In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...

As a global feature of fingerprints, singular point plays important roles in fingerprint model, synthesis fingerprint, fingerprint classification, fingerprint alignment and so on. In our previous work, a rapid and effective fingerprint singular points detection method was proposed. That method detects singular points based on partitioning the orientation field into a serious non-overlapping hom...

An advanced current measure probe is described for biological applications. Singular points on the body skin emit a semi-constant current that could be potentially useful for a medical diagnosis of the body organs to which any singular point is connected. In order to achieve an accurate and reliable analysis of the emitted current, all the error sources have been studied in order to design a re...

• Introduction 1. Example: rotationally symmetric eigenfunctions on R 2. Example: translation-equivariant eigenfunctions on H 3. Beginning of construction of solutions 4. K(x, t) is bounded 5. End of construction of solutions 6. Asymptotics of solutions 7. Appendix: asymptotic expansions • Bibliography According to [Erdélyi 1956], Thomé [1] found that differential equations with finite rank irr...

ly isomorphic to (C×)r−1 × (C), and hence also to (S1)r−1 × (R), where r = |J | is the number of branches and k = δ(C)− r+1 = 1 2 (μ(C) + 1 − r). The construction of the Jacobian variety J(C̃) of the non-singular curve C̃ in the large is standard in algebraic geometry. There is also a notion of Jacobian of a singular curve C , defined e.g. in [85], which, like the other, is an abelian group. Ther...