Projective Plane Research Articles

Accurate measurement of end position of inclined pipe with optimal projection plane of space

Accurate measurement of end position of inclined pipe with optimal projection plane of space

Lower bound for mr (2,41) and related code

A (k, n) - arc is a set of k points of a projective plane such that some n, but no n+1 of them, are collinear. The maximum size of a (k, n) - arc in PG(2 q) is denoted by mr(2, q). In this paper we found mr(2,41) for n = (2,3 ,...,40) ,In this work, we construct a complete (k, n)-arcs in the projective space over Galois field GF(41), we construct the complete(k,n+1)-arcs from the complete (k, n)-arcs, where 2 ≤ n ≤ 42 , by using computer program we added some points of index zero, and found all the complete (k, n)-arcs in PG(2,41) and [k,n,d]_code.

On possible symmetry groups of 27-vertex triangulations of manifolds like the octonionic projective plane

On possible symmetry groups of 27-vertex triangulations of manifolds like the octonionic projective plane

Disjoint maximal arcs in projective planes of order 16

Disjoint maximal arcs in projective planes of order 16

GPU Accelerated 3D Tomographic Reconstruction and Visualization From Noisy Electron Microscopy Tilt-Series.

We present a novel framework for 3D tomographic reconstruction and visualization of tomograms from noisy electron microscopy tilt-series. Our technique takes as an input aligned tilt-series from cryogenic electron microscopy and creates denoised 3D tomograms using a proximal jointly-optimized approach that iteratively performs reconstruction and denoising, relieving the users of the need to select appropriate denoising algorithms in the pre-reconstruction or post-reconstruction steps. The whole process is accelerated by exploiting parallelism on modern GPUs, and the results can be visualized immediately after the reconstruction using volume rendering tools incorporated in the framework. We show that our technique can be used with multiple combinations of reconstruction algorithms and regularizers, thanks to the flexibility provided by proximal algorithms. Additionally, the reconstruction framework is open-source and can be easily extended with additional reconstruction and denoising methods. Furthermore, our approach enables visualization of reconstruction error throughout the iterative process within the reconstructed tomogram and on projection planes of the input tilt-series. We evaluate our approach in comparison with state-of-the-art approaches and additionally show how our error visualization can be used for reconstruction evaluation.

634 vertex-transitive and more than $10^{103}$ non-vertex-transitive 27-vertex triangulations of manifolds like the octonionic projective plane

634 vertex-transitive and more than $10^{103}$ non-vertex-transitive 27-vertex triangulations of manifolds like the octonionic projective plane

A note on the Bricard property of projective planes

A note on the Bricard property of projective planes

On possible symmetry groups of 27-vertex triangulations of manifolds like the octonionic projective plane

On possible symmetry groups of 27-vertex triangulations of manifolds like the octonionic projective plane

Impact of the spatial orientation of the patient's head, metal artifact reduction, and tube current on cone-beam computed tomography artifact expression adjacent to a dental implant: A laboratory study using a simulated surgical guide.

The aim of this study was to evaluate image artifacts in the vicinity of dental implants in cone-beam computed tomography (CBCT) scans obtained with different spatial orientations, tube current levels, and metal artifact reduction algorithm (MAR) conditions. One dental implant and 2 tubes filled with a radiopaque solution were placed in the posterior region of a mandible using a surgical guide to ensure parallel alignment. CBCT scans were acquired with the mandible in 2 spatial orientations in relation to the X-ray projection plane (standard and modified) at 3 tube current levels: 5, 8, and 11 mA. CBCT scans were repeated without the implant and were reconstructed with and without MAR. The mean voxel and noise values of each tube were obtained and compared using multi-way analysis of variance and the Tukey test (α=0.05). Mean voxel values were significantly higher and noise values were significantly lower in the modified orientation than in the standard orientation (P<0.05). MAR activation and tube current levels did not show significant differences in most cases of the modified spatial orientation and in the absence of the dental implant (P>0.05). Modifying the spatial orientation of the head increased brightness and reduced spatial orientation noise in adjacent regions of a dental implant, with no influence from the tube current level and MAR.

Finding the complete List of Different K-Brackets for the Projective Plane PG (2, 8)

A k-arc in a plane PG (2, q) is a set of k point such that every line in the plane intersect it in at most two points and there is a line intersect it in exactly two points. A k-arc is complete if there is no k+1-arc containing it. This thesis is concerned with studies a k-arcs, k=4, 5,…., 10 and classification of protectively distinct k-arcs and distinct arcs under collineation. We prove by using computer program that the only complete k-arcs is for, k= 6, 10.

On maximizing line arrangements in the complex plane

Abstract In this note we provide a complete classification of weak combinatorics of the so-called maximizing line arrangements in the complex projective plane.

