Splitting Type Research Articles

Research of electric field strength on surface of conductor and its splitting type used in extra high voltage substation

Extra high voltage substation is an important part of the whole project locates in high altitude area, so corona audible noise exists around the operation equipment, mainly concentrated in the bundle conductor in the power station. This research on the split form and surface electric field intensity distribution of bundle conductor has a certain degree of theoretical and practical engineering application value. In this paper, an analysis of the classic formula illuminates the conductor split form, conductor diameter, bundle spacing and other factors how to affect the largest surface electric field intensity of the conductor. On this basis, we take a typical extra high voltage substation conductor as the research object. The three-dimensional model of the actual power station has been established with application of finite element simulation method in accordance with actual structure, and a preliminary calculation of surface electric field intensity also been obtained. According to the results, we analyze the reasons cause the serious corona. Then we design three-split conductor instead of two-split one, and make a comparative analysis between the two different forms. According to the three-split form mentioned above, the conductor diameter and bundle spacing are optimized. The research on the electrical field calculation and split form of bundle conductor provides references for the design of substation, and has practical value for the reduction of corona noise.

Universal degeneracy classes for vector bundles on [formula omitted] bundles

Given a vector bundle on a P1 bundle, the base is stratified by degeneracy loci measuring the splitting type of the vector bundle restricted to each fiber. The classes of these degeneracy loci in the Chow ring or cohomology ring of the base are natural invariants characterizing the degenerations of the vector bundle. When these degeneracy loci occur in the expected codimension, we find their classes. This yields universal formulas for degeneracy classes in terms of naturally arising vector bundles on the base. The existence of these formulas is applied to prove the non-emptiness of Brill-Noether splitting loci in [21]. Our results hold over arbitrary fields of any characteristic.

Splitting type viscosity methods for inclusion and fixed point problems on Hadamard manifolds

<abstract> In this article, we suggest and analyze the splitting type viscosity methods for inclusion and fixed point problem of a nonexpansive mapping in the setting of Hadamard manifolds. We derive the convergence of sequences generated by the proposed iterative methods under some suitable assumptions. Several special cases of the proposed iterative methods are also discussed. Finally, some applications to solve the variational inequality, optimization and fixed point problems are given on Hadamard manifolds. </abstract>

A refined Brill–Noether theory over Hurwitz spaces

Let $$f:C \rightarrow \mathbb {P}^1$$ be a degree k genus g cover. The stratification of line bundles $$L \in {{\,\mathrm{Pic}\,}}^d(C)$$ by the splitting type of $$f_*L$$ is a refinement of the stratification by Brill–Noether loci $$W^r_d(C)$$ . We prove that for general degree k covers, these strata are smooth of the expected dimension. In particular, this determines the dimensions of all irreducible components of $$W^r_d(C)$$ for a general k-gonal curve (there are often components of different dimensions), extending results of Pflueger (Adv Math 312:46–63, 2017) and Jensen and Ranganathan (Brill–Noether theory for curves of a fixed gonality, arXiv:1701.06579 , 2017). The results here apply over any algebraically closed field.

Riemann-Hilbert Boundary Value Problem with Piecewise Constant Transition Function

We prove that, for any Fuchsian system of differential equations on the Riemann sphere, there exists a rational matrix function whose partial indices coincide with the splitting type of the canonical vector bundle induced from the Fuchsian system. From this, we obtain solution of the Riemann-Hilbert boundary value problem for piecewise constant matrix function in terms of holomorphic sections of vector bundle and calculate the partial indices of the problem.

Mechanical Properties of Acid-corroded Sandstone Under Uniaxial Compression

Long-term exposure to chemical solutions can change the mineral composition and microstructure and may seriously affect the physical and mechanical properties of rocks. Therefore, to clarify the effects of long-term exposure and types of acids on the mechanical properties of rocks, and to develop the constitutive model of acid-immersed rocks, uniaxial compression tests were carried out on acid-immersed sandstone specimens. The sample weakened, and the brittle failure behavior became more ductile by the acid immersion to the aqueous solution of hydrochloric or sulfuric acids. The duration of the compaction stage of the stress–strain curve increased, that of the elastic stage decreased; the peak stress, elastic modulus, and Poisson's ratio decreased, and the peak point strains increased with the acidity and the immersion duration. The brittle shear failure of the untreated specimen became more axial splitting type failure with acidity. The damage variable of the combined effects of chemical and stress was introduced, and a statistical damage model considering the compaction stage of the stress–strain curve was established based on the damage variable. The model well-simulated the experimentally obtained stress–strain curves of the acid-immersed specimens. Finite element models reflecting the characteristics of the acid-immersed sandstone were established based on CT images.

