A generalised cole-hopf transformation for nonlinear parabolic and hyperbolic equations

The Cole-Hopf transformation has been generalized to generate a large class of nonlinear parabolic and hyperbolic equations which are exactly linearizable. These include model equations of exchange processes and turbulence. The methods to solve the corresponding linear equations have also been indicated.La transformation de Cole et de Hopf a été généralisée en vue d'engendrer une classe d'équations nonlinéaires paraboliques et hyperboliques qui peuvent être rendues linéaires de façon exacte. Elles comprennent des équations modèles de procédés d'échange et de turbulence. Les méthodes pour résoudre les équations linéaires correspondantes ont également été indiquées.

Genome-wide expression profiling identifies deregulated miRNAs in malignant astrocytoma

Malignant astrocytoma includes anaplastic astrocytoma (grade III) and glioblastoma (grade IV). Among them, glioblastoma is the most common primary brain tumor with dismal responses to all therapeutic modalities. We performed a large-scale, genome-wide microRNA (miRNA) (n=756) expression profiling of 26 glioblastoma, 13 anaplastic astrocytoma and 7 normal brain samples with an aim to find deregulated miRNA in malignant astrocytoma. We identified several differentially regulated miRNAs between these groups, which could differentiate glioma grades and normal brain as recognized by PCA. More importantly, we identified a most discriminatory 23-miRNA expression signature, by using PAM, which precisely distinguished glioblastoma from anaplastic astrocytoma with an accuracy of 95%. The differential expression pattern of nine miRNAs was further validated by real-time RT-PCR on an independent set of malignant astrocytomas (n-72) and normal samples (n=7). Inhibition of two glioblastoma-upregulated miRNAs (miR-21 and miR-23a) and exogenous overexpression of two glioblastoma-downregulated miRNAs (miR-218 and miR-219-5p) resulted in reduced soft agar colony formation but showed varying effects on cell proliferation and chemosensitivity. Thus we have identified the miRNA expression signature for malignant astrocytoma, in particular glioblastoma, and showed the miRNA involvement and their importance in astrocytoma development. Modern Pathology (2010) 23, 1404-1417; doi:10.1038/modpathol.2010.135; published online 13 August 2010

Anatase-rutile transformation in Fe/TiO2, Th/TiO2 and Cu/TiO2 catalysts and its possible role in metal-support interaction

Based on in-situ Mossbauer and X-ray diffraction studies, it is shown that in the Fe/TiO2 catalyst, the anatase-rutile transformation of the TiO2 support is facilitated by the Fe2+ ions formed during the reduction. The transformation occurs at lower temperatures in Th/TiO2 and Cu/TiO2 compared to pure TiO2. In general, the transformation of anatase to rutile seems to occur at or below the temperature (approximately 770 K) at which strong-metal-support-interaction manifests itself.

Relative Contribution of Cell Proliferation and Microvascularity to Metastasis in Malignant Uveal Melanoma

