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.

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.

Valkolakki vai haalarit, vaiko molemmat : Koulutuspolitiikan vaikuttajien näkemykset toisen asteen kehityksestä

In the present research Finnish education policy-makers describe the transformation in upper secondary education in the 1990s. They answered questions related to equality and all-round education. The timeline of the research extends from the early development of the welfare state and equality policy to the 2000s. Its focus is on upper secondary education, which, in this paper, denotes general upper secondary education and vocational upper secondary education. The chronological analysis proceeds from the education committee of 1971 up to the youth education experiment of the 1990s. The voices of the then policy-makers are heard in this research. They were the ones who planned the reforms and/or made the decisions. This being the case, the interviewees include cabinet ministers, permanent secretaries, representatives of organisations and the research community as well as civil servants. The research material can be construed as contextual interpretations of the past, influenced by both the times and places where the narrations were given. The persons interviewed described their experiences and views on education policy. In their narratives they illustrated the transformation that occurred in relation to equality and all-round education. The narrative interviews painted a picture of the upper secondary education transformation and the matriculation examination as having a slowing effect on education policy reforms. It was not until the 1990s when the said examination began to make a difference to students in vocational upper secondary education Those interviewed named the persons who, in their opinion, had the most say in Finnish education policy. This list comprised a small circle of people who more or less agreed on the grand values of education policy, i.e. all-round education and equality. Only a small minority represented a radical view of equality, being true believers in universal upper secondary education implemented in accordance with comprehensive school reform. Finnish education policy was led from the perspective of traditional conception of equality from the 1970s to the 1980s. The transformation finally occurred in the 1990s when equality was understood to mean individual needs and the right to choose. As was the case with matriculation education, the insistence on all-round education also hampered the development of universal upper secondary education. The interviews revealed that any attempts to increase the academic syllabus of vocational education caused organisations as well as other policy-makers to oppose such development well into the 1980s. It was not until the youth education experiment of the 1990s that vocational education finally carved a path to higher education, when the polytechnic schools were made permanent. Three principal groups of key players emerged in the research: ministers of education, civil servants and organisations. The research showed that the ministers and civil servant education policy-makers of the 1990s also included only handful women. The circle of policy-makers was small and represented similar schools of thought. In the 1970s era of government committees, representatives of organisations actively participated in education policy. When the committee establishment was discontinued, this eliminated lobbying venues for the organisations. Nonetheless, the organisations regained their policymaking status in the 1990s. New lobbying organisations included the Finnish Entrepreneurs and the Union of Finnish Upper Secondary School Students. However, in contrast to the 1970s, only rarely would individuals rise from the ranks of organisations to the cadre of policy-makers. The interviewees had a twofold view of neo-liberalism Contrary to other policy-makers, representatives of the research community and organisations concur that neo-liberalism did exist in education policy decision-making in the 1990s.

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.

Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator

Using path integrals, we derive an exact expression-valid at all times t-for the distribution P(Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P(Q, t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t > infinity exactly recovers the heat distribution function obtained recently by Imparato et al. Phys. Rev. E 76, 050101(R) (2007)] from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen Phys. Rev. E 69, 056121 (2004)]; however, this calculation does not provide an expression for P(Q, t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q, t) for the case v=0.

Path-integral derivation of the superconformal anomaly for the N=1 supersymmetric Yang-Mills theory

Fujikawa's method of evaluating the supercurrent and the superconformal current anomalies, using the heat-kernel regularization scheme, is extended to theories with gauge invariance, in particular, to the off-shell N=1 supersymmetric Yang-Mills (SSYM) theory. The Jacobians of supersymmetry and superconformal transformations are finite. Although the gauge-fixing term is not supersymmetric and the regularization scheme is not manifestly supersymmetric, we find that the regularized Jacobians are gauge invariant and finite and they can be expressed in such a way that there is no one-loop supercurrent anomaly for the N=1 SSYM theory. The superconformal anomaly is nonzero and the anomaly agrees with a similar result obtained using other methods.

Path-integral derivation of the superconformal anomaly for the Wess-Zumino model

Fujikawa's method of evaluating the anomalies is extended to the on-shell supersymmetric (SUSY) theories. The supercurrent and the superconformal current anomalies are evaluated for the Wess-Zumino model using the background-field formulation and heat-kernel regularization. We find that the regularized Jacobians for SUSY and superconformal transformations are finite. The results can be expressed in a form such that there is no supercurrent anomaly but a finite nonzero superconformal anomaly, in agreement with similar results obtained using other methods.

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.

