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In this paper, a method using neural network for optimizing the grading ring of ±1100kV ultra-high voltage direct current (UHVDC) wall bushing is presented. Firstly, the finite element method (FEM) is applied to calculate the electric field distribution along hollow insulator surface with various pipe diameter, ring diameter and installation position of the grading ring and the optimal goal is set according to the FEM numerical results. Then the neural network model is built and trained with L- M algorithm using 300 sets of data calculated by the method of parametric scanning. Finally, the parameters of grading ring are optimized according to the neural network fitting results. The optimized grading ring uniforms the electric field distribution along the hollow insulator surface. This paper can provide a reference on structural design of UHVDC wall bushing.

This paper is a survey on the study of the behaviour of the composition of polynomials on the computation of Gr\"obner bases. This survey brings together some works published between 1995 and 2007. The authors of these papers gave answers to some questions in this subject for several types of Gr\"obner bases, over different monomials orderings and over different polynomials rings. Some of these answers are complete and some are not. Some papers of them were given to answer some open questions given in the first published paper of these papers and other some were given to generalize previous work. Note that, there are many other works in this subject over other special cases and types of Gr\"obner bases under the usual definition over arbitrary fields, over other types of bases, under the non-commutative case and with other methods of proofs and calculations., Comment: 38 pages

This paper is a survey on the study of the behaviour of the composition of polynomials on the computation of Gr��bner bases. This survey brings together some works published between 1995 and 2007. The authors of these papers gave answers to some questions in this subject for several types of Gr��bner bases, over different monomials orderings and over different polynomials rings. Some of these answers are complete and some are not. Some papers of them were given to answer some open questions given in the first published paper of these papers and other some were given to generalize previous work. Note that, there are many other works in this subject over other special cases and types of Gr��bner bases under the usual definition over arbitrary fields, over other types of bases, under the non-commutative case and with other methods of proofs and calculations., 38 pages

of the paper: "G. Picavet and M. Picavet-L'Hermitte, Modules with finitely many submodules, Int. Electron. J. Algebra, 19 (2016), 119-131.":We characterize ring extensions $R \subset S$ having FCP (FIP), where $S$ is the idealization of some $R$-module. As a by-product we exhibit characterizations of the modules that have finitely many submodules. Our tools are minimal ring morphisms, while Artinian conditions on rings are ubiquitous. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

A Theoretical Paper on Using Two-Sided Markets Theory as a Framework in a Valuation Setting.

In this paper, we refine the method introduced by Izadi and Baghalaghdam to search integer solutions to the Diophantine equation $X_1^5+X_2^5+X_3^5=Y_1^3+Y_2^3+Y_3^3$. We show that the Diophantine equation has infinitely many positive solutions., Comment: To appear in Math. J. Okayama Univ

Mir Abbas Jalali et al. [Phys. Rev. E 92, 032913(2015)] explained the retrograde turn of rings by aerodynamic phenomena due to the presence of a central hole in the ring as opposed to a disk. The results of our experiments suggest that the drag torque is not the main reason for the retrograde turn of the rings, and the results of theoretical research have shown that such a motion is possible for both the ring and the disk in the case of rolling without slipping., 5 pages, 6 figures

We associate to a good cell decomposition of a manifold M a quadratic algebra and show that the Koszulity of the algebra implies a restriction on the Euler characteristic of M . For a two-dimensional manifold M the algebra is Koszul if and only if the Euler characteristic of M is two.

A new property of a complete intersection in a graded Noetherian ring is proved; this result, in conjunction with the Jacobian criterion, is then applied to the description of the loci of singularities in a family of affine varieties introduced in a well-known paper on forms of many variables.

We prove that every curve in the biliaison class of an extremal curve in P3 can be connected to an extremal curve.

We fill a gap in the proof of one of the central theorems in Epp's paper, concerning $p$-cyclic extensions of complete discrete valuation rings., Comment: 3 pages

We present yet another algebraic proof of the unimodality of the binomial coefficients.

