Perpendicular Research Articles

Effect of Fibre Orientation on the Bond Properties of Softwood and Hardwood Interfaces

Increasing concerns regarding carbon emissions and climate change are prompting a shift toward the use of sustainable materials in the construction industry. Engineered timber products are gaining attention in the construction industry due to advancements in lamination techniques and adhesives as well as the renewable characteristics of wood. Bond properties play a significant role in engineered timber products. In Australia, Radiata Pine (RP, softwood) and Shining Gum (SG, hardwood) share a large proportion of local and native plantation forest resources. The present paper investigates the bond behaviours of Australian softwoods (RP–RP), hardwoods (SG–SG) and hybrid-wood (RP–SG) combinations in both parallel (PAL) and perpendicular (PER) bonding directions using one-component polyurethane adhesives. The results indicate that most of the softwood samples were subjected to wood-side (timber) failure, whereas hardwood samples failed due to delamination but exhibited higher strength and stiffness regardless of bond direction. In contrast, bond direction had a significant effect on the bond characteristics of hybrid configurations. Improved bond properties were observed when bonded in PAL directions; however, negative effects were seen when bonded in PER directions. Obtained characteristic (5th percentile) shear bond strengths for RP–RP–PAL, RP–SG–PAL and SG–SG–PAL samples were 3.88 MPa, 6.19 MPa and 8.34 MPa, whilst those for RP–RP–PER, RP–SG–PER and SG–SG–PER samples were 3.45 MPa, 2.96 MPa and 7.83 MPa, respectively.

Expert-Based cognitive models vs theory-based cognitive models: Which cognitive models match students’ cognition on ‘Parallel and Perpendicular Lines’ Better?

The cognitive model is a prominent element for supporting teachers' instructional needs regarding the confusing geometry topic named ‘Parallel and Perpendicular Lines’. Nonetheless, the mismatch between the derived cognitive models and the students’ cognition would threaten the validity of the diagnostic inferences made. While cognitive models could be developed by using different approaches, this study evaluated the model-data fit of the expert-based cognitive models which were developed by conducting expert task analysis and the theory-based cognitive models which were developed by reviewing the available theory. The study was conducted by adopting a cross-sectional research design. A total of 1 069 Grade Four students were selected by using two-stage cluster sampling. The findings indicated that the average model-data fit increased with the abilities of students for both theory-based and expert-based cognitive models on ‘Parallel and Perpendicular Lines’. Nonetheless, the theory-based cognitive models have a better model-data fit compared to the expert-based cognitive models. The findings imply the significance of the available theory of cognition in guiding the development of cognitive models. With satisfactory model-data fit, the theory-based cognitive models could serve as a guide for making diagnostic inferences on students' skill acquisition in the topic of 'Parallel and Perpendicular Lines'.

Application of 2-D and 3-D Geo-electrical Resistivity Tomography and Geotechnical soil Evaluation for Engineering site Investigation: A Case Study of Okerenkoko Primary School, Warri-Southwest, Delta State, Nigeria

