LOM and HOM damping study in a superconducting deflecting cavity for ALS at LBNL

Superconducting deflecting cavities can be used in synchrotron light source to generate subpicosecond X-ray pulses while the impedance of the lower order modes (LOM) and higher order modes (HOM) in the cavity should be kept below an accepted level to avoid beam instability. These modes can be damped by adding waveguide on beam pipe. Detailed simulation of Q in CST Microwave Studio is introduced and experiment results on an aluminum model cavity with damping waveguide are reported to make a comparison.     

Evaluation of the quality of clinical laboratories in the Slovak Republic: conceptual and contextual remarks

The paper demonstrates conceptual parallels and relationships between intellectual capital measurement methods and the evaluation of quality in clinical laboratories in the Slovak Republic. It explores further the contextual links of those parallels with the tangibility (or intangibility) of quality indicators of laboratory diagnostics. It also highlights the problems which laboratory staff in Slovakia are confronted with. Presented at the conference Quality in the Spotlight, March 2007, Antwerp, Belgium.     

Weak Barriers in Nonlinear Potential Theory

We characterize regular boundary points for p-harmonic functions using weak barriers. We use this to obtain some consequences on boundary regularity. The results also hold for 2007_9064_Article_IEq1.gif" alt="$\mathcal{A}$" align="middle" border="0">-harmonic functions under the usual assumptions on 2007_9064_Article_IEq2.gif" alt="$\mathcal{A}$" align="middle" border="0">, and for Cheeger p-harmonic functions in metric spaces.      

Failure of hypoellipticity for the canonical solution to $${\bar\partial_b}$$ on some nilpotent Lie groups

In this paper we show that Kohn’s solution to the \({\bar\partial_b}\) problem fails to be hypoelliptic on some class of high codimension submanifolds of \({\mathbb{C}^n}\). The examples presented here carry a Lie group structure which generalize the one-dimensional Heisenberg group.     

Duality and interpolation of anisotropic Triebel–Lizorkin spaces

We study properties of anisotropic Triebel–Lizorkin spaces associated with general expansive dilations and doubling measures on 2007_216_Article_IEq1.gif" alt="$${\mathbb{R}}^n$$" align="middle" border="0"> using wavelet transforms. This paper is a continuation of (Bownik in J Geom Anal 2007, to appear, Trans Am Math Soc 358:1469–1510, 2006), where we generalized the isotropic methods of dyadic 2007_216_Article_IEq2.gif" alt="$$\varphi$$" align="middle" border="0"> -transforms of Frazier and Jawerth (J Funct Anal 93:34–170, 1990) to non-isotropic settings. By working at the level of sequence spaces, we identify the duals of anisotropic Triebel–Lizorkin spaces. We also obtain several real and complex interpolation results for these spaces. The author was partially supported by the NSF grants DMS-0441817 and DMS-0653881. The author wishes to thank Michael Frazier and Dachun Yang for valuable comments and discussions on this work.     

Algorithms for finding clique-transversals of graphs

A clique-transversal of a graph G is a subset of vertices intersecting all the cliques of G. It is NP-hard to determine the minimum cardinality τ _c of a clique-transversal of G. In this work, first we propose an algorithm for determining this parameter for a general graph, which runs in polynomial time, for fixed τ _c . This algorithm is employed for finding the minimum cardinality clique-transversal of [`(3K₂)]\overline{3K_{2}} -free circular-arc graphs in O(n ⁴) time. Further we describe an algorithm for determining τ _c of a Helly circular-arc graph in O(n) time. This represents an improvement over an existing algorithm by Guruswami and Pandu Rangan which requires O(n ²) time. Finally, the last proposed algorithm is modified, so as to solve the weighted version of the corresponding problem, in O(n ²) time.     

Projectively condensed semigroups,generalized completely regular semigroups and projective orthomonoids

The class 2007_7038_Article_IEq1.gif" alt="$$ \mathcal{P}\mathcal{C} $$" align="middle" border="0"> of projectively condensed semigroups is a quasivariety of unary semigroups, the class of projective orthomonoids is a subquasivariety of 2007_7038_Article_IEq2.gif" alt="$$ \mathcal{P}\mathcal{C} $$" align="middle" border="0">. Some well-known classes of generalized completely regular semigroups will be regarded as subquasivarieties of 2007_7038_Article_IEq3.gif" alt="$$ \mathcal{P}\mathcal{C} $$" align="middle" border="0">. We give the structure semilattice composition and the standard representation of projective orthomonoids, and then obtain the structure theorems of various generalized orthogroups. Partially supported by a UGC (HK) grant #2060123 (04-05).     

Evaluation of recurrence relationships and numerical solutions for finite rotation matrix elements by using auxiliary functions

In this article, we derived several new recurrence relations of the rotation matrix elements by using Gauss’ recurrence formulas for hypergeometric functions and auxiliary functions2007_9290_Article_IEq1.gif" alt="$$A_{m^{\prime}, m}^j (\beta)$$" align="middle" border="0"> , and 2007_9290_Article_IEq2.gif" alt="$$B_{i, l}^k (\beta)$$" align="middle" border="0"> . The aim of this contribution is to obtain general algorithm to compute the rotation matrix elements, paying attention to the use recurrence relationships of the auxiliary functions that allow the treatment of the functions with high angular momentum quantum numbers.     

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 Unified Fixed Point Theory in Generalized Convex Spaces

Let B be the class of ＇better＇ admissible multimaps due to the author. We introduce new concepts of admissibility （in the sense of Klee） and of Klee approximability for subsets of G-convex uniform spaces and show that any compact closed multimap in B from a G-convex space into itself with the Klee approximable range has a fixed point. This new theorem contains a large number of known results on topological vector spaces or on various subclasses of the class of admissible G-convex spaces. Such subclasses are those of O-spaces, sets of the Zima-Hadzic type, locally G-convex spaces, and LG-spaces. Mutual relations among those subclasses and some related results are added.