Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.

Women’s adaptation to STEM domains promotes resilience and a lesser reliance on heuristic thinking

Experiences that compel people to challenge social stereotypes can promote enhanced cognitive flexibility on a range of judgmental domains. Women in STEM (science, technology, engineering, and math) fields are chronically exposed to such experiences and may therefore also demonstrate these benefits. Two studies examined the differential effects of counterstereotypical experiences on women from STEM and non-STEM fields. Results showed that imagining or recollecting these experiences led women from STEM fields to exhibit a lesser reliance on heuristic thinking compared to women from non-STEM fields, and this difference was mediated by self-perceived resilience to the negative impact of gender stereotyping. Implications for psychologists’ and educators’ understanding of the relationship between counterstereotypical experiences and heuristic thinking are discussed.

Numerical solution of a Cauchy problem for Laplace equation in 3-dimensional domains by integral equations

A numerical method based on integral equations is proposed and investigated for the Cauchy problem for the Laplace equation in 3-dimensional smooth bounded doubly connected domains. To numerically reconstruct a harmonic function from knowledge of the function and its normal derivative on the outer of two closed boundary surfaces, the harmonic function is represented as a single-layer potential. Matching this representation against the given data, a system of boundary integral equations is obtained to be solved for two unknown densities. This system is rewritten over the unit sphere under the assumption that each of the two boundary surfaces can be mapped smoothly and one-to-one to the unit sphere. For the discretization of this system, Weinert’s method (PhD, Göttingen, 1990) is employed, which generates a Galerkin type procedure for the numerical solution, and the densities in the system of integral equations are expressed in terms of spherical harmonics. Tikhonov regularization is incorporated, and numerical results are included showing the efficiency of the proposed procedure.

Non-manipulable domains for the Borda count

We characterize the preference domains on which the Borda count satises Arrow's "independence of irrelevant alternatives" condition. Under a weak richness condition, these domains are obtained by xing one preference ordering and including all its cyclic permutations ("Condorcet cycles"). We then ask on which domains the Borda count is non-manipulable. It turns out that it is non-manipulable on a broader class of domains when combined with appropriately chosen tie-breaking rules. On the other hand, we also prove that the rich domains on which the Borda count is non-manipulable for all possible tie-breaking rules are again the cyclic permutation domains.

Nash implementable domains for the Borda count

We characterize the preference domains on which the Borda count satisfies Maskin monotonicity. The basic concept is the notion of a "cyclic permutation domain" which arises by fixing one particular ordering of alternatives and including all its cyclic permutations. The cyclic permutation domains are exactly the maximal domains on which the Borda count is strategy-proof when combined with every possible tie breaking rule. It turns out that the Borda count is monotonic on a larger class of domains. We show that the maximal domains on which the Borda count satisfies Maskin monotonicity are the "cyclically nested permutation domains" which are obtained from the cyclic permutation domains in an appropriately specified recursive way. ------ *We thank József Mala for posing the question of Nash implementability on restricted domains that led to this research. We are very grateful to two anonymous referees and an associate editor for their helpful comments and suggestions. The second author gratefully acknowledges financial support from the Hungarian Academy of Sciences (MTA) through the Bolyai János research fellowship.

Studying Key Amino Acids in the Function of Ras Interference 1 (Rinl) SH2 and Vps9 Domains

Receptor mediated endocytosis effectively removes the "ears" with which a cell would "hear" a signal conveyed by extracellular signaling molecules, but does not necessarily block the signaling pathway in which the endocytosed receptor participates. In the process of signal attenuation, this newly formed vesicle is fused with a phagosome and the receptor molecules are degraded. Receptor mediated endocytosis as a way to attenuate epidermal growth factor (EGF) and insulin signaling will be the focus here. Ras Interference 1 (Rin 1) is a multifunctional protein involved in intracellular membrane trafficking and receptor mediated endocytosis through its Rab5 Guanine Exchange Factor and SH2 domains. The goal of this investigation is to determine the role of key amino acids involved in the interaction of Rinl with Epidermal Growth Factor Receptor and Rab5. To elucidate this role, a number of point mutations have been created and the effects of each mutation on Rin 1 function will be investigated. Key amino acids in the SH2 and Vps9 Domain were identified and effects of mutations on rate of endocytosis were observed.

Development of Knowledge Domains and an Instrument to Assess Probation Officers’ Knowledge of Offenders with Intellectual Disabilities

The purpose of this study was to develop knowledge domains and an instrument to assess probation officers’ knowledge levels of offenders with intellectual disabilities by utilizing a synthesis of subject matter analysis technique and a comprehensive review of literature. Results can be used to develop effective training for probation officers.

Stripe domains formation and their affect on three-dimensional and perpendicular magnetic recording

In this study, the formation of stripe domains in permalloy (NisoFe20) thin films was investigated mainly utilizing magnetic force microscopy. Stripe domains are a known phenomenon, which reduces the "softness" of magnetic material and introduces a significant source of noise when used in perpendicular magnetic media. For the particular setup mentioned in this report, a critical thickness for stripe domains initiation depended on the sputtering rate, the substrate temperature, and the film thickness. Beyond the stripe domain formation, an increase in the periodicity of highly ordered stripe domains was evident with increasing film thickness. Above a particular thickness, stripe domains periodicity decreased along with magnetic domain randomization. The results led to the inference that the perpendicular anisotropy responsible for the formation of stripe domains originated mainly from magnetostriction.

Homogenization of elliptic problems in thin domains with oscillatory boundaries

Los dominios finos, es decir, dominios sustancialmente más pequeños en alguna o varias de sus direcciones que en el resto, aparecen en muchos campos de la ciencia. Por ejemplo, dinámica de fluídos (lubricación, conducción de fluídos en tubos delgados, dinámica de oceanos...), mecánica de sólidos (barras delgadas, placas o cáscaras) o incluso en fisiología (circulación de la sangre). Así, el amplio número de posibles aplicaciones a situaciones reales ha hecho que la investigación de modelos de ecuaciones en derivadas parciales en dominios finos se convierta en un tema muy estudiado en los últimos años. Desde un punto de vista matemático, el estudio de las soluciones de una EDP en un dominio fino es un caso particular de la cuestión general relativa a cómo la variación de los dominios afecta al comportamiento de las soluciones de la EDP. En este marco, obtener la ecuación límite del modelo considerado, comparar la solución de la ecuación límite y las soluciones del problema en el dominio fino, analizar los coeficientes de la ecuación límite y comprender cómo la geometría del dominio afecta a la ecuación límite son algunos de los objetivos que deberían ser alcanzados. De hecho, es importante señalar que este tipo de cuestiones no sólo proporcionan importantes resultados teóricos sino que son muy relevantes desde el punto de vista de las aplicaciones. Por ejemplo, ser capaz de reducir el problema original a un problema mucho más sencillo, problema límite, que refleje las principales características del problema de partida puede ser muy útil para ingenieros y físicos...

The importance of subclasses of chitin synthase enzymes with myosin-like domains for the fitness of fungi

TG and CF are funded by FEDER funds through the Operational Programme Competitiveness Factors e COMPETE and national funds by FCT e Foundation for Science and Technology under the strategic project UID/NEU/04539/2013. C.F. is a recipient of a postdoctoral fellowship from FCT-Fundac¸ ~ao para a Ci^encia e Tecnologia (SFRH/BPD/63733/2009). NG is funded by The Wellcome Trust (080088, 086827, 075470, 099215 & 097377), the FungiBrain Marie Curie Network and the Medical Research Council (UK).