On $$ \mathcal{C} $$*-sets and decompositions of continuous and ηζ-continuous functions

The main purpose of this paper is to introduce the concepts of 2007_6111_Article_IEq2.gif" alt="$$ \mathcal{C} $$" align="middle" border="0">*-sets, 2007_6111_Article_IEq3.gif" alt="$$ \mathcal{C} $$" align="middle" border="0">*-continuous functions and to obtain new decompositions of continuous and ηζ-continuous functions. Moreover, properties of 2007_6111_Article_IEq4.gif" alt="$$ \mathcal{C} $$" align="middle" border="0">*-sets and some properties of 2007_6111_Article_IEq5.gif" alt="$$ \mathcal{C} $$" align="middle" border="0">-sets are discussed.      

A general form of Jordan-type double inequality for the generalized and normalized Bessel functions

In this note, a general form of Jordan-type double inequality involving the generalized and normalized Bessel functions is presented, and then some recent results concerning generalized and sharp work of Jordan’s inequality are extended. At the same time, the applications of the results above give two new infinite series for sinx/x and sinhx/x.     

Bounded universal functions in one and several complex variables

We show how to obtain functions that are universal for the ball of 2007_195_Article_IEq1.gif" alt="$$H^\infty(\Omega)$$" align="middle" border="0">, where 2007_195_Article_IEq2.gif" alt="$$\Omega \subset {\mathbb{C}}^n$$" align="middle" border="0">. The existence of our functions will follow from universality criteria, but we also show how to construct them. Then we study the connection between certain interpolating sequences, runaway automorphisms, and the existence of universal functions on domains in 2007_195_Article_IEq3.gif" alt="$${\mathbb{C}}^n$$" align="middle" border="0">.      

Self-Similar Stable Processes Arising from High-Density Limits of Occupation Times of Particle Systems

We extend results on time-rescaled occupation time fluctuation limits of the (d, α, β)-branching particle system (0 < α ≤ 2, 0 < β ≤ 1) with Poisson initial condition. The earlier results in the homogeneous case (i.e., with Lebesgue initial intensity measure) were obtained for dimensions d > α / β only, since the particle system becomes locally extinct if d ≤ α / β. In this paper we show that by introducing high density of the initial Poisson configuration, limits are obtained for all dimensions, and they coincide with the previous ones if d > α / β. We also give high-density limits for the systems with finite intensity measures (without high density no limits exist in this case due to extinction); the results are different and harder to obtain due to the non-invariance of the measure for the particle motion. In both cases, i.e., Lebesgue and finite intensity measures, for low dimensions [d < α (1 + β) / β and d < α (2 + β) / (1 + β), respectively] the limits are determined by non-Lévy self-similar stable processes. For the corresponding high dimensions the limits are qualitatively different: 2007_9067_Article_IEq1.gif" alt="$\mathcal{S}'\left( {\mathbb{R}^d } \right)$" align="middle" border="0">-valued Lévy processes in the Lebesgue case, stable processes constant in time on (0,∞) in the finite measure case. For high dimensions, the laws of all limit processes are expressed in terms of Riesz potentials. If β = 1, the limits are Gaussian. Limits are also given for particle systems without branching, which yields in particular weighted fractional Brownian motions in low dimensions. The results are obtained in the setup of weak convergence of 2007_9067_Article_IEq2.gif" alt="$\mathcal{S}'\left( {\mathbb{R}^d } \right)$" align="middle" border="0">-valued processes. Research supported by MNiSW grant 1P03A1129 (Poland; T. Bojdecki and A. Talarczyk) and by CONACyT grant 45684-F (Mexico; L.G. Gorostiza).     

Dirichlet Problem at Infinity for $\mathcal A$-Harmonic Functions

We study the Dirichlet problem at infinity for 2007_9051_Article_IEq2.gif" alt="$\mathcal A$" align="middle" border="0">-harmonic functions on a Cartan–Hadamard manifold M and give a sufficient condition for a point at infinity x ₀∈M(∞) to be 2007_9051_Article_IEq3.gif" alt="$\mathcal A$" align="middle" border="0">-regular. This condition is local in the sense that it only involves sectional curvatures of M in a set U∩M, where U is an arbitrary neighborhood of x ₀ in the cone topology. The results apply to the Laplacian and p-Laplacian, 1<p<∞, as special cases.      

The Resolvent Problem and $${{H^{\infty}}}$$ -calculus of the Stokes Operator in Unbounded Cylinders with Several Exits to Infinity