In the design of building structures, joint efforts must be decided to resolve the depth to competent layers across the intended site, and periodic subsidence monitoring and deformation assessment of all buildings, specifically high-rise buildings, should be a regular practice, to safeguard the durability of civil engineering structures, to avert the disastrous consequences of structural failure and collapse prevalent of late. It was this extremity that necessitated the adoption of an integrated methodology which employed DC resistivity tomography involving 2-D and 3-D techniques and geotechnical-soil analysis to evaluate subsoil properties for engineering site investigation at Okerenkoko primary school, in Warri-southwest area of Delta State, to adduce the phenomena responsible for the visible cracks/structural failure observed in the school buildings. Rectilinear set of 2-D resistivity data consisting of five (5) parallel and five (5) perpendicular lines were obtained in a 100 x 80 m2 rectangular grid using the Wenner array. Thirteen (13) Schlumberger soundings were also obtained on the site with half-current electrode separation of 200 m. The results brought to light the geological structure beneath the subsurface, which consists of four geoelectric layers identified as top soil, dry/lithified upper sandy layer, wet sand (water-saturated) and peat/clay/sandy clayey soil (highly water-saturated). The deeply-seated peat/clay materials (ρ ≤ 20 Ωm) were delineated in the study area to depths of 17.1 m and 19.8 m from 2-D and 3-D imaging respectively. The dominance of mechanically unstable peat/clay/sandy clay layers beneath the subsurface, which are highly mobile in response to volumetric changes, is responsible for the noticeable cracks/failure/subsidence detected on structures within the study site. The DC resistivity result was validated using geotechnical test of soil samples collected from boreholes covering the first 8.0 m on three of the profiles. Atterberg’s limits of the soil samples revealed plasticity indices of zero for all samples. Thus, the soil samples within the depth analyzed were representatives of sandy soil which does not possess any plasticity and their plasticity index is taken as zero. These findings apparently justify the subsoil conditions defined in the interpretation of 2-D and 3-D resistivity imaging data. 3-D images presented as horizontal depth slices revealed the dominance of very low resistivity materials i.e. peat/clay/sandy clay within the third, fourth and fifth layers at depths ranging from 5.38-8.68 m, 8.68-12.5 m and 12.5-16.9 m respectively. Hence, 3-D tomography amplified the degree of accuracy of the geoelectrical resistivity imaging. Resistivity contour maps of second, third and fourth layers for VES 1 to 13, displayed low resistivity direction predominantly towards the northeastern part of the site, and signifies that rocks within the northeastern part have low resistivity values, which connotes high porosity and establishes the groundwater flow trend in the study area. The methods employed in this study justifiably gave relevant information on the subsurface geology beneath the study site and its suitability for engineering practice. Thus, it is suggested that these methods should be appropriated as major tools for engineering site assessment projects and groundwater future studies.

An appropriate method for predicting the femoral angle on whole-body X-ray images from full-spine X-ray images

IntroductionThe importance of lower-limb compensation in patients with spinal malalignment due to spinal pathologies has been emphasized. The latest whole-body X-ray images (WBX) have enabled evaluations of whole-body alignment from head to toe. However, WBX is still not commonly available. Thus, the present study aimed to examine an alternative measurement method of the femoral angle on usual full-spine X-ray images (FSX) that approximates the femoral angle on WBX. MethodsA total of 50 patients (age, 52.8 ± 25.3 years; female, n = 26; male, n = 24) underwent WBX and FSX. The following parameters were measured on lateral view X-rays: WBX and FSX femoral angle (angle between the femoral axis and a perpendicular line); FSX femoral distance (distance from the center of femoral head to the distal femur on FSX); WBX intersection length (length between the center of the femoral head and the intersection point [the point at which the line connecting the center of the femoral head and the midpoint of the femoral condyle intersects the center line of the femur] on WBX). ResultsThe WBX femoral angle, and FSX femoral angle were 0.16 ± 4.2°, and −0.53 ± 4.1°, respectively. The FSX femoral distance was 102.7 ± 41.1 mm. An ROC curve analysis revealed that the cut-off value of the FSX femoral distance associated with minimal difference in the WBX and FSX femoral angles (<3°) was 73 mm (sensitivity 83.3%, specificity 87.5%, AUC 0.80). The WBX intersection length was 105.3 ± 27.3 mm. ConclusionTo calculate the femoral angle on FSX that approximates the WBX femoral angle, the femoral distance on FSX ≥73 mm is preferable. We suggest using the FSX femoral distance within the range of 80 mm–130 mm as a simple numerical value that meets all criteria.

Compact filtering magic‐T using a hybrid microstrip‐cavity structure

AbstractThis letter introduces a filtering magic‐T based on a hybrid microstrip‐cavity structure. TE011 and TE101 modes of the cavity are generated by the two perpendicular input microstrip lines to form the filtering responses. Because of the orthogonality of the feeding lines and the two resonant modes, in‐ and out‐of‐phase output currents and high port isolations are achieved. The measured filtering responses of the two input ports are in good agreement with each other and possess high‐frequency selectivity. The isolations of the input and output ports are below 41 and 22 dB, respectively. Moreover, benefiting from the hybrid microstrip‐cavity structure, only two cavity resonators are employed, which realizes compact size.

