Unit Element Research Articles

On hyperelliptic curves of odd degree and genus g with 6 torsion points of order 2g + 1

Let a hyperelliptic curve C of genus g defined over an algebraically closed field K of characteristic 0, given by the equation y2=f(x), where the polynomial f(x)∈K[x]is square-free and has odd degree 2g+1. The curve Ccontains a single “infinite” point O, which is the Weierstrass point. There is a classical embedding of C(K)into the group of K-points J(K)of the Jacobian variety Jof the curve C, identifying the point Owith the unit element of the group J(K). For 2≤g≤5, the article explicitly found representatives of birational equivalence classes such hyperelliptic curves Cwith a marked unique point at infinity Othat the set C(K)∩J(K)contains at least 6 torsion points of order 2g+1. It was previously known that for g=2there are exactly 5 such equivalence classes, and for g≥3an upper bound was known that depended only on the genus of g. We improve the previously known upper bound by almost 36 times.

Super Low Profile 5G mmWave Highly Isolated MIMO Antenna with 360∘ Pattern Diversity for Smart City IoT and Vehicular Communication

This study introduces a planar folded super low profile 5G mmWave monopole antenna for small IoT devices with superior efficiency and gain. Low-loss Rogers RT-5880 substrate material has been utilized to achieve higher efficiency, gain, and diversity performance in a relatively compact size. The unit element planar monopole antenna has been designed within 6.15×5.13×0.8mm3 with a partial ground. Four unit element antenna was orthogonally arranged on alternating sides of the substrate plane with narrow inter-component spacing in the multiple input multiple output (MIMO) system. The integration of the double negative (DNG) metamaterial array on the antenna led to a cumulative improvement in the overall performance of the antenna, which includes gain, efficiency, and isolation. The minimum isolation of the antenna increased by 11 dB with substrate-loaded metamaterial. The proposed MIMO antenna model with substrate-loaded metamaterial demonstrates 8 GHz instantaneous bandwidth (33.1 GHz - 41.1 GHz), 0.001 envelope correlation coefficient (ECC), diversity gain (DG) greater than 9.99 dB, channel capacity loss (CCL) less than 0.2bits/s/Hz, and a total active reflection coefficient (TARC) of 25 dB, which suggests that the diversity characteristics of the MIMO antenna system is impressive. Moreover, a densely packed 12-element antenna model has been introduced in this study with 360∘ pattern diversity, capable of receiving signals from any direction. Three 4-element MIMO systems have been arranged in an architecture to develop the 12-element MIMO system, and the size of the 12-element MIMO architecture is 15×15×15mm3. Despite having this compact size and dense packing, the 12-element MIMO antenna model shows similar diversity performance as the 4-element antenna model. Analog equivalent circuit models or resistor-inductor-capacitor (RLC) equivalent systems for the antenna models were created. A concept of a 128-element massive MIMO antenna has been presented to support the end devices, creating an application scenario of an IoT-interconnected smart city.

Wideband and Low-Profile Array of Tightly Coupled Dipole Subarrays

This letter introduces a novel wideband, low profile, tightly coupled dipole subarray for wireless communication systems. The proposed subarray, composed of 3 × 3 unit elements, offers a planar structure with high aperture efficiency. The unit element is a bow-tie-shaped tightly coupled dipole antenna covered by a frequency-selective surface for wideband operation. Using power dividers with quarter-wave transformers, the proposed subarray achieved an impressive impedance-matching bandwidth of 28.6–41.6 GHz (37.8%). This wideband performance was maintained in a 4 × 4 array configuration as well. The antenna’s low-profile design (0.08λc) and high aperture efficiency (77.2%) set it apart from existing wideband patch array antennas, making it a promising candidate for future wireless communication applications.

Prototype Facial Response to Cute Stimuli: Expression and Recognition.

Cute, kindchenschema stimuli can evoke a suite of cognitive, physiological, and behavioral tendencies thought to promote caregiving. This research investigated facial expression elements associated with this response to cuteness and assessed the recognizability of an expression combining these elements. In Studies 1 and 2, participants at a community outreach event (Study 1, n = 19) and undergraduate students (Study 2, n = 103) showed spontaneous facial displays while watching videos/photos of baby humans and animals. These were Facial Action Coding System (FACS)-coded, revealing characteristic and statistically distinctive action unit elements of facial expression responses to cuteness. In six follow-up online studies (combined N = 962), including replications with Syrian refugees (n = 103) and Chinese samples (n = 222), a "cuteness prototype" expression combining all elements identified across Studies 1 and 2 (i.e., oblique brows, chin raise, lip tightening, and Duchenne smile) was commonly interpreted as a response to cuteness. These findings add to a growing literature about caregiving-focused motivational states and associated emotion/affect.

