Ring R2 Research Articles

Skew constacyclic codes of lengths ps and 2ps over [formula omitted

Let R2=Fpm+uFpm, where u2=0. In this paper, we determine the algebraic structures of all skew constacyclic codes of lengths ps and 2ps over R2 for special automorphisms. We also characterize the structure of (Euclidean) dual of some special skew constacyclic codes of length 2ps and calculate the number of codewords of them. As a special case, if we restrict our attention to the polynomial ring R2[x], we obtain most of results for constacyclic codes of lengths ps and 2ps over R2.

Twisted Hessian curves over the ring 𝔽<i><SUB align="right">q</i>[<i>∈</i>], <i>∈</i><SUP align="right">2</SUP> = 0

No AccessTwisted Hessian curves over the ring 𝔽q[∈], ∈2 = 0Abdelâli Grini, Abdelhakim Chillali, Lhoussain El Fadil and Hakima MouanisAbdelâli GriniDepartment of Mathematics, Faculty of Science Dhar El Mahraz-Fez, S.M. Ben Abdellah University, Fez, Morocco, Abdelhakim ChillaliDepartment of Mathematics, Physical and Computer Sciences, FP, LSI, Taza, S.M. Ben Abdellah University, Fez, Morocco, Lhoussain El FadilDepartment of Mathematics, Faculty of Science Dhar El Mahraz-Fez, S.M. Ben Abdellah University, Fez, Morocco and Hakima MouanisDepartment of Mathematics, Faculty of Science Dhar El Mahraz-Fez, S.M. Ben Abdellah University, Fez, MoroccoPublished Online:November 28, 2022pp 181-189https://doi.org/10.1504/IJCAET.2023.127795PDF ToolsAdd to FavouritesDownload CitationsTrack Citations Share this article on social mediaShareShare onFacebookTwitterLinkedInReddit AboutAbstractThe goal of this work is to study some arithmetic proprieties of the twisted Hessian curves defined by a equation of type: aX3 + Y3 + Z3 = dXYZ on the local ring R2 = 𝔽q[X]/(X2), where p ≥ 5 is a prime number, q = pd and d ∈ ℕ*, such that -3 is not a square in 𝔽q. This paper consists of an introduction, section, and a conclusion. In the introduction, we review some fundamental arithmetic proprieties of finite local rings R2, which will be used in the remainder of this article. The section is devoted to the study the above mentioned twisted Hessian curves on these finite local rings for restriction to some specific characteristic p ≥ 5. Using these studies, we give essential properties and we define the group H2a,d, these properties, the classification of these elements and a bijection between the sets H2a,d and Ha0,d0 × 𝔽q, where Ha0,d0 is the twisted Hessian curve over the finite field 𝔽q.Keywordstwisted Hessian curves, finite over ring, cryptography, elliptic curves, local ring Previous article Next article FiguresReferencesRelatedDetails Volume 18Issue 1-32023 ISSN: 1757-2657eISSN: 1757-2665 HistoryPublished onlineNovember 28, 2022 Copyright © 2023 Inderscience Enterprises Ltd.Keywordstwisted Hessian curvesfinite over ringcryptographyelliptic curveslocal ringAuthors and AffiliationsAbdelâli Grini1 Abdelhakim Chillali2 Lhoussain El Fadil3 Hakima Mouanis4 1. Department of Mathematics, Faculty of Science Dhar El Mahraz-Fez, S.M. Ben Abdellah University, Fez, Morocco2. Department of Mathematics, Physical and Computer Sciences, FP, LSI, Taza, S.M. Ben Abdellah University, Fez, Morocco3. Department of Mathematics, Faculty of Science Dhar El Mahraz-Fez, S.M. Ben Abdellah University, Fez, Morocco4. Department of Mathematics, Faculty of Science Dhar El Mahraz-Fez, S.M. Ben Abdellah University, Fez, MoroccoPDF download

