Geometric Environment Research Articles

Analytical and geometric interpretation of the flat arrangement of points by means of metric geometry in the study of metric spaces

Abstract When studying metric spaces, students of higher education often have difficulties with understanding the basic concepts and properties of these spaces. This, to a large extent, is a consequence of the significant level of formalization of such concepts on the one hand, and the preservation of the corresponding formulations and names familiar to students from a school mathematics course. To overcome these difficulties, it is advisable to use methods of geometric interpretation and visualization of these properties. At the same time, it is appropriate to use elements of metric geometry. Its methods make it possible to interpret the geometric features of the mutual placement of points of metric space in Cartesian (rectangular) coordinate systems, which are familiar to students of higher education. Moreover, it becomes possible to visualize these features with the help of graphic editors, since they, as a rule, use numerical values of the coordinates of points to visualize them. Based on the definition of an angle as an ordered trio of points of an arbitrary metric space, and the angular characteristic of this angle, the fact of the flat placement of four points of a non-Euclidean metric space is established, and examples of digital visualization of this arrangement using the dynamic geometric environment GeoGebra 3D are given.

Single and mixed dithiocarbamato metal(III) complexes (Co, Rh, and Ir): Crystal and molecular structure description and interplay

This review focuses on the crystal and molecular structures of single and mixed dithiocarbamate ligands of cobalt, rhodium, and iridium in the +3 oxidation state. The complexities of their chelating and bridging modes come into play through modification of the substituents on the carbamate nitrogen atoms of the ligands and additional coordination of secondary phosphino-containing ligands, culminating in various applications such as biological, analytical, medicine, and catalysis. Other considerations include the geometrical coordination environments around the metal centres and their comparison with isostructural congeners. The distortions around the metal centres and their subsequent effects on the symmetries of bonds in the primary and secondary coordination spheres are discussed. The trans-effects of secondary P-ligands and their effects on geometrical alignment and structural stability have become valuable yardsticks in analyzing structural modifications and stabilities.

PTFE-Based Circular Terahertz Dielectric Waveguides

This paper presents the transmission characteristics of flexible solid circular dielectric waveguides in the terahertz frequency band. In this paper, we measured the electrical properties of certain polymers within 325–500 GHz. Through simulation and measurement, the transmission loss, bending loss, and electric field distribution of solid-core polymer dielectric waveguides were analyzed and discussed. Additionally, we considered the surrounding cladding of the dielectric waveguide, the signal-feeding mode transmitter, and the interconnection of the dielectric waveguide. Ultimately, in the operating frequency range of 325–500 GHz, we selected PTFE rods with diameters of 0.5 mm and 1 mm as the dielectric waveguides, with measured transmission loss of less than 30 dB/m and 33 dB/m, respectively, and bending loss of less than 1 dB/m. The described dielectric waveguide has engineering significance for short-distance connections in complex geometric environments and provides a reference for subsequent research.

A Machine Learning Method for RNA-Small Molecule Binding Preference Prediction.

The interaction between RNA and small molecules is crucial in various biological functions. Identifying molecules targeting RNA is essential for the inhibitor design and RNA-related studies. However, traditional methods focus on learning RNA sequence and secondary structure features and neglect small molecule characteristics, and resulting in poor performance on unknown small molecule testing. To overcome this limitation, we developed a double-layer stacking-based machine learning model called ZHMol-RLinter. This approach more effectively predicts RNA-small molecule binding preferences by learning RNA and small molecule features to capture their interaction information. ZHMol-RLinter also combines sequence and secondary structural features with structural geometric and physicochemical environment information to capture the specificity of RNA spatial conformations in recognizing small molecules. Our results demonstrate that ZHMol-RLinter has a success rate of 90.8% on the published RL98 testing set, representing a significant improvement over existing methods. Additionally, ZHMol-RLinter achieved a success rate of 77.1% on the unknown small molecule UNK96 testing set, showing substantial improvement over the existing methods. The evaluation of predicted structures confirms that ZHMol-RLinter is reliable and accurate for predicting RNA-small molecule binding preferences, even for challenging unknown small molecule testing. Predicting RNA-small molecule binding preferences can help in the understanding of RNA-small molecule interactions and promote the design of RNA-related drugs for biological and medical applications.

