Coefficients of Drinfeld modular forms and Hecke operators

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The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

International Society of Urological Pathology (ISUP) Consensus Conference on Handling and Staging of Radical Prostatectomy Specimens. Working group 3: extraprostatic extension, lymphovascular invasion and locally advanced disease.

The International Society of Urological Pathology Consensus Conference on Handling and Staging of Radical Prostatectomy Specimens in Boston made recommendations regarding the standardization of pathology reporting of radical prostatectomy specimens. Issues relating to extraprostatic extension (pT3a disease), bladder neck invasion, lymphovascular invasion and the definition of pT4 were coordinated by working group 3. It was agreed that prostate cancer can be categorized as pT3a in the absence of adipose tissue involvement when cancer bulges beyond the contour of the gland or beyond the condensed smooth muscle of the prostate at posterior and posterolateral sites. Extraprostatic extension can also be identified anteriorly. It was agreed that the location of extraprostatic extension should be reported. Although there was consensus that the amount of extraprostatic extension should be quantitated, there was no agreement as to which method of quantitation should be employed. There was overwhelming consensus that microscopic urinary bladder neck invasion by carcinoma should be reported as stage pT3a and that lymphovascular invasion by carcinoma should be reported. It is recommended that these elements are considered in the development of practice guidelines and in the daily practice of urological surgical pathology.

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

On absoluteness of categoricity in abstract elementary classes

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Hankel operators on holomorphic Hardy-Orlicz spaces

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Potential isomorphism of elementary substructures of a strictly stable homogeneous model

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Complex and real Hausdorff operators

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Moduli of smoothness and rate of a.e. convergence for some convolution operators

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Concomitant cisplatin and hyperfractionated radiotherapy in locally advanced head and neck cancer: 10-year follow-up of a randomized phase III trial (SAKK 10/94).

Purpose: To compare the long-term outcome of treatment with concomitant cisplatin and hyperfractionated radiotherapy versus treatment with hyperfractionated radiotherapy alone in patients with locally advanced head and neck cancer.Methods and Materials: From July 1994 to July 2000, a total of 224 patients with squamous cell carcinoma of the head and neck were randomized to receive either hyperfractionated radiotherapy alone (median total dose, 74.4 Gy; 1.2 Gy twice daily; 5 days per week) or the same radiotherapy combined with two cycles of cisplatin (20 mg/m(2) for 5 consecutive days during weeks 1 and 5). The primary endpoint was the time to any treatment failure; secondary endpoints were locoregional failure, metastatic failure, overall survival, and late toxicity assessed according to Radiation Therapy Oncology Group criteria.Results: Median follow-up was 9.5 years (range, 0.1-15.4 years). Median time to any treatment failure was not significantly different between treatment arms (hazard ratio [HR], 1.2 [95% confidence interval [CM 0.9-1.7; p = 0.17]). Rates of locoregional failure-free survival (HR, 1.5 [95% CI, 1.1-2.1;p = 0.021), distant metastasis-free survival (HR, 1.6 [95% CI, 1.1-2.5; p = 0.021), and cancer-specific survival (HR, 1.6 [95% CI, 1.0-2.5;p = 0.03]) were significantly improved in the combined-treatment arm, with no difference in major late toxicity between treatment arms. However, overall survival was not significantly different (HR, 1.3 [95% CI, 0.9-1.8; p = 0.11]).Conclusions: After long-term follow-up, combined-treatment with cisplatin and hyperfractionated radiotherapy maintained improved rates of locoregional control, distant metastasis-free survival, and cancer-specific survival compared to that of hyperfractionated radiotherapy alone, with no difference in major late toxicity. (C) 2012 Elsevier Inc.

Reduction theorems for operators on the cones of monotone functions

For a quasilinear operator on the semiaxis a reduction theorem is proved on the cones of monotone functions in Lp - Lq setting for 0 < q < ∞, 1<= p < ∞. The case 0 < p < 1 is also studied for operators with additional properties. In particular, we obtain critera for three-weight inequalities for the Hardy-type operators with Oinarov' kernel on monotone functions in the case 0 < q < p <= 1.