Generalizations of Lie Algebras

The generalizations of Lie algebras appeared in the modern mathematics and mathematical physics. In this paper we consider recent developments and remaining open problems on the subject. Some of that developments have been influenced by lectures given by Professor Jaime Keller in his research seminar. The survey includes Lie superalgebras, color Lie algebras, Lie algebras in symmetric categories, free Lie tau-algebras, and some generalizations with non-associative enveloping algebras: tangent algebras to analytic loops, bialgebras and primitive elements, non-associative Hopf algebras.

ScPdZn and ScPtZn with YAlGe type structure: group-subgroup relation and 45Sc solid state NMR spectroscopy

The intermetallic compounds ScPdZn and ScPtZn were prepared from the elements by high-frequency melting in sealed tantalum ampoules. Both structures were refined from single crystal X-ray diffractometer data: YAlGe type, Cmcm, a = 429.53(8), b = 907.7(1), c = 527.86(1) pm, wR2 = 0.0375, 231 F2 values, for ScPdZn and a = 425.3(1), b = 918.4(2), c = 523.3(1) pm, wR2 = 0.0399, 213 F2 values for ScPtZn with 14 variables per refinement. The structures are orthorhombically distorted variants of the AlB2 type. The scandium and palladium (platinum atoms) build up ordered networks Sc3Pd3 and Sc3Pt3 (boron networks) which are slightly shifted with respect to each other. These networks are penetrated by chains of zinc atoms (262 pm in ScPtZn) which correspond to the aluminum positions, i.e. Zn(ScPd) and Zn(ScPt). The corresponding group-subgroup scheme and the differences in chemical bonding with respect to other AlB2-derived REPdZn and REPtZn compounds are discussed. 45Sc solid state NMR spectra confirm the single crystallographic scandium sites. From electronic band structure calculations the two compounds are found metallic with free electron like behavior at the Fermi level. A larger cohesive energy for ScPtZn suggests a more strongly bonded intermetallic than ScPdZn. Electron localization and overlap population analyses identify the largest bonding for scandium with the transition metal (Pd, Pt).

Serum free testosterone, leptin and soluble leptin receptor changes in a 6-week strength-training programme

[EN] Strength training is usually associated with a reduction in fat mass and with muscle hypertrophy. The aim of the present study was to examine whether the serum free leptin index (FLI), measured by the molar excess of soluble leptin receptor (sOB-R) over leptin, is increased by 6 weeks of strength training. Eighteen male, physical education students were randomly assigned to two groups: a strength-training (n 12) and a control group (n 6). Body composition (lean body mass and body fat) determined by dual-energy X-ray absorptiometry (DXA), muscle performance and leptin, sOB-R, total testosterone and free testosterone concentrations were determined before and after training. Fat mass was reduced by 1 kg with strength training (P<0.05). Lean body mass of trained extremities was increased by 3% (P<0.05), while the concentration of free testosterone in serum was reduced by 17% (P<0.05) after training. However, despite the reduction in fat mass and free testosterone, serum leptin concentration was not significantly affected by strength training, even after accounting for the differences in body fat. By contrast, for a given fat mass, the sOB-R was increased by 13% (P<0.05) at the end of the strength-training programme, although the molar excess of sOB-R over leptin remained unchanged. Therefore, the quantity of free leptin available to bind to the target tissues was not significantly affected by the short strength-training programme, which elicited a 7% reduction in fat mass.

Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

Skeletal muscle (1) H MRSI before and after prolonged exercise. II. visibility of free carnitine

Carnitine (Car) buffers excess acetyl-CoA through the formation of acetylCar (AcCar). AcCar's acetyl group (AG-AcCar) gives rise to a peak at 2.13 ppm in ¹H MR spectra of skeletal muscle, whereas the trimethylammonium (TMA) groups of both, AcCar and Car, are thought to contribute to the TMA peak at 3.23 ppm. Surprisingly, in previous studies both resonances, AG-AcCar and TMA, increased after exercise. The aim of this study was to assess if the exercise-related TMA increase correlated with AcCar production. Magnetic resonance spectroscopic imaging (pulse repetition time/echo time = 1200/35 ms) was performed before and after prolonged exercise in the lower leg and thigh of eight runners and eight cyclists, respectively. TMA and AG-AcCar increased after exercise (P < 0.001). TMA's increase correlated with the AG-AcCar increase (R² = 0.73, P < 0.001, lower leg; R² = 0.28, P < 0.001, thigh). The correlation of ΔTMA with ΔAG-AcCar suggests that the TMA increase is due to AcCar formation. As total Car (Car + AcCar) remains unchanged with exercise, these findings suggest that the contribution of free Car to the TMA peak is limited and, therefore, is partly invisible in muscle ¹H MR spectra. This indicates that the biochemically relevant cytosolic content of free Car is considerably lower than the overall concentration determined by radioisotopic assays, a potentially important result with respect to regulation of substrate oxidation.