Enhancing radiation-resistance and peroxidase-like activity of single-atom copper nanozyme via local coordination manipulation

The inactivation of natural enzymes by radiation poses a great challenge to their applications for radiotherapy. Single-atom nanozymes (SAzymes) with high structural stability under such extreme conditions become a promising candidate for replacing natural enzymes to shrink tumors. Here, we report a CuN3-centered SAzyme (CuN3-SAzyme) that exhibits higher peroxidase-like catalytic activity than a CuN4-centered counterpart, by locally regulating the coordination environment of single copper sites. Density functional theory calculations reveal that the CuN3 active moiety confers optimal H2O2 adsorption and dissociation properties, thus contributing to high enzymatic activity of CuN3-SAzyme. The introduction of X-ray can improve the kinetics of the decomposition of H2O2 by CuN3-SAzyme. Moreover, CuN3-SAzyme is very stable after a total radiation dose of 500 Gy, without significant changes in its geometrical structure or coordination environment, and simultaneously still retains comparable peroxidase-like activity relative to natural enzymes. Finally, this developed CuN3-SAzyme with remarkable radioresistance can be used as an external field-improved therapeutics for enhancing radio-enzymatic therapy in vitro and in vivo. Overall, this study provides a paradigm for developing SAzymes with improved enzymatic activity through local coordination manipulation and high radioresistance over natural enzymes, for example, as sensitizers for cancer therapy.

Orbital Hybridization Induced Dipole Polarization and Room Temperature Magnetism of Atomic Co‐N4‐C toward Electromagnetic Energy Attenuation

AbstractManipulating the electronic structure and geometric coordination environment of single metal atoms has been considered as promising approach for enhancing dipole polarization and enriching electromagnetic attenuation mechanisms. However, achieving precise control of the dielectric polarization response at atomic scale remains a huge challenge. Herein, a metal‐acetate coordination complexes‐assisted strategy is proposed to prepare spatially isolated cobalt (Co) atoms embedded in accordion‐like nitrogen‐doped carbon (NC) matrix. The interactions between metal atoms and NC matrix are carefully tailored through the successive evolution of dispersion states of Co species, ranging from individual atoms to atomic clusters to nanoparticles. Density functional theory reveals that the orbital hybridization between the d electrons of embedded Co atoms and p electrons of coordinated N atoms induces the electron redistribution at N sites, enabling enhanced electric dipole polarization and robust room temperature magnetism (a saturation magnetization of 0.108 emu g−1 at 300 K). Consequently, Co‐SAs@NC exhibits optimal electromagnetic wave absorption properties with a minimum reflection loss of ‐54.4 dB and an effective absorption bandwidth of 8.4 GHz. This work demonstrates an efficient strategy for modulating electromagnetic response at atomic level and provides a novel insight into the d/p electrons orbital hybridization between single metal atoms and NC species.

METHODOLOGY FOR CREATING A DESIGN DOCUMENT SPECIFICATION FOR ASSEMBLIES IN THE SOLIDWORKS SYSTEM

The article describes the methods of development of design documents in the geometric modeling environment SolidWorks. Special attention is paid to the main design document (DD) – Specification. For the proposed valve design, the creation of a specification for the entire product, as well as the specifications of the assembly units included in the product, is considered. Examples of specifications for drawings are given: assembly, general type, drawings with a loose part and for combined DD. The examples considered in the article contribute to the formation of students' practical skills in the image of products and their components using the SolidWorks modeling system, the development of the ability to read drawings, as well as the deepening of knowledge of the state standards of the Unified System of Design Documentation (USDD).

Theoretical Investigation of Structural, Electronic and Optical Properties of Cs3MoO4(HCO3) with NLO Active Functional Units

