Let [Formula: see text] text], be fixed. also text]. We prove on assumption of the Generalized Riemann Hypothesis that each sufficiently large odd integer can represented in form where are for and decimal expansion does not contain digit The proof merges methods Maynard from his paper infinitude primes with restricted digits, results Balog Friedlander Piatetski-Shapiro Hardy–Littlewood circle m...

Up to now, microtubules have been described in the spermatids of all the species studied. In annelids (Webster and Richards, 1977), insects (Friedlander, 1976 ; Godula, 1979), whip scorpions (Phillips, 1976), fishes (Zirkin, 1975), amphibians (Picheral, 1972 ; Sandoz, 1974), sauropsidae (Nagano, 1962 ; Nicander, 1967 ; McIntosh and Porter, 1967 ; Marchand, 1977 ; Maretta, 1977) and such mammals...

In this paper we extend Witten–Helffer–Sjöstrand theory from selfadjoint Laplacians based on fiber wise Hermitian structures, to non-selfadjoint Laplacians based on fiber wise non-degenerate symmetric bilinear forms. As an application we verify, up to sign, the conjecture about the comparison of the Milnor–Turaev torsion with the complex valued analytic torsion, for odd dimensional manifolds. T...

Matthew Tan, Hiromi I. Wettersten, Kristy Chu, David L. Huso, Terry Watnick, Sharon Friedlander, Yosef Landesman, and Robert H. Weiss Graduate Group in Comparative Pathology, Division of Nephrology, Department of Internal Medicine, and Cancer Center, University of California, Davis, California; Department of Molecular and Comparative Pathobiology, Johns Hopkins University School of Medicine, Ba...

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Let N(a, m) be the least integer n (if exists) such that φ(n) ≡ a (mod m). Friedlander and Shparlinski proved that for any ε > 0 there exists A = A(ε) > 0 such that for any positive integer m which has no prime divisors p < (log m) and any integer a with gcd(a,m) = 1, we have the bound N(a,m) ¿ m. In the present paper we improve this bound to N(a,m) ¿ m.

In this paper we extend Witten–Helffer–Sjöstrand theory from selfadjoint Laplacians based on fiber wise Hermitian structures, to non-selfadjoint Laplacians based on fiber wise non-degenerate symmetric bilinear forms. As an application we verify, up to sign, the conjecture about the comparison of the Milnor–Turaev torsion with the complex valued analytic torsion, for odd dimensional manifolds. T...

The gluing formula of the zeta-determinant of a Laplacian given by Burghelea, Friedlander and Kappeler contains an unknown constant. In this paper we compute this constant to complete the formula under the assumption of the product structure near boundary. As applications of this result, we prove the adiabatic decomposition theorems of the zeta-determinant of a Laplacian with respect to the Dir...

Lawrence, N., Martin, A., Toner, G., Stockler, M., Buizen, L., Thomson, D., Gebski, V., Friedlander, M., Yeung, A., Wong, N., Grimison, P., et al (2016). Long-term outcomes of accelerated BEP (bleomycin, etoposide, cisplatin) for advanced germ cell tumours: updated analysis of an Australian multicenter phase II trial by the Australian and New Zealand Urogenital and Prostate Cancer Trials Group ...