Splitting Type Variational Problems with Linear Growth Conditions

Regularity properties of solutions to variational problems are established for a broad class of strictly convex splitting type energy densities of the principal form f : ℝ2 → ℝ, f(ξ1, ξ2) = f1(ξ1) + f2(ξ2), with linear growth. We show that, regardless of the corresponding property of f2, the assumption (t ∈ ℝ) $$ {c}_1{\left(1+\left|t\right|\right)}^{-{\upmu}_1}\le {f}_1^{\hbox{'}\hbox{'}}(t)\le {c}_2,\kern1em 1<{\upmu}_1<2, $$ is sufficient to obtain higher integrability of ∂1u for any finite exponent. We also include a series of variants of our main theorem. In the case f : ℝn → ℝ, similar results hold with the obvious changes in notation. Bibliography: 30 titles.

Volar, Splitting, and Collapsed Type of Die-Punch Fracture Treated by Volar Locking Plate (VLP): A Retrospective Study.

ObjectiveTo compare the results of different types of die‐punch fractures treated by volar locking plate (VLP).MethodsBetween January 2013 and February 2018, a total of 71 patients with die‐punch fracture of distal radius were treated by VLP and their medical records were retrospectively reviewed. Of them, 18 were classified as volar type, 24 as splitting type, and 28 as collapsed type of fracture, based on the preoperative radiographs and CT scans. The minimum follow‐up period was 12 months. Radiological parameters, wrist function, range of motion (ROM), and complications were evaluated and compared. Pearson chi‐square test was used to assess the difference of gender distribution, injury side, dominance, mechanism, type and classification of fracture, and postoperative complications, when necessary (P < 0.05), followed by pairwise comparisons using partitions of chi‐square test. Two‐tailed P value <0.05 was considered as statistically significant. For pairwise comparisons, adjustment of statistical level as P < 0.017 (0.05/3) was used. SPSS 21.0 was used to perform all the analyses.ResultsThe mean follow‐up time was 14.5 months, and at the mean of postoperative 8 weeks all patients obtained bony union, without delayed or non‐union. The grip strength was 26.6 ± 7.9 kg for patients in volar fracture group, 27.0 ± 9.4 kg in splitting group, and 26.2 ± 9.4 kg in collapsed group, without significant difference (P = 0.628).The disabilities of the arm, shoulder, and hand (DASH) (9.2 ± 10.0 for volar group, 8.8 ± 7.9 for splitting group, and 10.6 ± 8.7 for collapsed group) or Gartland–Werley score (5.1 ± 2.8 for volar group, 4.8 ± 3.2 for splitting group, and 6.4 ± 2.7 for collapsed group) either did not differ among the three groups (all P > 0.05). There was a poorer ROM in the group of collapsed fractures, but the difference was non‐significant for any parameter (P > 0.05). As for radiographic parameters, we did not find any significant difference for volar tilt, radial inclination, radial height, and ulnar variance (all P > 0.05), except for articular step‐off (P < 0.001). Pairwise comparisons showed a significantly greater step‐off (1.2 mm vs 0.4 mm, 0.5 mm) and higher rate of total complications in group of collapsed fracture (39.3%), compared to either volar (10.5%) or splitting type (12.5%).ConclusionsThe collapsed type of die‐punch fracture posed a greater articular step‐off and a higher rate of complications, especially secondary wrist osteoarthritis, which deserved more attention in clinical treatment.

Normal Bundles of Lines on Hypersurfaces

If X is a smooth hypersurface in complex projective space, the Fano variety of lines on X is stratified by the splitting type of the normal bundle of the line. We show that for general hypersurfaces, these strata have the expected dimension and, in this case, compute the class of the closure of the strata in the Chow ring of the Grassmannian of lines in projective space. For certain splitting types, we also provide upper bounds on the dimension of the strata that hold for all smooth X.