AbstractEmploying functional building units with microscopic second‐order NLO response has been proposed to explore high performance NLO materials. Herein, structural, electronic and optical properties of non‐centrosymmetric molybdenyl carbonate Cs3MoO4(HCO3) with NLO active functional units have been examined based on density functional theory. Theoretical results are consistent with experimentally mentioned data, confirming the reliable method. Detailed geometric structure, electronic attributes, linear optical properties, and nonlinear optical properties of Cs3MoO4(HCO3) are provided. Analysis of structures, compositions of bands and plots of charge density suggest that asymmetric functional building units [MoO4] and [HCO3] exhibit varying degrees of second‐order Jahn‐Teller distortions, and therefore have a significant impact on the electronic structure and optical properties of Cs3MoO4(HCO3). Maximum absolute value of SHG coefficients at 1064 nm is 0.671 pm/V for d15, which is nearly twice as much as that of KDP. Further researches are needed in future to validate and enhance optical anisotropy characteristic of Cs3MoO4(HCO3) for satisfying the phase matching conditions. Analysis results indicate that microscopic origins of SHG response in Cs3MoO4(HCO3) are complicated, such as geometric environment, induced polar asymmetric functional building units, and electronic properties. Continuous research on structure‐property relationship of NLO materials is needed for exploring more competitive NLO materials.

Deciphering the contributing motifs of reconstructed cobalt (II) sulfides catalysts in Li-CO2 batteries

Developing highly efficient catalysts is significant for Li-CO2 batteries. However, understanding the exact structure of catalysts during battery operation remains a challenge, which hampers knowledge-driven optimization. Here we use X-ray absorption spectroscopy to probe the reconstruction of CoSx (x = 8/9, 1.097, and 2) pre-catalysts and identify the local geometric ligand environment of cobalt during cycling in the Li-CO2 batteries. We find that different oxidized states after reconstruction are decisive to battery performance. Specifically, complete oxidation on CoS1.097 and Co9S8 leads to electrochemical performance deterioration, while oxidation on CoS2 terminates with Co-S4-O2 motifs, leading to improved activity. Density functional theory calculations show that partial oxidation contributes to charge redistributions on cobalt and thus facilitates the catalytic ability. Together, the spectroscopic and electrochemical results provide valuable insight into the structural evolution during cycling and the structure-activity relationship in the electrocatalyst study of Li-CO2 batteries.

Topological bias: how haloes trace structural patterns in the cosmic web

ABSTRACT We trace the connectivity of the cosmic web as defined by haloes in the Planck-Millennium simulation using a persistence and Betti curve analysis. We normalize clustering up to the second-order correlation function and use our systematic topological analysis to correlate local information and properties of haloes with their multiscale geometrical environment of the cosmic web (elongated filamentary bridges and sheetlike walls). We capture the multiscale topology traced by the halo distribution through filtrations of the corresponding Delaunay tessellation. The resulting nested alpha shapes are sensitive to the local density, perfectly outline the local geometry, and contain the complete information on the multiscale topology. We find a remarkable linear relationship between halo masses and topology: haloes of different mass trace environments with different topological signature. This is a topological bias, an environmental structure bias independent of the halo clustering bias associated with the two-point correlation function. This mass-dependent linear scaling relation allows us to take clustering into account and determine the overall connectivity from a limited sample of galaxies. The presence of topological bias has major implications for the study of voids and filaments in the observed distribution of galaxies. The (infra)structure and shape of these key cosmic web components will strongly depend on the underlying galaxy sample. Their use as cosmological probes, with their properties influenced by cosmological parameters, will have to account for the subtleties of topological bias. This is of particular relevance with the large upcoming galaxy surveys such as DESI, Euclid, and the Vera Rubin telescope surveys.

USING THE GEOGEBRA ENVIRONMENT IN THE MATHEMATICAL TRAININGOF ECONOMIC STUDENTS

The use of information technology in the learning process has of learning in institutions of higher education already become commonplace, but new tools that constantly help teachers and students. In order for education to really meet the demand of modern realities, it is necessary to continuously modernize the forms and methods of education. One such most relevant assistant in teaching mathematics is the Dynamic Mathematics System GeoGebra. The article deals with the issue of modernization of methodological systems for teaching mathematical disciplines studied by students of economic specialties. in IT areas. The possibilities of the GeoGebra tool are revealed, which are important for improving the quality of mathematical training of future economists in the context of the implementation of the didactic principle of visibility and the inclusion of students in research and project activities. Particular attention is paid to the practical aspects of using GeoGebra in solving plot, applied problems associated with the use of active techniques and methods of teaching mathematical disciplines, the growth of students’ creative and intellectual activity when working with topics that require visualization of mathematical concepts and objects. The conditions of methodologically expedient inclusion of Geogebra into the practice of teaching mathematical disciplines for the preparation of economists and the modernization of already existing methodological systems for teaching mathematical disciplines are highlighted. It has been proven that the use of the interactive geometric environment GeoGebra allows visualization of abstract mathematical concepts, which contributes to the fastest possible perception of the material, a deeper understanding of it and increases interest in the discipline being studied. In addition, the use of dynamic mathematics systems both in the classroom and in non-classroom work has a positive effect on the success of students. Completing mathematical tasks using the GeoGebra environment arouses students' cognitive interest in exact sciences and promotes the development of visual and creative thinking. GeoGebra should be considered a special visual environment not only for solving specific problems related to mathematics and mathematical modeling, but also an environment for the implementation of interdisciplinary projects of an integration nature.