HOMOMORPHISM AND ANTI-HOMOMORPHISM OF SPHERICAL CUBIC BI-IDEALS OF GAMMA NEAR-RINGS

The purpose of the article is to study about homomorphism and anti- homomorphism of spherical cubic bi-ideals of Gamma near-rings R1 and R2. If φ : R1 −→ R2 be a gamma homomorphism and (C U s1 , R1), (C U s2 , R2) are spher- ical cubic bi-ideals of gamma near-rings R1 and R2.Then the image (φ(C U s1 ), R2) and pre-image (φ−1(C U s ), R1) are also spherical cubic bi-ideals of gamma near- rings R2 and R1. If φ : R1 −→ R2 be an epimorphism of gamma near-rings R1 and R2 and (C U s , R2) is a SCS of R2 such that (φ−1(C U s ), R1) is a SCBI of 2 2 R1, then (C U s2 , R2) is a SCBI of R2.

The binary operations calculus in H

Let Fq be a finite field of q elements, where q is a power of a prime number p greater than or equal to 5, such that −3 is not a square in Fp. In this paper, we will study the twisted Hessian curve over the ring R2 = Fq[e], where the relation e^2 = 0. More precisely, we will give many various explicit formulas, which describe the binary operations calculus in H2a,d, where H2a,d is the twisted Hessian curve over R2, and we will reduce the cost of the complexity of the calculus in H2a,d.

Distance invariant method for normalization of indexed differentials

A distance from free to dummy indices is defined. The distance is invariant with respect to both monoterm symmetries and bottom antisymmetry. Using the distance invariant, we present an index-replacement algorithm. We then develop two normalization algorithms. One is with respect to monoterm symmetries and has complexity lower than known algorithms; the other allows one to determine the equivalence of indexed polynomials in the Einstein summation ring R2[∂̸].

A Fundamental Theorem of Powerful Set-Valued for F-Rough Ring

In this paper, we introduce the upper and lower approximations on the invers set-valued mapping and the approximations an established on a powerful set valued homomorphism from a ring R1 to power sets of a ring R2. Moreover, the properties of lower and upper approximations of a powerful set valued are studies. In addition, we will give a proof of the theorem of isomorphism over approximations F-rough ring as new result. However, we will prove the kernel of the powerful set-valued homomorphism is a subring of R1. Our result is introduce the first isomorphism theorem of ring as generalized the concept of the set valued mappings.

Galactic resonance rings: modelling of motions in the wide solar neighbourhood

Models of the Galaxy with analytical Ferrers bars can reproduce the residual velocities of OB-associations in the Sagittarius, Perseus and Local System stellar-gas complexes located within 3 kpc solar neighborhood. Ferrers ellipsoids with density distribution defined by power indices n=1 and 2 are considered. The success in the reproduction of the velocity in the Local System is due to the large velocity dispersion which weakens the resonance effects by producing smaller systematic motions. Model galaxies form nuclear, inner and outer resonance rings R1 and R2. The outer rings R2 manage to catch twice more particles than the rings R1. The outer Lindblad resonance of the bar (OLR) is located 0.4 kpc beyond the solar circle, R_OLR=R0+0.4 kpc, corresponding to the bar angular velocity of Omega_b=50 km s-1 kpc-1. The solar position angle with respect to the bar, theta_b, providing the agreement between model and observed velocities is 40-52 degrees. Unfortunately, models considered cannot reproduce the residual velocities in the Carina and Cygnus stellar-gas complexes. The redistribution of the specific angular momentum, L, is found near the Lindblad resonances of the bar (ILR and OLR): the average value of L increases (decreases) at the radii a bit smaller (larger) than those of the resonances that can be connected with the existence of two types of periodic orbits elongated perpendicular to each other there.

