Search results for: corneal curvature

Authors: M. Abdelmalek

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In this work, we study the hypersurfaces of constant weighted mean curvature embedded in weighted manifolds. We give a condition about these hypersurfaces to be minimal. This condition is given by the ellipticity of the weighted Newton transformations. We especially prove that two compact hypersurfaces of constant weighted mean curvature embedded in space forms and with the intersection in at least a point of the boundary must be transverse. The method is based on the calculus of the matrix of the second fundamental form in a boundary point and then the matrix associated with the Newton transformations. By equality, we find the weighted elementary symmetric function on the boundary of the hypersurface. We give in the end some examples and applications. Especially in Euclidean space, we use the above result to prove the Alexandrov spherical caps conjecture for the weighted case.

Keywords: weighted mean curvature, weighted manifolds, ellipticity, Newton transformations

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Authors: Aiman Alshare, Sahar Qaadan

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A curvature dependent force correction algorithm for planning force controlled grinding process with off-line programming flexibility is designed for ABB industrial robot, in order to avoid the manual interface during the process. The machining path utilizes a spline curve fit that is constructed from the CAD data of the workpiece. The fitted spline has a continuity of the second order to assure path smoothness. The implemented algorithm computes uniform forces normal to the grinding surface of the workpiece, by constructing a curvature path in the spatial coordinates using the spline method.

Keywords: ABB industrial robot, grinding process, offline programming, CAD data extraction, force correction algorithm

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Authors: Rindra Rantoson, Hichem Nouira, Nabil Anwer, Charyar Mehdi-Souzani

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Multiple measurements by means of various data acquisition systems are generally required to measure the shape of freeform workpieces for accuracy, reliability and holisticity. The obtained data are aligned and fused into a common coordinate system within a registration technique involving coarse and fine registrations. Standardized iterative methods have been established for fine registration such as Iterative Closest Points (ICP) and its variants. For coarse registration, no conventional method has been adopted yet despite a significant number of techniques which have been developed in the literature to supply an automatic rough matching between data sets. Two main issues are addressed in this paper: the coarse registration and the fine registration. For coarse registration, two novel automated methods based on the exploitation of discrete curvatures are presented: an enhanced Hough Transformation (HT) and an improved Ransac Transformation. The use of curvature features in both methods aims to reduce computational cost. For fine registration, a new variant of ICP method is proposed in order to reduce registration error using curvature parameters. A specific distance considering the curvature similarity has been combined with Euclidean distance to define the distance criterion used for correspondences searching. Additionally, the objective function has been improved by combining the point-to-point (P-P) minimization and the point-to-plane (P-Pl) minimization with automatic weights. These ones are determined from the preliminary calculated curvature features at each point of the workpiece surface. The algorithms are applied on simulated and real data performed by a computer tomography (CT) system. The obtained results reveal the benefit of the proposed novel curvature-based registration methods.

Keywords: discrete curvature, RANSAC transformation, hough transformation, coarse registration, ICP variant, point-to-point and point-to-plane minimization combination, computer tomography

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Authors: Rajender Singh, Nidhi Sharma, Aastha Chauhan, Meenakshi Barsaul, Jyoti Deswal, Chetan Chhikara

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Introduction: Pre-eclampsia and eclampsia are hypertensive disorders of pregnancy with multisystem involvement and are common causes of morbidity and mortality in obstetrics. It is believed that changes in retinal arterioles may indicate similar changes in the placenta. Therefore, this study was undertaken to evaluate the ocular manifestations in cases of pre-eclampsia and eclampsia and to deduce any association between the retinal changes and blood pressure, the severity of disease, gravidity, proteinuria, and other lab parameters so that a better approach could be devised to ensure maternal and fetal well-being. Materials and Methods: This was a hospital-based cross-sectional study conducted over a period of one year, from April 2021 to May 2022. 350 admitted patients with diagnosed pre-eclampsia, eclampsia, and pre-eclampsia superimposed on chronic hypertension were included in the study. A pre-structured proforma was used. After taking consent and ocular history, a bedside examination to record visual acuity, pupillary size, corneal curvature, field of vision, and intraocular pressure was done. Dilated fundus examination was done with a direct and indirect ophthalmoscope. Age, parity, BP, proteinuria, platelet count, liver and kidney function tests were noted down. The patients with positive findings only were followed up after 72 hours and 6 weeks of termination of pregnancy. Results: The mean age of patients was 26.18±4.33 years (range 18-39 years).157 (44.9%) were primigravida while 193(55.1%) were multigravida.53 (15.1%) patients had eclampsia, 128(36.5%) had mild pre-eclampsia,128(36.5%) had severe pre-eclampsia and 41(11.7%) had chronic hypertension with superimposed pre-eclampsia. Retinal changes were found in 208 patients (59.42%), and grade I changes were the most common. 82(23.14%) patients had grade I changes, 75 (21.4%) had grade II changes, 41(11.71%) had grade III changes, and 11(3.14%) had serous retinal detachment/grade IV changes. 36 patients had unaided visual acuity <6/9, of these 17 had refractive error and 19(5.4%) had varying degrees of retinal changes. 3(0.85%) out of 350 patients had an abnormal field of vision in both eyes. All 3 of them had eclampsia and bilateral exudative retinal detachment. At day 4, retinopathy in 10 patients resolved, and 3 patients had improvement in visual acuity. At 6 weeks, retinopathy in all the patients resolved spontaneously except persistence of grade II changes in 23 patients with chronic hypertension with superimposed pre-eclampsia, while visual acuity and field of vision returned to normal in all patients. Pupillary size, intraocular pressure, and corneal curvature were found to be within normal limits at all times of examination. There was a statistically significant positive association between retinal changes and mean arterial pressure. The study showed a positive correlation between fundus findings and severity of disease (p value<0.05) and mean arterial pressure (p value<0.005). Primigravida had more retinal changes than multigravida patients. A significant association was found between fundus changes and thrombocytopenia and deranged liver and kidney function tests (p value<0.005). Conclusion: As the severity of pre-eclampsia and eclampsia increases, the incidence of retinopathy also increases, and it affects visual acuity and visual fields of the patients. Thus, timely ocular examination should be done in all such cases to prevent complications.