The Extremely Red, Young L Dwarf PSO J318.5338-22.8603: a Free-Floating Planetary-Mass Analog to Directly Imaged Young Gas-Giant Planets

We have discovered using Pan-STARRS1 an extremely red late-L dwarf, which has (J - K)(MKO) = 2.78 and (J - K) (2MASS) = 2.84, making it the reddest known field dwarf and second only to 2MASS J1207-39b among substellar companions. Near-IR spectroscopy shows a spectral type of L7 +/- 1 and reveals a triangular H-band continuum and weak alkali (K I and Na I) lines, hallmarks of low surface gravity. Near-IR astrometry from the Hawaii Infrared Parallax Program gives a distance of 24.6 +/- 1.4 pc and indicates a much fainter J-band absolute magnitude than field L dwarfs. The position and kinematics of PSO J318.5-22 point to membership in the beta Pic moving group. Evolutionary models give a temperature of 1160(-40)(+30) K and a mass of 6.5(-1.0)(+1.3) M-Jup, making PSO J318.5-22 one of the lowest mass free-floating objects in the solar neighborhood. This object adds to the growing list of low-gravity field L dwarfs and is the first to be strongly deficient in methane relative to its estimated temperature. Comparing their spectra suggests that young L dwarfs with similar ages and temperatures can have different spectral signatures of youth. For the two objects with well constrained ages (PSO J318.5-22 and 2MASS J0355+11), we find their temperatures are approximate to 400 K cooler than field objects of similar spectral type but their luminosities are similar, i.e., these young L dwarfs are very red and unusually cool but not "underluminous." Altogether, PSO J318.5-22 is the first free-floating object with the colors, magnitudes, spectrum, luminosity, and mass that overlap the young dusty planets around HR 8799 and 2MASS J1207-39

Early molecular and cytogenetic response is predictive for long-term progression-free and overall survival in chronic myeloid leukemia (CML)

In the face of competing first-line treatment options for CML, early prediction of prognosis on imatinib is desirable to assure favorable survival or otherwise consider the use of a second-generation tyrosine kinase inhibitor (TKI). A total of 1303 newly diagnosed imatinib-treated patients (pts) were investigated to correlate molecular and cytogenetic response at 3 and 6 months with progression-free and overall survival (PFS, OS). The persistence of BCR-ABL transcript levels >10% according to the international scale (BCR-ABL(IS)) at 3 months separated a high-risk group (28% of pts; 5-year OS: 87%) from a group with >1-10% BCR-ABL(IS) (41% of pts; 5-year OS: 94%; P=0.012) and from a group with 1% BCR-ABL(IS) (31% of pts; 5-year OS: 97%; P=0.004). Cytogenetics identified high-risk pts by >35% Philadelphia chromosome-positive metaphases (Ph+, 27% of pts; 5-year OS: 87%) compared with 35% Ph+ (73% of pts; 5-year OS: 95%; P=0.036). At 6 months, >1% BCR-ABL(IS) (37% of pts; 5-year OS: 89%) was associated with inferior survival compared with 1% (63% of pts; 5-year OS: 97%; P<0.001) and correspondingly >0% Ph+ (34% of pts; 5-year OS: 91%) compared with 0% Ph+ (66% of pts; 5-year OS: 97%; P=0.015). Treatment optimization is recommended for pts missing these landmarks.

Addition of bevacizumab to chemotherapy in acute myeloid leukemia at older age: a randomized phase 2 trial of the Dutch-Belgian Cooperative Trial Group for Hemato-Oncology (HOVON) and the Swiss Group for Clinical Cancer Research (SAKK)

An urgent need for new treatment modalities is emerging in elderly patients with acute myeloid leukemia (AML). We hypothesized that targeting VEGF might furnish an effective treatment modality in this population. Elderly patients with AML were randomly assigned in this phase 2 study (n = 171) to receive standard chemotherapy (3 + 7) with or without bevacizumab at a dose of 10 mg/kg intravenously at days 1 and 15. In the second cycle, patients received cytarabine 1000 mg/m(2) twice daily on days 1-6 with or without bevacizumab. The complete remission rates in the 2 arms were not different (65%). Event-free survival at 12 months was 33% for the standard arm versus 30% for the bevacizumab arm; at 24 months, it was 22% and 16%, respectively (P = .42). The frequencies of severe adverse events (SAEs) were higher in the bevacizumab arm (n = 63) compared with the control arm (n = 28; P = .043), but the percentages of death or life-threatening SAEs were lower in the bevacizumab arm (60% vs 75% of SAEs). The results of the present study show that the addition of bevacizumab to standard chemotherapy does not improve the therapeutic outcome of older AML patients. This trial is registered as number NTR904 in The Nederlands Trial Register (www.trialregister.nl).