Linearly involved generalized Moreau enhanced models and their proximal splitting algorithm under overall convexity condition

The convex envelopes of the direct discrete measures, for the sparsity of vectors or for the low-rankness of matrices, have been utilized extensively as practical penalties in order to compute a globally optimal solution of the corresponding regularized least-squares models. Motivated mainly by the ideas in Zhang (2010 Ann. Stat. 38 894–942; Selesnick 2017 IEEE Trans. Signal Process. 65 4481–94; Yin et al 2019 IEEE Trans. Signal Process. 67 2595–607) to exploit nonconvex penalties in the regularized least-squares models without losing their overall convexities, this paper presents the linearly involved generalized Moreau enhanced (LiGME) model as a unified extension of such utilizations of nonconvex penalties. The proposed model can admit multiple nonconvex penalties without losing its overall convexity and thus is applicable to much broader scenarios in the sparsity-rank-aware signal processing. Under the general overall-convexity condition of the LiGME model, we also present a novel proximal splitting type algorithm of guaranteed convergence to a globally optimal solution. Numerical experiments in typical examples of the sparsity-rank-aware signal processing demonstrate the effectiveness of the LiGME models and the proposed proximal splitting algorithm.

Nodal curves with a contact-conic and Zariski pairs

Abstract To study the splitting of nodal plane curves with respect to contact conics, we define the splitting type of such curves and show that it can be used as an invariant to distinguish the embedded topology of plane curves. We also give a criterion to determine the splitting type in terms of the configuration of the nodes and tangent points. As an application, we construct sextics and contact conics with prescribed splitting types, which give rise to new Zariski-triples.

Irreducibility of the moduli space of orthogonal instanton bundles on $$\mathbb {P}^n$$

In order to obtain existence criteria for orthogonal instanton bundles on $$\mathbb {P}^n$$, we provide a bijection between equivalence classes of orthogonal instanton bundles with no global sections and symmetric forms. Using such correspondence we are able to provide explicit examples of orthogonal instanton bundles with no global sections on $$\mathbb {P}^n$$ and prove that every orthogonal instanton bundle with no global sections on $$\mathbb {P}^n$$ and charge $$c\ge 2$$ has rank $$r \le (n-1)c$$. We also prove that when the rank r of the bundles reaches the upper bound, $$\mathcal {M}_{\mathbb {P}^n}^{\mathcal {O}}(c,r)$$, the coarse moduli space of orthogonal instanton bundles with no global sections on $$\mathbb {P}^n$$, with charge $$c\ge 2$$ and rank r, is affine, smooth, reduced and irreducible. Last, we construct Kronecker modules to determine the splitting type of the bundles in $$\mathcal {M}_{\mathbb {P}^n}^{\mathcal {O}}(c,r)$$, whenever is non-empty.

Bundles of generalized theta functions over abelian surfaces

We study the Verlinde bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. In degree 0, the splitting type of these bundles is expressed in terms of indecomposable semihomogeneous factors. Furthermore, Fourier–Mukai symmetries of the Verlinde bundles are found consistently with strange duality. Along the way, a transformation formula for the theta bundles is derived, extending a theorem of Drézet–Narasimhan from curves to abelian surfaces.

Distributed Generalized Nash Equilibria Computation of Monotone Games via Double-Layer Preconditioned Proximal-Point Algorithms

In this paper, we investigate distributed generalized Nash equilibrium (GNE) computation of monotone games with affine coupling constraints. Each player can only utilize its local objective function, local feasible set and a local block of the coupling constraint, and can only communicate with its neighbours. We assume the game has monotone pseudo-subdifferential without Lipschitz continuity restrictions. We design novel center-free distributed GNE seeking algorithms for equality and inequality affine coupling constraints, respectively. A proximal alternating direction method of multipliers(ADMM) is proposed for the equality case, while for the inequality case, a parallel splitting type algorithm is proposed. In both algorithms, the GNE seeking task is decomposed into a sequential NE computation of regularized subgames and distributed update of multipliers and auxiliary variables, based on local data and local communication. Our two double-layer GNE algorithms need not specify the inner-loop NE seeking algorithm and moreover, only require that the strongly monotone subgames are inexactly solved. We prove their convergence by showing that the two algorithms can be seen as specific instances of preconditioned proximal point algorithms} (PPPA) for finding zeros of monotone operators. Applications and numerical simulations are given for illustration.

Unexpected curves arising from special line arrangements

In a recent paper arXiv:1602.02300v2, Cook II, Harbourne, Migliore and Nagel related the splitting type of a line arrangement in the projective plane to the number of conditions imposed by a general fat point of multiplicity $j$ to the linear system of curves of degree $j+1$ passing through the configuration of points dual to the given arrangement. If the number of conditions is less than the expected, we say that the configuration of points admits unexpected curves. In this paper, we characterize supersolvable line arrangements whose dual configuration admits unexpected curves and we provide other infinite families of line arrangements with this property.