Keywords: eclampsia, hypertensive, ocular, pre-eclampsia

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Authors: Jay Prakash Singh

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The aim of the present paper is to study properties of Quasi conformally flat LP-Sasakian manifolds with a coefficient α. In this paper, we prove that a Quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α is an η−Einstein and in a quasi conformally flat LP-Sasakian manifold M (n > 3) with a constant coefficient α if the scalar curvature tensor is constant then M is of constant curvature.

Keywords: LP-Sasakian manifolds, quasi-conformal curvature tensor, concircular vector field, torse forming vector field, Einstein manifold

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Authors: Daniel Aberdam

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Haploinsufficiency of PAX6 in humans is the main cause of congenital aniridia, a rare eye disease characterized by reduced visual acuity. Patients have also progressive disorders including cataract, glaucoma and corneal abnormalities making their condition very challenging to manage. Aniridia-related keratopathy (ARK), caused by a combination of factors including limbal stem-cell deficiency, impaired healing response, abnormal differentiation, and infiltration of conjunctival cells onto the corneal surface, affects up to 95% of patients. It usually begins in the first decade of life resulting in recurrent corneal erosions, sub-epithelial fibrosis with corneal decompensation and opacification. Unfortunately, current treatment options for aniridia patients are currently limited. Although animal models partially recapitulate this disease, there is no in vitro cellular model of AKT needed for drug/therapeutic tools screening and validation. We used genome editing (CRISPR/Cas9 technology) to introduce a nonsense mutation found in patients into one allele of the PAX6 gene into limbal stem cells. Resulting mutated clones, expressing half of the amount of PAX6 protein and thus representative of haploinsufficiency were further characterized. Sequencing analysis showed that no off-target mutations were induced. The mutated cells displayed reduced cell proliferation and cell migration but enhanced cell adhesion. Known PAX6 targets expression was also reduced. Remarkably, addition of soluble recombinant PAX6 protein into the culture medium was sufficient to activate endogenous PAX6 gene and, as a consequence, rescue the phenotype. It strongly suggests that our in vitro model recapitulates well the epithelial defect and becomes a powerful tool to identify drugs that could rescue the corneal defect in patients. Furthermore, we demonstrate that the homeotic transcription factor Pax6 is able to be uptake naturally by recipient cells to function into the nucleus.

Keywords: Pax6, crispr/cas9, limbal stem cells, aniridia, gene therapy

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Authors: Peter W. Woodruff, Georgios Ponirakis, Reem Ibrahim, Amani Ahmed, Hoda Gad, Ioannis N. Petropoulos, Adnan Khan, Ahmed Elsotouhy, Surjith Vattoth, Mahmoud K. M. Alshawwaf, Mohamed Adil Shah Khoodoruth, Marwan Ramadan, Anjushri Bhagat, James Currie, Ziyad Mahfoud, Hanadi Al Hamad, Ahmed Own, Peter Haddad, Majid Alabdulla, Rayaz A. Malik

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Introduction:- We aimed to test the hypothesis that, using corneal confocal microscopy (a non-invasive method for assessing corneal nerve fibre integrity), patients with schizophrenia would show neuronal abnormalities compared with healthy participants. Schizophrenia is a neurodevelopmental and progressive neurodegenerative disease, for which there are no validated biomarkers. Corneal confocal microscopy (CCM) is a non-invasive ophthalmic imaging biomarker that can be used to detect neuronal abnormalities in neuropsychiatric syndromes. Methods:- Patients with schizophrenia (DSM-V criteria) without other causes of peripheral neuropathy and healthy controls underwent CCM, vibration perception threshold (VPT) and sudomotor function testing. The diagnostic accuracy of CCM in distinguishing patients from controls was assessed using the area under the curve (AUC) of the Receiver Operating Characterstics (ROC) curve. Findings:- Participants with schizophrenia (n=17) and controls (n=38) with comparable age (35.7±8.5 vs 35.6±12.2, P=0.96) were recruited. Patients with schizophrenia had significantly higher body weight (93.9±25.5 vs 77.1±10.1, P=0.02), lower Low Density Lipoproteins (2.6±1.0 vs 3.4±0.7, P=0.02), but comparable systolic and diastolic blood pressure, HbA1c, total cholesterol, triglycerides and High Density Lipoproteins were comparable with control participants. Patients with schizophrenia had significantly lower corneal nerve fiber density (CNFD, fibers/mm2) (23.5±7.8 vs 35.6±6.5, p<0.0001), branch density (CNBD, branches/mm2) (34.4±26.9 vs 98.1±30.6, p<0.0001), and fiber length (CNFL, mm/mm2) (14.3±4.7 vs 24.2±3.9, p<0.0001) but no difference in VPT (6.1±3.1 vs 4.5±2.8, p=0.12) and electrochemical skin conductance (61.0±24.0 vs 68.9±12.3, p=0.23) compared with controls. The diagnostic accuracy of CNFD, CNBD and CNFL to distinguish patients with schizophrenia from healthy controls were, according to the AUC, (95% CI): 87.0% (76.8-98.2), 93.2% (84.2-102.3), 93.2% (84.4-102.1), respectively. Conclusion:- In conclusion, CCM can be used to help identify neuronal changes and has a high diagnostic accuracy to distinguish subjects with schizophrenia from healthy controls.