Temperature-Sensitive Src-Transformed Mdck Cells nn 3d Cultures as a Model of Malignant Transformation of Epithelial Cells

The equilibrium between cell proliferation, differentiation, and apoptosis is crucial for maintaining homeostasis in epithelial tissues. In order for the epithelium to function properly, individual cells must gain normal structural and functional polarity. The junctional proteins have an important role both in binding the cells together and in taking part in cell signaling. Cadherins form adherens junctions. Cadherins initiate the polarization process by first recognizing and binding the neighboring cells together, and then guiding the formation of tight junctions. Tight junctions form a barrier in dividing the plasma membranes to apical and basolateral membrane domains. In glandular tissues, single layered and polarized epithelium is folded into tubes or spheres, in which the basal side of the epithelial layer faces the outer basal membrane, and the apical side the lumen. In carcinogenesis, the differentiated architecture of an epithelial layer is disrupted. Filling of the luminal space is a hallmark of early epithelial tumors in tubular and glandular structures. In order for the transformed tumor cells to populate the lumen, enhanced proliferation as well as inhibition of apoptosis is required. Most advances in cancer biology have been achieved by using two-dimensional (2D) cell culture models, in which the cells are cultured on flat surfaces as monolayers. However, the 2D cultures are limited in their capacity to recapitulate the structural and functional features of tubular structures and to represent cell growth and differentiation in vivo. The development of three-dimensional (3D) cell culture methods enables the cells to grow and to be studied in a more natural environment. Despite the wide use of 2D cell culture models and the development of novel 3D culture methods, it is not clear how the change of the dimensionality of culture conditions alters the polarization and transformation process and the molecular mechanisms behind them. Src is a well-known oncogene. It is found in focal and adherens junctions of cultured cells. Active src disrupts cell-cell junctions and interferes with cell-matrix binding. It promotes cell motility and survival. Src transformation in 2D disrupts adherens junctions and the fibroblastic phenotype of the cells. In 3D, the adherens junctions are weakened, and in glandular structures, the lumen is filled with nonpolarized vital cells. Madin-Darby canine kidney (MDCK) cells are an epithelial cell type commonly used as a model for cell polarization. Its-src-transformed variants are useful model systems for analyzing the changes in cell morphology, and they play a role in src-induced malignant transformation. This study investigates src-transformed cells in 3D cell cultures as a model for malignant transformation. The following questions were posed. Firstly: What is the role of the composition and stiffness of the extracellular matrix (ECM) on the polarization and transformation of ts v-src MDCK cells in 3D cell cultures? Secondly: How do the culture conditions affect gene expression? What is the effect of v-src transformation in 2D and in 3D cell models? How does the shift from 2D to 3D affect cell polarity and gene expression? Thirdly: What is the role of survivin and its regulator phosphatase and tensin homolog protein (PTEN) in cell polarization and transformation, and in determining cell fate? How does their expression correlate with impaired mitochondrial function in transformed cells? In order to answer the above questions, novel methods of culturing and monitoring cells had to be created: novel 3D methods of culturing epithelial cells were engineered, enabling real time monitoring of a polarization and transformation process, and functional testing of 3D cell cultures. Novel 3D cell culture models and imaging techniques were created for the study. Attention was focused especially on confocal microscopy and live-cell imaging. Src-transformation disturbed the polarization of the epithelium by disrupting cell adhesion, and sensitized the cells to their environment. With active src, the morphology of the cell cluster depended on the composition and stiffness of the matrix. Gene expression studies revealed a broader impact of src transformation than mere continuous activity of src-kinase. In 2D cultures, src transformation altered the expression of immunological, actin cytoskeleton and extracellular matrix (ECM). In 3D, the genes regulating cell division, inhibition of apoptosis, cell metabolism, mitochondrial function, actin cytoskeleton and mechano-sensing proteins were altered. Surprisingly, changing the culture conditions from 2D to 3D affected also gene expression considerably. The microarray hit survivin, an inhibitor of apoptosis, played a crucial role in the survival and proliferation of src-transformed cells.

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.

Performance study of a pressure transducer with meandering-path thin film strain gauges

The performance of a pressure transducer with meandering-path thin film strain gauges has been studied. Details of the procedure followed to prepare the thin film strain gauge system on the pressure transducer diaphragm are given. The effect of post-deposition heat treatment on the resistance of the sensing films of the strain gauges and the insulating base layers are discussed. The output of the pressure transducer was studied with various input pressures and excitation voltages. It was found that up to a maximum of 10 V bridge excitation the output was stable and repetitive. The maximum non-linearity and hysteresis observed are ±0.15%, ±0.16% and ±0.14% FSO (full-scale output) for 5, 7.5 and 10 V excitation respectively. Information on the output behaviour of the pressure transducer with temperature is also included.

Path integral quantisation of topological field theories

Conditions for quantum topological invariance of classically topological field theories in the path integral formulation are discussed. Both the three-dimensional Chern-Simons system and a Witten-type topological field theory are shown to satisfy these conditions.