The correlations between galaxy properties in different environments of the cosmic web

Abstract We study the correlations between (u-r) colour, stellar mass, specific star formation rate (sSFR) and metallicity of galaxies in different geometric environments of the cosmic web using a volume limited sample from the SDSS. The geometric environment at the location of each galaxy is determined using the eigenvalues of the tidal tensor in three dimensions. We use the Pearson correlation coefficient (PCC) and the normalized mutual information (NMI) to quantify the correlations between these galaxy properties in sheets, filaments and clusters after matching the stellar mass distributions of the galaxies in these environments. A two-tailed t-test assesses the statistical significance of the observed differences between these relations in different geometric environments. The null hypothesis can be rejected at >99.99% significance level in most of the cases, suggesting that the scaling relations between the observable galaxy properties are susceptible to the geometric environments of the cosmic web.

Pt confined in Sn-ECNU-46 zeolite for efficient alkane dehydrogenation

Highly dispersed and stable Pt-based catalysts play a crucial role in constructing efficient catalytic systems for alkane dehydrogenation. In this study, a novel bimetallic Pt–Sn catalyst confined in extra-large-pore ECNU-46 zeolite (denoted as Pt/Sn-ECNU-46) is prepared by post-treatment. The open-site framework Sn species ((SiO)3Sn–OH) serve as anchors to interact with Pt species, favoring the high dispersion of Pt. On the other hand, the framework Sn species act as the second metal to regulate the geometrical and electronic environment of Pt species, thus suppressing their accumulation. Pt/Sn-ECNU-46 achieves a good performance in propane dehydrogenation reaction with high initial propane conversion (46%) and propylene selectivity (> 99%) as well as regeneration ability. In addition, Pt/Sn-ECNU-46 is also active in the dehydrogenation of n-hexane. This study explores the application of extra-large-pore zeolite as support in constructing metal-confined catalysts for alkane dehydrogenation.

Vision-based collective motion: A locust-inspired reductionist model.

Naturally occurring collective motion is a fascinating phenomenon in which swarming individuals aggregate and coordinate their motion. Many theoretical models of swarming assume idealized, perfect perceptual capabilities, and ignore the underlying perception processes, particularly for agents relying on visual perception. Specifically, biological vision in many swarming animals, such as locusts, utilizes monocular non-stereoscopic vision, which prevents perfect acquisition of distances and velocities. Moreover, swarming peers can visually occlude each other, further introducing estimation errors. In this study, we explore necessary conditions for the emergence of ordered collective motion under restricted conditions, using non-stereoscopic, monocular vision. We present a model of vision-based collective motion for locust-like agents: elongated shape, omni-directional visual sensor parallel to the horizontal plane, and lacking stereoscopic depth perception. The model addresses (i) the non-stereoscopic estimation of distance and velocity, (ii) the presence of occlusions in the visual field. We consider and compare three strategies that an agent may use to interpret partially-occluded visual information at the cost of the computational complexity required for the visual perception processes. Computer-simulated experiments conducted in various geometrical environments (toroidal, corridor, and ring-shaped arenas) demonstrate that the models can result in an ordered or near-ordered state. At the same time, they differ in the rate at which order is achieved. Moreover, the results are sensitive to the elongation of the agents. Experiments in geometrically constrained environments reveal differences between the models and elucidate possible tradeoffs in using them to control swarming agents. These suggest avenues for further study in biology and robotics.