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Authors: Jacek Turski

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The visual space geometries are constructed in the Riemannian geometry framework from simulated iso-disparity conics in the horizontalvisual plane of the binocular system with the asymmetric eyes (AEs). For the eyes fixating at the abathic distance, which depends on the AE’s parameters, the iso-disparity conics are frontal straight lines in physical space. For allother fixations, the iso-disparity conics consist of families of the ellipses or hyperbolas depending on both the AE’s parameters and the bifoveal fixation. However, the iso-disparity conic’s arcs are perceived in the gaze direction asthe frontal lines and are referred to as visual geodesics. Thus, geometriesof physical and visual spaces are different. A simple postulate that combines simulated iso-disparity conics with basic anatomy od the human visual system gives the relative depth for the fixation at the abathic distance that establishes the Riemann matric tensor. The resulting geodesics are incomplete in the gaze direction and, therefore, give thefinite distances to the horizon that depend on the AE’s parameters. Moreover, the curvature vanishes in this eyes posture such that visual space is flat. For all other fixations, only the sign of the curvature canbe inferred from the global behavior of the simulated iso-disparity conics: the curvature is positive for the elliptic iso-disparity curves and negative for the hyperbolic iso-disparity curves.

Keywords: asymmetric eye model, iso-disparity conics, metric tensor, geodesics, curvature

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Authors: S. Jagadeesh Kumar

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Face detection and recognition is an authoritative technology for image database management, video surveillance, and human computer interface (HCI). Face recognition is a rapidly nascent method, which has been extensively discarded in forensics such as felonious identification, tenable entree, and custodial security. This paper recommends an erudite technique using curvature analysis (CA) that has less false positives incidence, operative in different light environments and confiscates the artifacts that are introduced during image acquisition by ring correction in polar coordinate (RCP) method. This technique affronts mean and median filtering technique to remove the artifacts but it works in polar coordinate during image acquisition. Investigational fallouts for face detection and recognition confirms decent recitation even in diagonal orientation and stance variation.

Keywords: curvature analysis, ring correction in polar coordinate method, face detection, face recognition, human computer interaction

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Authors: Ujjval J. Solanki, Prof.(Dr.) P.J. Gundaliya, Prof.M.D. Barasara

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The application of Falling Weight Deflectometer is to evaluate structural performance of the flexible pavement. The exercise of back calculation is required to know the modulus of elasticity of existing in-service pavement. The process of back calculation needs in-depth field experience for the input of range of modulus of elasticity of bituminous, granular and subgrade layer, and its required number of trial to find such matching moduli with the observed FWD deflection on the field. The study carried out at Barnala-Mansa State Highway Punjab-India using FWD before and after overlay; the deflections obtained at 0 on the load cell, 300, 600, 900,1200, 1500 and 1800 mm interval from the load cell these seven deflection results used to calculate Surface Curvature Index (SCI), Base damage Index (BDI), Base curvature index (BCI). This SCI, BCI and BDI indices are useful to predict the structural performance of in-service pavement and also useful to identify homogeneous section for condition assessment. The SCI, BCI and BDI range are determined for before and after overlay the range of SCI 520 to 51 BDI 294 to 63 BCI 83 to 0.27 for old pavement and SCI 272 to 23 BDI 228 to 28, BCI 25.85 to 4.60 for new pavement. It also shows good correlation with back calculated modulus of elasticity of all the three layer.

Keywords: back calculation, base damage index, base curvature index, FWD (Falling Weight Deflectometer), surface curvature index

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Authors: Aberdam Edith, Sangari Linda, Petit Isabelle, Aberdam Daniel

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Background and Rationale: Transparent avascularised cornea is essential for normal vision and depends on limbal stem cells (LSC) that reside between the cornea and the conjunctiva. Ocular burns or injuries may destroy the limbus, causing limbal stem cell deficiency (LSCD). The cornea becomes vascularised by invaded conjunctival cells, the stroma is scarring, resulting in corneal opacity and loss of vision. Grafted autologous limbus or cultivated autologous LCS can restore the vision, unless the two eyes are affected. Alternative cellular sources have been tested in the last decades, including oral mucosa or hair follicle epithelial cells. However, only partial success has been achieved by the use of these cells since they were not able to uniformly commit into corneal epithelial cells. Human pluripotent stem cells (iPSC) display both unlimited growth capacity and ability to differentiate into any cell type. Our goal was to design a standardized and reproducible protocol to produce transplantable autologous LSC from patients through cell reprogramming technology. Methodology: First, keratinocyte primary culture was established from a small number of plucked hair follicles of healthy donors. The resulting epithelial cells were reprogrammed into induced pluripotent stem cells (iPSCs) and further differentiate into corneal epithelial cells (CEC), according to a robust protocol that recapitulates the main step of corneal embryonic development. qRT-PCR analysis and immunofluorescent staining during the course of differentiation confirm the expression of stage specific markers of corneal embryonic lineage. First appear ectodermal progenitor-specific cytokeratins K8/K18, followed at day 7 by limbal-specific PAX6, TP63 and cytokeratins K5/K14. At day 15, K3/K12+-corneal cells are present. To amplify the iPSC-derived LSC (named COiPSC), intact small epithelial colonies were detached and cultivated in limbal cell-specific medium. In that culture conditions, the COiPSC can be frozen and thaw at any passage, while retaining their corneal characteristics for at least eight passages. To evaluate the potential of COiPSC as an alternative ocular toxicity model, COiPSC were treated at passage P0 to P4 with increasing amounts of SDS and Benzalkonium. Cell proliferation and apoptosis of treated cells was compared to LSC and the SV40-immortalized human corneal epithelial cell line (HCE) routinely used by cosmetological industrials. Of note, HCE are more resistant to toxicity than LSC. At P0, COiPSC were systematically more resistant to chemical toxicity than LSC and even to HCE. Remarkably, this behavior changed with passage since COiPSC at P2 became identical to LSC and thus closer to physiology than HCE. Comparative transcriptome analysis confirmed that COiPSC from P2 are similar to a mixture of LSC and CEC. Finally, by organotypic reconstitution assay, we demonstrated the ability of COiPSC to produce a 3D corneal epithelium on a stromal equivalent made of keratocytes. Conclusion: COiPSC could become valuable for two main applications: (1) an alternative robust tool to perform, in a reproducible and physiological manner, toxicity assays for cosmetic products and pharmacological tests of drugs. (2). COiPSC could become an alternative autologous source for cornea transplantation for LSCD.