Tamoxifen after adjuvant chemotherapy for premenopausal women with lymph node-positive breast cancer: International Breast Cancer Study Group Trial 13-93

PURPOSE: The value of adjuvant tamoxifen after chemotherapy for premenopausal women with breast cancer has not been adequately assessed. PATIENTS AND METHODS: Between 1993 and 1999, International Breast Cancer Study Group Trial 13-93 enrolled 1,246 assessable premenopausal women with axillary node-positive, operable breast cancer. All patients received chemotherapy (cyclophosphamide plus either doxorubicin or epirubicin for four courses followed by immediate or delayed classical cyclophosphamide, methotrexate, and fluorouracil for three courses), which was followed by either tamoxifen (20 mg daily) for 5 years or no further treatment. The primary end point was disease-free survival (DFS). Tumors were classified as estrogen receptor (ER) -positive (n = 735, 59%) if immunohistochemical (IHC) or ligand-binding assays (LBA) were clearly positive. The ER-negative group included all other tumors (n = 511, 41%). A subset of the ER-negative group was defined as ER absent (n = 108, 9%) if IHC staining was none or if the LBA result was 0 fmol/mg cytosol protein. The median follow-up time was 7 years. RESULTS: Tamoxifen improved DFS in the ER-positive cohort (hazard ratio [HR] for tamoxifen v no tamoxifen = 0.59; 95% CI, 0.46 to 0.75; P < .0001) but not in the ER-negative cohort (HR = 1.02; 95% CI, 0.77 to 1.35; P = .89). Tamoxifen had a detrimental effect on patients with ER-absent tumors compared with no tamoxifen in an unplanned exploratory analysis (HR = 2.10; 95% CI, 1.03 to 4.29; P = .04). Patients with ER-positive tumors who achieved chemotherapy-induced amenorrhea had a significantly improved outcome (HR for amenorrhea v no amenorrhea = 0.61; 95% CI, 0.44 to 0.86; P = .004), whether or not they received tamoxifen. CONCLUSION: Tamoxifen after adjuvant chemotherapy significantly improved treatment outcome in premenopausal patients with endocrine-responsive disease, but its use as adjuvant therapy for patients with ER-negative tumors is not recommended.

Multicycle dose-intensive chemotherapy for women with high-risk primary breast cancer: results of International Breast Cancer Study Group Trial 15-95

PURPOSE: To compare adjuvant dose-intensive epirubicin and cyclophosphamide chemotherapy administered with filgrastim and progenitor cell support (DI-EC) with standard-dose anthracycline-based chemotherapy (SD-CT) for patients with early-stage breast cancer and a high risk of relapse, defined as stage II disease with 10 or more positive axillary nodes; or an estrogen receptor-negative or stage III tumor with five or more positive axillary nodes. PATIENTS AND METHODS: Three hundred forty-four patients were randomized after surgery to receive seven cycles of SD-CT over 22 weeks, or three cycles of DI-EC (epirubicin 200 mg/m2 plus cyclophosphamide 4 gm/m2 with filgrastim and progenitor cell support) over 6 weeks. All patients were assigned tamoxifen at the completion of chemotherapy. The primary end point was disease-free survival (DFS). RESULTS: After a median follow-up of 5.8 years (range, 3 to 8.4 years), 188 DFS events had occurred (DI-EC, 86 events; SD-CT, 102 events). The 5-year DFS was 52% for DI-EC and 43% for SD-CT, with hazard ratio of DI-EC compared with SD-CT of 0.77 (95% CI, 0.58 to 1.02; P = .07). The 5-year overall survival was 70% for DI-EC and 61% for SD-CT, with a hazard ratio of 0.79 (95% CI, 0.56 to 1.11; P = .17). There were eight cases (5%) of anthracycline-induced cardiomyopathy (two fatal) among those who received DI-EC. Women with hormone receptor-positive tumors benefited significantly from DI-EC. CONCLUSION: There was a trend in favor of DI-EC with respect to disease-free survival. A larger trial or meta-analysis will be required to reveal the true effect of dose-intensive therapy.