ЕОМЕТРІЯ ТА ТОПОЛОГІЯ ПРОЄКТИВНОЇ ПЛОЩИНИ

The topological structure and geometric properties of the projective plane are described, as well as its group of movements that generate projective transformations of the Euclidean plane.

Exploring the use of bimodal transcranial direct current stimulation to enhance movement in individuals with patellofemoral pain-A sham-controlled double blinded pilot study.

In individuals with patellofemoral pain (PFP), addressing increased knee valgus during weight-bearing activities typically involves strengthening weak hip muscles. However, recent literature highlights the role of altered descending central control in abnormal movements associated with PFP. While transcranial direct current stimulation (tDCS) has demonstrated the capacity to enhance neuroplasticity, its application targeting the corticomotor function of gluteal muscles in PFP remains unexplored. This study aimed to investigate the effects of combining bimodal tDCS with exercise on frontal plane kinematics in individuals with PFP. The hypothesis was that bimodal tDCS, specifically targeting the corticomotor function of the gluteal muscles, would augment the effectiveness of exercise interventions in improving frontal plane kinematics compared to sham stimulation. Ten participants with PFP participated in two sessions involving either bimodal tDCS or sham stimulation, concurrently with hip strengthening exercises. Weight-bearing tasks, including single leg squat, single leg landing, single leg hopping, forward step-down, and lateral step-down, were performed and recorded before and after each session. Pain visual analog scale (VAS) scores were also documented. A one-way ANOVA with repeated measures was employed to compare kinematics, while a Friedman test was used to compare VAS across the three conditions (pre-test, post-tDCS, and post-Sham). We observed no significant differences in trunk lean angle, hip and knee frontal plane projection angles, or dynamic valgus index among the three conditions during the five weight-bearing tasks. VAS scores did not differ across the three conditions. A single session of tDCS did not demonstrate immediate efficacy in enhancing frontal plane kinematics or relieving pain in individuals with PFP. Considering observed positive outcomes in other neurological and orthopedic populations with multi-session tDCS applications, suggesting potential cumulative effects, further research is essential to explore the effects of multi-session tDCS on weight-bearing movement and underlying neurophysiology in individuals with PFP.

Relationship Between Knee Frontal Plane Projection Angle and Lower Limb Muscle Activity in Female Athletes.

Anterior cruciate ligament injuries are directly related to the control of dynamic knee valgus in the landing of a jump, and this is mainly due to the correct activation and neuromuscular function of the lower-extremity muscles. The aim of the study is to assess the relationship between lower limb muscle activity during a single-legged drop jump and knee frontal plane projection angle (FPPA). A correlation study. Thirty healthy collegiate female athletes were included in the study. Main outcomes measures were peak knee FPPA and muscle activity (% of maximal voluntary isometric contraction). Peak knee FPPA during a single-legged drop jump test was identified using a 2-dimensional motion analysis system. Muscle activity was assessed using a surface electromyograph for gluteus maximus, gluteus medius, biceps femoris, semitendinosus, vastus medialis quadriceps, vastus lateralis quadriceps, medial gastrocnemius, and lateral gastrocnemius. All variables were assessed for both dominant and nondominant limbs. A correlation analysis between peak knee FPPA and muscle activity was performed. Statistical significance was set at P <.05. A mean peak knee FPPA of 14.52° and 13.38° was identified for dominant and nondominant limb single-legged drop jump test, respectively. Muscle activity (% of maximal voluntary isometric contraction) for muscles assessed ranged from 43.97% to 195.71% during the single-legged drop jump test. The correlation analysis found no significant correlation between any of the muscles assessed and peak knee FPPA during the single-legged drop jump test (Pearson coefficient between -.3 and .1). There is no association between muscle activity from the lower limb muscles and the knee FPPA during a single-legged drop jump in female athletes. Thus, different muscle properties should be assessed in order to understand such an important movement as the knee FPPA during a jump.

Prediction of toluene/water partition coefficients of SAMPL9 compounds: comparison of the molecular dynamics force fields GAFF/RESP and GAFF/IPolQ-Mod + LJ-fit.