Keywords: Limbal stem cell deficiency, iPSC, cornea, limbal stem cells

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Authors: C. T. Cheung, R. K. P. Ng, T. Y. Lo, Zhou Jinyun

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This paper aims at manipulating loop alignment in knitting a three-dimensional (3D) shape by its geometry. Two loop alignment methods are introduced to handle a surface with positive Gaussian curvature. As weft knitting is a two-dimensional (2D) knitting mechanism that the knitting cam carrying the feeders moves in two directions only, left and right, the knitted fabric generated grows in width and length but not in depth. Therefore, a 3D shape is required to be flattened to a 2D plane with surface area preserved for knitting. On this flattened plane, dimensional measurements are taken for loop alignment. The way these measurements being taken derived two different loop alignment methods. In this paper, only plain knitted structure was considered. Each knitted loop was taken as a basic unit for loop alignment in order to achieve the required geometric dimensions, without the inclusion of other stitches which give textural dimensions to the fabric. Two loop alignment methods were experimented and compared. Only one of these two can successfully preserve the dimensions of the shape.

Keywords: 3D knitting, 3D shape, loop alignment, positive Gaussian curvature

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Authors: Suba Periyal Subramaniam, Babette Scheres, Altomare Corrado, Holger Schuttrumpf

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Due to the climatic change and the usage of coastal areas, there is an increasing risk of dike failures along the coast worldwide. Wave run-up plays a key role in planning and design of a coastal structure. The coastal dike lines are bent either due to geological characteristics or due to influence of anthropogenic activities. The effect of the curvature of coastal dikes on wave run-up and overtopping is not yet investigated. The scope of this research is to find the effects of the dike curvature on wave run-up by employing numerical model studies for various dike opening angles. Numerical simulation is carried out using DualSPHysics, a meshless method, and OpenFOAM, a mesh-based method. The numerical results of the wave run-up on a curved dike and the wave transformation process for various opening angles, wave attacks, and wave parameters will be compared and discussed. This research aims to contribute a more precise analysis and understanding the influence of the curvature in the dike line and thus ensuring a higher level of protection in the future development of coastal structures.

Keywords: curved dikes, DualSPHysics, OpenFOAM, wave run-up

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Authors: Hao Wang, Shengchun Wang, Weidong Wang

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On the influence of train vibration and environmental noise on the measurement of track wear, we proposed a method for automatic extraction of circular arc on the inner or outer side of the rail waist and achieved the high-precision registration of rail profile. Firstly, a polynomial fitting method based on truncated residual histogram was proposed to find the optimal fitting curve of the profile and reduce the influence of noise on profile curve fitting. Then, based on the curvature distribution characteristics of the fitting curve, the interval search algorithm based on dynamic window’s maximum curvature entropy was proposed to realize the automatic segmentation of small circular arc. At last, we fit two circle centers as matching reference points based on small circular arcs on both sides and realized the alignment from the measured profile to the standard designed profile. The static experimental results show that the mean and standard deviation of the method are controlled within 0.01mm with small measurement errors and high repeatability. The dynamic test also verified the repeatability of the method in the train-running environment, and the dynamic measurement deviation of rail wear is within 0.2mm with high repeatability.

Keywords: curvature entropy, profile registration, rail wear, structured light, train-running

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Authors: Dnyanesh P. Mathur, Gregory L. Slater

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Gravitation and the expansion of the universe at a large scale are generally regarded as two completely distinct phenomena. Yet, in general, relativity theory, they both manifest as 'curvature' of spacetime. We propose a hypothesis which treats these two 'curvature-producing' phenomena as aspects of an underlying process. This process treats spacetime itself as composed of discrete units (Plancktons) and is 'dynamic' in the sense that these elements of spacetime are continually being both created and annihilated. It is these two complementary processes of Planckton creation and Planckton annihilation which manifest themselves as - 'cosmic expansion' on the one hand and as 'gravitational attraction’ on the other. The Planckton hypothesis treats spacetime as a perfect fluid in the same manner as the co-moving frame of reference of Friedman equations and the Gullstrand-Painleve metric; i.e.Planckton hypothesis replaces 'curvature' of spacetime by the 'flow' of Plancktons (spacetime). Here we discuss how this perspective may allow a unified description of both cosmological and gravitational acceleration as well as providing a mechanism for inducing an irreducible action at every point associated with the creation and annihilation of Plancktons, which could be identified as the zero point energy.

