Normal Surfaces Research Articles

Globally subanalytic CMC surfaces in ℝ3 with singularities

AbstractIn this paper we present a classification of a class of globally subanalytic CMC surfaces in ℝ3 that generalizes the recent classification made by Barbosa and do Carmo in 2016. We show that a globally subanalytic CMC surface in ℝ3 with isolated singularities and a suitable condition of local connectedness is a plane or a finite union of round spheres and right circular cylinders touching at the singularities. As a consequence, we obtain that a globally subanalytic CMC surface in ℝ3 that is a topological manifold does not have isolated singularities. It is also proved that a connected closed globally subanalytic CMC surface in ℝ3 with isolated singularities which is locally Lipschitz normally embedded needs to be a plane or a round sphere or a right circular cylinder. A result in the case of non-isolated singularities is also presented. It also presented some results on regularity of semialgebraic sets and, in particular, it proved a real version of Mumford's Theorem on regularity of normal complex analytic surfaces and a result about C1 regularity of minimal varieties.

Smooth deformations of singular contractions of class VII surfaces

We consider normal compact surfaces $Y$ obtained from a minimal class VII surface $X$ by contraction of a cycle $C$ of $r$ rational curves with $C^2<0$. Our main result states that, if the obtained cusp is smoothable, then $Y$ is globally smoothable. The proof is based on a vanishing theorem for $H^2(\Theta_Y)$. If $r<b_2(X)$ any smooth small deformation of $Y$ is rational, and if $r=b_2(X)$ (i.e. when $X$ is a half-Inoue surface) any smooth small deformation of $Y$ is an Enriques surface. The condition "the cusp is smoothable" in our main theorem can be checked in terms of the intersection numbers of the cycle, using the Looijenga conjecture (which has recently become a theorem). Therefore this is a "decidable" condition. We prove that this condition is always satisfied if $r<b_2(X)\leq 11$. Therefore the singular surface $Y$ obtained by contracting a cycle $C$ of $r$ rational curves in a minimal class VII surface $X$ with $r<b_2(X)\leq 11$ is always smoothable by rational surfaces. The statement holds even for unknown class VII surfaces.

Complete algebraic vector fields on affine surfaces

Let [Formula: see text] be the subgroup of the group [Formula: see text] of holomorphic automorphisms of a normal affine algebraic surface [Formula: see text] generated by elements of flows associated with complete algebraic vector fields. Our main result is a classification of all normal affine algebraic surfaces [Formula: see text] quasi-homogeneous under [Formula: see text] in terms of the dual graphs of the boundaries [Formula: see text] of their SNC-completions [Formula: see text].

The Examples of Design of Normal Cycle Shells and Analyses of Stress-Strain State by Variation-Difference Method

The variation-difference method is a convenient numerical method for shells of complex forms. It is enough when only cinematic boundary conditions are satisfied because the method is based on the principle of Lagrange. Another advantage of the variation-difference method is the better opportunity to create computer programs based on it. For shell analysis in orthogonal coordinate system as well as for shell analysis in principal curvatures the system of equations describing stress-strain state can be simplified. In this paper the difference between analysis in orthogonal coordinate system and analysis in principal curvatures of the surface is considered. The main distinction of the analysis of shells in orthogonal curvilinear coordinate system is the necessity of determination of components which include curvature of torsion of coordinate lines. The addition of these components in the equations of the theory of shells for the coordinate system in principal curvatures gives possibility to analyze shells in common orthogonal coordinate system. In this article shell analysis in orthogonal coordinate system is applied to shells based on normal cyclic surfaces.

Singularities of Non-Developable Surfaces in Three-Dimensional Euclidean Space

We study the singularity on principal normal and binormal surfaces generated by smooth curves with singular points in the Euclidean 3-space. We discover the existence of singular points on such binormal surfaces and study these singularities by the method of singularity theory. By using structure functions, we can characterize the ruled surface generated by special curves.

Shells analysis in orthogonal curvilinear coordinate system with variation-difference method

The variation-difference method is a convenient numerical method for shells of complex forms. It is enough when only cinematic boundary conditions are satisfied because the method is based on the principle of Lagrange. Another advantage of the variation-difference method is the better opportunity to create computer programs based on it. For shell analysis in orthogonal coordinate system as well as for shell analysis in principal curvatures the system of equations describing stress-strain state can be simplified. In this paper the difference between analysis in orthogonal coordinate system and analysis in principal curvatures of the surface is considered. The main distinction of the analysis of shells in orthogonal curvilinear coordinate system is the necessity of determination of components which include curvature of torsion of coordinate lines. The addition of these components in the equations of the theory of shells for the coordinate system in principal curvatures gives possibility to analyze shells in common orthogonal coordinate system. In this article shell analysis in orthogonal coordinate system is applied to shells based on normal cyclic surfaces.

