Displaying similar documents to “A new approach to fracture mechanics.”

Static-kinematic duality in beams, plates, shells and its central role in the finite element method

Alberto Carpinteri (2017)

Curved and Layered Structures

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Static and kinematic matrix operator equations are revisited for one-, two-, and three-dimensional deformable bodies. In particular, the elastic problem is formulated in the details in the case of arches, cylinders, circular plates, thin domes, and, through an induction process, shells of revolution. It is emphasized how the static and kinematic matrix operators are one the adjoint of the other, and then demonstrated through the definition of stiffness matrix and the application of virtual...

The problem of kings.

Larsen, Michael (1995)

The Electronic Journal of Combinatorics [electronic only]

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Sufficient conditions to be exceptional

Charles R. Johnson, Robert B. Reams (2016)

Special Matrices

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A copositive matrix A is said to be exceptional if it is not the sum of a positive semidefinite matrix and a nonnegative matrix. We show that with certain assumptions on A−1, especially on the diagonal entries, we can guarantee that a copositive matrix A is exceptional. We also show that the only 5-by-5 exceptional matrix with a hollow nonnegative inverse is the Horn matrix (up to positive diagonal congruence and permutation similarity).

A note on the matrix Haffian.

Heinz Neudecker (2000)

Qüestiió

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This note contains a transparent presentation of the matrix Haffian. A basic theorem links this matrix and the differential ofthe matrix function under investigation, viz ∇F(X) and dF(X). Frequent use is being made of matrix derivatives as developed by Magnus and Neudecker.

On a nonnegative irreducible matrix that is similar to a positive matrix

Raphael Loewy (2012)

Open Mathematics

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Let A be an n×n irreducible nonnegative (elementwise) matrix. Borobia and Moro raised the following question: Suppose that every diagonal of A contains a positive entry. Is A similar to a positive matrix? We give an affirmative answer in the case n = 4.