Keywords: discrete spacetime, spacetime flow, zero point energy, planktons

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Authors: Bae Doobyong, Yoo Jaejun, Park Ilgyu, Choi Seowon, Oh Chang Kook

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Variation of slip coefficient in slip-critical connections of curved plates. This paper presents the results of analytical investigations of slip coefficients in slip-critical bolted connections of curved plates. It may depend on the contact stress distribution at interface and the flexibility of spliced plate. Non-linear FEM analyses have been made to simulate the behavior of bolted connections of curved plates with various radiuses of curvature and thicknesses.

Keywords: slip coefficient, curved plates, slip-critical bolted connection, radius of curvature

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Authors: Mohammed M. Mahdy Tawfeek

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Objective: The aim of this work is to compare the outcome of photoactivated chromophore for keratitis-cross linking (PACK-CXL) window absorption (WA) alone with combined PACK-CXL WA and standard anti-microbial therapy (SAT) for the treatment of infectious keratitis. Patients and Methods: This is a randomized prospective comparative clinical trial. Thirty eyes with clinically suspected infectious keratitis were randomly assigned into two equal groups of 15 eyes each: Group (A) was treated by PACK-CXL WA alone and group (B) was treated by PACK-CXL WA combined with SAT. Identification of organisms was made by lab study before treatment. Corneal healing was evaluated by corneal examination and anterior segment OCT (AS-OCT). Written informed consent was obtained from all participants and the study was approved by the research ethics committee of the Faculty of Medicine, Zagazig University. The work has been carried out in accordance with The Code of Ethics of the World Medical Association (Declaration of Helsinki) for studies involving humans. Results: Complete healing and resolution (Successful treatment) were observed in 10 eyes (66.7%) of a group (A) and 14 eyes (93.3%) of group (B) and failure was observed in 5 eyes (33.3%) of a group (A) and one eye (6.67%) of group (B). They were statistically significant (P =0.042 and 0.003) in a comparison between both groups regarding success and failure of treatment, respectively. Complete corneal healing was reported in the third month postoperatively in 10 eyes (66.7%) of group (A) and 14 eyes (93.3%) of group (B). Complications were absent in 12 patients (80%) in group (A) and 14 patients (93.3%) of group (B); however, perforation and impending perforation were found in 3 patients of group (A) and only one patient of group (B). Conclusion: PACK-CXL is a promising, non-invasive treatment option for infectious keratitis, especially when performed with the window absorption (WA) technique, either alone or combined with SAT. It has a synergistic effect with a standard antimicrobial treatment that gives good outcome results in the treatment of infectious keratitis. Also, it avoids the antibiotics resistance that has become rapidly spreading worldwide.

Keywords: corneal cross linking, infectious keratitis, PACK-CXL, window absorption

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Authors: V. Polenta, S. D. Garvey, D. Chronopoulos, A. C. Long, H. P. Morvan

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A parametric study on circular thin-walled pipes subjected to pure bending is performed. Both straight and curved pipes are considered. Ratio D/t, initial pipe curvature and internal pressure are the parameters varying in the analyses. The study is mainly FEA-based. It is found that negative curvatures (opposite to bending moment) considerably increase stiffness and buckling limit of the pipe when no internal pressure is acting and, similarly, positive curvatures decrease the stiffness and buckling limit. For internal pressurised pipes the effects of initial pipe curvature are less relevant. Results show that this phenomenon is in relationship with the cross-section deformation due to bending moment, which undergoes relevant ovalisation for no pressurised pipes and little ovalisation for pressurised pipes.

Keywords: buckling, curved pipes, internal pressure, ovalisation, pure bending, thin-walled pipes

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Authors: Wenfeng Xie

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Bulk/hull cavitation evolution induced by an underwater explosion (UNDEX) near a free surface (bulk) or a deformable structure (hull) is numerically investigated using a multiphase compressible fluid solver coupled with a one-fluid cavitation model. A series of two-dimensional computations is conducted with varying material elasticity and surface curvature. Results suggest that material elasticity and surface curvature influence the peak pressures generated from UNDEX shock and cavitation collapse, as well as the bulk/hull cavitation regions near the surface. Results also show that such effects can be different for bulk cavitation generated from UNDEX-free surface interaction and for hull cavitation generated from UNDEX-structure interaction. More importantly, results demonstrate that shock wave focusing caused by a concave solid surface can lead to a larger cavitation region and thus intensify the cavitation reload. The findings can be linked to the strength and the direction of reflected waves from the structural surface and reflected waves from the expanding bubble surface, which are functions of material elasticity and surface curvature. Shockwave focusing effects are also observed for axisymmetric simulations, but the strength of the pressure contours for the axisymmetric simulations is less than those for the 2D simulations due to the difference between the initial shock energy. The current method is limited to two-dimensional or axisymmetric applications. Moreover, the thermal effects are neglected and the liquid is not allowed to sustain tension in the cavitation model.