Uveal melanoma (UM) is the second most common primary intraocular cancer worldwide. It is a relatively rare cancer, but still the second most common type of primary malignant melanoma in humans. UM is a slowly growing tumor, and gives rise to distant metastasis mainly to the liver via the bloodstream. About 40% of patients with UM die of metastatic disease within 10 years of diagnosis, irrespective of the type of treatment. During the last decade, two main lines of research have aimed to achieve enhanced understanding of the metastasis process and accurate prognosis of patients with UM. One emphasizes the characteristics of tumor cells, particularly their nucleoli, and markers of proliferation, and the other the characteristics of tumor blood vessels. Of several morphometric measurements, the mean diameter of the ten largest nucleoli (MLN) has become the most widely applied. A large MLN has consistently been associated with high likelihood of dying from UM. Blood vessels are of paramount importance in metastasis of UM. Different extravascular matrix patterns can be seen in UM, like loops and networks. This presence is associated with death from metastatic melanoma. However, the density of microvessels is also of prognostic importance. This study was undertaken to help understanding some histopathological factors which might contribute to developing metastasis in UM patients. Factors which could be related to tumor progression to metastasis disease, namely nucleolar size, MLN, microvascular density (MVD), cell proliferation, and The Insulin-like Growth Factor 1 Receptor(IGF-1R), were investigated. The primary aim of this thesis was to study the relationship between prognostic factors such as tumor cell nucleolar size, proliferation, extravascular matrix patterns, and dissemination of UM, and to assess to what extent there is a relationship to metastasis. The secondary goal was to develop a multivariate model which includes MLN and cell proliferation in addition to MVD, and which would fit better with population-based, melanoma-related survival data than previous models. I studied 167 patients with UM, who developed metastasis even after a very long time following removal of the eye, metastatic disease was the main cause of death, as documented in the Finnish Cancer Registry and on death certificates. Using an independent population-based data set, it was confirmed that MLN and extravascular matrix loops and networks were unrelated, independent predictors of survival in UM. Also, it has been found that multivariate models including MVD in addition to MLN fitted significantly better with survival data than models which excluded MVD. This supports the idea that both the characteristics of the blood vessels and the cells are important, and the future direction would be to look for the gene expression profile, whether it is associated more with MVD or MLN. The former relates to the host response to the tumor and may not be as tightly associated with the gene expression profile, yet most likely involved in the process of hematogenous metastasis. Because fresh tumor material is needed for reliable genetic analysis, such analysis could not be performed Although noninvasive detection of certain extravascular matrix patterns is now technically possible,in managing patients with UM, this study and tumor genetics suggest that such noninvasive methods will not fully capture the process of clinical metastasis. Progress in resection and biopsy techniques is likely in the near future to result in fresh material for the ophthalmic pathologist to correlate angiographic data, histopathological characteristics such as MLN, and genetic data. This study supported the theory that tumors containing epithelioid cells grow faster and have poorer prognosis when studied by cell proliferation in UM based on Ki-67 immunoreactivity. Cell proliferation index fitted best with the survival data when combined with MVD, MLN, and presence of epithelioid cells. Analogous with the finding that high MVD in primary UM is associated with shorter time to metastasis than low MVD, high MVD in hepatic metastasis tends to be associated with shorter survival after diagnosis of metastasis. Because the liver is the main organ for metastasis from UM, growth factors largely produced in the liver hepatocyte growth factor, epidermal growth factor and insulin-like growth factor-1 (IGF-1) together with their receptors may have a role in the homing and survival of metastatic cells. Therefore the association between immunoreactivity for IGF-1R in primary UM and metastatic death was studied. It was found that immunoreactivity for IGF-IR did not independently predict metastasis from primary UM in my series.

Structural synthesis by transformation of binary chains Strukturelle synthese durch umwandlung binaerer ketten

The paper presents a general method of structural synthesis which can be used to derive all possible simple- and multiple-jointed chains of positive, zero or negative degree-of-freedom. In this method all possible chains with N links and F degrees-of-freedom are derived by the transformation of the corresponding “binary chains” with N binary links and F degrees-of-freedom. The method is illustrated by applying to the case of chains with degrees-of-freedom 1,2,0 and −1.

A real transformation for modal analysis of flexible damped spacecraft

Modal approach is widely used for the analysis of dynamics of flexible structures. However, space analysts yet lack an intimate modal analysis of current spacecraft which are rich with flexibility and possess both structural and discrete damping. Mathematical modeling of such spacecraft incapacitates the existing real transformation procedure, for it cannot include discrete damping, demands uncomputable inversion of a modal matrix inaccessible due to its overwhelming size and does not permit truncation. On the other hand, complex transformation techniques entail more computational time and cannot handle structural damping. This paper presents a real transformation strategy which averts inversion of the associated real transformation matrix, allows truncation and accommodates both forms of damping simultaneously. This is accomplished by establishing a key relation between the real transformation matrix and its adjoint. The relation permits truncation of the matrices and leads to uncoupled pairs of coupled first order equations which contain a number of adjoint eigenvectors. Finally these pairs are solved to obtain a literal modal response of forced gyroscopic damped flexibile systems at arbitrary initial conditions.

