An accurate spline polynomial cubature formula for double integration with logarithmic singularity

The paper studied the integration of logarithmic singularity problem J(ӯ) = ∫∫Δζ(ӯ)log|ӯ - ӯ 0∗|dA, where ӯ=(α,β), y0=(α0,β0) the domain Δ is rectangle Δ = [r1, r2] × [r3, r4], the arbitrary point ӯ ϵ Δ and the fixed point ӯ0 ϵ Δ. The given density function ζ(ӯ), is smooth on the rectangular domain Δ and is in the functions class C2,τ (Δ). Cubature formula (CF) for double integration with logarithmic singularities (LS) on a rectangle Δ is constructed by applying type (0, 2) modified spline function DΓ(P). The results obtained by testing the density functions ζ(ӯ) as linear and absolute value functions shows that the constructed CF is highly accurate

cDNA microarrays - providing insight into organism/chemotherapeutic interactions

The messenger ribonucleic acid (mRNA) complement of a cell or organism is affected by its environment. The cell dictates its mRNA transcript quantities by regulating the rates of their transcription from genes. By examining changes in the number of mRNA transcripts that arise in response to chemotherapeutic exposure, it is possible to gain insight into how biological systems respond to external stimuli

Investigating the biological significance of metallointercalators with cDNA microarrays

The double helix coded sequence of nucleotide bases with its protective sugar phosphate backbone forms deoxyribonucleic acid (DNA) which is the genetic blueprint of all living things. All the information required for the development, operation and maintenance of cells is contained in a sequence of adenine (A), thymine (T), cytosine (C) and guanine (G) bases, where adenine is paired with thymine and cytosine is paired with guanine [1]. The DNA sequence is made usable by transcription of the nucleotide sequence into single stranded messenger RNA (mRNA). This means that the four member nucleic acid base code sequence is converted into a 22 member amino acid code [2]

The sea urchin egg and cortical vesicles as model systems to dissect the fast, Ca2+-triggered steps of regulated exocytosis

Exocytosis is a fundamental process utilized by all eukaryotic organisms; this elegantly efficient process mediates such diverse functions as fertilization, synaptic transmission, and wound healing. Membrane fusion, the defining step of this process, has been well conserved through evolution. However, the mechanisms defining the priming, docking, and merger of two apposed native bilayer membranes have not been fully elucidated. Sea urchin cortical vesicles are locked at a stage just prior to Ca2+-triggered membrane fusion and are thus an ideal system for fully defining the mechanisms underlying this process. Here we describe detailed methods to isolate these native secretory vesicles, monitor the fusion process, assess the minimal essential biochemical components, and identify their ultrastructural interactions that define the triggered exocytotic pathway