Keywords: cavitation, UNDEX, fluid-structure interaction, multiphase

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Authors: Mancho Manev

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The concept of almost paracontact Riemannian manifolds (abbr., apcR manifolds) was introduced by I. Sato in 1976 as an analogue of almost contact Riemannian manifolds. The notion of an apcR manifold of type (p,q) was defined by S. Sasaki in 1980, where p and q are respectively the numbers of the multiplicity of the structure eigenvalues 1 and -1. It also has a simple eigenvalue of 0. In our work, we consider (2n+1)-dimensional apcR manifolds of type (n,n), i.e., the paracontact distribution of the studied manifold can be considered as a 2n-dimensional almost paracomplex Riemannian distribution with almost paracomplex structure and structure group O(n) × O(n). The aim of the present study is to introduce a new class of apcR manifolds. Such a manifold is obtained using the construction of a certain Riemannian cone over it, and the resulting manifold is a paraholomorphic paracomplex Riemannian manifold (abbr., phpcR manifold). We call it a para-Sasaki-like Riemannian manifold (abbr., pSlR manifold) and give some explicit examples. We study the structure of pSlR spaces and find that the paracontact form η is closed and each pSlR manifold locally can be considered as a certain product of the real line with a phpcR manifold, which is locally a Riemannian product of two equidimensional Riemannian spaces. We also obtain that the curvature of the pSlR manifolds is completely determined by the curvature of the underlying local phpcR manifold. Moreover, the ξ-directed Ricci curvature is equal to -2n, while in the Sasaki case, it is 2n. Accordingly, the pSlR manifolds can be interpreted as the counterpart of the Sasaki manifolds; the skew-symmetric part of ∇η vanishes, while in the Sasaki case, the symmetric part vanishes. We define a hyperbolic extension of a (complete) phpcR manifold that resembles a certain warped product, and we indicate that it is a (complete) pSlR manifold. In addition, we consider the hyperbolic extension of a phpcR manifold and prove that if the initial manifold is a complete Einstein manifold with negative scalar curvature, then the resulting manifold is a complete Einstein pSlR manifold with negative scalar curvature. In this way, we produce new examples of a complete Einstein Riemannian manifold with negative scalar curvature. Finally, we define and study para contact conformal/homothetic deformations by deriving a subclass that preserves the para-Sasaki-like condition. We then find that if we apply a paracontact homothetic deformation of a pSlR space, we obtain that the Ricci tensor is invariant.

Keywords: almost paracontact Riemannian manifolds, Einstein manifolds, holomorphic product manifold, warped product manifold

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Authors: Mohammad Ghandehari Motlagh

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Purpose: To evaluate validity of simplified Javal’s rule (Total Ast=Corneal Ast-0.50@9) in 147 pre-op cataract eyes. Methods: Due to change in lens tissue and structure in a cataract crystalline lens, we conceive the simplified javal’s rule may not be valid in cataract cases.In this cross-sectional study,147 pre-op cataract eyes without oblique astigmatism were enrolled in this study. Ocular biometry (with IOL master 500)and keratometry and refraction findings were recorded. Results: Mean age of our patients was 64.95 yrs/old (SD+_9.86) that confirms on senile cataract. Mean Axial length and average keratometry were respectively 23.86 and 44.62.Prevalence of systemic diseases diabet and high blood pressure were respectively 43 (29.25%) and 44 (29.93%)and shows importance of these diseases. The Corneal astigmatism axis is correlated with refractive astigmatism in cataract eyes (R=0.493). Simplified Javal’s rule is valid in cataract eyes (P<0.001). Conclusion: Simplified Javal’s rule is a valid formula in pre-op cataract eyes and can be used for keratometry results confirmation.

Keywords: javals rule, cataract, keratometry, ocular axial length

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Authors: A. Benzian

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The generalization of relativistic theory of gravity based essentially on the principle of equivalence stipulates that for all bodies, the grave mass is equal to the inert mass which leads us to believe that gravitation is not a property of the bodies themselves, but of space, and the conclusion that the gravitational field must curved space-time what allows the abandonment of Minkowski space (because Minkowski space-time being nonetheless null curvature) to adopt Riemannian geometry as a mathematical framework in order to determine the curvature. Therefore the work presented in this paper begins with the evolution of the concept of gravity then tensor field which manifests by Riemannian geometry to formulate the general equation of the gravitational field.

Keywords: inertia, principle of equivalence, tensors, Riemannian geometry

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Authors: Kang Lin Peng

Abstract:

Space tourism emerged in 2001 and became famous in 2021, following the development of space technology. The space market is twisted because of the excess demand. Space tourism is currently rare and extremely expensive, with biased luxury product pricing, which is the seller’s market that consumers can not bargain with. Spaceship companies such as Virgin Galactic, Blue Origin, and Space X have been charged space tourism prices from 200 thousand to 55 million depending on various heights in space. There should be a reasonable price based on a fair basis. This study aims to derive a spacetime pricing model, which is different from the general pricing model on the earth’s surface. We apply general relativity theory to deduct the mathematical formula for the space tourism pricing model, which covers the traditional time-independent model. In the future, the price of space travel will be different from current flight travel when space travel is measured in lightyear units. The pricing of general commodities mainly considers the general equilibrium of supply and demand. The pricing model considers risks and returns with the dependent time variable as acceptable when commodities are on the earth’s surface, called flat spacetime. Current economic theories based on the independent time scale in the flat spacetime do not consider the curvature of spacetime. Current flight services flying the height of 6, 12, and 19 kilometers are charging with a pricing model that measures time coordinate independently. However, the emergence of space tourism is flying heights above 100 to 550 kilometers that have enlarged the spacetime curvature, which means tourists will escape from a zero curvature on the earth’s surface to the large curvature of space. Different spacetime spans should be considered in the pricing model of space travel to echo general relativity theory. Intuitively, this spacetime commodity needs to consider changing the spacetime curvature from the earth to space. We can assume the value of each spacetime curvature unit corresponding to the gradient change of each Ricci or energy-momentum tensor. Then we know how much to spend by integrating the spacetime from the earth to space. The concept is adding a price p component corresponding to the general relativity theory. The space travel pricing model degenerates into a time-independent model, which becomes a model of traditional commodity pricing. The contribution is that the deriving of the space tourism pricing model will be a breakthrough in philosophical and practical issues for space travel. The results of the space tourism pricing model extend the traditional time-independent flat spacetime mode. The pricing model embedded spacetime as the general relativity theory can better reflect the rationality and accuracy of space travel on the universal scale. The universal scale from independent-time scale to spacetime scale will bring a brand-new pricing concept for space traveling commodities. Fair and efficient spacetime economics will also bring to humans’ travel when we can travel in lightyear units in the future.