Unraveling Lewis acid-base sites in defected MOFs for catalyzing dicyclopentadiene hydrogenation via a DFT study and descriptor exploration

The 12-connected UiO-66 MOFs with great defect regulation ability have attracted significant attention due to the easily tunable electronic structure and surface electrostatic potential distribution of metal nodes. In this density functional theory (DFT) study, we systematically explored the effect of bi-active site types as the frustrated Lewis pair (FLP) and classical Lewis pair (LP) as well as metal elements of secondary building units (SBUs) on the catalytic hydrogenation of dicyclopentadiene (DCPD) to tetrahydrodicyclopentadiene (THDCPD). These design strategies effectively modulate the frontier molecular orbital energy level that determines the binding strength between MOFs and adsorbed species *Hδ+-Hδ- and charges transfer before and after H2 chemisorption. We also found that the heterolytic H2 adsorption energy and charges transfer linearly correlate with the energy barrier. In order to unravel the clear-cut designing strategies and further simplify computational complexity, we firstly proposed the ADCH charges difference between the Lewis acid and the Lewis base centers (ΔQM-O) as an intrinsic descriptor for catalytic activity of DCPD into THDCPD, which can effectively describe the reactivity and electrostatic effects of oppositely charged bi-active sites in the system. Furthermore, the defective UiO-66(Ce) MOF with moderate ΔQM-O effectively balance the contradiction between the barriers of two primitive reaction: the heterolytically H2 dissociation to *Hδ+-*Hδ- and the desorption of the active hydrogen species to hydrogenate 8,9-dihydrodicyclopentadiene (8,9-DHDCPD), resulting in the optimal catalytic performance. This work provides a deep understanding of the catalytic mechanism of MOFs with multiple active sites and might open up avenues for the rational design of novel hydrogenation catalysts.

Monitoring of thick-walled pressure elements to determine transient temperature and stress distributions using the measured fluid's pressure and wall's temperature

The paper presents a new stress monitoring method for cylindrical pressure elements of the power unit. It can be used to monitor a power unit's start-up, shutdown, and load change to reduce the unit's connection time to the power grid. The outer surface of the component is thermally insulated. Circumferential thermal stress at the point of its concentration at the hole edge is determined based on the stress determined at a greater distance from the hole. The circumferential thermal and pressure stresses at the hole edge are calculated by multiplying the stress values determined for the non-weakened wall by the respective concentration factors. In addition, the heat transfer coefficient (HTC) at the inner surface of the pressure element is necessary to determine the thermal stress concentration factor. Heat transfer correlations available in the literature are used to calculate HTC. The transient element wall temperature is measured five to 12 mm from the inner surface of the cylindrical component. An analysis of the measurement point locations on the accuracy of temperature and stress determining at the inner component surface was investigated. A practical application of the proposed method using real measurement data is presented.

ON THE ISSUE OF ENSURING THE OPERABILITY OF FREIGHT CAR AXLE BOXES

The article is devoted to analysing the reliability of freight car axle boxes. Wheelsets and axle boxes are especially important for ensuring the traffic safety of trains. The study examined cases of cars uncoupling from a train along the route due to technical faults resulting in delays in train movement. The analysis covered the period of 1995–2023. It found that failures of car axle boxes and automatic brakes predominated. After a significant decrease from 2000–2014, the number of roller axle box failures in recent years fluctuated at 30% of the total number of uncouplings. The analysis obtained a dependency for the change in car detachments due to roller bearing failures, calculated per 1,000 cars in the operating fleet. Despite fluctuations in the number of railcars, the safety level of operations in recent years remained virtually at the same level. The study highlighted that excessive heating accompanies damage in the elements of the axle box unit. It considered methods for detecting possible failures and their advantages and disadvantages. The authors identified the primary causes of axle box component failures. Cylindrical bearings and end mountings remain the most dangerous for failure probability. We demonstrated that the axle box design with cylindrical bearings has a fundamental flaw. Axial forces are perceived through the rolling friction of the ends of the rollers against the ring flanges, leading to the formation of ‘chevron’ scratches and dents on the roller ends, which are stress concentrators. The study established that the surface of the axle box housing is constantly in contact with the side frame of the freight car bogie and wears out. It results in pinching of the axle box body and contributes to the appearance of additional permanent forces acting on the axle box assembly. The end-bearing mounts are weakened and destroyed. Skewed rollers in the bearings cause fatigue failure of the rolling races. It leads to increased heating of the axle box assemblies and uncoupling of the car. A promising direction is the improvement of axle box bodies. Keywords: rolling stock, traffic safety, reliability, axle box assembly, roller bearing, axle box body, failure.

