An efficient method to approximate eigenfunctions and high-index eigenvalues of regular Sturm–Liouville problems

2016 ◽  
Vol 279 ◽  
pp. 249-257
Author(s):  
M. Dehghan
Keyword(s):  
Efficient Method ◽  
High Index ◽  
Sturm Liouville

scholarly journals A miniaturized biotyping system for strain discrimination inEscherichia coli

1993 ◽  
Vol 111 (1) ◽  
pp. 81-88
Author(s):  
P. B. Crichton ◽  
J. M. J. Logan ◽  
D. C. Old
Keyword(s):  
Escherichia Coli ◽  
Efficient Method ◽  
High Index ◽  
Inescherichia Coli ◽  
E Coli

SummaryA two-tier miniaturized scheme of eight tests was devised for biotyping strains ofEscherichia coliin microwell plates. Primary biotypes were defined by positive and negative reactions in tests for fermentation of raffinose, sorbose, dulcitol and 2-deoxy-D-ribose and for decarboxylation of ornithine when read after specified periods of incubation; subtypes were identified within primary biotypes according to results in secondary tests for rhamnose fermentation, lysine decarboxylation and motility. The method gave reproducible results on different occasions of testing.Among 100E. colistrains from various sources, 26 of the 32 possible primary biotypes and 56 full biotypes, as defined by results in both primary and secondary tests, were identified, thus demonstrating a high index of strain discrimination (D = 0·98).The scheme is recommended as a simple, reliable, inexpensive and efficient method of differentiating strains ofE. coli.

scholarly journals Efficient computation of high index Sturm–Liouville eigenvalues for problems in physics

2009 ◽  
Vol 180 (2) ◽  
pp. 241-250 ◽  
Author(s):  
V. Ledoux ◽  
M. Van Daele ◽  
G. Vanden Berghe
Keyword(s):  
High Index ◽  
Efficient Computation ◽  
Sturm Liouville

scholarly journals Some notes on conformable fractional Sturm–Liouville problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wei-Chuan Wang
Keyword(s):  
Asymptotic Expansion ◽  
Eigenvalue Problem ◽  
Efficient Method ◽  
Sturm Liouville

AbstractThe conformable fractional eigenvalue problem $$\begin{aligned} -D_{x}^{\alpha }D_{x}^{\alpha }y+q(x)y=\lambda \rho (x)y \end{aligned}$$ − D x α D x α y + q ( x ) y = λ ρ ( x ) y is considered. We employ an easy and efficient method to derive its eigenvalue asymptotic expansion. On the basis of this result, we also investigate Ambarzumyan problems related to this eigenvalue problem as an application.

The usefulness of high index low symmetry zone axes for holz line analysis

1987 ◽  
Vol 45 ◽  
pp. 384-385
Author(s):  
C. M. Sung ◽  
D. B. Williams
Keyword(s):  
Lattice Parameter ◽  
High Order ◽  
Zone Axis ◽  
High Index ◽  
High Symmetry ◽  
Second Phases ◽  
Line Patterns ◽  
Low Symmetry ◽  
Line Analysis

Researchers have tended to use high symmetry zone axes (e.g. <111> <114>) for High Order Laue Zone (HOLZ) line analysis since Jones et al reported the origin of HOLZ lines and described some of their applications. But it is not always easy to find HOLZ lines from a specific high symmetry zone axis during microscope operation, especially from second phases on a scale of tens of nanometers. Therefore it would be very convenient if we can use HOLZ lines from low symmetry zone axes and simulate these patterns in order to measure lattice parameter changes through HOLZ line shifts. HOLZ patterns of high index low symmetry zone axes are shown in Fig. 1, which were obtained from pure Al at -186°C using a double tilt cooling holder. Their corresponding simulated HOLZ line patterns are shown along with ten other low symmetry orientations in Fig. 2. The simulations were based upon kinematical diffraction conditions.

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

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