We present yet another algebraic proof of the unimodality of the binomial coefficients.

In section 8.3 of our paper "Duality and Flat Base Change on Formal Schemes" (http://arXiv.org/abs/alg-geom/9708006) some important results concerning localization of, and preservation of coherence by, basic duality functors, were based on the false statement that any closed formal subscheme of an open subscheme of the completion P of a relative projective space is an open subscheme of a closed formal subscheme of P. In this note, the said results are provided with solid foundations.

This submission consists of two papers: 1) an erratum that corrects an error in the proof of Proposition 4.3 in my paper "The Homogeneous Coordinate Ring of a Toric Variety", and 2) the original (unchanged) version of the paper, published in 1995. The original paper introduced the homogeneous coordinate ring of a toric variety (now called the total coordinate ring or Cox ring) and gave a quotient construction. The paper also studied sheaves on a toric variety, and in Section 4 described its automorphism group. The error in the proof of Proposition 4.3 resulted from the faulty assumption that a certain set of graded endomorphisms forms a ring; rather, it is a monoid under composition. The erratum notes this error and gives a correct proof of the proposition., Erratum: 6 pages, LaTeX; Original paper: 28 pages, TeX C Version 3.0 with AMS fonts

The idea of residuation goes back to Dedekind, who introduced it into ideal theory. Residuation now plays an important role in several fields of mathematics, especially commutative ring theory. Let R be a commutative ring with identity. The residual of an ideal B with respect to an ideal A is the ideal A: B = {x ∈ R | xB ⊆ A. Here A: B is the largest ideal X of R with the property that BX ⊆ A. Residuation may be defined in other algebraic structures and may be defined independently of multiplication.

Electrical grade natural fibers continue to play an important role as components in dielectric systems.

The main goal of this short paper is to prove the existence of rank 2 simple and special Ulrich bundles on a wide class of elliptic surfaces: namely, on regular Weierstrass fibrations \(\pi : S\rightarrow \mathbb {P}^1\). Alongside we also show the existence of rank 2 weakly Ulrich sheaves on arbitrary Weierstrass fibrations \(S\rightarrow C_0\) and we deal with the (non-)existence of rank one Ulrich bundles on them.

In all molecules, a current density is induced when the molecule is subjected to an external magnetic field. In turn, this current density creates a particular magnetic field. In this work, the bifurcation value of the induced magnetic field is analyzed in a representative set of aromatic, non‐aromatic and antiaromatic monocycles, as well as a set of polycyclic hydrocarbons. The results show that the bifurcation value of the ring‐shaped domain adequately classifies the studied molecules according to their aromatic character. For aromatic and nonaromatic molecules, it is possible to analyze two ring‐shaped domains, one diatropic (inside the molecular ring) and one paratropic (outside the molecular ring). Meanwhile, for antiaromatic rings, only a diatropic ring‐shaped domain (outside the molecular ring) is possible to analyze, since the paratropic domain (inside the molecular ring) is irreducible with the maximum value (attractor) at the center of the molecular ring. In some of the studied cases, i. e., in heteroatomic species, bifurcation values do not follow aromaticity trends and present some inconsistencies in comparison to ring currents strengths, showing that this approximation provides only a qualitative estimation about (anti)aromaticity.

The structures and interaction energies of water clusters with ring stacking motifs are studied by using ab initio calculations. The structures of the water clusters are constructed by stacking either single rings or multi‐rings of tetramer, pentamer, and hexamer. We found that, in the single‐ring‐stacking motif, the most stable isomers exhibit an alternative clockwise‐anticlockwise stacking pattern. We also show that four‐layer single‐ring‐stacking isomers are not energetically favorable in comparison with those of two‐layer multi‐ring‐stacking isomers. The relative stability of the isomers is also analyzed in terms of H‐bond strength and elastic distortions of the water molecules.