Histologic Analysis of 2 Alternative Donor Sites of the Ipsilateral Elbow in the Treatment of Capitellar Osteochondritis Dissecans

To compare the histologic features of the cartilage from the capitellum with 2 proposed alternative donor sites from the ipsilateral elbow in the treatment of capitellar osteochondritis dissecans (OCD): the nonarticulating part of the radial head and the nonarticulating lateral side of the olecranon tip. Ten human cadaveric elbow specimens with macroscopically normal articular surfaces were used to obtain 5-mm osteochondral grafts: 10 from the capitellum (60° anteriorly relative to the humeral shaft), 10 from the radial head (nonarticulating part at 80°), and 4 from the olecranon (lateral side of the olecranon tip). Grafts were fixated in formalin (4% formaldehyde), decalcified, and processed into standard 8-μm-thick hematoxylin and eosin-and Toluidine Blue-stained sections. These were assessed for cartilage thickness, shape of articular surface, and 13 histologic parameters of the International Cartilage Repair Society II. Olecranon scores were excluded from statistical analysis. Mean cartilage thickness was 1.5 ± 0.22mm at the capitellum; 1.3 ± 0.34mm at the radial head; and 1.9 ± 1.0mm at the olecranon. There was no difference in cartilage thickness between the capitellum and radial head (P= .062). All grafts demonstrated a convex articular surface. International Cartilage Repair Society II scores ranged from 82 to 100 for the capitellum, from 81 to 100 for the radial head, and from 67 to 87 for the olecranon tip. There was less chondrocyte clustering at the capitellum (84 ± 14) than in the radial head (94 ± 3.2; P= .019). Mid/deep zone assessment of the capitellum scored higher (97 ± 6.7) than the radial head (91 ± 4.6; P= .038). This study demonstrates appropriate histologic similarities between the cartilage from the capitellum and 2 alternative donor sites of the ipsilateral elbow in the treatment of capitellar OCD: the nonarticulating part of the radial head and the nonarticulating lateral side of the olecranon tip. From an histologic point of view, there seem to be no obstacles to use grafts from these alternative donor sites for reconstruction of the capitellum when performing osteochondral autologous transplantation.

Two Dimensional Model for Backwater Geomorphology: Darby Creek, PA

Predicting morphological alterations in backwater zones has substantial merit as it potentially influences the life of millions of people by the change in flood dynamics and land topography. While there is no two-dimensional river model available for predicting morphological alterations in backwater zones, there is an absolute need for such models. This study presents an integrated iterative two-dimensional fluvial morphological model to quantify spatio-temporal fluvial morphological alterations in normal flow to backwater conditions. The integrated model works through the following steps iteratively to derive geomorphic change: (1) iRIC model is used to generate a 2D normal water surface; (2) a 1D water surface is developed for the backwater; (3) the normal and backwater surfaces are integrated; (4) an analytical 2D model is established to estimate shear stresses and morphological alterations in the normal, transitional, and backwater zones. The integrated model generates a new digital elevation model based on the estimated erosion and deposition. The resultant topography then serves as the starting point for the next iteration of flow, ultimately modeling geomorphic changes through time. This model was tested on Darby Creek in Metro-Philadelphia, one of the most flood-prone urban areas in the US and the largest freshwater marsh in Pennsylvania.

Treewidth, crushing and hyperbolic volume

We prove that there exists a universal constant $c$ such that any closed hyperbolic 3-manifold admits a triangulation of treewidth at most $c$ times its volume. The converse is not true: we show there exists a sequence of hyperbolic 3-manifolds of bounded treewidth but volume approaching infinity. Along the way, we prove that crushing a normal surface in a triangulation does not increase the carving-width, and hence crushing any number of normal surfaces in a triangulation affects treewidth by at most a constant multiple.

Easy-cleaning surfaces functionalized with an interface-binding recombinant lipase

Surface fabrication is an effective method for functional materials development. This work investigated the use of cellulose-binding domain (CBD) fused detergent lipase for fabrication of easy-cleaning surfaces. As a result, the CBD conjugated Lipase-A (LipA-CBD) demonstrated a multi-layer self-assemble on cotton fabric surface and enhanced hydrophobicity as detected by both scanning electron microscope and water contact angle measurement. Compared to the normal cotton surfaces, such self-assembly bioactive surfaces afforded effective easy-cleaning functionality against both water and lipids based stains with the most significant stain removing ratio as examined through the simulated laundering test. Additionally, this surface assembled LipA-CBD presented good thermal stability with 15 days of half-life detected for 70°C and over 60 days for room temperature. Although there is a gradual decrease in sun irradiation stability and laundering durability, the functionality could be quickly recovered by re-applying the LipA-CBD as the self-assembly coating in the rinsing process. These results presented a green, simple and timesaving method to develop new easy-cleaning cotton fabrics via interfacial self-assembly of biomacromolecules.

