Large deviations of infinite intersections of events in Gaussian processes

Consider events of the form {_Zs≥ζ(s),s∈S}$\{Z_s\ge \zeta \left(s\right),s\in S\}$, where Z$Z$ is a continuous Gaussian process with stationary increments, ζ$\zeta$ is a function that belongs to the reproducing kernel Hilbert space R$R$ of process Z$Z$, and S⊂R$S\subset \mathbb{R}$ is compact. The main problem considered in this paper is identifying the function β^∗∈R${\beta }^{\ast }\in R$ satisfying β^∗(s)≥ζ(s)${\beta }^{\ast }\left(s\right)\ge \zeta \left(s\right)$ on S$S$ and having minimal R$R$-norm. The smoothness (mean square differentiability) of Z$Z$ turns out to have a crucial impact on the structure of the solution. As examples, we obtain the explicit solutions when ζ(s)=s$\zeta \left(s\right)=s$ for s∈[0,1]$s\in [0,1]$ and Z$Z$ is either a fractional Brownian motion or an integrated Ornstein–Uhlenbeck process.     

Uniform Convexity and Associate Spaces

We prove that the associate space of a generalized Orlicz space L^?(·) is given by the conjugate modular ?* even without the assumption that simple functions belong to the space. Second, we show that every weakly doubling Φ-function is equivalent to a doubling Φ-function. As a consequence, we conclude that L^?(·) is uniformly convex if ? and ?* are weakly doubling.     

Overview of differential equations with non-standard growth

Differential equations with non-standard growth have been a very active field of investigation in recent years. In this survey we present an overview of the field, as well as several of the most important results. We consider both existence and regularity questions. Finally, we provide a comprehensive list of papers published to date.     

Analysis of acetylcholine and choline in microdialysis samples by liquid chromatography/tandem mass spectrometry

A sensitive liquid chromatography/electrospray ionisation tandem mass spectrometric (LC/ESI-MS/MS) method was developed for the analysis of acetylcholine and choline in microdialysis samples. A Ringer's solution that contains high (150 mM) concentrations of inorganic salts was used to extract acetylcholine and choline from a rat or mouse brain. The separation of acetylcholine, choline, an internal standard acetyl-beta-methylcholine, endogenous compounds and inorganic cations was achieved with hydrophilic interaction chromatography using a diol column. The eluent consisted of 20 mM ammonium formate (pH 3.3) and acetonitrile (20:80) which is favourable for the ESI process. Limits of detection (signal-to-noise (S/N) ratio = 3) of 0.02 nM (0.2 fmol) for acetylcholine and 1 nM (10 fmol) for choline were observed using standards diluted in Ringer's solution. A good linearity was obtained from the limit of quantitation: 0.1 nM (S/N ratio = 10) to 50 nM (r = 0.999) for acetylcholine and within the concentration range of 100-3500 nM (r = 0.998) for choline. The between-day repeatability of the method was good; RSD was 3.1% at 1 nM level of acetylcholine and 3.5% at 1000 nM level of choline. The recoveries for addition of 1 or 2.5 nM acetylcholine and 0.2 or 1 microM choline in microdialysis balancing samples were between 93 and 101% indicating that no suppressing endogenous compounds were co-eluting with acetylcholine or choline. The developed method was applied to the analysis of microdialysis balancing samples collected from rat and mouse brains.     

Steiner triple systems of order 19 and 21 with subsystems of order 7

Steiner triple systems (STSs) with subsystems of order 7 are classified. For order 19, this classification is complete, but for order 21 it is restricted to Wilson-type systems, which contain three subsystems of order 7 on disjoint point sets. The classified STSs of order 21 are tested for resolvability; none of them is doubly resolvable.     

There are exactly five biplanes with k = 11

A biplane is a 2‐(k(k ? 1)/2 + 1,k,2) symmetric design. Only sixteen nontrivial biplanes are known: there are exactly nine biplanes with k < 11, at least five biplanes with k = 11, and at least two biplanes with k = 13. It is here shown by exhaustive computer search that the list of five known biplanes with k = 11 is complete. This result further implies that there exists no 3‐(57, 12, 2) design, no 112₁₁ symmetric configuration, and no (324, 57, 0, 12) strongly regular graph. The five biplanes have 16 residual designs, which by the Hall–Connor theorem constitute a complete classification of the 2‐(45, 9, 2) designs. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 117–127, 2008     

Determination of Mn, Fe, and Cu in chemically-treated wood pulps by the XRF addition method

A rapid X-ray fluorescence addition method has been developed for quantification of the technically most important metals in wood pulp matrix (Mn, Fe, and Cu). Pretreatment consisted of just two steps: first, acid was added to the sample to achieve homogeneous distribution of the metals; the pulp was then pressed lightly on to Mylar film. Total analysis time was less than 10 min. The concentration range investigated was up to 15 mg kg^–1 for Mn and up to 5 mg kg^–1 for Fe and Cu. Metal concentrations in Scandinavian pulps are not expected to exceed these amounts. The quantification limit was 2 mg kg^–1 for all three metals. The reproducibilities and repeatabilities were concentration-dependent and varied between 3 and 19% and between 1 and 17%, respectively. The squares of the linear correlation coefficients between measured intensity and added metal concentration were 0.994, 0.950, and 0.932 for Mn, Fe, and Cu, respectively.     

The Steiner triple systems of order 19

Using an orderly algorithm, the Steiner triple systems of order are classified; there are pairwise nonisomorphic such designs. For each design, the order of its automorphism group and the number of Pasch configurations it contains are recorded; of the designs are anti-Pasch. There are three main parts of the classification: constructing an initial set of blocks, the seeds; completing the seeds to triple systems with an algorithm for exact cover; and carrying out isomorph rejection of the final triple systems. Isomorph rejection is based on the graph canonical labeling software nauty supplemented with a vertex invariant based on Pasch configurations. The possibility of using the (strongly regular) block graphs of these designs in the isomorphism tests is utilized. The aforementioned value is in fact a lower bound on the number of pairwise nonisomorphic strongly regular graphs with parameters .

     

Correlation of aluminum doping and lithiation temperature with electrochemical performance of LiNi1-xAlxO2 cathode material

Journal of Solid State Electrochemistry - This article presents a process for producing LiNi1-xAlxO2 (0 &lt;  ×  &lt; 0.05) cathode material with...