Synthesis of Orbital Angular Momentum Antennas for Target Localization

AbstractThe exploitation of Orbital Angular Momentum (OAM) is proposed to design circular‐support continuous aperture distributions and concentric‐ring arrays for target‐localization applications. The proposed approach allows generating a single isolated null of the field in the target direction, which is of interest with respect to common techniques leading to a line (or perpendicular lines) of power‐pattern zeroes in the spectral plane. In the presented design procedure, the optimal continuous aperture source is first identified by resorting to the most suitable OAM vortex and effective tools such as the Singular Value Decomposition of the involved operator and a smart Convex Programming optimization. Then, by exploiting fast deterministic algorithms, this continuous source is discretized into circular‐ring arrays emulating it at best. Relevant applications including equispaced arrays, sum‐difference reconfigurable arrays, and isophoric sparse arrays are presented. The proposed approach is also compared with the state‐of‐the‐art techniques and assessed through full‐wave electromagnetic simulations.

Influence of the Operator`s Experience, Working Time, and Working Position on the Quality of the Margin Width: In Vitro Study

Background and Objectives: Appropriate tooth preparation is mandatory to obtain a perfect marginal fit of fixed restorations. The heavy chamfer is the most commonly used finish line, especially for minimally invasive tooth preparation. The aim of the study was to compare the width of the finish line obtained during tooth preparation performed by experienced (university lecturers) and inexperienced persons (dental students) in different working times and positions. Materials and Methods: Forty left upper-second molars were prepared on the simulator by each participant, totalizing 160 prepared teeth. A new round-end tapered diamond was used to obtain the 0.5 mm width of the heavy chamfer. The prepared teeth were photographed using a Canon D5300 camera with a macro lens attached to a tripod. The measurements were made with the Image-Pro Insight software selecting the same eight reference points. From these points, perpendicular lines were drawn above the finish line to the axial walls and the distance between the chamfer's outer edge and the axial wall's inner edge was measured. GraphPad Instat and NCSS Dowson Edition software were used. The statistical significance was set at p < 0.05. The mean (M) and standard deviation (SD) were calculated. The used tests: one sample t-test, ANOVA test, and Tukey-Kramer Multiple Comparisons Test. Results: Statistically significant differences were obtained according to the experience of the participant, preparation time, patient's position, and the chamfer width on the prepared tooth different surfaces. Conclusions: Daytime or weeklong tiredness and patient position do not affect the width of the heavy chamfer prepared by experienced and inexperienced persons. The experience and the operator's working position influence the width of the prepared finish line.

Transformer High-Voltage Primary Coil Quality Detection Method Based on Machine Vision

Aiming at the problems of low efficiency and low accuracy in manual detection of winding angle and wire spacing during automatic winding of high-voltage primary coils of transmission and distribution transformers, a detection scheme using machine vision is proposed. Firstly, the coil image is acquired by the industrial camera, the detection region is segmented, and the ROI (region of interest) image is pre-processed. For winding angle detection, we propose a slicing method for image graying to reduce the interference caused by uneven light irradiation. The gray image is converted to a binary image, and wire skeleton extraction is performed; the skeleton is identified using the Hough transform for feature straight lines, and the winding angle is then calculated. For wire spacing detection, we propose an intersection of the perpendicular lines method, which extracts edge coordinates using contour images and performs endpoint pixel expansion and shape classification. Use the intersection of the vertical lines to determine the centroid coordinates of the wire outline, calculate the pixel distance of the adjacent centroid, and obtain the wire spacing by combining pixel calibration. Comparison experiments have shown that the solution has a high detection accuracy (0.01 mm), and the error of the integrated detection results is not higher than 10%, which enables the real-time detection of coil winding status and corrects the winding process according to the visual real-time detection result to improve the finished product quality of coils.

