Ring Elements Research Articles

A Note on Symmetric Elements of Division Rings with Involution

A Note on Symmetric Elements of Division Rings with Involution

Tripotent elements in quaternion rings over ℤp

Abstract In this paper, we discuss tripotent1 elements in the finite ring ℍ/ℤp. We provide examples and establish conditions for tripotency. We follow similar methods used in [3] for idempotent elements in ℍ/ℤp.

Evidence of declining trees resilience under long term heavy metal stress combined with climate change heating

Annually resolved tree rings enable us to distinguish past pollution and climate change effects on chronic tree decline, which affects significant areas around the world. The aim of the current study was to establish a pattern for the assimilation of heavy metals in regular and declining Quercus robur L. trees. Using laser ablation-inductively coupled plasma mass spectrometry (LA-ICP-MS), ICP-MS, and atomic absorption spectroscopy (AAS), the present and historical changes in element levels were investigated. Twenty different environmental species, including water, soil, sediments, mushrooms, acorn, leaves, branches, bark, and wood, were analyzed. Time profiles of elements in earlywood tree rings were investigated. We demonstrated higher HM contamination in the present background with increasing Pb and Cd levels. The presence of Li and Sr in groundwater was reported for the first time. We found significant differences (p < 0.001) between declined (D) and normally (N) growing trees only in the 1960–2019 period (Levene's t-test), which was sustained by a significant negative trend in D‒ chronology (MK-test, two-tailed). The bootstrapped correlation showed a weak positive relationship between D‒ chronology and soil moisture and a negative relationship with temperature and evapotranspiration. Declined trees were less resistant to environmental stress factors than N‒ growing trees at present (2012 compared to 1953). Mn, Cu, Cd, Pb, Zn, and Ni contents in tree rings correlated with climate-induced drought conditions, explaining the increasing elemental contents after 1980. A significant relationship between earlywood tree rings, climate and HM contamination explained different response patterns for normal and declining trees. Metal availability is increasing with climate change effects, leading to higher rates and future concerns, especially considering the high environmental health risk of some elements, such as Pb and Cd.

Role of zero-divisor graph in power set ring

The first article about graph theory was written by Leonhard Euler the famous Swiss mathematician which was published in 1736. Primarily, the idea of graph was not important as point of mathematics because it mostly deals with recreational puzzles. But the recent improvement in mathematics specially, its application brought a strong revolution in graph theory. Therefore, this article is written under the title of (Role of Zero-divisor graph in power set ring). This study clarifies the role of the zero-fraction graph in the strength ring and the library research method was used for the collection of information from the past research. This study first introduces the zero-divisor graph set of alternatives in R ring. Then presents the Role of Zero-divisor graph in power set ring. Whereas the vertex is denoted with K1 and the elements of an optional ring which are not zero-divisors they are the vertices without edges of that ring in zero-divisor graph. Next, we will study when a graph is planar in power set ring. The research found out that if the element numbers of set X  is less than 4, the graph of zero-divisor graph ring of P X( ) is planar and if the element numbers of set X is greater than or equals to 4, the zero-divisor graph ring is not planar.

Perspectivity and von Neumann regularity

We investigate connections between von Neumann regularity of endomorphisms and perspectivity of direct summands in modules. This leads to a new classification of those rings whose regular elements are strongly regular, which turn out to be exactly the rings R whose idempotents are central modulo the Jacobson radical J(R). An important component of our work is an investigation of the left and right associate relations on idempotents, as well as chains of these relations. As applications we give new characterizations of strongly regular elements and of idempotents that are central modulo the Jacobson radical. We also introduce a new class of regular elements that we call pc-regular elements, related to perspectivity in complement summands. These pc-regular elements are exactly the special clean elements. Generalizing the well-known fact that unit-regular rings are special clean, we then show that the unit-regular elements of any regular ring satisfying general comparability are special clean. Consequently, unit-regular endomorphisms of quasi-continuous modules are special clean, answering, in the positive, a conjecture of Lam.

