Poly(amidoamine) (PAMAM) dendrimer-based nanodevices are of recent interest in targeted cancer therapy. Characterization of mono- and multifunctional PAMAM-based nanodevices remains a great challenge because of their molecular complexity. In this work, various mono- and multifunctional nanodevices based on PAMAM G5 (generation 5) dendrimer were characterized by UV-Vis spectrometry, (1)H NMR, si...

Abstract This paper presents several properties and relations that satisfy the components of a bicomplex holomorphic function. It also exhibits analogies differences with case analytic functions.

Suppose that a circular fire spreads in the plane at unit speed. A single fire fighter can build a barrier at speed v > 1. How large must v be to ensure that the fire can be contained, and how should the fire fighter proceed? We contribute two results. First, we analyze the natural curve FFv that develops when the fighter keeps building, at speed v, a barrier along the boundary of the expanding...

A classical theorem of Hausdorff-Young shows that when 1 < p < 2, the system of equations rp(n) = cn (-oo < n < oo) admits a solution <p in Lq{~tt,<tt) whenever {c„} E /', Here, as usual, <p denotes the complex Fourier transform of <p and q is the conjugate exponent given by p~l + q~l = 1. The purpose of this note is to show that if a set {Xn} of real or complex numbers is "sufficiently close" ...

1. 〈x + z,y〉 = 〈x,y〉+ 〈z,y〉 2. 〈cx,y〉 = c〈x,y〉 3. 〈x,y〉 = 〈y,x〉, where the bar denotes complex conjugation. 4. 〈x,x〉 > 0 if x 6= 0 Note that if z is a complex number, then the statement “z ≥ 0” means that z is real and non-negative. Notice that if F = R, (3) is just 〈x,y〉 = 〈y,x〉. Definition. Let A ∈ Mm×n(F ). We define the conjugate transpose or adjoint of A to be the n ×m matrix A∗ such that ...

Let H = (hij) and G = (gij) be two m × n, m ≤ n, random matrices, each with i.i.d complex zero-mean unit-variance Gaussian entries, with correlation between any two elements given by E[hijg ⋆ pq ] = ρ δipδjq such that |ρ| < 1, where ⋆ denotes the complex conjugate and δij is the Kronecker delta. Assume {sk} m k=1 and {rl} m l=1 are unordered singular values of H and G, respectively, and s and r...

Let G be a real connected semisimple Lie group. For each v′, v, g ∈ G, we prove that lim m→∞ [a(vgv)] = s · b(g), where a(g) denotes the a-component in the Iwasawa decomposition of g = kan and b(g) ∈ A+ denotes the unique element that conjugate to the hyperbolic component in the complete multiplicative Jordan decomposition of g = ehu. The element s in the Weyl group of (G, A) is determined by y...