Differentiation of Integrals pdf

Exam questions and solutions in PDF

Differentiation of Integrals

Exam questions and solutions in LaTex

Applications of Partial Differentiation

Exercises and solutions for an applications of partial differentiation course. Diagrams for the questions are all together in the support.zip file, as .eps files

Partial Differentiation

Exercises and solutions about partial differentiation.

Geometric characterization of red blood cells. Differentiation of normal and pathologic samples

Introduction. Fractal geometry measures the irregularity of abstract and natural objects with the fractal dimension. Fractal calculations have been applied to the structures of the human body and to quantifications in physiology from the theory of dynamic systems.Material and Methods. The fractal dimensions were calculated, the number of occupation spaces in the space border of box counting and the area of two red blood cells groups, 7 normal ones, group A, and 7 abnormal, group B, coming from patient and of bags for transfusion, were calculated using the method of box counting and a software developed for such effect. The obtained measures were compared, looking for differences between normal and abnormal red blood cells, with the purpose of differentiating samples.Results. The abnormality characterizes by a number of squares of occupation of the fractal space greater or equal to 180; values of areas between 25.117 and 33.548 correspond to normality. In case that the evaluation according to the number of pictures is of normality, must be confirmed with the value of the area applied to adjacent red blood cells within the sample, that in case of having values by outside established and/or the greater or equal spaces to 180, they suggest abnormality of the sample.Conclusions. The developed methodology is effective to differentiate the red globules alterations and probably useful in the analysis of bags of transfusion for clinical use 

Veterinary differentiation : how veterinary education can adequately support the developing profession

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Biochemical differentiation between Ophidion Barbatum and o. Rochei (Pisces, Ophidiidae)

El gènere Ophidion esta representat al Mediterrani per dues espècies, 0. barbatum L. i O. rochei Müller. Són dues espècies molt similars en aspecte i difícils d'identificar només a partir dels seus caràcters morfològics externs. El treball descriu en primer lloc, i a partir de dades obtingudes per tècniques electroforètiques, alguns marcadors bioquímics que permeten diferenciar les dues espècies. En segon lloc, i a partir del càlcul de la 'Distància Genètica de Nei', es fa una estimació del temps de divergència entre O. barbatum i 0. rochei

Differentiation and coordination within a composite training policy providing efficient support namely to isolated museum professionals

In Portugal, namely in municipal museums, the reduced percentage of museum professionals that have a stable administrative position imposes a high degree of polyvalence allowing them to coordinate, often by themselves, the quotidian activities at the museum(s) they run.

Molecular genetic differentiation in earthworms inhabiting a heterogeneous Pb-polluted landscape

A Pb-mine site situated on acidic soil, but comprising of Ca-enriched islands around derelict buildings was used to study the spatial pattern of genetic diversity in Lumbricus rubellus. Two distinct genetic lineages ('A' and 'B'), differentiated at both the mitochondrial (mtDNA COII) and nuclear level (AFLPs) were revealed with a mean inter-lineage mtDNA sequence divergence of approximately 13%, indicative of a cryptic species complex. AFLP analysis indicates that lineage A individuals within one central 'ecological island' site are uniquely clustered, with little genetic overlap with lineage A individuals at the two peripheral sites. FTIR microspectroscopy of Pb-sequestering chloragocytes revealed different phosphate profiles in residents of adjacent acidic and calcareous islands. Bioinformatics found over-representation of Ca pathway genes in ESTPb libraries. Subsequent sequencing of a Ca-transport gene, SERCA, revealed mutations in the protein's cytosolic domain. We recommend the mandatory genotyping of all individuals prior to field-based ecotoxicological assays, particularly those using discriminating genomic technologies.

Differentiation status of limbal epithelial cells cultured on intact and denuded amniotic membrane before and after air-lifting

We have investigated differences in bovine limbal epithelial cell differentiation when expanded upon intact (amniotic epithelial cells and basement membrane remaining) and denuded human amniotic membrane, a commonly used substrate in ophthalmic surgery for corneal stem cell transplantation. Ex vivo expansion of the epithelial cells, in supplemented media, continued for 2 weeks followed by 1 week under ‘air-lifting’ conditions. Before and after air-lifting the differentiated (K3/K12 positive) and undifferentiated (K14 positive) cells were quantified by immunohistochemistry, Western blotting and quantitative PCR. Limbal epithelial cells expanded upon amniotic membrane formed 4-6 stratified layers, both on intact and denuded amniotic membrane. On denuded amniotic membrane the proportion of differentiated cells remained unaltered following airlifting. Within cells grown on intact amniotic membrane, however, the number of differentiated cells increased significantly following air-lifting. These results have important implications for both basic and clinical research. Firstly, they show that bovine limbal epithelia can be used as an alternative source of cells for basic research investigating ex vivo limbal stem cells expansion. Secondly, these findings serve as a warning to clinicians that the affect of amniotic membrane on transplantable cells is not fully understood; the use of intact or denuded amniotic membrane can produce different results in terms of the amount of differentiation, once cells are exposed to the air.