Dual-Band Frequency Absorber Based on Split-Ring Resonators for WiMAX and WLAN Bands

In this paper, a dual-band compact absorber design based on split-ring resonator for WiMAX and WLAN bands is presented. Top plate of a unit cell in the proposed design is composed of three concentric circular split ring (SR) elements covers an area of π×13.42 mm2 and placed on a FR4 substrate with 1.5 mm thickness, dielectric constant of 4.3 and loss tangent of 0.025. Also, six miniature metallic loadings are appropriately inserted between the SR elements. The back side of the substrate is covered full ground plane for shielding transmission from port 1 to port 2. In the design, SR elements are primary resonator of the proposed absorber and provide a dual band of absorption at the respective frequencies. The metallic loadings are used for fine frequency tuning where the absorption peaks occur. Hence, the absorption frequency of the design can be easily tuned by means of sliding the loadings between the rings without changing any design parameters. The proposed compact absorber excited by incident electromagnetic wave provides 0.92 and 0.97 absorption peaks at 3.52 GHz WiMAX and 5.16 GHz WLAN bands, respectively. The design and analysis of the absorber are performed by means of CST Microwave Studio based on frequency domain solver. In this paper, the absorber design with novel configuration is introduced in detail and its corresponding electric field distributions and absorption characteristics at the related bands are presented. Also, the proposed SRR-based absorber design is compared with the previously reported dual or multi bands absorbers in terms of dimensions, resonance frequencies and number of bands.

Commuting-like elements in prime rings with derivations

Commuting-like elements in prime rings with derivations

About proregular sequences and an application to prisms

Let denote an ordered sequence of elements of a commutative ring R. Let M be an R-module. We recall the two notions that is M-proregular given by Greenlees and May and Lipman and show that both notions are equivalent. As a main result we prove a cohomological characterization for to be M-proregular in terms of Čech cohomology. This implies also that is M-weakly proregular if it is M-proregular. A local-global principle for proregularity and weakly proregularity is proved. This is used for a result about prisms as introduced by Bhatt and Scholze.

DNA codes over finite local Frobenius non-chain rings of length 4

A one to one correspondence between the elements of a finite local Frobenius non-chain ring of length 4 and k-tuples of DNA codewords is established. Using this map the structure of DNA codes over finite local Frobenius non-chain rings of length 4 is determined, the length of the code is relatively prime to the characteristic of the residue field of the ring.

A novel Ku/K band reflectarray antenna with reduced phase slope and phase sensitivity

The design, development, fabrication, and testing of a wideband reflectarray antenna with a novel concentric ring element operating over Ku/K band frequencies is presented in this paper. The element characterization is performed using the infinite array approach and is inferred that the proposed unit cell offers a higher phase variation of 643° by changing the size of the concentric rings. The proposed reflectarray antenna has a circular geometry and is constructed using 437 elements with an element separation of 0.43λ0. The proposed reflectarray offers a 3 dB gain bandwidth of 35% (15–21 GHz). The aperture efficiency is estimated to be 58.78% at 16.5 GHz. The prototype reflectarray is fabricated and tested to validate the simulation results. The measured peak gain of the reflectarray is 28.4 dBi with a side lobe level of −17.6 dB. The measured cross-polarization level is less than −32 dB. Furthermore, it is inferred that the proposed unit cell has a reduced maximum phase sensitivity of 246°/mm with a gain selectivity of 6 dB at the lowest operating frequency. The proposed broadband reflectarray with enhanced performance characteristics is suitable for application in satellite communication and aeronautical radio navigation.

Left uniquely generated elements in rings

An element a in a ring R is left uniquely generated (or left UG) if, whenever Ra = Rb, a = ub for a unit u in R, and is left strongly UG if, whenever Ra = Rb, a = ub = bu for a unit u in R. A ring is a left UG (resp. left strongly UG) ring if each of its elements is left UG (resp. left strongly UG). Motivated by a result of Marks [15] that a (von Neumann) regular ring is left UG iff it is unit-regular, we establish characterizations of a regular left UG element and, respectively, a regular left strongly UG element. As applications, many notable consequences are presented and connections with commutativity of rings are discussed.