Trapping two types of particles using a focused partially coherent circular edge dislocations beam

A focused partially coherent circular edge dislocations beam used to trap Rayleigh dielectric sphere with different refractive indices is studied. The dependence of radiation forces on the number of circular edge dislocations p, the spatial correlation length σ0, relative refractive index nr, and particle radius a are analyzed and illustrated by numerical examples. It is shown that the focused partially coherent circular edge dislocations beam can be used to trap high index of refraction particles at focus F and bright ring R2, and simultaneously to capture low index of refraction particles at dark ring R1. It is much easier to capture the high index of refraction particles at focus F and the low index of refraction particles at dark ring as for the larger number of circular edge dislocations p and the spatial correlation length σ0, therefore it is necessary to optimally choose on p and σ0 for obtaining an optimal optical guiding. The ranges of the radius for two types of particles stably captured also have been determined. The obtained results are useful for analyzing the trapping efficiency of circular edge dislocations beams applied in micromanipulation technology.

Structural, spectral, quantum chemical and thermal studies on a new NLO crystal: guanidinium cinnamate

New organic non-linear optical (NLO) single crystals of guanidinium cinnamate were crystallized by solvent evaporation solution growth technique and the crystal and molecular structure were determined by single crystal X-ray diffraction. The crystal packing is dominated by classical N–H···O hydrogen bonding interactions. Due to deficiency of acceptor atoms compared to the donor sites, two unusual ring R2 1(6) motifs are formed through two N–H···O hydrogen bonds. These ring motifs are further connected through chain C2 2(6) or C2 2(8) motifs along the b-axis of the unit cell. Further, these chain and ring motifs are cross-linked through another N–H···O hydrogen bond leading to classical ring R2 2(8) motif. These chain and ring motifs are interlinked with each other to form secondary ring R6 6(14)/R6 6(16) motifs. The molecular geometry of the asymmetric part of the unit cell was optimized theoretically by density functional theory using the B3LYP function with 6-311 + + G(d,p) basis set. The optimized molecular geometry and computed vibrational spectra are compared with experimental results which showed significant agreement. The intermolecular interactions of the title compound were analyzed by the Hirshfeld surfaces. The computed hyperpolarizability values showed that the compound is a good candidate for NLO applications. The chemical hardness, electro-negativity and chemical potential of the molecule were computed by HOMO–LUMO plot. The lower band gap of the frontier orbitals indicates the suitability of fabrication of the material for non-linear optoelectronic applications.

Enhancement of Light-to-Dark Current Ratio Via Coupling Effect for MIS (p) Tunnel Diode Photo Sensors