On the unit-Jacobson graph

In this paper, we introduce the unit-Jacobson graph, which is defined by the unit elements and the elements of the Jacobson radical of a commutative ring [Formula: see text] with nonzero identity. We give relationships between this new graph concept and some special rings such as [Formula: see text]-clean rings, [Formula: see text]-rings, local rings, and cartesian rings. Moreover, we investigate the concepts of the dominating set, diameter, and girth on the unit-Jacobson graph.

An AI-assisted terahertz reconfigurable metamaterial in standard 180-nm CMOS

For large-scale terahertz (THz) reconfigurable metamaterials (RM), each unit element needs to be controlled by an independent voltage source. This leads to a huge solution space for control words to achieve the required RM performance specification. In this paper, we propose a fast AI-assisted control-word generation scheme to reduce the computation cost of electromagnetic (EM) simulations (Forward Model) and to speed up iterations for control word searches (Inverse Model). We demonstrate the effectiveness of our models by designing and fabricating a 12 × 9 RM array with a Bi-layer Bi-Split-Ring Resonator structure (B-BSRR) in standard 180 nm CMOS technology. The terahertz RM can be electrically reconfigured, providing active metamaterials with an amplitude modulation depth of around 0–1.7 dB at 0.49 THz. The results show that our Forward Model can predict the S-parameters between 100 GHz and 800 GHz with a mean absolute error of 0.61 dB. Our method is more than 200 times faster than traditional full-wave simulation methods. The Inverse Model can generate required control words within a 1.3 dB error margin in less than 200 iterations.

On the cubic Shimura lift to $\operatorname{PGL}(3)$: The fundamental lemma

The classical Shimura correspondence lifts automorphic representations on the double cover of \mathrm{SL}_{2} to automorphic representations on \mathrm{PGL}_{2} . Here we take key steps towards establishing a relative trace formula that would give a new global Shimura lift, from the triple cover of \mathrm{SL}_{3} to \mathrm{PGL}_{3} , and also characterize the image of the lift. The characterization would be through the non-vanishing of a certain global period involving a function in the space of the automorphic minimal representation \Theta_{\mathrm{SO}_8} for split \mathrm{SO}_{8}(\mathbb{A}) , consistent with a conjecture of Bump, Friedberg and Ginzburg (2001). In this paper, we first analyze a global distribution on \mathrm{PGL}_{3}(\mathbb{A}) involving this period and show that it is a sum of factorizable orbital integrals. The same is true for the Kuznetsov distribution attached to the triple cover of \mathrm{SL}_{3}(\mathbb{A}) . We then match the corresponding local orbital integrals for the unit elements of the spherical Hecke algebras; that is, we establish the fundamental lemma.

What's the Situation With Intelligent Mesh Generation: A Survey and Perspectives.

Intelligent Mesh Generation (IMG) represents a novel and promising field of research, utilizing machine learning techniques to generate meshes. Despite its relative infancy, IMG has significantly broadened the adaptability and practicality of mesh generation techniques, delivering numerous breakthroughs and unveiling potential future pathways. However, a noticeable void exists in the contemporary literature concerning comprehensive surveys of IMG methods. This paper endeavors to fill this gap by providing a systematic and thorough survey of the current IMG landscape. With a focus on 113 preliminary IMG methods, we undertake a meticulous analysis from various angles, encompassing core algorithm techniques and their application scope, agent learning objectives, data types, targeted challenges, as well as advantages and limitations. We have curated and categorized the literature, proposing three unique taxonomies based on key techniques, output mesh unit elements, and relevant input data types. This paper also underscores several promising future research directions and challenges in IMG.

SIFAT ELEMENTER DARI RING TERGENERALISASI

Ring is a study of algebraic structures, which is defined as a non-empty set containing two binary operations. Regarding the first binary operation, the set is a group, and the second binary operation is a semigroup, and both operations fulfill the left distributive and right distributive properties. The generalized ring concept is an extension of the ring concept, namely that for the first binary operation, each element has an identity element that is not necessarily the same. This research aims to prove the elementary properties of generalized rings and the properties of generalized rings associated with the G-ring structure. Furthermore, this research also proves the properties of subsets related to identity elements in generalized rings. The results of this research are that the fundamental properties of the generalized ring are valid, which are analogous to the fundamental properties of the ring, and sufficient conditions for a generalized ring to be a G-ring are obtained. Furthermore, if the generalized ring has a unit element, it forms an abelian group with all elements having the same identity, and the generalized ring contains all identity elements.

