Darboux curves in three dimensional Heisenberg group

In this paper, a new characterization for darboux curves in Heis₃ is completely given. Then, a new classification for translation surface , which is generated by darboux curve in Heis₃ is obtained.

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A Research on the Morphology and Composition of Flocs (Part 1: Floc Breaage Disregarded)

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.726-731.1566 ◽

2013 ◽

Vol 726-731 ◽

pp. 1566-1572 ◽

Cited By ~ 1

Author(s):

Shi Qiang Ding ◽

Qing Na Li ◽

Xin Rong Pang ◽

Ji Run Xu

Keyword(s):

Dimensional Space ◽

Three Dimensional ◽

New Classification ◽

Suspension Viscosity ◽

Primary Particles ◽

Long Time ◽

Relationship Of ◽

The Relationship ◽

Three Dimensional Space ◽

Floc Breakage

The characteristics of flocs aggregated in flocculation have been paid more and more attention for a long time. In this paper, a new classification and analyses method dealing with the flocs is developed. The flocs formed after flocculation is divided into four kinds, including the left primary particles, linear flocs with all component particles in a line, planar flocs with all component particles on a plane and volumetric flocs with all component particles in a three-dimensional space. By analyzing the formation approaches of different kind of flocs regardless of the floc breakage, the number of every kind of floc is analyzed to be related with the suspension concentration mathematically. After comparing the different items in the models describing the relationship of floc number and concentration, a series of simplified expressions are presented. Lastly, a mathematical equation relating the measurable suspension viscosity with the numbers of different flocs is obtained.

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Microbial Dextran-Hydrolyzing Enzymes: Fundamentals and Applications

Microbiology and Molecular Biology Reviews ◽

10.1128/mmbr.69.2.306-325.2005 ◽

2005 ◽

Vol 69 (2) ◽

pp. 306-325 ◽

Cited By ~ 128

Author(s):

Elvira Khalikova ◽

Petri Susi ◽

Timo Korpela

Keyword(s):

Sequence Data ◽

Three Dimensional ◽

Side Reaction ◽

Sequence Information ◽

New Classification ◽

Wide Range ◽

Hydrolyzing Enzymes ◽

Complex Polymer ◽

Sequence Similarities ◽

Primary Sequence Data

SUMMARY Dextran is a chemically and physically complex polymer, breakdown of which is carried out by a variety of endo- and exodextranases. Enzymes in many groups can be classified as dextranases according to function: such enzymes include dextranhydrolases, glucodextranases, exoisomaltohydrolases, exoisomaltotriohydrases, and branched-dextran exo-1,2-α-glucosidases. Cycloisomalto-oligosaccharide glucanotransferase does not formally belong to the dextranases even though its side reaction produces hydrolyzed dextrans. A new classification system for glycosylhydrolases and glycosyltransferases, which is based on amino acid sequence similarities, divides the dextranases into five families. However, this classification is still incomplete since sequence information is missing for many of the enzymes that have been biochemically characterized as dextranases. Dextran-degrading enzymes have been isolated from a wide range of microorganisms. The major characteristics of these enzymes, the methods for analyzing their activities and biological roles, analysis of primary sequence data, and three-dimensional structures of dextranases have been dealt with in this review. Dextranases are promising for future use in various scientific and biotechnological applications.

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A Functional Classification Framework for the Conceptual Design of Layered Manufacturing Technologies

Volume 5: 13th Design for Manufacturability and the Lifecycle Conference; 5th Symposium on International Design and Design Education; 10th International Conference on Advanced Vehicle and Tire Technologies ◽

10.1115/detc2008-49353 ◽

2008 ◽

Author(s):

Christopher B. Williams ◽

Farrokh Mistree ◽

David W. Rosen

Keyword(s):

Conceptual Design ◽

Three Dimensional ◽

Layered Manufacturing ◽

Functional Classification ◽

New Classification ◽

Metal Artifacts ◽

Three Dimensional Printing ◽

Classification Framework ◽

Manufacturing Technologies ◽

Dimensional Printing

There exist many different layered manufacturing technologies for the realization of prototypes and fully-functional artifacts. Although extremely different in solution principle and embodiment, there exists functional commonality between each technology. This commonality affords the authors an opportunity to propose a new classification framework for layered manufacturing technologies. In addition to using it as a means of classifying existing processes, the authors present the framework as a tool to aid a designer in the conceptual design of new layered manufacturing technologies. The authors close the paper with an example of such an implementation; specifically, the conceptual design of a novel means of obtaining metal artifacts from three-dimensional printing.

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Einstein–Weyl geometry, dispersionless Hirota equation and Veronese webs

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004114000164 ◽

2014 ◽

Vol 157 (1) ◽

pp. 139-150 ◽

Cited By ~ 22

Author(s):

MACIEJ DUNAJSKI ◽

WOJCIECH KRYŃSKI

Keyword(s):

Heisenberg Group ◽

Twistor Space ◽

Three Dimensional ◽

Poisson Structures ◽

Weyl Geometry ◽

Hirota Equation ◽

Five Dimensions ◽

Dispersionless Hirota Equation

AbstractWe exploit the correspondence between the three–dimensional Lorentzian Einstein–Weyl geometries of the hyper–CR type and the Veronese webs to show that the former structures are locally given in terms of solutions to the dispersionless Hirota equation. We also demonstrate how to construct hyper–CR Einstein–Weyl structures by Kodaira deformations of the flat twistor space$T\mathbb{CP}^1$, and how to recover the pencil of Poisson structures in five dimensions illustrating the method by an example of the Veronese web on the Heisenberg group.

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