Randomized trial comparing axillary clearance versus no axillary clearance in older patients with breast cancer: first results of International Breast Cancer Study Group Trial 10-93

Axillary clearance in early breast cancer aims to improve locoregional control and provide staging information but is associated with undesirable morbidity. We therefore investigated whether avoiding axillary surgery in older women would result in improved quality of life (QL) with similar disease-free survival (DFS) and overall survival (OS).

An in vivo study of a growth-factor enhanced, cell free, two-layered collagen-tricalcium phosphate in deep osteochondral defects

Focal osteochondral defects are still a challenging problem in joint surgery. We have developed a two-layered implant consisting of a basal porous beta-tricalcium phosphate (TCP) for bone reconstruction and a superficial fibrous collagen type I/III layer for cartilage regeneration. Fifty-four osteochondral defects in the trochlear groove of 27 Göttinger Minipigs were created and either left untreated, treated with the implant alone, or the implant augmented with an additional growth factor mixture, which was assumed to stimulate cell and tissue differentiation. Follow-up was 6, 12 and 52 weeks with n=6 for each group. The repair tissue was evaluated for its gross appearance and biomechanical properties. Histological sections were semi-quantitatively scored for their histomorphological structure. Treatment with the two-layered implant improved defect filling and subchondral bone repair at 6 and 12 weeks follow-up. The TCP was replaced by cancellous bone at 52 weeks. Cartilage repair tissue mainly consisted of fibrocartilage and showed a moderate cell density up to the joint surface. Growth factor treatment improved the mechanical and histomorphological properties of the cartilage repair tissue at 12, but not at 52 weeks postoperatively. In conclusion, the two-layered collagen-TCP implant augmented with chondroinductive growth factors seems a promising new option for the treatment of deep osteochondral defects in joint surgery.

Human group II 14 kDa phospholipase A2 activates human platelets

Recombinant human group II phospholipase A2 (sPLA2) added to human platelets in the low microg/ml range induced platelet activation, as demonstrated by measurement of platelet aggregation, thromboxane A2 generation and influx of intracellular free Ca2+ concentration and by detection of time-dependent tyrosine phosphorylation of platelet proteins. The presence of Ca2+ at low millimolar concentrations is a prerequisite for the activation of platelets by sPLA2. Mg2+ cannot replace Ca2+. Mg2+, given in addition to the necessary Ca2+, inhibits sPLA2-induced platelet activation. Pre-exposure to sPLA2 completely blocked the aggregating effect of a second dose of sPLA2. Albumin or indomethacin inhibited sPLA2-induced aggregation, similarly to the inhibition of arachidonic acid-induced aggregation. Platelets pre-treated with heparitinase or phosphatidylinositol-specific phospholipase C lost their ability to aggregate in response to sPLA2, although they still responded to other agonists. This suggests that a glycophosphatidylinositol-anchored platelet-membrane heparan sulphate proteoglycan is the binding site for sPLA2 on platelets. Previous reports have stated that sPLA2 is unable to activate platelets. The inhibitory effect of albumin and Mg2+, frequently used in aggregation studies, and the fact that isolated platelets lose their responsiveness to sPLA2 relatively quickly, may explain why the platelet-activating effects of sPLA2 have not been reported earlier.

CA15-3 and alkaline phosphatase as predictors for breast cancer recurrence: a combined analysis of seven International Breast Cancer Study Group trials

BACKGROUND: We evaluated the ability of CA15-3 and alkaline phosphatase (ALP) to predict breast cancer recurrence. PATIENTS AND METHODS: Data from seven International Breast Cancer Study Group trials were combined. The primary end point was relapse-free survival (RFS) (time from randomization to first breast cancer recurrence), and analyses included 3953 patients with one or more CA15-3 and ALP measurement during their RFS period. CA15-3 was considered abnormal if >30 U/ml or >50% higher than the first value recorded; ALP was recorded as normal, abnormal, or equivocal. Cox proportional hazards models with a time-varying indicator for abnormal CA15-3 and/or ALP were utilized. RESULTS: Overall, 784 patients (20%) had a recurrence, before which 274 (35%) had one or more abnormal CA15-3 and 35 (4%) had one or more abnormal ALP. Risk of recurrence increased by 30% for patients with abnormal CA15-3 [hazard ratio (HR) = 1.30; P = 0.0005], and by 4% for those with abnormal ALP (HR = 1.04; P = 0.82). Recurrence risk was greatest for patients with either (HR = 2.40; P < 0.0001) and with both (HR = 4.69; P < 0.0001) biomarkers abnormal. ALP better predicted liver recurrence. CONCLUSIONS: CA15-3 was better able to predict breast cancer recurrence than ALP, but use of both biomarkers together provided a better early indicator of recurrence. Whether routine use of these biomarkers improves overall survival remains an open question.