Helical ensembles solve more structures by MR with AMPLE than do ideal helices and at no greater CPU cost., The conventional approach in molecular replacement is the use of a related structure as a search model. However, this is not always possible as the availability of such structures can be scarce for poorly characterized families of proteins. In these cases, alternative approaches can be explored, such as the use of small ideal fragments that share high, albeit local, structural similarity with the unknown protein. Earlier versions of AMPLE enabled the trialling of a library of ideal helices, which worked well for largely helical proteins at suitable resolutions. Here, the performance of libraries of helical ensembles created by clustering helical segments is explored. The impacts of different B-factor treatments and different degrees of structural heterogeneity are explored. A 30% increase in the number of solutions obtained by AMPLE was observed when using this new set of ensembles compared with the performance with ideal helices. The boost in performance was notable across three different fold classes: transmembrane, globular and coiled-coil structures. Furthermore, the increased effectiveness of these ensembles was coupled to a reduction in the time required by AMPLE to reach a solution. AMPLE users can now take full advantage of this new library of search models by activating the ‘helical ensembles’ mode.

An algorithm for modelling the background of X-ray diffraction images in the presence of ice rings is presented., An algorithm for modelling the background for each Bragg reflection in a series of X-ray diffraction images containing Debye–Scherrer diffraction from ice in the sample is presented. The method involves the use of a global background model which is generated from the complete X-ray diffraction data set. Fitting of this model to the background pixels is then performed for each reflection independently. The algorithm uses a static background model that does not vary over the course of the scan. The greatest improvement can be expected for data where ice rings are present throughout the data set and the local background shape at the size of a spot on the detector does not exhibit large time-dependent variation. However, the algorithm has been applied to data sets whose background showed large pixel variations (variance/mean > 2) and has been shown to improve the results of processing for these data sets. It is shown that the use of a simple flat-background model as in traditional integration programs causes systematic bias in the background determination at ice-ring resolutions, resulting in an overestimation of reflection intensities at the peaks of the ice rings and an underestimation of reflection intensities either side of the ice ring. The new global background-model algorithm presented here corrects for this bias, resulting in a noticeable improvement in R factors following refinement.

Let I be the Stanley–Reisner ideal of a simplicial complex Δ. In this short paper, we shall give a formula of vanishing of the local cohomology modules for S/I(r) in the case Δ is a union of disjoint matroids, where I(r) is the rth symbolic power of I. As an application, we will improve a previous result in Minh and Nakamura (Nagoya Math. J. 213, 127–140, 2014) for the k-Buchsbaumness of S/I(r).

In this short paper, we show that properties of an ideal I of a ring R are related to those of the homogeneous ideal I(+)IM of a ring R(+)M.

Let K be a field of characteristic 0 and consider exterior algebras of finite dimensional K-vector spaces. In this short paper we exhibit principal quadric ideals in a family whose Castelnuovo-Mumford regularity is unbounded. This negatively answers the analogue of Stillman's Question for exterior algebras posed by I. Peeva. We show that these examples are dual to modules over polynomial rings that yield counterexamples to a conjecture of J. Herzog on the Betti numbers in the linear strand of syzygy modules., 7 pages - Complete rewrite of previous draft with new section and shorter proofs

The purpose of this short paper is to give a structure theorem for certain Gorenstein ideals.

In the title compound, C26H26N2O2, the piperidine ring exhibits a chair conformation. The phenyl rings are attached to the central heterocycle in an equatorial position. The dihedral angle between the planes of the phenyl rings is 57.58 (8)°. In the crystal, C—H...O interactions connect the molecules into zigzag chains along [001].

In the title compound, C14H12ClN5, the dihydropyridine ring adopts a shallow boat conformation. The dihedral angle between the plane of this ring and that of the chlorobenzene ring is 69.15 (15)°. In the crystal, molecules are linked by N—H...N and N—H...Cl hydrogen bonds, generating (001) sheets.

