The entropy of irreducible stochastic matrix measures its mixing properties. We show that this quantity is subadditive and strongly subadditive. 1Instytut Matematyki Uniwersytet Jagielloński Reymonta 4, 30-059 Kraków, Poland mail: [email protected] 1 1 Preliminaries Let N ∈ N. We denote the simplex of probability vectors (finite probability distributions) by ∆N = { p ∈ R : pi ≥ 0 for i = 1,...

Hyperspectral remote sensing has been used in many fields, such as agriculture, military detection and mineral exploration. Hyperspectral image (HSI), despite its high spectral resolution, has lower spatial resolution than panchromatic image (PI). Therefore, it is useful yet still challenging to effectively fuse HSI and PI to obtain images with both high spectral resolution and high spatial res...

He also defines, following Hardy, Littlewood and Polya [3] a partial ordering of w-dimensional real vectors: a<b if, and only if, there exists a d.s. matrix P such that a = Pb. In the above named article, the author investigates a conjecture of S. Kakutani to the effect that, if two d.s. matrices are such that Pi& <P3a for every real vector a, then Pi<P3. For this purpose he constructs a linear...

A new thermally conductive polyimide composite film has been developed. It is based on a dispersion of different particle sizes of boron nitride (BN) in a polyimide (PI) precursor, polyamic acid (PAA). Subsequently, thermal imidization of PAA at 350 degrees C produced the corresponding polyimide composites. 3-Mercaptopropionic acid was used as the surfactant to modify the BN surface for the dis...

We derive an exact, continuous-variable path integral (PI) representation of the canonical partition function for electronically nonadiabatic systems. Utilizing the Stock-Thoss (ST) mapping for an N-level system, matrix elements of the Boltzmann operator are expressed in Cartesian coordinates for both the nuclear and electronic degrees of freedom. The PI discretization presented here properly c...

The relationships between membranes and intramembrane compartments of isolated heart mitochondria are inadequately defined to express the induced morphological changes associated with the structural organization . The inner membrane and matrix are the major structural entities which undergo transformation upon alteration of metabolism or incubation conditions . To better express these morpholog...

Pathways for net biochemical reactions can be calculated by using a computer program that solves systems of linear equations. The coefficients in the linear equations are the stoichiometric numbers in the biochemical equations for the system. The solution of the system of linear equations is a vector of the stoichiometric numbers of the reactions in the pathway for the net reaction; this is ref...

Retroviruses acquire a lipid envelope during budding from the membrane of their hosts. Therefore, the composition of this envelope can provide important information about the budding process and its location. Here, we present mass spectrometry analysis of the lipid content of human immunodeficiency virus type 1 (HIV-1) and murine leukemia virus (MLV). The results of this comprehensive survey fo...

BACKGROUND/AIMS High phosphate (Pi) levels and extracellular matrix (ECM) accumulation are associated with chronic kidney disease progression. However, how high Pi levels contribute to ECM accumulation in mesangial cells is unknown. The present study investigated the role and mechanism of high Pi levels in ECM accumulation in immortalized human mesangial cells (iHMCs). METHODS iHMCs were expo...

Let G = (V G,EG) be a connected graph on n vertices, with diameter D, adjacency matrix A, and distance function ∂. Assume that A has d + 1 distinct eigenvalues λ0 > λ1 > · · · > λd with corresponding multiplicities m0 = 1, m1, . . ., md. From the spectrum of G we then define an inner product 〈·, ·〉4 on the vector space Rd[x] of real polynomials of degree at most d. It is well-known that Rd[x] h...