(Mo + N) codoped TiO2 for enhanced visible-light photoactivity

A series of Ti_1−xMo_xO_2−yN_y samples were prepared by using sol-gel method and characterized by X-ray diffraction, transmission electron microscopy and UV-vis absorption spectroscopy. All Ti_1−xMo_xO_2−yN_y samples are anatase phase. It is found that Mo, N mono-doping can increase visible light absorption, while (Mo + N) co-doping can greatly enhance absorption in whole visible region. Results of our first-principles band structure calculations reveal that (Mo + N)-doping, especially passivated co-doping can increase the up-limit of dopant concentration and create more impurity bands in the band gap of TiO₂, which leads to a greatly increase of its visible-light absorption without a decrease of its redox potential. It reveals that (Mo + N) co-doped TiO₂ is promising for a photocatalyst with high photocalystic activity under visible light.     

über die Definition von effektiven Zufallstests

Summary We continue the discussion on the definition of random sequences from Part I. We will show that the idea of Kolmogoroff to characterize random sequences by their program complexity can be formulated in such a way as to let this definition coÏncide with the others given in Part I. Another equivalent definition of random sequences can be derived from the games of chance. A sequence is random, if and only if no player who calculates his pool by effective methods can raise his fortune indefinitely when playing on this sequence. Finally we will study transformations which preserve the random property of a sequence. We will prove that the original concept of v. Mises can also be modified in such a manner as to coÏncide with all our other definitions. A sequence is random, if and only if it satisfies the strong law of large numbers and if every sequence obtained from it by a constructive measure-preserving transformation is random, too.

---

---

Die Arbeit stellt einen Teil der Habilitationsschrift dar, die der Mathematisch-Naturwissenschaftlichen FakultÄt der UniversitÄt des Saarlandes vom Verfasser vorgelegt wurde.     

Über den Satz von Poincaré in der Störungstheorie Briot-Bouquetscher Differentialgleichungen

The well known theorem of H. Poincaré concerning the analytic continuation and representation along a curve of solutions of differential equations depending on a parameter is generalized to solutions of Differential Equations of Briot-Bouquet type depending on a parameter.

---

---

Herrn Professor Dr. N. Hofreiter zum 70. Geburtstag     

Measuring the Michel parameter ξ'

Unlike the majority of Michel parameters which are consistent with the Standard Model V-A interaction, the experimental value of ξ″(=0.65±0.36) [1] is poorly known. Our experiment will measure the longitudinal polarization, P _L , of positrons emitted from the decay of polarized muons. The value of P _L , equal to unity in the Standard Model, will decrease for high energy positrons emitted antiparallel to the muon spin if the combination of Michel parameters ξ″/ξξ′ − 1 deviates from the Standard Model value of zero. This revised version was published online in August 2006 with corrections to the Cover Date.     

LM-g splines

As an extension of the notion of an L-g spline, three mathematical structures called LM-g splines of types I, II, and III are introduced. Each is defined in terms of two differential operators the coefficients a_j, J = 0,…, n − 1, and b_i, I = 0,…, m, are sufficiently smooth; and b_m is bounded away from zero on [0, T]. Each of the above types of splines is the solution of an optimization problem more general than the one used in the definition of the L-g spline and hence it is recognized as an entity which is distinct from and more general mathematically than the L-g spline. The LM-g splines introduced here reduce to an L-g spline in the special case in which m = 0 and b₀ = constant ≠ 0. After the existence and uniqueness conditions, characterization, and best approximation properties for the proposed splines are obtained in an appropriate reproducing kernel Hilbert space framework, their usefulness in extending the range of applicability of spline theory to problems in estimation, optimal control, and digital signal processing are indicated. Also, as an extension of recent results in the generalized spline literature, state variable models for the LM-g splines introduced here are exhibited, based on which existing least squares algorithms can be used for the recursive calculation of these splines from the data.