In the title compound, C30H31N3O2S, the fused pyrrolidine ring bearing three substituents adopts an envelope conformation with the C atom bearing the benzoyl group as the flap. The other fused pyrrolidine ring adopts a twisted conformation about one of its C—C bonds. The dihedral angle between the isatin ring system and the methylthiazole ring is 25.95 (8)°. An intramolecular C—H...O interaction closes anS(8) ring. In the crystal, molecules are linked by C—H...O interactions, generatingC(11) chains propagating in [001].

In the title compound, C21H19NO2S2, the seven-membered thiazepine ring adopts a slightly distorted twist boat conformation. The dihedral angle between the benzene rings is 67.4 (2)°. The mean plane of the thiophene ring is twisted by 59.3 (2) and 87.7 (2)° from the mean planes of the benezene rings. In the crystal, inversion dimers linked by pairs of C—H...O hydrogen bonds generateR22(20) loops.

In the title compound C24H17BrN2O5S, the phenyl ring makes dihedral angles of 85.4 (2) and 8.8 (2)° with the indole ring system and the nitrobenzene ring, respectively, while the indole ring system and nitrobenzene ring make a dihedral angle of 80.1 (2)°. In the crystal, weak C—H...O interactions link the molecules, forming a two-dimensional network parallel to thebcplane.

In this short paper, our main result gives and internal characterization in A of when the smash products of graded rings have the ideal intersection property. This result generalizes S. Montgomery and D. Passman’s result on criteria for the smash products of graded rings to be prime or simple.

In the title compound, C14H13ClN2O5S, the chlorine-substituted tetrahydrofuran ring adopts a twist conformation and the other tetrahydrofuran ring an envelope conformation with the O atom as the flap. The pyrrolidine ring adopts a twist conformation. In the crystal, C—H...O hydrogen bonds link the molecules into zigzag chains running along the b-axis direction.

In the title compound, C22H16Br2O2, which has approximate non-crystallographic inversion symmetry, the dihedral angles between the central ring and the pendant rings are 89.1 (4) and 82.4 (3)°; the dihedral angle between the pendant rings is 12.1 (4)°. In the crystal, the packing is influenced by van der Waals forces and no aromatic π–π stacking is observed.

In the title compound, C29H32N2O2, the piperidine ring exists in a chair conformation (the bond-angle sum at the sp2-hybridized C atom is 359.79°). The phenyl rings and the methyl group substituted on the heterocyclic ring are in equatorial orientations. In the crystal, pairs of C—H...π interactions result in the formation of inversion dimers.

In the title compound, C39H36N2O4S, the piperidine ring adopts a twisted half-chair conformation. In the pyrrolo­thia­zole fused-ring system, the pyrrole ring adopts an envelope conformation (with the C atom bound to the thia­zole ring being the flap atom) and the thia­zole ring also exhibits an envelope conformation (with the N atom bound to the pyrrole ring as the flap). The mol­ecular structure features a weak intra­molecular C—H⋯O inter­action. In the crystal, a C—H⋯O inter­action forms a linear chain along the diagonal of the ac plane, generating a C(14) graph-set motif. A weak C—H⋯π inter­action also occurs.

In the title compound, C19H20N2O6, the pyrone and pyran rings adopt envelope conformations with the same common C atom as the flap, the dihedral angle between the planes of the remaining ring atoms being 68.27 (4)°. The planar atoms of the pyran ring and the diazacyclic ring are almost coplanar, the dihedral angle between their mean planes being 3.29 (7)°. Moreover, the planar atoms of the pyrone ring and benzene ring of the coumarin unit are also close to coplanar, the dihedral angle between their mean planes being 8.03 (9)°. The methoxy group lies in the plane of the benzene ring, with a dihedral angle between their mean planes of 9.4 (2)°. In the crystal, the molecules are linked by C—H...O hydrogen bonds resulting in sheets of molecules in theacplane.

