For a complete measure space (X,Σ,μ), we give conditions which force Lp(X,μ), for 1 ≤ p < ∞, to be isometrically isomorphic to p(Γ) for some index set Γ which depends only on (X,μ). Also, we give some new characterizations which yield the inclusion Lp(X,μ)⊂ Lq(X,μ) for 0<p < q.

In this paper, we study certain Fuchsian groups H (p1, . . . , pn) , called generalized Hecke groups. These groups are isomorphic to ∏∗ n j=1Zpj . Let Γ be a subgroup of finite index in H (p1, . . . , pn) . By Kurosh’s theorem, Γ is isomorphic to Fr ∗ ∏∗ k i=1Zmi , where Fr is a free group of rank r , and each mi divides some pj . Moreover, H/Γ is Riemann surface. The numbers m1, . . . , mk are...

OBJECTIVE Elevated γ-Glutamyltransferase serum levels are associated with increased risk of overall cancer incidence and several site-specific malignancies. In the present prospective study we report on the associations of serum γ-Glutamyltransferase with the risk of breast cancer in a pooled population-based cohort considering established life style risk factors. METHODS Two cohorts were inc...

A few pages in Siegel [9, p. 115 (§2)] describe how, starting with a fundamental polygon for compact Riemann surface, one can construct symplectic basis of its homology. This note retells that construction, specializing to the case where surface is associated subgroup Γ finite index PSL 2 (ℤ). One then obtains by classical procedures generating system minimal number hyperbolic elements and pres...

The nonlinear coefficients, n4, of the time-dependent refractive index for argon are calculated in the non-resonant optical regime. Second-order polynomial fitting of DC-Kerr, γ((2))(-ω; ω, 0, 0), electric field induced second harmonic generation (ESHG), γ((2))(-2ω; ω, ω, 0), and static second-order hyperpolarizability, γ((2))(0; 0, 0, 0), is performed using an auxiliary electric field approach...

A stability result for the compressible Navier-Stokes system with transport equation for entropy s is shown. The proof comes as an outcome of the isentropic case and additional properties of the effective viscous flux. We deal with the pressure term in the form ρ γ e s with adiabatic index γ > 3/2; therefore the crucial renormalization method is restricted.

Bacground Toxoplasma gondii is an intracellular obligate protozoan parasite that infects most warm-blooded animals including humans. It can cause congenital infection with clinical symptoms ranging from mild to severe including microcephaly. At the cellular level, infection T. gondii causes apoptosis in some tissues and it is induced by proinflammatory cytokines, such as IFN-γ and TNF-α. The pu...

We consider an inverse boundary value problem for the Maxwell equations with boundary data assumed known only in accessible part Γ of the boundary. We aim to prove a uniqueness result using the Dirichlet to Neumann data with measurements limited to an open part of the boundary and we seek to reconstruct the complex refractive index n in the interior of a body. Further, using the impedance map r...

The Schultz molecular topological index (MTI) is compared with the Wiener index (W) of a molecular graph. It is shown that 2VminW < MTI e 4VmaxW holds for any (connected) graph Γ, with Vmin and Vmax denoting the smallest and the largest valency, respectively, of the vertices of Γ. For molecular graphs these bounds can be further improved. For instance, for benzenoid systems we have the followin...