The location of unilateral axillary lymphadenopathy after COVID-19 vaccination compared with that of metastasis from breast cancer without vaccination

PurposeUnilateral axillary lymphadenopathy is known to occur after coronavirus disease (COVID-19) vaccination. Post-vaccination lymphadenopathy may mimic the metastatic lymph nodes in breast cancer, and it is challenging to distinguish between them. This study investigated whether the localization of axillary lymphadenopathy on magnetic resonance imaging (MRI) could be used to distinguish reactive lymphadenopathy after COVID-19 vaccines from metastatic nodes.Materials and methodsWe retrospectively examined preoperative MRI images of 684 axillae in 342 patients who underwent breast cancer surgery from June to October 2021. Lymphadenopathy was defined as cortical thickening or short axis ≥ 5 mm. The axilla was divided into ventral and dorsal parts on the axial plane using a perpendicular line extending from the most anterior margin of the muscle group, including the deltoid, latissimus dorsi, or teres major muscles, relative to a line along the lateral chest wall. We recorded the presence or absence of axillary lymphadenopathy in each area and the number of visible lymph nodes.ResultsOf 80 axillae, 41 and 39 were included in the vaccine and metastasis groups, respectively. The median time from the last vaccination to MRI was 19 days in the vaccine group. The number of visible axillary lymph nodes was significantly higher in the vaccine group (median, 15 nodes) than in the metastasis group (7 nodes) (P < 0.001). Dorsal lymphadenopathy was observed in 16 (39.0%) and two (5.1%) axillae in the vaccine and metastasis groups, respectively (P < 0.001). If the presence of both ventral and dorsal lymphadenopathy is considered indicative of vaccine-induced reaction, this finding has a sensitivity of 34.1%, specificity of 97.4%, and positive and negative predictive values of 93.3％ and 58.5%, respectively.ConclusionThe presence of deep axillary lymphadenopathy may be an important factor for distinguishing post-vaccination lymphadenopathy from metastasis. The number of axillary lymph nodes may also help.

Association between Bilateral Sagittal Split Osteotomy Setback and Autorotation of the Mandible

Introduction: The study aimed to evaluate the autorotation for Class III malocclusions after the bilateral sagittal split osteotomy (BSSO) setback procedure . Methodology: This retrospective study includes lateral cephalograms of eight males and three females total of 11 patients who had undergone BSSO, without any other additional surgeries. The Frankfurt-Horizontal (F-H) plane was used as a reference and manual superimposition was done. Considering stable mandibular landmarks, reference line perpendicular (RLp) and reference line (RL) were drawn as x and y coordinates, respectively. Pre- and postsurgical statistics were used to compare using paired t-test where P &lt; 0.05 was set for statistical significance. Results: Superimposed tracings showed no significant difference in pre- and postsurgical treatments. There was no statistically significant amount of autorotation after the BSSO setback procedure (P = 0.714). Conclusion: Hence, BSSO setback surgery will not cause any significant amount of autorotation of the mandible. If autorotation is required it must be incorporated into treatment planning.

Cramér-Rao Bounds of Near-Field Positioning Based on Electromagnetic Propagation Model

The adoption of large-scale antenna arrays at high-frequency bands is widely envisioned in the beyond 5G wireless networks. This leads to the near-field regime where the wavefront is no longer planar but spherical, bringing new opportunities and challenges for communications and positioning. In this paper, we improve the near-field positioning technology from the classical <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">spherical wavefront model</i> (SWM) to the more accurate and true <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">electromagnetic propagation model</i> (EPM). A generic near-field positioning model with different observation capabilities for three electric field types ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vector</i> , <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">scalar</i> , and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">overall scalar electric field</i> ) is developed based on the complete EPM. For these three observed electric field types, the Cramér-Rao bound (CRB) is adopted to evaluate the achievable estimation accuracy. The expressions of the CRBs for different electric field observations are derived by combining electromagnetic propagation concepts with estimation theory. Closed-form expressions can be further obtained as the terminal is assumed to be on the central perpendicular line (CPL) of the receiving antenna surface. Moreover, the above discussions are extended to the system with multiple receiving antennas. In this case, the CRBs using various electric field types are derived and the effect of different numbers of receiving antennas is deeply investigated. Numerical results are provided to quantify the CRBs and validate the analytical results. Also, the impact of different system parameters, including electric field type, wavelength, size of the receiving antenna, and number of antennas, is evaluated.