MIS tunnel diodes have been used as sensing devices since MIS tunnel currents are very sensitive to surrounding signals. It is found that MIS tunnel currents are perimeter-dependent due to magnifying of finging-field effect. And, it is shown that MIS saturation currents have a strong relationship with Schottky barrier height which indicates that a slight change of Schottky barrier height would make a big move of MIS tunnel currents. In this work, a structure of concentric circle is used. Photo response is examined by light-to-dark current ratio Ilight/Idark. It is found that MIS tunnel currents can be controlled by the voltage bias of the nearby MOS capacitor since the voltage bias of the nearby MOS capacitor(VG) determines the amount of minority carriers underneath the gate and therefore the diffusion currents to the MIS sensing tunnel diode. As a result, by well controlling VG, Ilight/Idark ratio can be effectively enhanced. It is also shown that under different intensities of illumination, the maximum of Ilight/Idark occurred at different value of VG. The underlying mechanism will be explained later. Fig.1(a),(b) show the top and schematic view of the concentric circle device with radius of inner ring R1=170um, and outer ring R2=675um. Fig.2 shows the MIS tunnel currents ITD versus VTD with VG floating. It is found there are different mechanisms dominating when VTD is biased at negative and positive voltage. When VTD is biased at negative voltage, ITD increases with oxide thickness decreasing. This can be explained by gate-injection theory. However, when VTD is biased at positive voltage, ITD increases with oxide thickness increasing. This can be explained by Schottky barrier theory, that is when oxide thickness increases, the voltage drop on the oxide will increase so the Schottky barrier height will decrease causing the increase of the tunnel current ITDshown in Fig.2. Fig.3(a) shows the MIS tunnel currents ITD of different oxide thicknesses at dark and with light versus VTD with VG floating. Solid line and dash line represent the dark current and light current respectively. Note that the illumination intensity is 7mW/cm2.Three different oxide thicknesses were extracted out. Fig.3(b) shows the Ilight/Idark versus VTD with VG floating. From the figure, it is shown that the Ilight/Idark is of one order. Fig.3(c) shows the MIS tunnel currents ITD of different oxide thicknesses at dark and with light versus VG while VTD fixed at 2.5V. Fig.3(d) shows the Ilight/Idark versus VG with VTD fixed at 2.5V. Surprisingly, it is found that when VG is biased around -0.5V, Ilight/Idark can be enhanced to two orders. The underlying mechanism is that when VG is biased near the flat-band, there are nearly no charges underneath the gate, so there are few charges accumulating underneath the tunnel diode causing the low tunnel current and hence the enhancement of Ilight/Idarkratio. In the following, the intensity of light was enhanced to 15mW/cm2. Fig.4(a) shows the MIS tunnel currents ITD of different oxide thicknesses at dark and with light versus VTD with VG floating. Also, three different oxide thicknesses were extracted out. Fig.4(b) shows the corresponding Ilight/Idark versus VTD with VG floating. It is shown that the Ilight/Idark is of two orders. Fig.4(c) shows the MIS tunnel currents ITD of different oxide thicknesses at dark and with light versus VG while VTD fixed at 2.5V. Fig. 4(d) shows the Ilight/Idark versus VG with VTD fixed at 2.5V. Amazingly, it is found that when VG is biased near -0.9V, the Ilight/Idarkratio can be effectively enhanced to four orders. What’s interesting is that the maximum of Ilight/Idark ratio occurred at different value of VG compared to the light intensity is 7mW/cm2. The reason is that when implementing weak illumination which is 7mW/cm2, the number of light-induced carriers is relatively low which means the tunnel currents are still affected by the charges from the gate. As a result, it can be inferred that light currents change relatively high while sweeping VG. However, when implementing stronger illumination which is 15 mW/cm2, the number of light-induced carriers will increase, so the coupling effect from the gate will reduce causing light currents move relatively slightly while sweeping VG. Consequently, the maximum of Ilight/Idarkratio will occur at where the dark currents is lowest. This work was supported by the Ministry of Science and Technology of Taiwan, ROC, under Contract No. Most 105-2221-E-002-180-MY3 and NTU-ERP-105R89081 [1] C. S. Liao and J. G. Hwu, ECS Trans., 75, 77 (2016). [2] W.C. Kao and J.G Hwu, ECS Trans., 72(2), 223 (2016) Figure 1

Structural insights, protein-ligand interactions and spectroscopic characterization of isoformononetin

Isoformononetin, a methoxylated isoflavone present in medicinal plants, has non-estrogenic bone forming effect via differential mitogen-activated protein kinase (MAPK) signaling. Spectroscopic (FT-Raman, FT-IR, UV–vis and NMR spectra) and quantum chemical calculations using density functional theory (DFT) and 6-311++G(d,p) as a large basis set have been employed to study the structural and electronic properties of isoformononetin. A detailed conformational analysis is performed to determine the stability among conformers and the various possibilities of intramolecular hydrogen bonding formation. Molecular docking studies with different protein kinases were performed on isoformononetin and previously studied isoflavonoid, formononetin in order to understand their inhibitory nature and the effect of functional groups on osteogenic or osteoporosis associated proteins. It is found that the oxygen atoms of methoxy, hydroxyl groups attached to phenyl rings R1, R3 and carbonyl group attached to pyran ring R2, play a major role in binding with the protein kinases that is responsible for the osteoporosis; however, no hydrophobic interactions are observed between rings of ligand and protein. The electronic properties such as HOMO and LUMO energies were determined by time-dependent TD-DFT which predict that conformer II is a little bit more stable and chemically low reactive than conformer I of isoformononetin. To estimate the structure-activity relationship, the molecular electrostatic potential (MEP) surface map, and reactivity descriptors are calculated from the optimized geometry of the molecule. From these results, it is also found that isoformononetin is kinetically more stable, less toxic, weak electrophile and chemically less reactive than formononetin. The atoms in molecules and natural bond orbital analysis are applied for the detailed analysis of intra and intermolecular hydrogen bonding interactions.

