Length Distortion Research Articles

On the univalence of certain polyharmonic mappings with bounded length distortions

On the univalence of certain polyharmonic mappings with bounded length distortions

On prime end distortion estimates of mappings with the Poletsky condition in domains with the Poincar´e inequality

This article is devoted to the study of mappings with bounded andfinite distortion defined in some domain of the Euclidean space. Weconsider mappings that satisfy some upper estimates for thedistortion of the modulus of families of paths, where the order ofthe modulus equals to $p,$ $n-1<p\leqslant n.$ The main problemstudied in the manuscript is the investigation of the boundarybehavior of such mappings, more precisely, the distortion of thedistance under mappings near boundary points. The publication isprimarily devoted to definition domains with ``bad boundaries'', inwhich the mappings not even have a continuous extension to theboundary in the Euclidean sense. However, we introduce the conceptof a quasiconformal regular domain in which the specified continuousextension is valid and the corresponding distance distortionestimates are satisfied; however, both must be understood in thesense of the so-called prime ends. More precisely, such estimateshold in the case when the mapping acts from a quasiconformal regulardomain to an Ahlfors regular domain with the Poincar\'e inequality.The consideration of domains that are Ahlfors regular and satisfythe Poincar\'e inequality is due to the fact that, lower estimates forthe modulus of families of paths through the diameter of thecorresponding sets hold in these domains. (There are the so-calledLoewner-type estimates). We consider homeomorphisms and mappingswith branching separately. The main analytical condition under whichthe results of the paper were obtained is the finiteness of theintegral averages of some majorant involved in the defining modulusinequality under infinitesimal balls. This condition includes thesituation of quasiconformal and quasiregular mappings, because forthem the specified majorant is itself bounded in a definitiondomain. Also, the results of the article are valid for more generalclasses for which Poletsky-type upper moduli inequalities aresatisfied, for example, for mappings with finite length distortion.

Unveiling the geometrical and mechanical properties of Σ3 (111) grain boundaries in Ni-based alloys: From interfacial insights

Understanding the properties of interfaces and grain boundaries is pivotal for advancing the design and performance of modern materials and devices. The mechanical strength and durability of materials are significantly influenced by the integrity of these interfaces and grain boundaries. In this study, we employ density functional theory calculations to investigate the geometries, electronic properties, and mechanical behaviors of Σ3 (111) grain boundaries in Ni, AlNi3, and FeNi3 systems. Result reveals that these grain boundaries exhibit trigonal, hexagonal, and hexagonal close-packed structures with minimal bond length distortions, attributed to specific misorientation angles of 60°. They also demonstrate bonding characteristics akin to their corresponding polycrystalline bulk materials, indicating stability and twist character with anti-phase boundaries. Evaluation of grain boundary energetics indicates low energy values and stability across the studied systems. Furthermore, we conduct a detailed examination of the interfacial grain boundary structures of Σ3 (111) Ni/AlNi3 and Σ3 (111) Ni/FeNi3, revealing trigonal closed space configurations with twist character and anti-phase boundaries. Electron localization in interfacial regions suggests a metallic nature of interfacial bonds, supported by density of state calculations and positive Cauchy pressure. Assessment of mechanical properties indicate ductile behavior due to structural heterogeneity, moderate anisotropy. Overall, present study underscores the enhanced mechanical properties resulting from heterogeneity, offering promise for future applications in advanced materials and devices. Additionally, a comparative analysis with highlights the advancements and contributions of this study to the existing body of knowledge.

