20 W single longitudinal mode Nd:YVO<Subscript>4</Subscript> retro-reflection ring laser operated as a self-intersecting master oscillator power amplifier

We demonstrate the stable operation of a 20 W single longitudinal mode TEM₀₀ Nd:YVO₄ ring laser at 1064 nm. Unidirectionality of 2500:1 was imposed through retro-reflection of one of the output arms. An additional extra-cavity pass of the intra-cavity gain medium, in a self-intersecting master oscillator power amplifier setup, is shown to improve the stable TEM₀₀ operation power from ≈15 to 20.0 W. The spatial quality improvement involves splitting of the gain region into oscillator and amplifier sections leading to enhanced fundamental mode selection. It is believed that the segregation is, at least in part, self-organising.     

On a nonlinear multigrid algorithm with primal relaxation for the image total variation minimisation

Digital image restoration has drawn much attention in the recent years and a lot of research has been done on effective variational partial differential equation models and their theoretical studies. However there remains an urgent need to develop fast and robust iterative solvers, as the underlying problem sizes are large. This paper proposes a fast multigrid method using primal relaxations. The basic primal relaxation is known to get stuck at a ‘local’ non-stationary minimum of the solution, which is usually believed to be ‘non-smooth’. Our idea is to utilize coarse level corrections, overcoming the deadlock of a basic primal relaxation scheme. A further refinement is to allow non-regular coarse levels to correct the solution, which helps to improve the multilevel method. Numerical experiments on both 1D and 2D images are presented.     

Children’s use of realistic considerations in problem solving: some English evidence

This is the second of two papers exploring children’s responses to an extended version of a division-with-remainder problem intended to elicit general rather than particular realistic considerations during mathematical problem solving. Responses to two problems are analyzed. The first is a ‘realistically’ contextualised item drawn from national tests in England whose ambiguities have been previously discussed (Cooper, 1992); the second is a version of this problem revised to encourage a wider range of realistic responses. In Cooper and Harries (2002), the responses of children at the end of their first year of secondary schooling were analyzed. Here the responses of children at the end of their primary schooling are analyzed and compared with the previous results. It is shown that many children, given suitable encouragement, are willing and able to enter into an extended form of realistic thinking during problem solving, although the original test item renders this invisible.     

Derivations on Real and Complex JB*-Triples

At the regional conference held at the University of California,Irvine, in 1985 [24], Harald Upmeier posed three basic questionsregarding derivations on JB*-triples: (1) Are derivations automatically bounded? (2) When are all bounded derivations inner? (3) Can bounded derivations be approximated by inner derivations? These three questions had all been answered in the binary cases.Question 1 was answered affirmatively by Sakai [17] for C*-algebrasand by Upmeier [23] for JB-algebras. Question 2 was answeredby Sakai [18] and Kadison [12] for von Neumann algebras andby Upmeier [23] for JW-algebras. Question 3 was answered byUpmeier [23] for JB-algebras, and it follows trivially fromthe Kadison–Sakai answer to question 2 in the case ofC*-algebras. In the ternary case, both question 1 and question 3 were answeredby Barton and Friedman in [3] for complex JB*-triples. In thispaper, we consider question 2 for real and complex JBW*-triplesand question 1 and question 3 for real JB*-triples. A real orcomplex JB*-triple is said to have the inner derivation propertyif every derivation on it is inner. By pure algebra, every finite-dimensionalJB*-triple has the inner derivation property. Our main results,Theorems 2, 3 and 4 and Corollaries 2 and 3 determine whichof the infinite-dimensional real or complex Cartan factors havethe inner derivation property.     

Fifteen consecutive integers with exactly four prime factors

We describe a successful search for a sequence of fifteen consecutive integers, each the product of exactly four prime factors. Fifteen is best possible.

     

Non-Birational Twisted Derived Equivalences in Abelian GLSMs

In this paper we discuss some examples of abelian gauged linear sigma models realizing twisted derived equivalences between non-birational spaces, and realizing geometries in novel fashions. Examples of gauged linear sigma models with non-birational Kähler phases are a relatively new phenomenon. Most of our examples involve gauged linear sigma models for complete intersections of quadric hypersurfaces, though we also discuss some more general cases and their interpretation. We also propose a more general understanding of the relationship between Kähler phases of gauged linear sigma models, namely that they are related by (and realize) Kuznetsov’s ‘homological projective duality.’ Along the way, we shall see how ‘noncommutative spaces’ (in Kontsevich’s sense) are realized physically in gauged linear sigma models, providing examples of new types of conformal field theories. Throughout, the physical realization of stacks plays a key role in interpreting physical structures appearing in GLSMs, and we find that stacks are implicitly much more common in GLSMs than previously realized.     

Strongly Even‐Cycle Decomposable Graphs

A graph is strongly even‐cycle decomposable if the edge set of every subdivision with an even number of edges can be partitioned into cycles of even length. We prove that several fundamental composition operations that preserve the property of being Eulerian also yield strongly even‐cycle decomposable graphs. As an easy application of our theorems, we give an exact characterization of the set of strongly even‐cycle decomposable cographs.     

On exceptional groups of order p5

A finite group G is exceptional if it has a quotient Q whose minimal faithful permutation degree is greater than that of G. We say that Q is a distinguished quotient.The smallest examples of exceptional p-groups have order $p^5$. For an odd prime p, we classify all pairs $(G,Q)$ where G has order $p^5$ and Q is a distinguished quotient. (The case $p=2$ has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order $p^5$ with at least one exceptional quotient tends to 1/2.     

Development and validation of a sensitive liquid‐chromatography tandem mass spectrometry assay for mycophenolic acid and metabolites in HepaRG cell culture: Characterization of metabolism interactions between p‐cresol and mycophenolic acid

Mycophenolic acid (MPA), a frequently used immunosuppressant, exhibits large inter‐patient pharmacokinetic variability. This study (a) developed and validated a sensitive liquid chromatography–tandem mass spectrometry (LC–MS/MS) assay for MPA and metabolites [MPA glucuronide (MPAG) and acyl‐glucuronide (AcMPAG)] in the culture medium of HepaRG cells; and (b) characterized the metabolism interaction between MPA and p‐cresol (a common uremic toxin) in this in vitro model as a potential mechanism of pharmacokinetic variability. Chromatographic separation was achieved with a C₁₈ column (4.6 × 250 mm,5 μm) using a gradient elution with water and methanol (with 0.1% formic acid and 2 mm ammonium acetate). A dual ion source ionization mode with positive multiple reaction monitoring was utilized. Multiple reaction monitoring mass transitions (m/z) were: MPA (320.95 → 207.05), MPAG (514.10 → 303.20) and AcMPAG (514.10 → 207.05). MPA‐d₃ (323.95 → 210.15) and MPAG‐d₃ (517.00 → 306.10) were utilized as internal standards. The calibration curves were linear from 0.00467 to 3.2 μg/mL for MPA/MPAG and from 0.00467 to 0.1 μg/mL for AcMPAG. The assay was validated based on industry standards. p‐Cresol inhibited MPA glucuronidation (IC₅₀ ≈ 55 μm ) and increased MPA concentration (up to >2‐fold) at physiologically relevant substrate‐inhibitor concentrations (n = 3). Our findings suggested that fluctuations in p‐cresol concentrations might be in part responsible for the large pharmacokinetic variability observed for MPA in the clinic.