Wideband radar cross section reduction based on absorptive coding metasurface with compound stealth mechanism* *Project supported by the National Natural Science Foundation of China (Grant Nos. 61871280, 61372012, and 61671315).

A scheme of combing wave absorption and phase cancellation mechanisms for widening radar cross section (RCS) reduction band is proposed. An absorptive coding metasurface implementing this scheme is derived from traditional circuit analog absorber (CAA) composed of resistive ring elements which characterize dual resonances behavior. It is constructed by replacing some of the CAA elements by another kind of resistive ring elements which is singly resonant in between the original two resonant bands and has reflection phase opposite to that of the original elements at resonance. Hence the developed metasurface achieves an improved low-RCS band over which the lower and higher sub-bands are mainly contributed by wave absorption mainly while the middle sub-band is formed by joint effect of wave absorption and anti-phase cancellation mechanisms. The polarization-independent wideband RCS reduction property of the metasurface is validated by full-wave simulation results of a preliminary and an advanced design examples which employ the same element configuration but different element layout schemes as partitioned distribution and random coding. The advanced design also exhibits broadband bistatic low-RCS property and keeps a stable specular RCS reduction performance with regard to incident elevation angle up to 35°. The advanced design is fabricated and the experimental results of the sample agrees qualitatively well with their simulated counterparts. The measured figure of merit (i.e., low-RCS bandwidth ratio versus electrical thickness) of the sample is 40.572, which is superior to or comparable with those for most of other existing metasurface with compound RCS reduction mechanism. The proposed compound metasurface technique also features simple structure, light weight, low cost and easy fabrication compared with other techniques. This makes it promising in applications such as radar stealth and electromagnetic compatibility.

Development of an X-Band Reflectarray Antenna for Satellite Communications

An X-band reflectarray antenna using 16 × 12 double square ring elements for satellite communications is proposed in this paper. The feed is a 4 × 3 elements microstrip patch array designed to create edge taper of approximately − 10 dB. A prototype with right-hand circular polarization (RHCP) is manufactured and tested, and the good agreements between simulations and measurements are demonstrated. The good performance is obtained with the aperture efficiency of 40.7% and the 3-dB gain bandwidth of about 10% which is beneficial to nanosatellites.

On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined Neutrosophic Linear Equations

This paper studies the problem of determining invertible elements (units) in any n-refined neutrosophic ring. It presents the necessary and sufficient condition for any n-refined neutrosophic element to be invertible, idempotent, and nilpotent. Also, this work introduces some of the elementary algebraic properties of n-refined neutrosophic matrices with a direct application in solving n-refined neutrosophic algebraic equations.

Hybrid Polarization-Phase Tuning Methodology for Reflectarray Antennas

A hybrid polarization-phase tuning methodology is presented for reflectarray antenna designs. First, three representative phasing approaches for reflectarray designs are briefly reviewed, and it is pointed out that when the polarization conversion is considered, these phasing approaches can be combined together to achieve more versatile functionalities and better performance. It is theoretically derived that using the mirror combining approach (MCA), broadband reflectarray elements with polarization conversion can be achieved. Using the rotational combining approach (RCA), both amplitude and phase of the reflected cross-polarization waves can be controlled. Next, a split ring element has been designed as an example to demonstrate the theoretical analysis. By using the MCA, the designed element achieves a linear 360° phase coverage, which suggests its capability of wideband operation. By using the RCA, the designed element achieves continuous amplitude modulation from 0 to 1 and full 360° phase coverage. Finally, a Ka-band reflectarray prototype with broadband behavior is designed, fabricated, and measured. It has achieved high-gain pencil beams pointing at predesigned directions. The measured gain at 20 GHz is 35.6 dBi with the aperture efficiency of 54.4% under linear-polarization (LP) excitation, and the gain is 35.4 dBi with the aperture efficiency of 52% under circular-polarization (CP) excitation. The measured 1 dB gain bandwidth is 18.5% (19-22.7 GHz) and 12.5% (19.3-21.8 GHz) under LP and CP excitation, respectively.