Singularity properties of killing magnetic curves in Minkowski 3-space

We define the coordinate equations of killing magnetic curves [Formula: see text] in [Formula: see text] with the magnetic vector field [Formula: see text] under the frame [Formula: see text]. In particular, this yields to describe the geometrical properties and singularities of the magnetic curves and the magnetic normal binormal surfaces. Meanwhile, we establish the relationships between singularity types of the magnetic normal binormal surfaces and geometrical invariants of the magnetic curves. As an application, we give an example to explain the main results in this paper, where we give the classification of singularity types of the magnetic curves.

The Lipman–Zariski Conjecture in Low Genus

Abstract We prove the Lipman–Zariski conjecture for complex surface singularities of genus 1 and also for those of genus 2 whose link is not a rational homology sphere. As an application, we characterize complex $2$-tori as the only normal compact complex surfaces whose smooth locus has trivial tangent bundle. We also deduce that all complex-projective surfaces with locally free and generically nef tangent sheaf are smooth, and we classify them.

Sodium atom beam collisions with the liquid glycerol surface: Mass effects of deuteration

Gas-phase sodium atom collisions with liquid glycerol were investigated by atomic beam scattering from normal and deuterated surfaces. The scattering signal of the recoiling effusive Na atom beam was monitored by a mass spectrometer. Because all thermally equilibrated Na atoms ionize into the liquid surface, this system was uniquely suited to interrogate the subtle kinematic effect of glycerol deuteration on the collisional energy transfer process within the impulsive scattering regime. An interplay of kinematic and vibrational effects explains the Na scattering behavior from variously deuterated glycerol surfaces, extending our fundamental understanding of collisional energy transfer, and ultimately, chemical reaction dynamics.

The Calculation Of The Normal Height Of The State Geodetic Network Point Based On The Local Quasigeoid Model

The data obtained during GPS observations is the basis for the creation of local quasigeoid models and obtaining differences in the heights of normal and ellipsoid surfaces of WGS-84. The network of satellite base stations located in the Rostov region is used as points of the state geodetic network (SGN). The gravimetric model is used as a model of the quasigeoid height (QH). The model of the quasigeoid is calculated and developed on the basis of gravimetric data. Five base stations located within the city of Rostov-on-Don are selected to obtain the normal heights of SGN points. The above points are recalculated from the local system to the WGS-84 system. The equation of the plane, approximating the local quasigeoid is constructed. The gravimetric heights of the quasigeoid are obtained by substituting the coordinate values of each point. The calculation of the normal heights of points is made after an estimation of the model accuracy.

Determination of H+ and Ca2+ fluxes in cold-stored banana fruit using non-invasive micro-test technology

Ion concentration changes significantly under stress conditions such as chilling. Accurate assessment of the concentration, flow velocity and flow direction of ions is pivotal to understanding the mechanism of stress response of fruits and vegetables. Fibroin is a newly reported edible coating material effective in delaying fruit senescence and alleviating chilling injury. In the present study, banana fruit were fibroin-treated before cold-stored, and non-invasive micro-test technology (NMT) was employed to determine H+ and Ca2+ fluxes across the non-wound surfaces of pericarp cuboids of the fibroid-treated banana fruit. When the wound surfaces of banana pericarp cuboids were coated with food grease, H+ and Ca2+ fluxes across the wound surfaces fluctuated around 0 nmol m−2 s-1, indicating that ion flow across the wound surfaces of the pericarp cuboids had been completely prevented by food grease coating. This coating method was employed to coat the wound surfaces while H+ and Ca2+ fluxes across the normal surfaces of the pericarp cuboids of fibroin-treated cold-stored banana fruit were determined. The results suggested that fibroin treatment alleviated chilling injury by reducing H+ and Ca2+ effluxes. Utilization of food grease coating on wound surfaces will greatly improve our ability to reveal the mechanism of chilling injury in fruits and vegetables by learning ion fluxes in tissues and organs.

Optimal bounds for T-singularities in stable surfaces

We explicitly bound T-singularities on normal projective surfaces W with one singularity, and KW ample. This bound depends only on KW2, and it is optimal when W is not rational. We classify and realize surfaces attaining the bound for each nonnegative Kodaira dimension of the minimal resolution of W. This answers effectiveness of bounds (see [1], [2], [17]) for those surfaces.