ALGORITHM FOR CONSTRUCTING THE TRIPLE UNIT GRAPH OF TYPE II OF RING Z_n USING PYTHON

Let be a commutative ring with as the set of all unit elements in . This paper introduces a new graph associated with the ring , called the triple unit graph of type II, denoted by with the vertex set is − {0,1}. In TU2(R), two distinct vertices, and , are adjacent if there exists with and such that . This paper focuses on the algorithm for constructing using Python. This research uses the literature study research method. The Python programming language can be used to observe the characteristic result of the graph. From the patterns generated by the algorithm, some characteristics of are obtained. For example, if is a prime and , then is a connected graph, a complete graph, a regular graph, and a Hamiltonian graph

A wideband polarization diversified MIMO antenna with improved isolation using machine learning optimized metasurface absorber

This communication presents a model and optimization of a dual-sense circularly polarized (RHCP/LHCP) 2-port MIMO antenna with increased isolation. The antenna operates in a broad frequency range of 1.76–4.0 GHz and is loaded with a metasurface. It has dimensions of 98.5 × 39 mm2 and an edge-to-edge distance of 55.5 mm. The MIMO antenna is created by replicating a single unit and placing it in a mirrored configuration around the y-axis. The dimensions of the unit antenna are 40 × 39 × 0.8 mm3 and it is printed on a substrate made of FR4 with a thickness of 0.8 mm. The substrate has a relative permittivity (ε r) of 4.4 and a loss tangent (tanδ) of 0.02. The isolation between the ports may be enhanced by including a metasurface absorber, increasing from 12 dB to 23 dB. To verify the wideband and CP properties, we examine the MIMO antenna unit element for its reflection coefficient, peak gain (4.2 dB), radiation efficiency (about 90%), axial ratio, and surface current distribution. Machine learning is used to improve the design of metasurface unit cells to achieve optimum absorption. The Envelope correlation coefficient (ECC), Diversity gain (DG), and Channel capacity loss (CCL) of the proposed metasurface absorber-enabled antenna are simulated and calculated to prove its MIMO identity. The HFSS simulations are consistent with the experimental results obtained from the developed model.

On finite groups in which the twisted conjugacy classes of the unit element are subgroups

We consider groups G such that the set [G,φ]={g-1gφ|g∈G}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[G,\\varphi ]=\\{g^{-1}g^{\\varphi }|g\\in G\\}$$\\end{document} is a subgroup for every automorphism φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi $$\\end{document} of G, and we prove that there exists such a group G that is finite and nilpotent of class n for every n∈N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\in \\mathbb N$$\\end{document}. Then there exists an infinite not nilpotent group with the above property and the Conjecture 18.14 of Khukhro and Mazurov (The Kourovka Notebook No. 20, 2022) is false.

On center graphs of finite associative rings

UDC 512.5 We consider a finite associative ring R , which may have or may not have a unit element. We also examine its center denoted by Z ( R ) . Our main focus is on the introduction of two distinct graphs associated with R , namely, the center graph denoted by G C ( R ) and the strict center graph denoted by G C ( R ) ¯ . We present the properties of G C ( R ) and explore its implications on the nature of Z ( R ) . Specifically, we demonstrate that if G C ( R ) is complete, then Z ( R ) is an ideal in R . Furthermore, in the case where R is a unital ring, the completeness of G C ( R ) leads to the conclusion that R is a commutative ring. As a specific application of our results, we provide an explicit construction of the graph G C ¯ ( T 2 ( p ) ) , where T 2 ( p ) represents the ring of upper-triangular matrices with entries in the ring ℤ / p ℤ and p is a prime integer. In our investigations of the center graph and strict center graph, we aim to shed light on the properties of finite associative rings and their centers, thus providing valuable insights and applications in the ring theory.

Computational and experimental substantiation of the operability of seals of localizing safety system elements of power units with VVER

