scholarly journals A new method for lattice reduction using directional and hyperplanar shearing

2022 ◽  
Vol 78 (1) ◽  
Author(s):  
Cyril Cayron
Keyword(s):  
Geometric Method ◽  
New Method ◽  
Lattice Reduction ◽  
Metric Tensor ◽  
Lll Algorithm ◽  
Unit Cells ◽  
The Absolute

A geometric method of lattice reduction based on cycles of directional and hyperplanar shears is presented. The deviation from cubicity at each step of the reduction is evaluated by a parameter called `basis rhombicity' which is the sum of the absolute values of the elements of the metric tensor associated with the basis. The levels of reduction are quite similar to those obtained with the Lenstra–Lenstra–Lovász (LLL) algorithm, at least up to the moderate dimensions that have been tested (lower than 20). The method can be used to reduce unit cells attached to given hyperplanes.

scholarly journals Lattice reduction in two dimensions: analyses under realistic probabilistic models

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Brigitte Vallée ◽  
Antonio Vera
Keyword(s):  
Dynamical Systems ◽  
Probabilistic Models ◽  
Two Dimensions ◽  
Lattice Reduction ◽  
Lll Algorithm ◽  
Transfer Operators ◽  
International Audience ◽  
Dimension 2

International audience The Gaussian algorithm for lattice reduction in dimension 2 is precisely analysed under a class of realistic probabilistic models, which are of interest when applying the Gauss algorithm "inside'' the LLL algorithm. The proofs deal with the underlying dynamical systems and transfer operators. All the main parameters are studied: execution parameters which describe the behaviour of the algorithm itself as well as output parameters, which describe the geometry of reduced bases.

A new method for the absolute counting of 239Np

1958 ◽  
Vol 7 (4) ◽  
pp. 339-342 ◽  
Author(s):  
F.H. Cripps ◽  
J.W. Weale
Keyword(s):  
New Method ◽  
The Absolute

scholarly journals The behaviour of trypsin towards α-N-methyl-α-N-toluene-p-sulphonyl-l-lysine β-naphthyl ester. A new method for determining the absolute molarity of solutions of trypsin

1968 ◽  
Vol 107 (1) ◽  
pp. 97-102 ◽  
Author(s):  
D. T. Elmore ◽  
J. J. Smyth
Keyword(s):  
Methyl Ester ◽  
Convenient Method ◽  
Substrate Concentration ◽  
Competitive Inhibitor ◽  
New Method ◽  
Spectrophotometric Measurement ◽  
Bovine Thrombin ◽  
The Absolute ◽  
Hydrolysis Of

1. α-N-Methyl-α-N-toluene-p-sulphonyl-l-lysine β-naphthyl ester (MTLNE) was synthesized as its hydrobromide and shown to be slowly hydrolysed by bovine pancreatic trypsin. The acylation step, however, is so much faster than deacylation of the acyl-enzyme that spectrophotometric measurement of the ‘burst’ of β-naphthol provides a convenient method for determining the absolute molarity of trypsin solutions. 2. By using the same stock solution of trypsin, application of this method at pH4·0 and pH7·0 as well as that of Bender et al. (1966) at pH3·7 gave concordant results. 3. Provided that [S]0>[E]0, the size of the ‘burst’ is independent of substrate concentration. 4. In the trypsin-catalysed hydrolysis of α-N-toluene-p-sulphonyl-l-arginine methyl ester, MTLNE functions as a powerful non-competitive inhibitor. 5. There is no detectable reaction between MTLNE and either bovine pancreatic α-chymotrypsin at pH4·0 or bovine thrombin at pH6·0.

Stresses Analysis on Coarse Grain Zn Film during Tensile Loading

2006 ◽  
Vol 524-525 ◽  
pp. 723-728
Author(s):  
Wen Jun Huang ◽  
Vincent Ji ◽  
Wilfrid Seiler
Keyword(s):  
Steel Substrate ◽  
Strain Tensor ◽  
Tensile Loading ◽  
New Method ◽  
Coarse Grain ◽  
Initial State ◽  
Metric Tensor ◽  
Coarse Grains ◽  
Deformed State ◽  
Galvanized Coating

The advance of the XRD technique allows us to reach the properties of each coarse grain. This paper has demonstrated a new method to determine stress in a single crystal for multicrystal material and this new method could be specially applied for any symmetric crystalline systems. The strain tensor ε is determined by the change of the metric tensor G before the initial state and after the deformed state in the crystal reference system. Then stress tensor at grain scale is calculated by the Hooks law. The stress evaluations are carried out in coarse grains of a thin galvanized coating on a steel substrate during tensile loading. This study allows us to link the microstructure evolution to the elastic heterogeneity at grain scale or between the grains.

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