Some new matrix versions of Kantorovich-Type inequalities for Hermitian matrix are proposed in this paper. We consider what happens to these inequalities when the positive definite matrix is allowed to be positive semidefinite singular or indefinite.

The problem addressed in this paper is both the detection and localization of a point reflector embedded in a medium by sensor array imaging when the array response matrix is measured in a noisy environment. We construct a detection test based on reverse-migration of the array response matrix that is the most powerful for a given false alarm rate and prove that it is more efficient than the one...

We introduce and study the partial singular braid monoid PSBn, a monoid that contains both the inverse braid monoid IBn and the singular braid monoid SBn. Our main results include a characterization of Green’s relations, a presentation in terms of generators and relations, and a proof that PSBn embeds in the semigroup algebra C[IBn].

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This paper investigates how changing the growth rate of the sequence of penalty weights affects the asymptotics of Lasso-type estimators. The cases of non-singular and nearly singular design are considered.

Multiplicative backward stability results are presented for two algorithms which compute the singular value decomposition of dense matrices. These algorithms are the classical onesided Jacobi algorithm, with a stringent stopping criterion, and an algorithm which uses one-sided Jacobi to compute high accurate singular value decompositions of matrices given as rank-revealing factorizations. When ...

In [5], Colding-Ilmanen-Minicozzi-White showed that within the class of closed smooth self-shrinkers in R, the entropy is uniquely minimized at the round sphere. They conjectured that, for 2 ≤ n ≤ 6, the round sphere minimizes the entropy among all closed smooth hypersurfaces. Using an appropriate weak mean curvature flow, we prove their conjecture. For these dimensions, our approach also gives...

The main result is a computation of the Nahm transform of a SU(2)-instanton over R× T , called spatially-periodic instanton. It is a singular monopole over T , a solution to the Bogomolny equation, whose rank is computed and behavior at the singular points is described.

In this paper we provide concrete constructions of idempotents to represent typical singular matrices over a given ring as a product of idempotents and apply these factorizations for proving our main results. We generalize works due to Laffey ([12]) and Rao ([3]) to noncommutative setting and fill in the gaps in the original proof of Rao’s main theorems (cf. [3], Theorems 5 and 7 and [4]). We a...

Computer technology these days is most focused on storage space and speed. Considerable advancements in this direction can be achieved through the usage of digital image compression techniques. In this paper we present a well studied singular value decomposition based JPEG image compression technique. Singular Value Decomposition is a way of factorizing matrices into a series of linear approxim...