Characterization of micro pore optics for full-field X-ray fluorescence imaging

Elemental mapping images can be achieved through step scanning imaging using pinhole optics or micro pore optics (MPO), or alternatively by full-field X-ray fluorescence imaging (FF-XRF). X-ray optics for FF-XRF can be manufactured with different micro-channel geometries such as square, hexagonal or circular channels. Each optic geometry creates different imaging artefacts. Square-channel MPOs generate a high intensity central spot due to two reflections via orthogonal channel walls inside a single channel, which is the desirable part for image formation, and two perpendicular lines forming a cross due to reflections in one plane only. Thus, we have studied the performance of a square-channel MPO in an FF-XRF imaging system. The setup consists of a commercially available MPO provided by Photonis and a Timepix3 readout chip with a silicon detector. Imaging of fluorescence from small metal particles has been used to obtain the point spread function (PSF) characteristics. The transmission through MPO channels and variation of the critical reflection angle are characterized by measurements of fluorescence from copper and titanium metal fragments. Since the critical angle of reflection is energy dependent, the cross-arm artefacts will affect the resolution differently for different fluorescence energies. It is possible to identify metal fragments due to the form of the PSF function. The PSF function can be further characterized using a Fourier transform to suppress diffuse background signals in the image.

Singularly Degenerate Heteroclinic Cycles with Nearby Apple-Shape Attractors

Compared with most known singularly degenerate heteroclinic cycles consisting of two different equilibria of a line or a curve, or two parallel lines of semi-hyperbolic equilibria, little seems to be noticed about the one that connects two perpendicular lines of semi-hyperbolic equilibria, i.e. [Formula: see text] and [Formula: see text], [Formula: see text], which is found in the mathematical chaos model: [Formula: see text], [Formula: see text], [Formula: see text] when [Formula: see text] and [Formula: see text]. Surprisingly, apple-shape attractors are also created nearby that kind of singularly degenerate heteroclinic cycles in the case of small [Formula: see text]. Further, some other rich dynamics are uncovered, i.e. global boundedness, Hopf bifurcation, limit cycles coexisting with one chaotic attractor, etc. We not only prove that the ultimate bound sets and globally exponentially attracting sets perfectly coincide under the same parameters, but also illustrate four limit cycles coexisting with one chaotic attractor, the saddle in the origin, and other two stable nontrivial node-foci, which are also trapped in the obtained globally exponentially attracting set, extending the recently reported results of the Lü-type subsystem. In addition, combining theoretical analysis and numerical simulation, the bidirectional forming mechanism of that kind of singularly degenerate heteroclinic cycles is illustrated, and their collapses may create three-scroll/apple-shape attractors, or limit cycles, etc. Finally, conservative chaotic flows are numerically found in the new system. We expect that the outcome of the study may provide a reference for subsequent research.

A New Methodology to Assess Spatial Response Models for Satellite Imagers Using the Optical Design Parameters of a Generic Sensor as Independent Variables

Several types of analytic models are currently used to estimate the spatial response of satellite imagers, the accuracy of these models being critical for applications requiring precise knowledge about the spatial response of a given imager. The assessment of these models is complicated because the actual spatial response of an imager depends on its optical design, so evaluations based on a single kind of design are inherently biased. To reduce this bias, a new assessment methodology based on a generic imaging sensor is proposed; the key optical design’s parameters of this sensor are selected as independent variables, so the error of any spatial response model can be computed within a broad domain of possible optical designs. Assuming a generic sensor with annular optical aperture and square detector elements, the optical factor <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> and the aperture obstruction ratio ε are selected as key design parameters, allowing the error of spatial response models to be computed in the ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> , ε) plane. This approach is used to assess the separable Point Spread Function ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PSF</i> ) model, which assumes that the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PSF</i> is equal to the product of two perpendicular line spread functions, concluding that it is only valid when <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> ≤ 0.35 for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PSF</i> ≥ 0.1. This methodology can be used to assess other types of spatial response models for different shapes of optical apertures and detect or elements. We contend that our approach provides a standard assessment procedure that will help end users select the correct model for their specific application.