Keywords: space tourism, spacetime pricing model, general relativity theory, spacetime curvature

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Authors: Konstanca Nikolajevic, Nicolas Belanger, David Duvivier, Rabie Ben Atitallah, Abdelhakim Artiba

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Finding the optimal 3D path of an aerial vehicle under flight mechanics constraints is a major challenge, especially when the algorithm has to produce real-time results in flight. Kinematics models and Pythagorian Hodograph curves have been widely used in mobile robotics to solve this problematic. The level of difficulty is mainly driven by the number of constraints to be saturated at the same time while minimizing the total length of the path. In this paper, we suggest a pragmatic algorithm capable of saturating at the same time most of dimensioning helicopter 3D trajectories’ constraints like: curvature, curvature derivative, torsion, torsion derivative, climb angle, climb angle derivative, positions. The trajectories generation algorithm is able to generate versatile complex 3D motion primitives feasible by a helicopter with parameterization of the curvature and the climb angle. An upper ”motion primitives’ concatenation” algorithm is presented based. In this article we introduce a new way of designing three-dimensional trajectories based on what we call the ”Dubins gliding symmetry conjecture”. This extremely performing algorithm will be soon integrated to a real-time decisional system dealing with inflight safety issues.

Keywords: robotics, aerial robots, motion primitives, helicopter

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Authors: Amir Hossein Haji, Nabeel Al-Rawahi, Gholamreza Vakili-Nezhaad

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An innovative design has been examined for a gas-oil separator based on pressure reduction over an airfoil surface. The primary motivations are to shorten the release trajectory of the bubbles by minimizing the thickness of the oil layer as well as improving uniform pressure reduction zones. Restricted airflow over an airfoil is investigated for its effect on the pressure drop enhancement and the maximum attainable attack angle prior to the stall condition. Aerodynamic separation is delayed based on numerical simulation of Wortmann FX 63137 Airfoil in a confined domain using FLUENT 6.3.26. The proposed set up results in higher pressure drop compared with the free stream case. With the aim of optimum power consumption we have pursued further restriction to an air jet case over the airfoil. Then, a curved strip model is suggested for the air jet which can be applied as an analysis/design tool for the best performance conditions. Pressure reduction is shown to be inversely proportional to the curvature of the upper airfoil profile. This reduction occurs within the tracking zones where the air jet is effectively attached to the airfoil surface. The zero slope condition is suggested to estimate the onset of these zones after which the minimum curvature should be searched. The corresponding zero slope curvature is applied for estimation of the maximum pressure drop which shows satisfactory agreement with the simulation results.

Keywords: airfoil, air jet, curved fluid flow, gas-oil separator

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Authors: Rajib Husain, Munirujzaman Osmani, Mohammad Shamsal Islam

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Purpose: To compare the safety, efficacy and visual outcome of phacoemulsification vs. manual small-incision cataract surgery (SICS) for the treatment of cataract in Bangladesh. Objectives: 1. To assess the Visual outcome after cataract surgery 2. To understand the post-operative complications and early rehabilitation 3. To identified which surgical procedure more attractive to the patients 4. To identify which surgical procedure is occurred fewer complications. 5. To find out the socio-economic and demographic characteristics of study patients Setting: Chittagong Eye Infirmary and Training Complex, Chittagong, Bangladesh. Design: Retrospective, randomised comparison of 300 patients with visually significant cataracts. Method: The present study was designed as a retrospective hospital-based research. The sample size was 300 and study period was from July, 2012 to July, 2013 and assigned randomly to receive either phacoemulsification or manual small-incision cataract surgery (SICS). Preoperative and post-operative data were collected through a well designed collection format. Three follow-up were done; i) during discharge ii) 1-3 weeks & iii) 4-11 weeks post operatively. All preoperative and surgical complications, uncorrected and best-corrected visual acuity (BCVA) and astigmatism were taken into consideration for comparison of outcome Result: Nearly 95% patients were more than 40 years of age. About 52% patients were female, and 48% were male. 52% (N=157) patients came to operate their first eye where 48% (N=143) patients were visited again to operate their second eye. Postoperatively, five eyes (3.33%) developed corneal oedema with >10 Descemets folds, and six eyes (4%) had corneal oedema with <10 Descemets folds for Phacoemulsification surgeries. For SICS surgeries, seven eyes (4.66%) developed corneal oedema with >10 Descemets folds and eight eyes (5.33%) had corneal oedema with < 10 descemets folds. However, both the uncorrected and corrected (4-11 weeks) visual acuities were better in the eyes that had phacoemulsification (p=0.02 and p=0.03), and there was less astigmatism (p=0.001) at 4-11 weeks in the eye that had phacoemulsification. Best-corrected visual acuity (BCVA) of final follow-up 95% (N=253) had a good outcome, borderline 3.10% (N=40) and poor outcome was 1.6% (N=7). The individual surgeon outcome were closer, 95% (BCVA) in SICS and 96% (BCVA) in Phacoemulsification at 4-11 weeks follow-up respectively. Conclusion: outcome of cataract surgery both Phacoemulsification and SICS in CEITC was more satisfactory according to who norms. Both Phacoemulsification and manual small-incision cataract surgery (SICS) shows excellent visual outcomes with low complication rates and good rehabilitation. Phacoemulsification is significantly faster, and modern technology based surgical procedure for cataract treatment.