Research on compensation method for starlight emission accuracy based on star point focal length traversal

Star simulators are essential equipment for ground calibration of star sensors and are widely used in the aerospace field. Aiming at the problem that it is difficult to further improve the emission accuracy of the current star simulator due to the lack of comprehensive analysis of the factors affecting the error, a comprehensive error transfer model consisting of star point position deviation, principal point position deviation, focal length deviation, distortion deviation, and object plane tilt deviation was established. Analyzed the design basis for distortion tolerance of the optical system of the star simulator, and the required distortion tolerance for a 0–30° field of view with starlight emission accuracy better than 5″, 10″, and 20″ was determined. A mapping model between star point position and starlight emission accuracy has been established, and a compensation method for starlight emission accuracy based on star point focal length traversal has been proposed. Taking field of view of Φ20° and theoretical starlight emission accuracy better than 16″ as an example, a stellar simulation optical system has been designed, on this basis, an experimental platform was built and compared with existing unified focal length compensation and star map region partition compensation methods, verifying the performance of the starlight emission accuracy compensation method based on comprehensive focal length. The experimental results show that the maximum error of uncorrected starlight emission accuracy is 82.14". After three corrections using the unified focal length compensation method, the starlight emission accuracy is 15.27". Using the compensation method of star map region partition to achieve a starlight emission accuracy of 13.39". The starlight emission accuracy compensation method based on star point focal length traversal is used after one correction, achieve a starlight emission accuracy of 11.23″, The proposed method is superior to existing methods in terms of difficulty and accuracy in correction, and can provide new research ideas and advanced technical means for the development of high-precision star simulators.

Dynamic Projection Method of Electronic Navigational Charts for Polar Navigation

Electronic navigational charts (ENCs) are geospatial databases compiled in strict accordance with the technical specifications of the International Hydrographic Organization (IHO). Electronic Chart Display and Information System (ECDIS) is a Geographic Information System (GIS) operated by ENCs for real-time navigation at sea, which is one of the key technologies for intelligent ships to realize autonomous navigation, intelligent decision-making, and other functions. Facing the urgent demand for high-precision and real-time nautical chart products for polar navigation under the new situation, the projection of ENCs for polar navigation is systematically analyzed in this paper. Based on the theory of complex functions, we derive direct transformations of Mercator projection, polar Gauss-Krüger projection, and polar stereographic projection. A rational set of dynamic projection options oriented towards polar navigation is proposed with reference to existing specifications for the compilation of the ENCs. From the perspective of nautical users, rather than the GIS expert or professional cartographer, an ENCs visualization idea based on multithread-double buffering is integrated into Polar Region Electronic Navigational Charts software, which effectively solves the problem of large projection distortion in polar navigation applications. Taking the CGCS2000 reference ellipsoid as an example, the numerical analysis shows that the length distortion of the Mercator projection is less than 10% in the region up to 74°, but it is more than 80% at very high latitudes. The maximum distortion of the polar Gauss-Krüger projection does not exceed 10%. The degree of distortion of the polar stereographic projection is less than 1% above 79°. In addition, the computational errors of the direct conversion formulas do not exceed 10−9 m throughout the Arctic range. From the point of view of the computational efficiency of the direct conversion model, it takes no more than 0.1 s to compute nearly 8 million points at 1′×1′ resolution, which fully meets the demand for real-time nautical chart products under information technology conditions.

Differences in Maxillary and Mandibular Premolar Length Distortion at Various Angulation Angles of Periapical Radiographs

Background: Periapical radiographic techniques are usually used in root canal treatment. Distortion on bisecting technique periapical radiographs is relatively more common, especially on premolars located at the curved jaw area. Objective: To determine the difference in the length distortion of the maxillary and mandibular premolars at various exposure angles of periapical radiographs. Methods: The research conducted using observational analytic research, and the research design is cross-sectional. The sample used in this study were 30 upper premolars X-rayed using the periapical bisecting technique with a reference angle from the first literature book +30 and a reference angle from the second literature book +40 and 30 lower premolars X-rayed at -10 and -15 angles. Results: On the independent sample T-test, p value<0.05 for both the upper and lower premolars, so it can be concluded that there is a significant difference in distortion with a reference angle of +30 and +40 on upper premolars and -10 and -15 reference angles on the lower premolars. Discussion: Distortion of periapical radiographs with bisecting technique occurs more easily. The placement of the periapical sensor must be as close as possible to the object so that the correct position of the periapical sensor also plays a role in the formation of distortion. Conclusion: There is a significant difference in the length distortion of the upper and lower premolars on the angle of exposure periapical bisecting radiographs from the two reference books.