Strongly EP elements in rings with involution

The purpose of this paper is to give some sufficient and necessary conditions for an element to be a strongly [Formula: see text] element through some transformations of equations.

Design of aperiodic spherical antenna arrays for wideband performance

This paper illustrates a highly nonlinear problem related to the design of aperiodic antenna arrays using spherical geometry for maximum performance. This synthesis of aperiodic spherical antenna arrays considers two design cases: (1) aperiodic arrays with a nonuniform spacing between rings assuming equal element spacings on the same ring (ASANRUE case) and (2) aperiodic arrays with a nonuniform spacing between rings and between antenna elements of the same ring (ASANRNE case). This process is carried out by using the differential evolution (DE) optimization technique with the goal of finding the optimum angular position of each element on the elevation and azimuthal planes to achieve the maximum performance in terms of the side lobe level, directivity, and number of antenna elements used in the array for three design objectives: natural response of the radiation pattern, beam scanning, and the restriction of a minimum distance among elements. The innovative contribution of this paper is the application of the differential evolution algorithm to a nontrivial and highly complex design problem: the aperiodic element distribution over a spherical antenna arrangement. The advantage of this approach with respect to the state of the art on the topic of spherical array design is that a lower side lobe level and maximum directivity for a spherical antenna array can be obtained for aperiodic element distributions with a reduced number of antenna elements and hence a smaller radius, which means less complexity and lower fabrication costs. Simulation results based on CST Microwave Studio are provided to take mutual coupling into account.

Dual Frequencies Usage by Full and Incomplete Ring Elements

Full and incomplete ring patch elements antenna can be mixed to generate a variety of responses with respect to the direction of polarization. Dual frequencies requirement in numerous usage like in tracking radar can be achieved by combining the patches. To obtain the favored operating frequency, a straightforward design of a ring patch and also the addition of a gap have been utilized. Various sizes of the gap and the gap's position within a ring have been examined in the study. In order to investigate the element conduct, the surface current distribution, return loss, as well as reflection phase, are monitored. The evaluation revealed that the ring element with a smaller width would offer a sharp gradient of reflection phase that lowers its bandwidth performance. Meanwhile, the element performance was not affected by the gap's placement at the upper and lower part of the ring. However, the gap's size of 0.2 mm placed at the left or right position of the ring has shifted up the resonant frequency from 8.1 GHz to 11.8 GHz. For this study, it was shown that the mixture of full and incomplete ring elements has the potential to be utilized as an antenna to comprehend the operation of monopulse.

Identity-Based Proxy Re-encryption over NTRU Lattices for Cloud Computing

Identity-based proxy re-encryption (IB-PRE) is a kind of public key cryptography that allows a proxy to convert the ciphertext based on Alice’s identity into another ciphertext of the same message for Bob. It has important applications in cloud computing, distributed systems and secure e-mail forwarding. So far, the existing lattice-based IB-PRE schemes are designed on the general lattice and their security is based on the learning with errors (LWE) assumption. In this paper, we propose an IB-PRE scheme over NTRU lattices with the desirable properties of anonymity, unidirectionality, backward collusion safeness and multi-hop. Our IB-PRE scheme is provable secure under adaptive chosen-plaintext and adaptive chosen-identity attacks. And, in the random oracle model, the security of our scheme is based on the decisional Ring-LWE assumption. Besides, the key and ciphertext sizes of our IB-PRE scheme are short, only one or two ring elements, and our scheme could encrypt n bits in each encryption process.

Extensions of Cline’s formula for some new generalized inverses

Let a, b, c, d be elements in a unital associative ring R. In this note, we generalize Cline?s formula for some new generalized inverses such as strong Drazin inverse, generalized strong Drazin inverse, Hirano inverse and generalized Hirano inverse to the case when acd = dbd and dba = aca. As a particular case, some recent results are recovered.