Cavities spatial distribution confined by microcrystalline cellulose particles determines tablet disintegration patterns

Cavities and the architectures inside tablet play a decisive role for the permeation of water within tablet to initiate disintegration phenomenon. The present study aims to establish inner structure characterization methodology based on synchrotron radiation X-ray microcomputed tomography (SR-μCT) for microcrystalline cellulose (MCC) tablets and to correlate the cavities and 'their attributes to tablet disintegration phenomenon. The three-dimensional (3D) morphological architecture and quantitative data of single particles for 12 specifications of MCC, and respective MCC tablets' cavities structure were obtained through advanced SR-μCT studies. The image processing techniques were established to study the morphology of voids and porosity in an axial and radial direction based on the highly resolved 3D structure of tablets. The in-situ visualization of morphological disintegration behavior indicates that there were two patterns of disintegrations, which can be cataloged as laminating type (LT) and splitting type (ST) disintegrations. The principal component analysis (PCA) was used for multivariate data analysis to get the meaningful correlation among disintegration behaviors, cavities morphology, single particles attributes, and the cavities spatial arrangement within the tablets. These findings have deepened insights into inner structures of tablets and single particle structural attributes to tablet disintegration, reflecting the mechanism of disintegration mode, and the significance of pharmaceutical structure evaluated via SR-μCT.

Splitting types of bundles of logarithmic vector fields along plane curves

We give a formula relating the total Tjurina number and the generic splitting type of the bundle of logarithmic vector fields associated to a reduced plane curve. By using it, we give a characterization of nearly free curves in terms of splitting types. Several applications to free and nearly free arrangements of lines are also given, in particular a proof of a form of Terao’s Conjecture for arrangements having a line with at most four intersection points.

Multiple crack extension model of steel anchor bolts subjected to impact loading

Steel anchor bolts embedded in concrete are designed based on standards that assume to have a uniform stress along with single crack failure. However, experimental evidence has shown that the steel anchor bolt failure is governed by a combination of failure patterns such as cone and splitting type failure, hence the assumptions of uniform stress and single crack failure are not valid. In this regards the presented manuscript details an analytical model related to the anchor bolt failure subjected to impact loading. Impact loading is such that is introduced using a Schmidt Hammer in order to judge the pull-out strength steel bolts. The presented analytical model takes into consideration multiple crack extension scenarios, such as interfacial cracking initiated from top and bottom of steel bolt along with the case of simultaneous crack extension. The presented model is further capable of taking into consideration a variety of anchor types such as straight, hooked and bent type of anchors. The theoretical and experimental results comparison proved that the presented analytical model was capable of predicting the peak load capacity and could also simulate the pre and post peak failure mechanism. The proposed model can be employed by professionals to judge the deformational response of various types of steel anchor bolts.

Normal bundles of rational curves in projective space

Let $$b_{\bullet }$$ be a sequence of integers $$1 < b_1 \le b_2 \le \cdots \le b_{n-1}$$ . Let $${\text {M}}_e(b_{\bullet })$$ be the space parameterizing nondegenerate, immersed, rational curves of degree e in $$\mathbb {P}^n$$ such that the normal bundle has the splitting type $$\bigoplus _{i=1}^{n-1}\mathcal {O}(e+b_i)$$ . When $$n=3$$ , celebrated results of Eisenbud, Van de Ven, Ghione and Sacchiero show that $${\text {M}}_e(b_{\bullet })$$ is irreducible of the expected dimension. We show that when $$n \ge 5$$ , these loci are generally reducible with components of higher than the expected dimension. We give examples where the number of components grows linearly with n. These generalize an example of Alzati and Re.

Image classification for Die-punch fracture of intermediate column of the distal radius.

The aim of the study was to analyze the imaging findings of Die-punch fracture of intermediate column of the distal radius, and to explore the clinical application value of image classification. The clinical data of 45 patients who were admitted to our hospital from May 2010 to October 2016 were analyzed retrospectively. All patients met the inclusion criteria for Die-punch fracture. X-ray and CT scan were performed to examine the fracture, and the results were assessed by two doctors in a double blind method. Finally, the image classification of Die-punch fracture was formulated. According to the imaging features of Die-punch fracture, it was divided into four types: type I (dorsal type, 15 cases), type II (volar type, 8 cases), type III (splitting type, 10 cases), type IV (collapsed type, 12 cases). The accuracy rate of CT was 100% (45/45). The misclassification rate of X-ray was 15.6% (7/45) and the missed diagnosis rate was 11.1% (5/45). CT examination could accurately diagnose Die-punch fracture and perform preoperative image classification.