Feasible region determination without local interference of 3 + 2 axis machining for arbitrary revolving tools

The 3 + 2 axis machining technology is of high feasibility and strong rigidity. Its feasible region determination is a prerequisite and indispensable. This paper focuses on feasible region determination without local interference for arbitrary revolving tools in 3 + 2 axis machining. A unified definition of revolving tools is firstly raised, and the normal vector surfaces are mapped to areas on a same unit sphere. The feasible region determination is transformed into a covering problem between two areas on a unit sphere, which are the normal vector surface of the tool and the negative normal vector surface of the machining area. This method is independent of tool geometry types. If the normal vector surfaces are determined, then the feasible region is obtained. To get more maneuverability, in the actual determination process, the negative normal vector surface of the machining area is approximated by a revolving surface on a unit sphere which is called as its γ-revolving surface in this paper, and the error is analyzed. The γ-revolving surface is obtained by the steepest descent method to search the minimum revolving surface in a certain sense. The covering problem between two revolving surfaces on a unit sphere is solved on a plane, which equals to consider the covering between their generatrices. In the validation, the feasibility of tool axes in feasible regions’ different positions is verified, and the method is used in tool selection.

Toward cognitive support for automated defect detection

With the development of cognitive computing, machine learning techniques, and big data analytics, cognitive support is crucial for automated industrial production. The real-time automated visual inspection in industrial production is a challenging task. Speed and accuracy are crucial factors for the process of automating the defect detection. Many statistical and spectrum analysis approaches have been introduced; however, they suffer from high computational cost with average performance. This paper proposes a neighborhood-maintaining approach, which is based on the minimum ratio for fast and reliable inspection of industrial products. The minimum ratio between local neighborhood sliding windows is used as a similarity measure for localizing defection. Extreme learning machine is then adapted to classify surfaces to defect or normal. A defect detection accuracy on textile fabrics has achieved 98.07% with 91.29% sensitivity and 99.67% specificity. The minimum ratio shows highly discriminant power to distinguish between normal and abnormal surfaces. A defective region produces a smaller value of minimum ratio than that of a defect-free region. Experimental results show superior speed and accuracy performance over many existing defect detection methods.

Observers Agreement in Perception of Non-Cavitated Approximal Dental Caries by Intraoral Digital CCD Radiography at Different Exposure Parameters and Corresponding Required Radiation Dose

Objectives: To evaluate the diagnostic accuracy of Charged Coupled device (CCD) in detection of Non- Cavitated Approximal caries at different exposure parameters in relation to radiation dose in vitro. Study Design: Seventy-eight surfaces of extracted teeth were inserted in acid gel to create non-cavitated proximal caries with different depth, and then Radiographs have been taken to all teeth by CCD sensor. Radiographs were interpreted by three observers. The lesions were classified as (N) No lesion, (D1) Less than ½ enamel thickness, (D2) more than halfway of enamel but not involve DEJ. (D3) Dentin caries. Teeth were randomly selected for histological analysis after consensus from three oral and maxillofacial radiologists as Gold standard. The corresponding radiation dose was measured by unfors meter device at different exposure parameters. Results: The histological examination showed that the distribution of lesions was 39.8% Sound, both enamel lesions are equal 17.8%, Dentin lesions 24.6. The sensitivity and specificity of CCD to detect normal surfaces were 0.95, D1 was 0.37, D2 was 0.74 and D3 was 0.86. As the lesions depth increased, the sensitivity increased. The higher image quality was produced by using exposure parameters (70 KvP, 160 ms) and (70 KvP, 200 ms). While, (60 KvP, 200 ms) and (60 KvP, 250 ms) produced the worse image quality. Conclusion: Regard the balance between the higher diagnostic accuracy of digital images and minimum radiation dose: using exposure parameters as (70 KvP, 160 ms) is considered the best image quality and relative dose (81 mSv). While, (70 KvP, 125ms) and (66 KvP, 160 ms) are little bit lower quality and corresponding dose are (63), (73) respectively. Although (70 KvP, 200 ET) produce higher image quality but its relative dose is high (101mSv).

A higher-dimensional generalization of Mumford's rational pullback for Weil divisors

Mumford defined a rational pullback for Weil divisors on normal surfaces, which is linear, respects effectivity, and satisfies the projection formula. In higher dimensions, the existence of small resolutions of singularities precludes such general results. We single out a higher-dimensional situation that resembles the surface case and show for it that a rational pullback for Weil divisors exists, which is also linear, respects effectivity, and satisfies the projection formula.