In the title compound, C20H19NO5, the dihedral angle between the mean plane of the pyran ring (which has a half-chair conformation) and the benzene ring of the chromeno ring system is 7.21 (7)°. The dihedral angle between the mean plane of the chromeno ring system and the isoxazole ring is 21.78 (6)°, while the isoxazole ring forms a dihedral angle of 72.60 (8)° with the attached phenyl ring. In the crystal, molecules are linkedviapairs of C—H...O hydrogen bonds, forming inversion dimers with anR22(10) ring motif. These dimers are linkedviaC—H...N hydrogen bonds, forming chains along [001].

In the title compound, C17H11BrN2O2, the five-membered isoxazole ring has an envelope conformation with the C atom bearing the phenyl ring as the flap. The pyran ring has a half-chair conformation. In the chromeno ring system, the dihedral angle between the mean plane of the pyran ring and the benzene ring is 4.68 (2)°. The dihedral angle between the mean planes of the chromeno ring system and the isoxazole ring is 13.79 (15)°. The latter forms a dihedral angle of 34.10 (17)° with the phenyl ring. In the crystal, molecules are linked by C—H...N hydrogen bonds, forming an undulating two-dimensional network parallel to theabplane.

In the title compound, C24H26O5, the 2H-chromene ring system is essentially planar, with a maximum deviation of 0.029 (2) Å from the best-fit mean plane incorporating both rings. The dihedral angle between the 2H-chromene ring system and the benzene ring is 21.00 (1)°. In the crystal, pairs of C—H...O hydrogen bonds generate anR22(8) ring pattern. These contacts are bolstered by weaker bifurcated C—H...O hydrogen bonds.

In the title compound, C18H18N2O, the morpholine ring adopts a chair conformation with the exocyclic N—C bond in an equatorial orientation. The dihedral angles between the central benzene ring and the morpholine ring (all atoms) and the cyanobenzene ring are 87.87 (7) and 52.54 (7)°, respectively. No significant intermolecular interactions are observed in the crystal structure.

The crystal structure of 1-[Bis(4-fluorophenyl)methyl]piperazine has been detd. The dihedral angle between the benzene rings was 73.40(3)°. The piperazine ring was close to an ideal chair conformation and the N-H hydrogen was in an equatorial position. In the crystal, mols. were linked via weak C-H···F hydrogen bonds. [on SciFinder(R)]

In the title molecule, C19H18Cl2O4, the cyclohexane ring adopts a chair conformation. The furan ring is essentially planar and forms a dihedral angle of 82.1 (1)° with the benzene ring. In the crystal, weak C—H...O interactions are present.

In the title compound, C17H14O5S, the coumarin ring system is nearly planar, with a maximum deviation of 0.034 (2) Å from the mean plane. The dihedral angle between the benzene ring and the coumarin ring system is 56.11 (6)°. The crystal packing is stabilized by C—H...O hydrogen bonding, which forms a three-dimensional framework.

In the title compound, C30H20N2, the anthracene ring system is approximately planar [maximum deviation = 0.035 (2) Å] and is nearly perpendicular to the central pyridine ring, making a dihedral angle of 75.73 (7)°. The terminal pyridine ring and the phenyl ring are oriented at dihedral angles of 8.11 (10) and 13.22 (10)°, respectively, to the central pyridine ring.

In the title compound, C26H26N2O6S, the benzene ring is positioned axially to the thiazolopyrimidine ring and bisects it with a dihedral angle of 80.94 (7)°. The pyrimidine ring adopts a flattened boat conformation. In the crystal, pairs of bifurcated C—H...O hydrogen bonds link the molecules into chains along thecaxis.

The complete molecule of the title compound, C19H34N2S, is generated by crystallographic twofold symmetry, with the C=S group lying on the rotation axis. A short C—H...S contact occurs in the molecule. The five-membered ring is twisted and the cyclohexyl ring adopts a chair conformation. The dihedral angle between the mean plane of the five-membered ring and the basal plane of the cyclohexyl ring is 75.32 (13)°.