Unlinking singular loci from regular fibers and its application to submersions

To the basic assumptions that the map [Formula: see text] is a proper, flat morphism between complex manifolds should be added the hypothesis that the fibres of π are all generically reduced complex spaces. The existence of a non-empty open neighbourhood in [Formula: see text] plays an essential role in the proof of the main theorem, and does not follow automatically from the hypotheses as they were originally stated.

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SINGULAR LOCI IN HOLOMORPHIC FAMILIES

International Journal of Mathematics ◽

10.1142/s0129167x98000129 ◽

1998 ◽

Vol 09 (03) ◽

pp. 277-293

Author(s):

ADAM HARRIS

Keyword(s):

Vector Bundles ◽

A Priori ◽

Complex Structure ◽

Compact Complex Manifold ◽

Entire Family ◽

Analytic Subset ◽

Degeneracy Loci ◽

Singular Spaces ◽

Singular Loci ◽

Complex Projective

Let [Formula: see text] be a proper flat morphism between manifolds, and [Formula: see text] an analytic subset, such that the fibres Xt, for all [Formula: see text], determine a locally trivial deformation of a compact complex manifold. Non-generic fibres Xt, for t ∈ A, may be taken a priori to be singular spaces, or to have a smooth complex structure which is biholomorphically distinct from their generic neighbours. The main theorem of this article provides a sufficient condition for local triviality of the entire family [Formula: see text], in terms of the dimension of A and of the singular subvarieties of certain "degeneracy loci" in [Formula: see text]. Several specific applications of the main theorem are subsequently examined, some of which correspond sharply with examples of "structure-jumping" in complex deformations and "jumping loci" of vector bundles on complex projective space.

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Singular loci of Bruhat–Hibi toric varieties

Journal of Algebra ◽

10.1016/j.jalgebra.2007.10.033 ◽

2008 ◽

Vol 319 (11) ◽

pp. 4759-4779 ◽

Cited By ~ 2

Author(s):

J. Brown ◽

V. Lakshmibai

Keyword(s):

Toric Varieties ◽

Singular Loci

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Power law fluid flow through a bundle of regular fibers

Applied Mathematical Modelling ◽

10.1016/j.apm.2015.01.067 ◽

2015 ◽

Vol 39 (21) ◽

pp. 6425-6437 ◽

Cited By ~ 2

Author(s):

J.A. Kolodziej ◽

M. Mierzwiczak ◽

M. Ciałkowski

Keyword(s):

Fluid Flow ◽

Power Law ◽

Power Law Fluid ◽

Flow Through ◽

Regular Fibers

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Singular loci of Schubert varieties for classical groups

Bulletin of the American Mathematical Society ◽

10.1090/s0273-0979-1987-15466-8 ◽

1987 ◽

Vol 16 (1) ◽

pp. 83-91 ◽

Cited By ~ 12

Author(s):

V. Lakshmibai

Keyword(s):

Schubert Varieties ◽

Classical Groups ◽

Singular Loci

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Singularity properties of null killing magnetic curves in Minkowski 3-space

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887820501418 ◽

2020 ◽

Vol 17 (09) ◽

pp. 2050141 ◽

Cited By ~ 1

Author(s):

Jianguo Sun

Keyword(s):

Vector Field ◽

Magnetic Vector ◽

Geometrical Properties ◽

Singular Loci ◽

Magnetic Curve

We reconstruct the Cartan Equations of null Killing magnetic curve [Formula: see text] in [Formula: see text] with Killing magnetic vector field [Formula: see text] under the new Cartan frame [Formula: see text], which describe some new geometrical properties of [Formula: see text]. The singularity properties of the rectifying surfaces and the binormal osculating surfaces of null Killing magnetic curves are given. As an application, two examples are given to explain the main results, where the singular loci of null Killing magnetic curves are obtained.

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Improving the adsorption performance and surface roughening of rayon fibers via enzymatic treatment with cellulase

Textile Research Journal ◽

10.1177/0040517520932394 ◽

2020 ◽

pp. 004051752093239

Author(s):

Tetsuya Takahashi ◽

Makoto Hayashi ◽

Yudai Watanabe ◽

Hiroyuki Sadatomi ◽

Kentaro Matsumoto ◽

...

Keyword(s):

Air Pollutants ◽

Dye Adsorption ◽

Wet Spinning ◽

Surface Roughening ◽

Ammonia Gas ◽

Volatile Organic ◽

Cellulase Treatment ◽

Blue Solution ◽

Regular Fibers ◽

Very High

In recent years, expectations have increased for the development of filters for removing air pollutants. Rayon fibers have rough surfaces and excellent adsorption characteristics. Therefore, rayon is a promising material for such filters. By further roughening its surface, its adsorptivity to substances such as volatile organic compounds can likely be improved. The surface of rayon fibers was roughened via wet spinning carried out by adding oleic acid to a raw viscose. As a result, porous fibers containing several pores with a diameter of about 0.5–1.0 µm were obtained. A weight reduction treatment of the porous rayon fibers with cellulase, a cellulose-degrading enzyme, resulted in the appearance of several streaks and asperities on their surfaces. To investigate the adsorption behavior of the rayon fibers after cellulase treatment, dye adsorption was examined using an aqueous methylene blue solution. The porous rayon fibers adsorbed much more dye than the regular fibers. In addition, the fibers absorbed more dye after treatment with cellulase than without treatment in both fibers. The deodorizing function of the rayon fibers was also investigated using ammonia gas. The porous rayon fibers treated with cellulase had a very high deodorizing effect. In the proposed study, rayon fibers (which are porous inside) were treated with cellulase, and their surface was found to be considerably rough.

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