This work gives a detailed account of the orthogonal projection method in the theory of two- and three-body scattering, which is based on the employment of orthogonal projecting pseudopotentials. The method is applied to a number of physical problems, of which the following the most important: ...
We study the Mie-like scattering from an open subwavelength resonator made of a high-index dielectric material, when its parameters are tuned to the regime of interfering resonances. We uncover a novel mechanism of superscattering, closely linked to stro
For the sake of convenience, we assume that H is a Hamiltonian matrix of a certain quantum system. This assumption is just for convenience, does not alter our conclusion. Assuming orthogonal complete basis being |ei > , where the subscript i refers the i-th basis, the projection of |ei ...
Answer to: Find the projection of u onto v. Then write u as the sum of two orthogonal vectors, one of which is proj_\text{v}u. u = (5, 6), v = (10,...
Linear elasticity is one of the more successful theories of mathematical physics. Its pragmatic success in describing the small deformations of many materials is uncontested. The origins of the three-dimensional theory go back to the beginning of the 19t
Let V be a subspace of R n . To find the matrix of the orthogonal projection onto V , the way we first discussed, takes three steps: (1) Find a basis v 1 , v 2 , . . . , v m for V . (2) Turn the basis v i into an orthonormal basis u i , using the Gram-Schmi...
for the projection operators on the sectors with spins 0 and 1. Finally, it was shown that the DKP-algebra admits supersymmetric generalization [16]. Further, the Duffin–Kemmer–Petiau algebra is closely related to an entirely different branch of theoretical physics, namely, the theory of para...
Recognition of objects from sensory stimuli is essential for survival. To that end, sensory networks in the brain must form object representations invariant to stimulus changes, such as size, orientation and context. Although Hebbian plasticity is known
The cranial vault in humans is highly variable, clinically relevant, and heritable, yet its genetic architecture remains poorly understood. Here, we conduct a joint multi-ancestry and admixed multivariate genome-wide association study on 3D cranial vault
The planes x = 2 and y = 3 in Figure 12.3 intersect in a line parallel to the z-axis. This line is described by the pair of equations x = 2, y = 3. A point (x , y , z) lies on the line if and only if x = 2 and y = 3. Similarly, the line of intersection of the...