Isotherm migration along orthogonal flow lines in two dimensions

A novel approach to the solution of transient heat flow problems in two dimensions is described. The movements of isotherms along orthogonal flow lines are tracked in successive small intervals of time by solving a locally one-dimensional IMM form of radial heat equation. The determination of the new orientation of the orthogonal system at the end of each time interval is based on geometrical considerations. The method is applied to the moving boundary problem presented by the solidification of a square prism of fluid and the results compared with those obtained by the enthalpy method

Reference incidence angles in constant stagger cascades

Fortran 4 computer program for design application of stagger angle replacing inlet flow angle for given blade cascad

Hyperasymptotic solutions for certain partial differential equations

We present the hyperasymptotic expansions for a certain group of solutions of the heat equation. We extend this result to a more general case of linear PDEs with constant coefficients. The generalisation is based on the method of Borel summability, which allows us to find integral representations of solutions for such PDEs.Comment: 17 page

One-Watt level mid-IR output, singly resonant, continuous-wave optical parametric oscillator pumped by a monolithic diode laser

We report more than 1.1 Watt of idler power at 3373 nm in a singly resonant optical parametric oscillator (SRO), directly pumped by a single-frequency monolithic tapered diode laser. The SRO is based on a periodically poled MgO:LiNbO3 crystal in a four mirror cavity and is excited by 8.05 W of 1062 nm radiation. The SRO pump power at threshold is 4 W. The internal slope-efficiency and conversion efficiency reach 89% and 44% respectively. The signal and idler waves are temperature tuned in the range of 1541 to 1600 nm and 3154 to 3415 nm respectively. To the best of our knowledge, this is the highest output obtained for a diode pumped optical parametric oscillator (OPO), and the first time a SRO is directly pumped by a monolithic tapered diode laser

Derived equivalence classification of the cluster-tilted algebras of Dynkin type E

We obtain a complete derived equivalence classification of the cluster-tilted algebras of Dynkin type E. There are 67, 416, 1574 algebras in types E6, E7 and E8 which turn out to fall into 6, 14, 15 derived equivalence classes, respectively. This classification can be achieved computationally and we outline an algorithm which has been implemented to carry out this task. We also make the classification explicit by giving standard forms for each derived equivalence class as well as complete lists of the algebras contained in each class; as these lists are quite long they are provided as supplementary material to this paper. From a structural point of view the remarkable outcome of our classification is that two cluster-tilted algebras of Dynkin type E are derived equivalent if and only if their Cartan matrices represent equivalent bilinear forms over the integers which in turn happens if and only if the two algebras are connected by a sequence of "good" mutations. This is reminiscent of the derived equivalence classification of cluster-tilted algebras of Dynkin type A, but quite different from the situation in Dynkin type D where a far-reaching classification has been obtained using similar methods as in the present paper but some very subtle questions are still open.Comment: 19 pages. v4: completely rewritten version, to appear in Algebr. Represent. Theory. v3: Main theorem strengthened by including "good" mutations (cf. also arXiv:1001.4765). Minor editorial changes. v2: Third author added. Major revision. All questions left open in the earlier version by the first two authors are now settled in v2 and the derived equivalence classification is completed. arXiv admin note: some text overlap with arXiv:1012.466

On Hierarchy and Equivalence of Relativistic Equations for Massive Fields

A non-canonical correspondence of the complete sets of solutions to the Dirac and Klein-Gordon free equations in Minkowski space-time is established. This allows for a novel viewpoint on the relationship of relativistic equations for different spins and on the origin of spinor transformations. In particular, starting from a solution to the Dirac equation, one obtains a chain of other solutions to both Dirac and Klein-Gordon equations. A comparison with the massless case is performed, and examples of non-trivial singular solutions are presented. A generalization to Riemannian space-time and inclusion of interactions are briefly discussed.Comment: 7 pages, twocolumn. Problem of construction the hierarchy of solutions in the massive case reformulate

The PML-RAR alpha transcript in long-term follow-up of acute promyelocytic leukemia patients

Background and Objectives. Detection of PML-RAR alpha transcripts by RT-PCR is now established as a rapid and sensitive method for diagnosis of acute promyelocytic leukemia (APL), Although the majority of patients in longterm clinical remission are negative by consecutive reverse transcription polymerase chain reaction (RT-PCR) assays, negative tests are still observed in patients who ultimately relapse. Conversion from negative to positive PCR has been observed after consolidation and found to be a much stronger predictor of relapse. This study reports on 47 APL patients to determine the correlation between minimal residual disease (MRD) status and clinical outcome in our cohort of patients. Design and Methods. The presence of PML-RAR alpha t transcripts was investigated in 47 APL patients (37 adults and 10 children) using a semi-nested reverse transcriptase-polymerase chain reaction to evaluate the prognostic value of RT-PCR tests. Results. All patients achieved complete clinical remission (CCR) following induction treatment with all-trans retinoic acid (ATRA) and chemotherapy (CHT) or ATRA alone. Patients were followed up between 2 and 117.6 months (median: 37 months). Relapses occurred in 11 patients (9 adults and 2 children) between 11.4 and 19 months after diagnosis (median: 15.1 months) while 36 patients (28 adults and 8 children) remained in CCR, Seventy-five percent of patients carried the PML-RARa long isoform (bcr 1/2) which also predominated among the relapsed cases (9 of 11) but did not associate with any adverse outcome (p = 0.37), For the purpose of this analysis, minimal residual disease tests were clustered into four time-intervals: 0-2 months, 3-5 months, 5-9 months and 10-24 months. Interpretation and Conclusions. Children showed persisting disease for longer than adults during the first 2 months of treatment, At 2 months, 10 (50%) of 20 patients who remained in CCR and 4 (80%) of 5 patients who subsequently relapsed were positive. Patients who remained in CCR had repeatedly negative results beyond 5.5 months from diagnosis. A positive MRD test preceded relapse in 3 of 4 tested patients. The ability of a negative test to predict CCR (predictive negative value, PNV) was greater after 6 months (> 83%), while the ability of a positive test to predict relapse (predictive positive value, PPV) was most valuable only beyond 10 months (100%). This study (i) highlights the prognostic value of RT-PCR monitoring after treatment of APL patients but only from the end of treatment, (ii) shows an association between conversion to a positive test and relapse and (iii) suggests that PCR assessments should be carried out at 3-month intervals to provide a more accurate prediction of hematologic relapses but only after the end of treatment, (C) 2001, Ferrata Storti Foundatio