Quantum Codes From Cyclic Codes Over The Ring R2

Let R2 denotes the ring F2 + μF2 + υ2 + μυF2 + wF2 + μwF2 + υwF2 + μυwF2. In this study, we construct quantum codes from cyclic codes over the ring R2, for arbitrary length n, with the restrictions μ2 = 0, υ2 = 0, w2 = 0, μυ = υμ, μw = wμ, υw = wυ and μ (υw) = (μυ) w. Also, we give a necessary and sufficient condition for cyclic codes over R2 that contains its dual. As a final point, we obtain the parameters of quantum error-correcting codes from cyclic codes over R2 and we give an example of quantum error-correcting codes form cyclic codes over R2.

Evidence of the Galactic outer ring R 1 R 2 ′ $R_{1}R_{2}'$ from young open clusters and OB-associations

The distribution of young open clusters in the Galactic plane within 3 kpc from the Sun suggests the existence of the outer ring R1R2' in the Galaxy. The optimum value of the solar position angle with respect to the major axis of the bar, theta_b, providing the best agreement between the distribution of open clusters and model particles is theta_b=35 +/- 10 degrees. The kinematical features obtained for young open clusters and OB-associations with negative Galactocentric radial velocity VR indicate the solar location near the descending segment of the outer ring R2.

New extremal binary self-dual codes from a modified four circulant construction

In this work, we propose a modified four circulant construction for self-dual codes and a bordered version of the construction using the properties of λ-circulant and λ-reverse circulant matrices. By using the constructions on F2, we obtain new binary codes of lengths 64 and 68. We also apply the constructions to the ring R2 and considering the F2 and R1-extensions, we obtain new singly-even extremal binary self-dual codes of lengths 66 and 68. More precisely, we find 3 new codes of length 64, 13 new codes of length 66 and 21 new codes of length 68. These codes all have weight enumerators with parameters that were not known to exist in the literature.

Classical Cepheids in the Galactic outer ring R1R ′2

AbstractThe kinematics and distribution of classical Cepheids within ∼3 kpc from the Sun suggest the existence of the outer ring R1R ′2 in the Galaxy. The optimum value of the solar position angle with respect to the major axis of the bar, θb, providing the best agreement between the distribution of Cepheids and model particles, is θb = 37° ±13°. The kinematical features obtained for Cepheids with negative galactocentric radial velocity VR are consistent with the solar location near the descending segment of the outer ring R2. The sharp rise of extinction toward of the Galactic center can be explained by the presence of the outer ring R1 near the Sun. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Some results on cyclic codes over the ring $R_{2,m}$

Let Rk;m be the ring F2m(u1;u2; � � � ;uk)= ⟨ u 2;uiuj ujui ⟩ . In this paper, cyclic codes of arbitrary length n over the ring R2;m are completely characterized in terms of unique generators and a way for determination of these generators is investigated. A F2m -basis for these codes is also derived from this representation. Moreover, it is proven that there exists a one-to-one correspondence between cyclic codes of length 2n, n odd, over the ring Rk 1;m and cyclic codes of length n over the ring Rk;m. By determining the complete structure of cyclic codes of length 2 over R2;m, a mass formula for the number of these codes is given. Using this and the mentioned correspondence, the number of ideals of the rings R2;m and R3;m is determined. As a corollary, the number of cyclic codes of odd length n over the rings R2;m and R3;m is obtained.