The relevance of this work is determined by the need to predict the operation of sealing assemblies for elements of localizing safety systems (LSSs) of power units with VVER, which include (penetrations, hatches, locks, doors and other elements of hermetic fencing (GF) in operational modes. Operational modes are understood as modes of normal operation, modes of violation of normal operation, as well as emergency situations. During the manufacture and operation of LSS elements, the problem arises of uneven protrusion of a double-row rubber seal from the grooves in the web of the LSS element, which leads to the need to clarify the integral compression force of the seal as a whole for this element. The problem is caused by the imperfection of the manufacturing technology of large canvases for LSS elements (doors, hatches, locks: the perimeter of the seals can reach 10-20 m, the diameter of the canvas 2-6 m) and the need to withstand stringent technological requirements for flatness, parallelism and marginal deviations in linear and angular dimensions. The manufacture of overall structures is complicated by the presence of welded joints, heat treatment, and the complexity of metalworking. Compression force of the PNAE rubber gasket-7-002-86 it is not regulated, therefore, for the reliable design of gasket compression mechanisms, the magnitude of this force was determined. Based on the obtained results of tests of rubber seals for tightness and cyclic loading [7], an assessment of the tightness of the applied rubber seals is performed, calculations of deformations of rubber seals are performed using the FEM software package. Recommendations have been developed to increase the reliability of seal assemblies for elements of localizing safety systems (LSSs) of VVER power units in operational modes and to select the compression value to determine the necessary force to ensure tightness at the beginning of operation and after 5000 opening-closing cycles.

The retina's neurovascular unit: Müller glial sheaths and neuronal contacts.

The neurovascular unit (NVU), comprising vascular, glial and neural elements, supports the energetic demands of neural computation, but this aspect of the retina's trilaminar vessel network is poorly understood. Only the innermost vessel layer - the superficial vascular plexus (SVP) - is ensheathed by astrocytes, like brain capillaries, whereas glial ensheathment in other layers derives from radial Müller glia. Using serial electron microscopy reconstructions from mouse and primate retina, we find that Müller processes cover capillaries in a tessellating pattern, mirroring the tiled astrocytic endfeet wrapping brain capillaries. However, gaps in the Müller sheath, found mainly in the intermediate vascular plexus (IVP), permit different neuron types to contact pericytes and the endothelial cells directly. Pericyte somata are a favored target, often at spine-like structures with a reduced or absent vascular basement lamina. Focal application of adenosine triphosphate (ATP) to the vitreal surface evoked Ca2+ signals in Müller sheaths in all three vascular layers. Pharmacological experiments confirmed that Müller sheaths express purinergic receptors that, when activated, trigger intracellular Ca2+ signals that are amplified by IP3-controlled intracellular Ca2+ stores. When rod photoreceptors die in a mouse model of retinitis pigmentosa (rd10), Müller sheaths dissociate from the deep vascular plexus (DVP) but are largely unchanged within the IVP or SVP. Thus, Müller glia interact with retinal vessels in a laminar, compartmentalized manner: glial sheathes are virtually complete in the SVP but fenestrated in the IVP, permitting direct neural-to-vascular contacts. In the DVP, the glial sheath is only modestly fenestrated and is vulnerable to photoreceptor degeneration.

Computational Protocol for the Spectral Assignment of NMR Resonances in Covalent Organic Frameworks.

Solid-state nuclear magnetic resonance spectroscopy is routinely used in the field of covalent organic frameworks to elucidate or confirm the structure of the synthesized samples and to understand dynamic phenomena. Typically this involves the interpretation and simulation of the spectra through the assumption of symmetry elements of the building units, hinging on the correct assignment of each line shape. To avoid misinterpretation resulting from library-based assignment without a theoretical basis incorporating the impact of the framework, this work proposes a first-principles computational protocol for the assignment of experimental spectra, which exploits the symmetry of the underlying building blocks for computational feasibility. In this way, this protocol accommodates the validation of previous experimental assignments and can serve to complement new NMR measurements.

Scutoids as Building Blocks for Topologically Interlocking Material Systems

Topologically interlocking material (TIM) systems are constrained assemblies of building blocks with geometry such that individual unit elements cannot be removed from the assembly without complete disassembly. These assemblies can bear load in the absence of adhesive bonds. TIM systems with scutoid‐shaped building blocks are investigated. Scutoids are prism‐like shapes with two polygonal faces and contain vertices on the lateral sides which enable geometric interlocking. The quasi‐static mechanical behavior of two types of scutoid‐based TIM systems is investigated and compared to reference tetrahedron‐based TIM systems. TIM systems are realized as plate‐type assemblies and a central point‐force load is considered. The computational analysis is conducted with the finite‐element method. Scutoid‐based TIM systems are found, in aggregate, to match or exceed the performance of the tetrahedra‐based systems. It is documented that TIM systems in general, but scutoid‐based systems in particular, emerge to possess chiral characteristics. The combination of building block symmetry and assembly symmetry together determines the type of chirality in the mechanical response. Experimental data validates the computational finding. In summary, considering scutoids as building blocks for load‐carrying TIM assemblies opens the pathway to new classes of mechanical behavior in systems where structure and microstructure strongly interact with each other.