Straight impact crater rim segments on Mercury

ABSTRACT The formation of straight impact crater rims is widely accepted to be influenced by preexisting lithospheric structure. We investigate the distribution and orientations of straight crater rim segments across Mercury. We devise a mapping workflow aimed at minimizing distortions of length and orientation that arise when working on projected image mosaics on a global scale and produce a global map of the rims of 7,145 impact craters with diameters between 20 and 400 km. We extract straight rim segments that maintain consistent orientations for at least 10 km to assess their frequency and orientation. Our dataset shows that 83% of craters have straight rim segments that show strong east–west orientations at the poles and weak north–south or random orientations at lower latitudes. This emphasizes the importance of lithospheric structure for impact cratering on Mercury. Our map dataset provides valuable insights for future investigations into the tectonic evolution of Mercury.

Assessment of Distortion of Radiovisiographical Tooth Length Compared to Actual Tooth Length: In-vivo and In-vitro Study

Background: Determination of appropriate or exact working length measurement with radiovisiography (RVG) during root canal treatment (RCT) is an essential for the long-term success. As, there are several controversies with the distortion of RVG image in assessing the working tooth length (WTL) during RCT compared to actual tooth length (ATL). So, this study was aimed to assess the frequency of distortion of radiovisiographical tooth length (RTL) compared to actual tooth length (ATL). Methods: An analytical (in-vivo and in-vitro) study was conducted at Department of Conservative Dentistry and Endodontics, BSMMU. The patient indicated for extraction purpose of orthodontic treatment was considered as the study population. Human premolar teeth (n=20) were selected as study sample by purposive sampling technique which met the inclusion and exclusion criteria. The RTL measurements were carried out with RVG images before and after tooth extraction (in-vivo and in-vitro setting). Then the ATL measurements of extracted tooth samples were carried out with both Inch Architectural Scale Ruler and Endodontic Ruler individually three concordant times. Statistical analysis: The data was analyzed using T test and presented in frequency and percentages with tables. Results: For 95% of study samples, the differences from actual and radiovisiographical tooth length were <0.5 mm. Total 19 tooth samples (out of 20) showed acceptable level of coincidence except one sample showed non-acceptable level of coincidence. There was no sample revealed exact level of coincidence. There was a significant difference between the distortion category; yes (95%)/ no (5%) (P 0.001). The radiovisiological tooth lengths among all samples were same in both in-vivo and in-vitro setting. Study results also revealed the average distortion of RTL to ATL was 2.61±0.97 mm when RVG was done without using RVG sensor positioner. Conclusion: RVG tooth length images exhibited no distortion with the exact anatomical tooth lengths when the RTL was carried out with RVG sensor positioner. It’s recommended that to overcome the RVG image distortion, the RTL measurement ought to be carried out with RVG sensor positioner allowing RVG sensor/film parallel to long axis of tooth; RVG beam position perpendicular (900) to long axis of tooth.

Boosting Electrocatalytic Carbon Dioxide Reduction via Self-Relaxation of Asymmetric Coordination in Fe-Based Single Atom Catalyst.

