A Scaling Method and its Applications to Problems in Fractional Dimensional Space

A scaling method is proposed to find (1) the volume and the surface area of a generalized hypersphere in a fractional dimensional space and (2) the solid angle at a point for the same space. It is demonstrated that the total dimension of the fractional space can be obtained by summing the dimension of the fractional line element along each axis. The regularization condition is defined for functions depending on more than one variable. This condition is applied (1) to find a closed form expression for the fractional Gaussian integral, (2) to establish a relationship between a fractional dimensional space and a fractional integral, (3) to develop the Bochner theorem, and (4) to obtain an expression for the fractional integral of the Mittag–Leffler function. Some possible extensions of this work are also discussed

Solutions of a particle with fractional δ\delta-potential in a fractional dimensional space

A Fourier transformation in a fractional dimensional space of order \la (0<\la\leq 1) is defined to solve the Schr\"odinger equation with Riesz fractional derivatives of order \a. This new method is applied for a particle in a fractional $\delta$-potential well defined by V(x) =- \gamma\delta^{\la}(x), where $\gamma>0$ and \delta^{\la}(x) is the fractional Dirac delta function. A complete solutions for the energy values and the wave functions are obtained in terms of the Fox H-functions. It is demonstrated that the eigen solutions are exist if 0< \la<\a. The results for \la= 1 and \a=2 are in exact agreement with those presented in the standard quantum mechanics

Computer-Based Intensity Measurement Assists Pathologists in Scoring Phosphatase and Tensin Homolog Immunohistochemistry - Clinical Associations in NSCLC Patients of the European Thoracic Oncology Platform Lungscape Cohort.

Phosphatase and tensin homolog (PTEN) loss is frequently observed in NSCLC and associated with both phosphoinositide 3-kinase activation and tumoral immunosuppression. PTEN immunohistochemistry is a valuable readout, but lacks standardized staining protocol and cutoff value. After an external quality assessment using SP218, 138G6 and 6H2.1 anti-PTEN antibodies, scored on webbook and tissue microarray, the European Thoracic Oncology Platform cohort samples (n = 2245 NSCLC patients, 8980 tissue microarray cores) were stained with SP218. All cores were H-scored by pathologists and by computerized pixel-based intensity measurements calibrated by pathologists. All three antibodies differentiated six PTEN+ versus six PTEN- cases on external quality assessment. For 138G6 and SP218, high sensitivity and specificity was found for all H-score threshold values including prospectively defined 0, calculated 8 (pathologists), and calculated 5 (computer). High concordance among pathologists in setting computer-based intensities and between pathologists and computer in H-scoring was observed. Because of over-integration of the human eye, pixel-based computer H-scores were overall 54% lower. For all cutoff values, PTEN- was associated with smoking history, squamous cell histology, and higher tumor stage (p &lt; 0.001). In adenocarcinomas, PTEN- was associated with poor survival. Calibration of immunoreactivity intensities by pathologists following computerized H-score measurements has the potential to improve reproducibility and homogeneity of biomarker detection regarding epitope validation in multicenter studies

Entwicklung einer gepulsten sub-#mu#m-Fluessigmetallionenquelle und Integration in ein abbildendes Flugzeit-Sekundaerionen-Massenspektrometer (TOF-SIMS) Schlussbericht

Available from TIB Hannover: F94B0405+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEBundesministerium fuer Forschung und Technologie (BMFT), Bonn (Germany)DEGerman

MOVE - Modellierung einer verteilten Archtitektur fuer die Entwicklung unternehmensuebergreifender Informationssysteme und deren Validierung im Handelsbereich Schlussbericht

Available from TIB Hannover: F99B715+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEBundesministerium fuer Bildung und Forschung (BMBF), Bonn (Germany)DEGerman