Sensing and Deep CNN-Assisted Semi-Blind Detection for Multi-User Massive MIMO Communications

Attaining precise target detection and channel measurements are critical for guiding beamforming optimization and data demodulation in massive multiple-input multiple-output (MIMO) communication systems with hybrid structures, which requires large pilot overhead as well as substantial computational complexity. With benefits from the powerful detection characteristics of MIMO radar, we aim for designing a novel sensing-assisted semi-blind detection scheme in this paper, where both the inherent low-rankness of signal matrix and the essential knowledge about geometric environments are fully exploited under a designated cooperative manner. Specifically, to efficiently recover the channel factorizations via the formulated low-rank matrix completion problem, a low-complexity iterative algorithm stemming from the alternating steepest descent (ASD) method is adopted to obtain the solutions in case of unknown noise statistics. Moreover, we take one step forward by employing the denoising convolutional neural network (DnCNN) to preprocess the received signals due to its favorable performance of handling Gaussian denoising. The overall paradigm of our proposed scheme consists of three stages, namely (1) target parameter sensing, (2) communication signal denoising and (3) semi-blind detection refinement. Simulation results show that significant estimation gains can be achieved by the proposed scheme with reduced training overhead in a variety of system settings.

Noble metal free double helix binuclear Cu(I) complex as catalyst for carboxylative cyclization of propargylamines with atmospheric carbon dioxide toward oxazolidinones synthesis under mild conditions

The application of economically abundant, renewable and C1-feedstock, carbon dioxide into organically important compounds is considered as the hot topic in modern aspects. In this prospective, a binuclear double helix copper (I) complex (1) was synthesized through insitu reaction between quinolone-2-carbaldehyde and succino-hydrazide with copper (II) nitrate hexahydrate. Single crystal X-ray analysis of complex 1, clearly explained that both tetra co-ordinated Cu(I) ions are in tetrahedral geometric environment, having suprmolecular network arrangement via weak interaction of H-bonding, π…π stacking and CH…π stacking. The complex 1 was found to be effectively active catalyst in carboxylative cyclization reaction of propargylic amines with carbon dioxide towards oxazolidinones synthesis under atmospheric pressure and mild reaction conditions. Due to the initiation of side reaction by –NH2 group of primary propargyliamines, which reduces the yield percentage of respective oxazolidinones as a result the carboxylative cyclization reaction of primary propargylic amines, was rarely developed. In this work both primary and secondary propargylamines smoothly undergoes through this catalytic reaction and produced high percentage of desired oxazolidinones product. Again neat condition for this catalytic reaction makes the methodology more environmentally benign and sustainable. The complex 1 showed luminescent property. Moreover DFT methods were utilized in order to explain the probable mechanistic pathway of carboxylative cyclization reaction.

Efficient Binocular Rendering of Volumetric Density Fields With Coupled Adaptive Cube-Map Ray Marching for Virtual Reality.

Creating visualizations of multiple volumetric density fields is demanding in virtual reality (VR) applications, which often include divergent volumetric density distributions mixed with geometric models and physics-based simulations. Real-time rendering of such complex environments poses significant challenges for rendering quality and performance. This article presents a novel scheme for efficient real-time rendering of varying translucent volumetric density fields with global illumination (GI) effects on high-resolution binocular VR displays. Our scheme proposes creative solutions to address three challenges involved in the target problem. First, to tackle the doubled heavy workloads of binocular ray marching, we explore the anti-aliasing principles and more advanced potentials of ray marching on interior cube-map faces, and propose a coupled ray-marching technique that converges to multi-resolution cube maps with interleaved adaptive sampling. Second, we devise a fully dynamic ambient GI approximation method that leverages spherical-harmonics (SH) transform information of the phase function to reduce the huge amount of ray sampling required for GI while ensuring fidelity. The method catalyzes spatial ray-marching reuse and adaptive temporal accumulation. Third, we deploy a two-phase ray-tracing algorithm with a tiled k-buffer to achieve fast processing of order-independent transparency (OIT) for multiple volume instances. Consequently, high-quality and high-performance real-time dynamic volume rendering can be achieved under constrained budgets controlled by developers. As our solution supports mixed mesh-volume rendering, the test results prove the practical usefulness of our approach for high-resolution binocular VR rendering on hybrid multi-volumetric and geometric environments.