Addressing the limitations arising from the consistent catalytic behavior observed for various intermediates during the electrochemical carbon dioxide reduction reaction (CO2 RR) poses a significant challenge in the optimization of catalytic activity. In this study, we aimed to address this challenge by constructing an asymmetric coordination Fe single atom catalyst (SCA) with a dynamically evolved structure. Our catalyst, consisting of a Fe atom coordinated with one S atom and three N atoms (Fe-S1 N3 ), exhibited exceptional selectivity (CO Faradaic efficiency of 99.02 %) and demonstrated a high intrinsic activity (TOF of 7804.34 h-1 ), and remarkable stability. Using operando XAFS spectra and Density Functional Theory (DFT) calculations, we elucidated the self-relaxation of geometric distortion and dynamic evolution of bond lengths within the catalyst. These structure changes enabled independent regulation of the *COOH and *CO intermediate adsorption energies, effectively breaking the linear scale relationship and enhancing the intrinsic activity of CO2 RR. This study provides valuable insights into the dynamic evolution of SACs and paves the way for targeted catalyst designs aimed to disrupt the linear scaling relationships.

Boosting Electrocatalytic Carbon Dioxide Reduction via Self‐Relaxation of Asymmetric Coordination in Fe‐Based Single Atom Catalyst

AbstractAddressing the limitations arising from the consistent catalytic behavior observed for various intermediates during the electrochemical carbon dioxide reduction reaction (CO2RR) poses a significant challenge in the optimization of catalytic activity. In this study, we aimed to address this challenge by constructing an asymmetric coordination Fe single atom catalyst (SCA) with a dynamically evolved structure. Our catalyst, consisting of a Fe atom coordinated with one S atom and three N atoms (Fe−S1N3), exhibited exceptional selectivity (CO Faradaic efficiency of 99.02 %) and demonstrated a high intrinsic activity (TOF of 7804.34 h−1), and remarkable stability. Using operando XAFS spectra and Density Functional Theory (DFT) calculations, we elucidated the self‐relaxation of geometric distortion and dynamic evolution of bond lengths within the catalyst. These structure changes enabled independent regulation of the *COOH and *CO intermediate adsorption energies, effectively breaking the linear scale relationship and enhancing the intrinsic activity of CO2RR. This study provides valuable insights into the dynamic evolution of SACs and paves the way for targeted catalyst designs aimed to disrupt the linear scaling relationships.

On the Definition of Standard Parallels in Map Projections

The article belongs to the field of theoretical research on map projections. It is observed that there is no unique and generally accepted definition of standard parallels in the cartographic literature. For some authors, a standard line is a line along which there is no distortion, and for others, it is a line along which there is no distortion of length. At the same time, it is forgotten that the length distortions at any point generally change and depend on the direction. The main goal of this article is very simple: the sentence “linear deformation is zero in all directions” is expressed using a mathematical formula. Besides that, the paper introduces equidistance in a broader sense. This is a novelty in the theory of map projections. Equidistance is defined at a point, along a line and in an area, especially in the direction of the parallels and especially in the direction of the meridian. This enables an unambiguous definition of standard parallels. Theoretical considerations are illustrated with examples of cylindrical projections. The practical value of the proposed approach is manifested in the possibility of a better understanding of the distribution of distortions in any map projection used.

The Crystal Chemistry of Voltaite-Group Minerals from Post-Volcanic and Anthropogenic Occurrences

Five samples of voltaite-group minerals from post-volcanic occurrences (geothermal fields and solfatara at pyroclastic flow) and from pseudofumaroles born by coal fires are characterized by single-crystal X-ray diffraction, scanning electron microscopy and electron microprobe analysis. The studied minerals include ammoniomagnesiovoltaite, ammoniovoltaite, voltaite and magnesiovoltaite. The quadrilateral of chemical compositions is determined by monovalent cations such as (NH4)+ and K+ and divalent cations such as Fe2+ and Mg2+. Minor Al can occur in the Fe3+ site. Minor amounts of P, V can occur in the S site. Ammonium members are described from geothermal fields, expanding the mineral potential of this type of geological environment. All minerals are cubic, space group Fd-3c, a = 27.18–27.29 Å, V = 20079–20331 Å3, Z = 16. No clear evidence of symmetry lowering (suggested for synthetic voltaites) is observed despite the chemical variation in the studied samples. Ammonium species tend to have a larger a lattice parameter than potassium ones due to longer <A–O> distances (A = N or K). The systematically shorter <Me2+–ϕ>obs (Me2+ = Fe, Mg; ϕ = O, H2O) in comparison to <Me2+–ϕ>calc bond lengths can be explained as a consequence of mean bond length variation due to significant bond length distortion in Me2+ϕ6 octahedra Me2–O2—2.039–2.055 Å; Me2–O4—2.085–2.115 Å; and Me2–Ow5—2.046–2.061 Å, with bond length distortion estimated as from 0.008 to 0.014 for different samples.

