim Breternitz ◽  
Susan Schorr

Binary III–V nitrides such as AlN, GaN and InN in the wurtzite-type structure have long been considered as potent semiconducting materials because of their optoelectronic properties, amongst others. With rising concerns over the utilization of scarce elements, a replacement of the trivalent cations by others in ternary and multinary nitrides has led to the development of different variants of nitrides and oxide nitrides crystallizing in lower-symmetry variants of wurtzite. This work presents the symmetry relationships between these structural types specific to nitrides and oxide nitrides and updates some prior work on this matter. The non-existence of compounds crystallizing in Pmc21, formally the highest subgroup of the wurtzite type fulfilling Pauling's rules for 1:1:2 stoichiometries, has been puzzling scientists for a while; a rationalization is given, from a crystallographic basis, of why this space group is unlikely to be adopted.


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