A Vicarious One-Pot Transformation of a Fluorocyclitol to a Polycyclitol: Observation of a Formal 4-Fold Axial-Equatorial Epimerization on a Conformationally Locked Scaffold

A conformationally locked fluoropentol undergoes an interesting transformation to (trans,anti,trans,anti,trans)-perhydro-2,3,4a,6,7,8a-naphthalenehexol essentially under conditions of base-induced transesterification. The proposed rationale for the observed metamorphosis involves a nucleophilic displacement of fluoride, and subsequent stereo- and regioselective anti-Furst-Plattner-type ring-opening of the epoxide thus formed.

An in situ electron microscope investigation of the icosahedral-to-decagonal quasicrystalline transformation in Al-20 at.% Mn

The solid-state transformation behaviour of the icosahedral phase in rapidly solidified Al-20 at.% Mn has been investigated by in situ heating experiments in the transmission electron microscope. As-rapidly-solidified Al-20 at.% Mn consists mainly of a dendritic icosahedral phase, with a small amount of interdendritic f.c.c. agr-Al. During subsequent heat treatment at temperatures below about 500°C, the dendritic icosahedral phase grows and consumes the interdendritic agr-Al. At about 500°C the decagonal phase nucleates near icosahedral dendrite and grain boundaries and then grows into the icosahedral matrix by lateral motion of ledges 10-20 nm high across facet planes normal to the twofold symmetry axes. At about 600°C the decagonal phase transforms into a crystalline phase. The present study suggests that solid-state decomposition of the icosahedral phase is the mechanism of decagonal phase formation in as-rapidly-solidified Al-Mn alloys.

Genetic transformation of Brassica nigra by agrobacterium based vector and direct plasmid uptake

Genetic transformation systems have been established for Brassica nigra (cv. IC 257) by using an Agrobacterium binary vector as well as by direct DNA uptake of a plasmid vector. Both the type of vectors carried nptII gene and gus gene. For Agrobacterium mediated transformation, hypocotyl tissue explants were used, and up to 33% of the explants produced calli on selection medium. All of these expressed B-glucuronidase gene on histochemical staining. Protoplasts isolated from hypocotyl tissues of seedlings could be transformed with a plasmid vector by FEG mediated uptake of vector DNA. A number of fertile kanamycin resistant plants were obtained using both the methods, and their transformed nature was confirmed by Southern blot analysis and histochemical staining for GUS. Backcrossed and selfed progenies of these transformed plants showed the presence of npt and gus genes.

Phase Transformation Introduced by Mechanical and Chemical Surface Preparations of Tetragonal Zirconia Polycrystals

Cutting of Y2O3-doped TZP rods by a low-speed diamond saw introduces an unidentified, metastable phase X (x-ZrO2) coexisting with the tetragonal (t-ZrO2) and the monoclinic (m-ZrO2) phases initially present in the sample. Further mechanical deformation of the cut surface by indentation or polishing sustains the x-ZrO2. Chemical etching removes the x-ZrO2 and increases the m-ZrO2content.

Transformation formula for exponential sums involving fourier coefficients of modular forms

In 1984 Jutila [5] obtained a transformation formula for certain exponential sums involving the Fourier coefficients of a holomorphic cusp form for the full modular group SL(2, Z). With the help of the transformation formula he obtained good estimates for the distance between consecutive zeros on the critical line of the Dirichlet series associated with the cusp form and for the order of the Dirichlet series on the critical line, [7]. In this paper we follow Jutila to obtain a transformation formula for exponential sums involving the Fourier coefficients of either holomorphic cusp forms or certain Maass forms for congruence subgroups of SL(2, Z) and prove similar estimates for the corresponding Dirichlet series.

Grain size effect on the phase transformation temperature of nanostructured CuFe2O4

We report a large decrease in tetragonal to cubic phase transformation temperature when grain size of bulk CuFe2O4 is reduced by mechanical ball milling. The change in phase transformation temperature was inferred from in situ high temperature conductivity and x-ray diffraction measurements. The decrease in conductivity with grain size suggests that ball milling has not induced any oxygen vacancy while the role of cation distribution in the observed decrease in phase transformation temperature is ruled out from in-field Fe-57 Mossbauer and extended x-ray absorption fine structure measurements. The reduction in the phase transformation temperature is attributed to the stability of structures with higher crystal symmetry at lower grain sizes due to negative pressure effect. (C) 2011 American Institute of Physics. doi: 10.1063/1.3493244]