The SAMPL9 blind challenge aims to predict the toluene/water partition coefficient of 16 active pharmaceutical ingredients. In this work, the transfer free energy between the solvation in water and toluene is predicted by molecular dynamics simulations using the MBAR method [M. R. Shirts and J. D. Chodera, J. Chem. Phys., 2008, 129, 123105] with replica exchange molecular dynamics [Y. Sugita, A. Kitao and Y. Okamoto, J. Chem. Phys., 2000, 113, 6042-6051]. Thereby, simulation results using the force field GAFF/IPolQ-Mod + LJ-fit [A. Mecklenfeld and G. Raabe, ADMET and DMPK, 2020, 8, 274-296] are compared to simulations with the standard GAFF/RESP model [J. Wang, R. M. Wolf, J. W. Caldwell, P. A. Kollman and D. A. Case, J. Comput. Chem., 2004, 25, 1157-1174]. By statistical evaluation of RMSD and R2, we compare the results with other participants of the blind challenge. Furthermore, we provide a detailed analysis of solvation structures using the combined distribution function for simulations in water and the plane projection analysis for simulations in toluene, and we work out differences and similarities of the two force fields. These studies allow to gain important insights to increase the understanding of the mechanism of interactions between the drugs and the solvent.

Sex differences in factors of pelvis and lower-limb joint kinematics influencing dynamic knee valgus during single-leg squat.

Dynamic knee valgus (DKV) during dynamic activity is associated with patellofemoral pain, one of the most common sports disorders, especially in females. No studies have examined the factors that can lead to DKV in females as compared to males while addressing the influence of factors on each other. To identify factors of pelvis and lower joints kinematics affecting DKV during single-leg squat (SLS) in females compared to males with multiple regression analysis. Forty-four healthy young people (24 females, 20 males) performed SLS, and pelvis, hip, knee, and ankle 3D kinematics were recorded. The 2D knee frontal plane projection angle (FPPA) was adopted as the DKV measurement. Multiple regression analysis was performed to determine the relationship between FPPA and the kinematics of each joint and segment. Hip adduction and pelvic contralateral rotation were explanatory factors for FPPA in females. Hip adduction, hip internal rotation, and knee external rotation were explanatory factors in males. The lower limb or pelvic motion factors affecting DKV during SLS differ between the sexes, with pelvic contralateral rotation being extracted only in women, possibly due to differences in pelvic width.

Subfield subcodes of projective Reed-Muller codes

Explicit bases for the subfield subcodes of projective Reed-Muller codes over the projective plane and their duals are obtained. In particular, we provide a formula for the dimension of these codes. For the general case over the projective space, we generalize the necessary tools to deal with this case as well: we obtain a universal Gröbner basis for the vanishing ideal of the set of standard representatives of the projective space and we show how to reduce any monomial with respect to this Gröbner basis. With respect to the parameters of these codes, by considering subfield subcodes of projective Reed-Muller codes we obtain long linear codes with good parameters over a small finite field.

Stereographic Projection of Theoretical Orientation Relationships Between Crystals of Any Types in Phase Transformation and Precipitation

AbstractStereographic projection is a classic technology to represent the angular relationships of lattice planes and directions. In some cases, it is necessary to project arbitrary lattice planes or directions of a crystal onto an arbitrary lattice plane of another crystal, e.g., when representing orientation relationships (ORs) in phase transformation or precipitation. Commercial EBSD (electron backscatter diffraction) software cannot illustrate theoretical orientation relationships based purely on the parallelism conditions. This work presents a generalized and unified formulation for stereographic projection of any lattice planes or directions onto any lattice planes of any crystals in the 32 point groups, which is utilized to represent the theoretical orientation relationships between any crystal types. Examples are given to illustrate the correlations of common orientation relationships in both cubic and hexagonal crystals. A procedure is also established to color code and simultaneously project all low‐index Miller/Bravais planes or directions of a crystal onto an arbitrary lattice plane of the same crystal, which can be utilized to visualize the crystal symmetry and determine the standard stereographic triangle (SST). All these illustrations are realized in a computer program written in C++ using the OpenGL graphic libraries.

A phantom on a rational surface

We construct a non-full exceptional collection of maximal length consisting of line bundles on the blow-up of the projective plane in 10 general points. As a consequence, the orthogonal complement of this collection is a universal phantom category. This provides a counterexample to a conjecture of Kuznetsov and to a conjecture of Orlov.

MORSE AND CODIMENSION 1 FUNCTIONS ON THE PROJECTIVE PLANE

The topological properties of functions on two-dimensional spaces are described using an invariant called the Reeb graph. In the case of Morse functions on closed oriented two-dimensional manifolds, this serves as a complete topological invariant for homotopy equivalence. For non-oriented two-dimensional manifolds and manifolds with boundaries, additional information is required to construct a complete topological invariant. If a linear order is imposed on the set of vertices, it becomes a complete topological invariant with respect to topological equivalence. The research explores the topological classification of Morse functions and functions of corank 1 on the projective plane. In these cases, the Reeb graph is an oriented rooted tree. An analytical expression is derived for the number of oriented Reeb graphs with a root. For functions of corank 1 and a fixed number of critical points, all possible Reeb graphs are constructed.