Evaluation of the Level of Dural Sac Tip in Saudi Population: A Magnetic Resonance Imaging Study.

Background For the success of procedures such as caudal block, craniospinal irradiation (CSI), and management of lower back pain and to minimize the risk of dural puncture the exact level of dural sac (DS) termination should be known. Objective The evaluation of DS tip location in the Saudi population and exploring possible significant factors that could be used as predictors in clinical prognosis. Methods A total of 200 patients' lumbar sagittal Weighted T2 Magnetic Resonance Imaging (MRI) study were randomly selected from a single-center hospital in-between 2020 and 2021. The DS tip location was determined by generating a perpendicular line from the longitudinal axis of its termination to the corresponding level. Then naming it after an intervertebral disk or a corresponding vertebrate that is divided into three thirds (upper, middle, and lower). Results In most cases, the level of DS termination is at the middle part of S2 (26.5%), followed by the upper part of S2 (25.1%), and the lower part of S2 (20%). In Saudi nationals, the DS tip was in the middle S2 level at 21.5%, upper S2 level at 19.1%, and lower S2 level at 17%. Factors such asage, sex, cause of referral, and nationality had no statistical significance in relation to DS tip location. Conclusion The DS termination level in the Saudi population ranges from disk between L5-S1 to the lower third of S3. Moreover, nationality, age, and cause of referral were not significant in determining the DS termination level. Therefore, it is still important to individualize patients' treatment by using MRI for each case that requires it.

A fast and accurate numerical approach for electromagnetic inversion

This paper deals with the solution of Maxwell's equations to model the electromagnetic fields in the case of a layered earth. The integrals involved in the solution are approximated by means of a novel approach based on the splitting of the reflection term. The inverse problem, consisting in the computation of the unknown underground conductivity distribution from a set of modeled magnetic field components, is also considered. Two optimization algorithms are applied, based on line- and global-search methods, and a new minimization approach is presented. Several EM surveys from the ground surface are simulated, considering the horizontal coplanar (HCP) and perpendicular (PRP) magnetic dipolar configurations. The numerical experiments, carried out for the study of river-levees integrity, allowed to estimate the errors associated to these kind of investigations, and confirm the reliability of the technique.

RESTORATION OF DISCONTINUOUS FUNCTIONS BY DISCONTINUOUS INTERLINATION SPLINES

Context. The problem of development and research of methods for approximation of discontinuous functions by discontinuous interlination splines and its further application to problems of computed tomography. The object of the study was the modeling of objects with a discontinuous internal structure.&#x0D; Objective. The aim of this study is to develop a general method for constructing discontinuous interlining polynomial splines, which, as a special case, include discontinuous and continuously differentiated splines.&#x0D; Method. Modern methods of restoring functions are characterized by new approaches to obtaining, processing and analyzing information. There is a need to build mathematical models in which information can be represented not only by function values at points, but also in the form of a set of function traces on planes or straight lines.&#x0D; At the same time, practice shows that among the multidimensional objects that need to be investigated, more problems are described by a discontinuous functions.&#x0D; The paper develops a general method for constructing discontinuous interlining polynomial splines, which, as a special case, include discontinuous and continuously differentiable splines. It is considered that the domain of the definition of the required twodimensional function is divided into rectangular elements. Theorems on interlination and approximation properties of such discontinuous constructions are formulated and proved. The method is developed for approximating discontinuous functions of two variables based on the constructed discontinuous splines. The input data are the traces of an unknown function along a given system of mutually perpendicular straight lines. The proposed method has not only theoretical significance but also practical application in the IT domain, especially in computing tomography, allowing more accurately restore the internal structure of the body.&#x0D; Results. The discontinuous interlination operator from known traces of the function of two variables on a system of mutually perpendicular straight lines is researched.&#x0D; Conclusions. The functions of two variables that are discontinuous at some points or on some lines are better approximated by discontinuous spline interlinants. At the same time, equally high approximation estimates can be obtained. The results obtained have significant advantages over existing methods of interpolation and approximation of discontinuous functions. In further research, the authors plan to develop a theory of discontinuous splines on areas of complex shape bounded by arcs of known curves.