It is proved that the Stokes operator in L^q -space on an infinite cylindrical domain of 2007_Article_300_TeX2GIFIEq2.gif" alt=" $${{\mathbb{R}^{n}}}$$ " align="middle" border="0"> , 2007_Article_300_TeX2GIFIEq3.gif" alt=" $${{n \geq 3}}$$ " align="middle" border="0"> , with several exits to infinity generates a bounded and exponentially decaying analytic semigroup and admits a bounded 2007_Article_300_TeX2GIFIEq4.gif" alt=" $${{H^{\infty}}}$$ " align="middle" border="0"> -calculus. For the resolvent estimates, the Stokes resolvent system with a prescribed divergence in an infinite straight cylinder with bounded cross-section 2007_Article_300_TeX2GIFIEq5.gif" alt=" $${{\Sigma}}$$ " align="middle" border="0"> is studied in L ^q 2007_Article_300_TeX2GIFIEq6.gif" alt=" $${{(\mathbb{R}; L^{r}_{\omega} (\Sigma))}}$$ " align="middle" border="0"> where 2007_Article_300_TeX2GIFIEq7.gif" alt=" $${{1 < q,r < \infty}}$$ " align="middle" border="0"> and 2007_Article_300_TeX2GIFIEq8.gif" alt=" $${{\omega \, \epsilon \, A_{r}(\mathbb{R}^{n-1})}}$$ " align="middle" border="0"> is an arbitrary Muckenhoupt weight. The proofs use cut-off techniques and the theory of Schauder decomposition of UMD spaces based on 2007_Article_300_TeX2GIFIEq9.gif" alt=" $${{\mathcal{R}}}$$ " align="middle" border="0"> -boundedness of operator families and on square function estimates involving Muckenhoupt weights.     

Global error bounds for the extended vertical LCP

A new necessary and sufficient condition for the row 2007_9134_Article_IEq1.gif" alt="$\mathcal{W}$" align="middle" border="0"> -property is given. By using this new condition and a special row rearrangement, we provide two global error bounds for the extended vertical linear complementarity problem under the row 2007_9134_Article_IEq2.gif" alt="$\mathcal{W}$" align="middle" border="0"> -property, which extend the error bounds given in Chen and Xiang (Math. Program. 106:513–525, 2006) and Mathias and Pang (Linear Algebra Appl. 132:123–136, 1990) for the P-matrix linear complementarity problem, respectively. We show that one of the new error bounds is sharper than the other, and it can be computed easily for some special class of the row 2007_9134_Article_IEq3.gif" alt="$\mathcal{W}$" align="middle" border="0"> -property block matrix. Numerical examples are given to illustrate the error bounds. The work was in part supported by a Grant-in-Aid from Japan Society for the Promotion of Science, and the National Natural Science Foundation of China (10671010).     

$${\mathcal{M}}$$ -decomposability and symmetric unimodal densities in one dimension

In this paper, we introduce the notion of 2007_144_Article_IEq2.gif" alt="$${\mathcal{M}}$$" align="middle" border="0"> -decomposability of probability density functions in one dimension. Using 2007_144_Article_IEq3.gif" alt="$${\mathcal{M}}$$" align="middle" border="0"> -decomposability, we derive an inequality that applies to all symmetric unimodal densities. Our inequality involves only the standard deviation of the densities concerned. The concept of 2007_144_Article_IEq4.gif" alt="$${\mathcal{M}}$$" align="middle" border="0"> -decomposability can be used as a non-parametric criterion for mode-finding and cluster analysis.     

Applying Bayesian neural networks to identify pion, kaon and proton in BES Ⅱ

The Monte-Carlo samples of pion, kaon and proton generated from 0.3 GeV/c to 1.2 GeV/c by the 'tester' generator from SIMBES which are used to simulate the detector of BES Ⅱ are identified with the Bayesian neural networks (BNN). The pion identification and misidentification efficiencies are obviously better at high momentum region using BNN than the methods of X2 analysis of dE/dX and TOF information.The kaon identification and misidentification efficiencies are obviously better from 0.3 GeV/c to 1.2 GeV/c using BNN than the methods of X2 analysis. The proton identification and misidentification efficiencies using BNN are basically consistent with the ones of X2 analysis. The anti-proton identification and misidentification efficiencies are better below 0.6 GeV/c using BNN than the methods of X2 analysis.     

LC-MS-MS Determination of Cyclo{(2S)-2-amino-8-[(aminocarbonyl)hydrazono] decanoyl-1-l-tryptophyl-l-isoleucyl-(2R)-2-piperidinecarbonyl} a Novel Histone Deacetylase Inhibitor in Rat Serum

A rapid and sensitive liquid chromatography-tandem mass spectrometry assay was developed for the determination of a novel histone deacetylase inhibitor, cyclo{(2S)-2-amino-8-[(aminocarbonyl)hydrazono]decanoyl-1-l-tryptophyl-l-isoleucyl-(2R)-2-piperidinecarbonyl} (SD-2007), in rat serum. The mobile phase consisted of acetonitrile and ammonium formate (10 mM) (85:15 v/v), and the flow rate was 0.25 mL min⁻¹. Chromatographic separations were achieved by isocratic elution on a C₁₈ column. Multiple reaction monitoring was based on the transition of m/z = 681.8 → 83.6 for SD-2007 and 372.1 → 176.1 for trazodone (internal standard). A linearity was observed over a concentration range from 2 to 1,000 ng mL⁻¹ (r ² > 0.999), with the lower limit of quantification at 2 ng mL⁻¹ with 100 μL of rat serum. The mean intra- and inter-day assay accuracy ranged from 98.5–109.7% to 95.2–102.7%, respectively, and the mean intra- and inter-day precision was between 4.3–11.3% and 2.9–13.3%. The developed assay was applied to a pharmacokinetic study of SD-2007 in rats after intravenous injection (dose 4 mg kg⁻¹).