This note gives converses to the well-known result: for any vector e u such that sin (u; e u) = O(), we have e u Ae u e u e u = + O(2) where is an eigenvalue and u is the corresponding eigenvector of a Her-mitian matrix A, and \ " denotes complex conjugate transpose. It shows that if e u Ae u=e u e u is close to A's largest eigenvalue, then e u is close to the corresponding eigenvector with an ...

the generalization of p-frame in banach spaces is considered in this paper. the concepts of an $tilde{x}$-frame and a system conjugate to $tilde{x}$-frame were introduced. analogues of the results on the existence of conjugate system were obtained. the stability of $tilde{x}$-frame having a conjugate system is studied.

Complex-conjugate-resolved Fourier-domain optical coherence tomography, where the quadrature components of the interferogram are obtained by simultaneous acquisition of the first and second harmonics of the phase-modulated interferogram, is applied to multisurface test targets and biological samples. The method provides efficient suppression of the complex-conjugate, dc, and autocorrelation art...

Concepts of the inner product and conjugate of matrix of complex numbers are defined here. Operations such as addition, subtraction, scalar multiplication and inner product are introduced using correspondent definitions of the conjugate of a matrix of a complex field. Many equations for such operations consist like a case of the conjugate of matrix of a field and some operations on the set of s...

Let G be a simple graph of order n and let V (G) be its vertex set. Let c = a + b √ m and c = a − b√m, where a and b are two nonzero integers and m is a positive integer such that m is not a perfect square. We say that A = [cij ] is the conjugate adjacency matrix of the graph G if cij = c for any two adjacent vertices i and j, cij = c for any two nonadjacent vertices i and j, and cij = 0 if i =...

This paper provides the duality structure of the optimal two-block H∞ problem. The dual description leads naturally to a numerical solution based on convex programming for LTI (including infinite dimensional) systems. Alignment conditions are obtained and show that the optimal solution is flat in general, and unique in the SISO case. It is also proved that under specific conditions a wellknown ...

The first edition of these notes was written by Professor Dyson. The second edition was prepared by Michael J. Moravcsik; he is responsible for the changes made in the process of re-editing. A * : complex conjugate transposed (Hermitian conjugate) A + : complex conjugate (not transposed) A : A * β = A * γ 4 = adjoint A −1 = inverse A T = transposed I = identity matrix or operator i

miRNAs as one of the potential therapeutic agents have been recently considered for cancer treatment. AS1411 (aptNCL) is a DNA aptamer specifically binding to nucleolin protein on the cancer cell surface with antiproliferative effect. The aim of the study was to develop a conjugate consisted of aptNCL (as targeted delivery of therapeutic agent) and miRNA let-7d (as a tumor suppressor) using two...

Curcumin is the natural bio-active component of turmeric (Curcuma longa L.) with known therapeutic properties; nevertheless, its biological applications are limited due to its poor bioavailability. To overcome this limitation, curcumin was conjugated with silica nanoparticles. Curcumin was separated from turmeric by microwave-assisted extraction and silica nanoparticles were developed from rice...