On isolated singularities of mappings with finite length distortion

On isolated singularities of mappings with finite length distortion

On isolated singularities of mappings with finite length distortion

Here we give a survey of various integral criteria in terms of inner dilatations $K_{I}$ for the removability of isolated singularities of mappings with finite length distortion in $\mathbb{R}^{n}$, $n\geq 2$, that are a natural extension of the well-known Martio-Vaisal a mappings with bounded length distortion. In particular, the survey includes many effective integral criteria of the types of BMO, bounded mean oscillation by John-Nirenberg, FMO, finite mean oscillation, Calderon-Zygmund, Lehto, and Orlicz.

Compressed and Expanded Lattices - Barriers to Spin-State Switching in Mn3+ Complexes.

We report the structural and magnetic properties of two new Mn3+ complex cations in the spin crossover (SCO) [Mn(R-sal2323)]+ series, in lattices with seven different counterions in each case. We investigate the effect on the Mn3+ spin state of appending electron-withdrawing and electron-donating groups on the phenolate donors of the ligand. This was achieved by substitution of the ortho and para positions on the phenolate donors with nitro and methoxy substituents in both possible geometric isomeric forms. Using this design paradigm, the [MnL1]+ (a) and [MnL2]+ (b) complex cations were prepared by complexation of Mn3+ to the hexadentate Schiff base ligands with 3-nitro-5-methoxy-phenolate or 3-methoxy-5-nitro-phenolate substituents, respectively. A clear trend emerges with adoption of the spin triplet form in complexes 1a-7a, with the 3-nitro-5-methoxy-phenolate donors, and spin triplet, spin quintet and thermal SCO in complexes 1b-7b with the 3-methoxy-5-nitro-phenolate ligand isomer. The outcomes are discussed in terms of geometric and steric factors in the 14 new compounds and by a wider analysis of electronic choices of Mn3+ with related ligands by comparison of bond length and angular distortion data of previously reported analogues in the [Mn(R-sal2323)]+ family. The structural and magnetic data published to date suggest a barrier to switching may exist for high spin forms of Mn3+ in those complexes with the longest bond lengths and highest distortion parameters. A barrier to switching from low spin to high spin is less clear but may operate in the seven [Mn(3-NO2-5-OMe-sal2323)]+ complexes 1a-7a reported here which were all low spin in the solid state at room temperature.

Adaptive synchroextracting transform and its application in bearing fault diagnosis

Time–frequency analysis methods can be used to characterize the time-varying characteristics of a signal. The postprocessing algorithm further enhances this ability. The synchroextracting transform is a typical postprocessing algorithm that has the advantage of energy aggregation. However, based on a short-time Fourier transform, shortcomings such as a fixed window length and amplitude distortion when processing frequency modulation signals are unavoidable. This paper proposes a time–frequency postprocessing algorithm with high adaptability, which is called the adaptive synchroextracting transform (ASET). The filter window width for the ASET is adaptive and is determined by the instantaneous frequency change rate for the signal. On this basis, the improved extraction operator can be used to achieve a high-resolution time–frequency​ representation. This algorithm can be used to better deal with strong frequency modulation signals and has better noise robustness while allowing for signal reconstruction. The effectiveness and practicability of the proposed algorithm are demonstrated by simulation signals and faulty bearing signals.