Keywords: phacoemulsification, SICS, cataract, Bangladesh, visual outcome of SICS

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Authors: Chaiyawat Musikapan, Ratchatin Chancharoen, Saknan Bongsebandhu-Phubhakdi

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For many recent years, soft robotic fingers were used for supporting the patients who had survived the neurological diseases that resulted in muscular disorders and neural network damages, such as stroke and Parkinson’s disease, and inflammatory symptoms such as De Quervain and trigger finger. Generally, the major hand function is significant to manipulate objects in activities of daily living (ADL). In this work, we proposed the model of soft actuator that manufactured by full 3D printing without the molding process and one material for use. Furthermore, we designed the model with a technique of multi cavitation cells (MC-Cells). Then, we demonstrated the curvature bending, fluidic pressure and force that generated to the model for assistive finger flexor and hand grasping. Also, the soft actuators were characterized in mathematics solving by the length of chord and arc length. In addition, we used an adaptive push-button switch machine to measure the force in our experiment. Consequently, we evaluated biomechanics efficiency by the range of motion (ROM) that affected to metacarpophalangeal joint (MCP), proximal interphalangeal joint (PIP) and distal interphalangeal joint (DIP). Finally, the model achieved to exhibit the corresponding fluidic pressure with force and ROM to assist the finger flexor and hand grasping.

Keywords: biomechanics efficiency, curvature bending, hand functional assistance, multi cavitation cells (MC-Cells), range of motion (ROM)

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Authors: Satyabrata Bera, Mintu Mondal

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Two-dimensional (2D) ferromagnetic materials have garnered significant attention due to their potential to host intriguing scientific phenomena such as the anomalous Hall effect, anomalous Nernst effect, and high transport spin polarization. This study focuses on the investigation of air-stable van der Waals(vdW) ferromagnets, FeGeTe₂ (FₙGT with n = 3, 4, and 5). Particular emphasis is placed on the Fe4GeTe2 (F4GT) compound, which exhibits a complex and fascinating magnetic behavior characterized by two distinct transitions: (i) paramagnetic (PM) to ferromagnetic (FM) around T C ∼ 270 K, and (ii) another spins reorientation transition (SRT) at T SRT ∼ 100 K . Scaling analysis of magnetocaloric effect confirms the second-order character of the ferromagnetic transition, while the same analysis at T SRT suggests that SRT is first-order phase transition. Moreover, the F4GT exhibits a large anomalous Hall conductivity (AHC), ∼ 490 S/cm at 2 K . The near-quadratic behavior of the anomalous Hall resistivity with the longitudinal resistivity suggests that a dominant AHC contribution arises from an intrinsic Berry curvature (BC) mechanism. Electronic structure calculations reveal a significant BC resulting from SOC-induced gapped nodal lines around the Fermi level, thereby giving rise to large AHC. Additionally, we reported exceptionally large anomalous Hall angle (≃ 10.6%) and Hall factor (≃ 0.22 V −1 ) values, the largest observed within this vdW family. The findings presented here, provide valuable insights into the fascinating magnetic and transport properties of 2D ferromagnetic materials, in particular, FₙGT family.

Keywords: 2D vdW ferromagnet, spin reorientation transition, anomalous hall effect, berry curvature

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Authors: Nikhat Iqbal Tamboli

Abstract:

INTRODUCTION: road traffic accidents (RTAs) are one of the leading and common causes of ocular injuries especially in developing countries like India which are preventable with certain measures and so it is of public health importance. AIM: To study incidence and clinical presentation of ocular morbidity in road traffic accidents. METHOD: Prospective cross-sectional study was conducted on 360 patients reported in department of ophthalmology. Detailed ocular examination and relevant investigations done. RESULTS: Incidence of ocular injuries is 23%. male:female ratio is 4.5:1.Cases having Sub conjunctival haemorrhage [74].eccymosis[217]. lid lcerations [164]orbital fracture[12] corneal tear [7]corneal abrasion[2] sclera tear[6] hyphaema[4] traumatic mydriasis [7]traumatic cataract [2]vitreous haemorrhage [1]traumatic optic neuropathy[1].Maximum cases in age group 20-40 years, with two wheeler vehicles 94.7% .Under influence of alcohol 13.3%. CONCLUSION: Younger age group with male preponderance is involved in ocular trauma due to road traffic accidents .maximum cases reported are with anterior segment injuries. Alcohol and two wheeler vehicles are common risk factors. Injuries involving cornea had bad prognosis and involving retina had worst prognosis.

Keywords: ocular morbidity, eye trauma, RTA, eye injury

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Authors: Adriano Valdes-Gomez, Francisco Javier Sevilla

Abstract:

We devise a numerical algorithm to simulate the diffusion of a Brownian particle restricted to the surface of a three-dimensional sphere when the particle is under the effects of an external potential that is coupled linearly. It is obtained using elementary geometry, yet, it converges, in the weak sense, to the solutions to the Smoluchowski equation. Rotations on the sphere, which are the analogs of linear displacements in euclidean spaces, are calculated using algebraic operations and then by a proper scaling, which makes the algorithm efficient and quite simple, especially to what may be the short-time propagator approach. Our findings prove that the global effects of curvature are taken into account in both dynamic and stationary processes, and it is not restricted to work in configuration space, neither restricted to the overdamped limit. We have generalized it successfully to simulate the Kramers or the Ornstein-Uhlenbeck process, where it is necessary to work directly in phase space, and it may be adapted to other two dimensional surfaces with non-constant curvature.

Keywords: diffusion on the sphere, Fokker-Planck equation on the sphere, non equilibrium processes on the sphere, numerical methods for diffusion on the sphere

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