A two-component outer ring and Galactic spiral structure

A model of the Galaxy with a ring R1R′2 can explain some large-scale morphological features of Galactic spiral structure. The Carina–Sagittarius arm could consist of two ascending segments of outer rings R1 and R2, which almost touch each other near the Carina region. The Perseus and Crux arms can be partially identified with the descending segments of ring R2. A model of a two-component outer ring can also explain the existence of some maxima in diagrams of (l, VLSR), which are supposed to correspond to directions tangential to the spiral arms. On the basis of numerical simulations, we propose two sketches of the ring structure of the Galaxy that include a bar, two outer rings, an inner ring and nuclear gas condensation, which may be a nuclear ring. Both sketches can explain the position of the Carina–Sagittarius arm with respect to the Sun.

Synthesis and a high field NMR study of a 2,2′-bipyridyl substituted β-cyclodextrin and its luminescent ReImetal complex

The synthesis and an NMR spectroscopic study of the substituted β-cyclodextrin derivative β-CD(per-OMe)bpy 3, and the metal complex β-CD(per-OMe)bpyRe(CO)3Br 4 are reported. The ligand 3 was prepared by condensation of monohydroxypermethylated β-cyclodextrin 1 with 6-bromomethyl-2,2′-bipyridine 2 under standard Williamson reaction conditions. The neutral complex, β-CD(per-OMe)bpyRe(CO)3Br 4, was obtained by treatment of the ligand 3 with Re(CO)5Br. 600 MHz two-dimensional NMR experiments (DQF-COSY, HOHAHA, ROESY) were used to establish the purity and structure of the ligand 3 and complex 4 in CDCl3. The two diastereotopic bipyridyl methylene protons (H7a, H7b) in ligand 3 appear as a singlet at 4.82 ppm. The protons H3′, H4′, H5′, and H6a′, 6b′ on the adjacent ring R2 are shifted downfield compared to the protons on the other six sugar rings. In the complex 4, the bipyridyl methylene protons (H7a, H7b) appear as 2 AX systems, R2H6a′ appears as a doublet of doublets and the aromatic protons appear as complex multiplets, consistent with the formation of two diastereomeric complexes 4a and 4b. While circular dichroism measurements suggest that the metal is directed over the cavity, NOE connectivities between the bipyridyl protons and the surface of the cyclodextrin cavity were not detected in ROESY experiments. Preorganized assemblies based on 4, in which the metal is directed over the cavity, provide ideal systems in which to study photochemical communication between the photoactive unit and a guest molecule encapsulated in the cyclodextrin cavity.

A characterization of perfect rings

J. P. Jans has shown that if a ring R is right perfect, then a certain torsion in the category Mod R of left ϋί-modules is closed under taking direct products. Extending his method, J. S. Alin and E. P. Armendariz showed later that this is true for every (hereditary) torsion in Mod R. Here, we offer a very simple proof of this result. However, the main purpose of this paper is to present a characterization of perfect rings along these lines: A ring R is right perfect if and only if every (hereditary) torsion in Mod R is fundamental (i.e., derived from prime torsions) and closed under taking direct products; in fact, then there is a finite number of torsions, namely 2 for a natural number n. Finally, examples of rings illustrating that the above characterization cannot be strengthened are provided. Thus, an example of a ring R± is given which is not perfect, although there are only fundamental torsions in Mod Ri, and only 4 = 2 of these. Furthermore, an example of a ring R2* is given which is not perfect and which, at the same time, has the property that there is only a finite number (namely, 3) of (hereditary) torsions in Mod i?2* all of which are closed under taking direct products. Moreover, the ideals of R2* form a chain (under inclusion) and Rad R2* is a nil idempotent ideal; all the other proper ideals are nilpotent and R2* can be chosen to have a (unique) minimal ideal.