Regulating the selective adsorption of OH* over the equatorial position of Co3O4via doping of Ru ions for efficient water oxidation reaction

The synthesized Ru-Co3O4 delivers a high performance towards the OER in alkaline (292 mV) and acidic (365 mV) media. Structural optimization demonstrates the distortion of bond length favours the selective adsorption of OH− which facilitates the OER.

K-anonymization of social network data using Neural Network and SVM: K-NeuroSVM

With the coming up of social network sites like Twitter, Facebook, LinkedIn, etc information sharing has seen tremendous growth in the past few years. Although people wish to interact with like-minded persons through such platforms, there is a lot of personal information about individuals that need to be secured. To maintain the privacy of sensitive information in a social network, efficient privacy-preserving techniques like k-anonymization, randomization, generalization, etc., are used. The majority of the proposed techniques apply edge editing and clustering based methods for creating k-anonymized social network graphs. Since these techniques distort the original properties of the graph to a great extent, various enhancements have been proposed which consider the addition of noisy nodes as one of the alternatives. In this paper, an improved version of k-degree-anonymization on social network graph has been provided which uses the hybridization of Neural Network and SVM, called NeuroSVM where average path length of the graph is preserved and addition of noisy nodes and noisy edges is reduced significantly. The proposed technique is evaluated on various parameters which include Average path length, Precision, Recall, F-measure, and Information loss. It has been experimentally proved that the proposed technique has less distortion in average path length as compared to existing techniques. The accuracy of the proposed technique is more than 75% and information loss is also reduced.

Using Optimal Transport to Improve Spherical Harmonic Quantification of Complex Biological Shapes.

The knowledge of the anatomical shape of both gross and microscopic structures is the key to understanding the effects of disease processes on cellular structure. Geometric morphometric methods, such as Procrustes superimposition, and Spherical Harmonics (SPHARM), have been used to capture the biological shape variation and group differences in morphology. Previous SPHARM-MAT techniques use the CALD algorithm to parameterize the mesh surface. It starts from initial mapping and performs local and global smoothing methods alternately to control the area and length distortions simultaneously. However, this parameterization may not be sufficient in complex morphological cases. To bridge this gap, we propose SPHARM-OT, an enhanced SPHARM surface modeling method using optimal transport (OT) for spherical parameterization. First, the genus 0 3D objects are conformally mapped onto a sphere. Then the optimal transport theory via spherical power diagram is introduced to minimize the area distortion. This new algorithm can effectively reduce the area distortion and lead to a better reconstruction result. We demonstrate the effectiveness of the method by applying it to the human sphenoidal paranasal sinuses.

An Automated Approach for Clipping Geographic Data before Projection that Maintains Data Integrity and Minimizes Distortion for Virtually Any Projection Method

Selecting a map projection is key to minimizing distortion and thus clear communication of spatial data and accurate spatial analysis. Methods exist for selecting projections based on the intended area of use but not for finding polygons that can be used to clip geographic data to ensure the data are projected correctly and within desired distortion limits. The projection methods available in the Proj library were examined to determine the nature of the errors and distortions they created based on global data and a wide variety of available settings. Approaches were then identified for each projection including simple bounding boxes and more complex clipping polygons. To make sure that errors were not introduced into the projected data, data integrity polygons (DIPs) were created by placing a grid of cells over the Earth and then finding a cell near the origin that was within the specified criteria. Adjacent cells were added to the DIPs that met the criteria until no additional cells could be added. The criteria included projected cell sides could not intersect with themselves or other cells, the order of the cell corners could not be reversed, and distortion within the cell had to be within specified limits. I found that up to two DIPs with a limit on length distortion of a factor of 4 provided a general solution for all but three projection methods. Limitations included the time to find DIPs at high resolution. Clipping polygons and visualizations of the results were made available on a website.