Evaluation of the anionic effect on the formation of biologically active {CuII-phenx; x = 1, 2, 3} fragments - Synthetic and structural variations, antimycobacterial and antiblastoma effects

Two cationic and molecular copper(II) complexes - mixed ligand [{Cu(phen)2benz}{Cu(phen)2Cl}]2+·2Cl-·benz-·H3O+·4·.5H2O (1), [Cu(benz)2phen] (2) (benz- = m-Cl-benzoate anion; phen = 1,10-phenantroline) and [Cu(phen)3]2+·2OTf-·2EtOH (3) (OTf = trifluoromethylsulfonate, triflate anion, CF3SO3-) were synthesized using various synthetic approaches and thoroughly characterized by spectroscopic methods and single crystal X-ray diffraction analysis. The structures of the complexes according to X-ray diffraction data are characterized by a diverse geometric environment of the complexing agent - the cationic form of 1 comprises two structurally nonequivalent moieties: the Cu (1) and Cu (2) complex-forming atoms coordinate, in chelate manner, two phen moieties each and the benz- (1)/Cl- (2) anions, respectively, thus forming different-ligand formula units, a trigonal–bipyramidal {Cu(1)N4Cl} and a pseudo octahedral one {Cu(2)N4O2}. The copper(II) ion in the complex 2 coordinates one phen ligand in a bidentate mode and two benz- anions to produce a distorted planar square environment {CuN2O2}. In complex 3, the copper(II) cation is surrounded by three phenanthroline fragments {Cu(phen)3}2+ and non-coordinated OTf- ions. The results of an EPR study 1 show that in the solid phase, intermolecular exchange interactions that cause exchange narrowing of the spectrum are efficient, whereas in solutions, resolved spectra of copper(II) ion with rhombic symmetry of the g-tensor are observed. An in vitro study of the biological properties of 1–3 toward nonpathogenic mycobacterial strain Mycolicibacterium smegmatis showed an increase in biological effectiveness depending on the structure of complexes (MIC, 1 (2 nmol/disk) > 3 (5 nmol/disk) > 2 (12.5 nmol/disk)). Complex 1 was also tested for antitumor activity against an ovarian adenocarcinoma SKOV3 demonstrated high efficiency: the IC50 value is almost 9 times higher than the activity of cisplatin.

DEVELOPMENT OF ASSIGNMENTS AND DESIGN DOCUMENTS IN ELECTRONIC FORM USING THE SOLID WORKS SYSTEM

The article describes the creation of a set of design documents (DD) in the geometric modeling environment SolidWorks. The main attention is paid to the development of electronic tasks for products that allow students of technical universities to study DD remotely. The programs and applications with which electronic design documents are studied are considered in detail. Special attention is paid to the main design document for the product – specifications. The DD examples considered in the article allow students to study the basics of DD development in electronic form, to form practical skills and abilities to display products on drawings, to deepen knowledge of state standards of the Unified System of Design Documentation. The purpose of this work is to develop electronically tasks and methods for creating DD based on these tasks for products for various purposes. This article may be useful to specialists whose work is related to the creation of DD, with the design and modeling of parts, assemblies, as well as teachers of technical universities engaged in teaching engineering students in remote operation.

Synergistic Co─Ir/Ru Composite Electrocatalysts Impart Efficient and Durable Oxygen Evolution Catalysis in Acid

AbstractExploring highly active and robust catalysts, which have low precious metal content, to boost the kinetically sluggish oxygen evolution reaction (OER) is a key concern for hydrogen production via proton exchange membrane water electrolysis (PEMWE). Here, rational engineering of the morphology and the local geometric ligand environment of Ir and Ru catalysts are presented by using defect‐rich, lanthanum‐ and lithium‐doped Co3O4 nanofiber (LLCF) as substrate that promotes the electrocatalytic OER. Two catalysts, IrCoOx@LLCF and RuCoOx@LLCF, achieve mass activities of 1013.5 A gIr−1 and 1911.4 A gRu−1 in 0.1 m HClO4 at 300 mV overpotential, respectively, which are 26 and 50 times higher than that of commercial IrO2 and RuO2. Operando X‐ray absorption spectroscopy unveils the reversible structure of IrCoOx during the OER and the suppression of over‐oxidation of Co and Ir, giving rise to high stability. Density functional theory calculations reveal that the local geometric ligand engineering optimizes the binding of oxygenated species to the active sites, resulting in strongly enhanced catalytic activity.