Related Experiment Video
Updated: Feb 19, 2026
07:19
Preparation of Extracellular Matrix Protein Fibers for Brillouin Spectroscopy
Published on: September 15, 2016
11.0K
Some new sharp bounds for the spectral radius of a nonnegative matrix and its application
Jun He1, Yan-Min Liu1, Jun-Kang Tian1
1School of Mathematics, Zunyi Normal College, Zunyi, Guizhou 563006 P.R. China.
Journal of Inequalities and Applications
|November 7, 2017
Abstract:
In this paper, we give some new sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix. Using these bounds, we obtain some new and improved bounds for the signless Laplacian spectral radius of a graph or a digraph.
Related Concept Videos
01:29Application of Nonlinear Inequalities
268
A nonlinear inequality describes a comparison involving an expression that curves or behaves more complexly than a straight line. These inequalities often appear in forms that include squares, products, or variables in the denominator.To solve such an inequality, one starts by rewriting it so that zero appears on one side. For example, the inequality: can be factored as: This form makes it easier to identify the values that cause the expression to equal zero. In this case, the...
268
01:19Routh-Hurwitz Criterion II
1.1K
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
1.1K
01:12Radius of Gyration of an Area
2.8K
The second moment of area, also known as the moment of inertia of area, is a crucial factor in understanding an object's resistance against bending deformation, or stiffness. To accurately estimate the second moment of area along any axis, one needs to concentrate all areas associated with that object into a thin strip, which should be placed parallel to that particular axis.
2.8K
01:25Applications Of NMR In Biology
4.6K
Nuclear magnetic resonance (NMR) spectroscopy is a very valuable analytical technique for researchers. It has been used for more than 50 years as an analytical tool. F. Bloch and E. Purcell formulated NMR in 1946 and won the 1952 Nobel Prize in Physics for their work. Biological macromolecules such as proteins, nucleic acids, lipids, and organic molecules including pharmaceutical compounds, can be studied using this versatile tool that exploits the magnetic properties of certain nuclei.
4.6K
00:57Root Mean Square
3.9K
If in an experiment, data values have a probability of being both positive and negative, neither the arithmetic mean, the geometric mean, nor the harmonic mean can be used to calculate the central tendency of the data set. In particular, if the positive and negative values are equally likely, the arithmetic mean is close to zero.
For example, consider the velocity of gas molecules in a container. The gas molecules are moving in different directions, which might impart positive and negative...
For example, consider the velocity of gas molecules in a container. The gas molecules are moving in different directions, which might impart positive and negative...
3.9K
01:15Routh-Hurwitz Criterion I
617
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
617