Inventory of close-to-nature forest stands using terrestrial mobile laser scanning

• Hand-held mobile LiDAR data of a close-to-nature forest in the leaf-on season. • Fully automatic processing using modified mean-shift and RANSAC algorithms. • 96.5 % detection and 3.5 cm DBH RMSE for trees with DBHs from 4 to 80 cm. • A comparison of different levels of low-intensity filtering is performed. • A walking trajectory consisting of concentric circles is recommended. In this work, we evaluated mobile laser scanning (MLS) technology for the acquisition of individual tree data in a close-to-natural forest structure. The data was collected during the leaf-on period in a single-tree selection forest stand. Individual tree positions and diameters at breast height (DBHs) were acquired in an automatic process. MLS data was collected on 1000 m 2 circular inventory plots. We compared three trajectories consisting of the plot perimeter and 1), two perpendicular lines, 2) an additional concentric circle, and 3) four parallel lines. We compared two algorithms for tree segmentation: 1) a density-based approach and 2) a modified mean-shift algorithm. The diameters were estimated using a modified random sample consensus (RANSAC) algorithm. We tested a series of intensity thresholds for filtering returns from green vegetation. We achieved the best results with an intensity threshold of 0.7 quantile of point intensities, and mean-shift segmentation, resulting in the correct identification of trees representing 96.5 % of basal area and an overestimation of 6.8 % of the total basal area. The algorithm omitted mainly small trees and trees at close distances. False detections mainly comprised unvalidated detections of real trees that were not field-measured as their diameter did not exceed the registration limit, or were caused by point structures representing leaves and understory vegetation. Diameters were estimated with a mean error of 0.03 cm and a root mean square error of 3.5 cm. A joinpoint regression model demonstrated that for small trees (<9 cm) the diameters were generally overestimated. Diameters above 12 cm were underestimated consistently by 1 cm. The trajectory comprising two concentric circles was the most efficient.

Magnetic flux ruled surfaces

There is a unique curve called striction curve that is not present on a surface except a ruled surface. This curve is defined as the shortest distance with the help of a common perpendicular line between two adjacent rulings. In this work, we present Lorentz forces and magnetic striction curves produced by the geodesic Frenet frame on the striction curve of the ruled surface defined by the spherical indicatrix curve in a magnetic field. We calculate magnetic vector fields of magnetic striction curves for , and . Furthermore, we define magnetic flux surfaces constructed by magnetic vector fields along magnetic striction curves. We obtain developability conditions for these surfaces according to their curvature functions. Finally, we give some examples about magnetic flux surfaces.

Characteristics of Giant Nodular Melanomas in Special Locations: a Case Series and Review of the Literature.

Nodular melanoma (NM) is a rare subtype of melanoma, responsible for more than 40% of melanoma deaths, characterized by rapid growth and high metastatic potential. Only a few case studies concerning the dermoscopic presentations of giant nodular melanoma have been reported so far. The aim of the study was to assess dermoscopic features of giant nodular melanomas in special locations, along with their clinical and histopathologic aspects. Among 120 patients with histopathologically confirmed melanoma treated by the Skin Cancer and Melanoma Team between September 2020 and February 2021, we identified six patients with giant nodular melanoma in special locations. We retrospectively assessed the archived dermoscopic images to determine the dermoscopic features of these tumors. The group consisted of six cases of giant melanoma in special locations, including the scalp (4/6) and the heel (2/6). The giant tumors were large in size (at least 5cm in diameter). The most common dermoscopic structures in polarized light included asymmetric distribution of dermoscopic structures, the presence of structureless, multicolored zones (showing three or more colors), and the presence of white perpendicular lines or small, pink globules. It seems that there are no significant differences in dermoscopy between small and giant melanomas; however, further studies should be conducted on a larger scale.