Weyl group multiple Dirichlet series II: The stable case

To each reduced root system Φ of rank r, and each sufficiently large integer n, we define a family of multiple Dirichlet series in r complex variables, whose group of functional equations is isomorphic to the Weyl group of Φ. The coefficients in these Dirichlet series exhibit a multiplicativity that reduces the specification of the coefficients to those that are powers of a single prime p. For each p, the number of nonzero such coefficients is equal to the order of the Weyl group, and each nonzero coefficient is a product of n-th order Gauss sums. The root system plays a basic role in the combinatorics underlying the proof of the functional equations.     

Light Fluence Rate and Tissue Oxygenation (StO2) Distributions Within the Thoracic Cavity of Patients Receiving Intraoperative Photodynamic Therapy for Malignant Pleural Mesothelioma

The distributions of light and tissue oxygenation (S_tO₂) within the chest cavity were determined for 15 subjects undergoing macroscopic complete resection followed by intraoperative photodynamic therapy (PDT) as part of a clinical trial for the treatment of malignant pleural mesothelioma (MPM). Over the course of light delivery, detectors at each of eight different sites recorded exposure to variable fluence rate. Nevertheless, the treatment-averaged fluence rate was similar among sites, ranging from a median of 40–61 mW cm⁻² during periods of light exposure to a detector. S_tO₂ at each tissue site varied by subject, but posterior mediastinum and posterior sulcus were the most consistently well oxygenated (median S_tO₂ >90%; interquartile ranges ~85–95%). PDT effect on S_tO₂ was characterized as the S_tO₂ ratio (post-PDT S_tO₂/pre-PDT S_tO₂). High S_tO₂ pre-PDT was significantly associated with oxygen depletion (S_tO₂ ratio < 1), although the extent of oxygen depletion was mild (median S_tO₂ ratio of 0.8). Overall, PDT of the thoracic cavity resulted in moderate treatment-averaged fluence rate that was consistent among treated tissue sites, despite instantaneous exposure to high fluence rate. Mild oxygen depletion after PDT was experienced at tissue sites with high pre-PDT S_tO₂, which may suggest the presence of a treatment effect.     

Convergent iterative solutions for a Sombrero-shaped potential in any space dimension and arbitrary angular momentum

We present an explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with an N-dimensional radial potential and an angular momentum l. For g large, the rate of convergence is similar to a power series in g⁻¹.     

Jarlskog invariant of the neutrino mapping matrix

The Jarlskog Invariant J_ν-map of the neutrino mapping matrix is calculated based on a phenomenological model which relates the smallness of light lepton masses m_e and m₁ (of ν₁) with the smallness of T violation. For small T violating phase χ_l in the lepton sector, J_ν-map is proportional to χ_l, but m_e and m₁ are proportional to . This leads to . Assuming , we find J_ν-map≅1.16×10^-2, consistent with the present experimental data.     

Gauge theory on a random lattice

A general formulation of gauge theory on a random lattice is developed and the strong coupling limit of the Wilson string tension worked out. The confining force found in this strong coupling limit is identical to that predicted by the relativistic string model. In particular, the force between two color-triplet charges is a constant for large separation and the tube of electric flux joining the charges fluctuates, giving it a net thickness proportional to the logarithm of its length.     

Mean Value Operators, Differential Operators and D'Atri Spaces

We study commutativity relations between differential operators and spherical means on Riemannian manifolds. The results show that all D'Atri spaces are ball-homogeneous. A further consequence characterizes complete nonpositively curved, simply connected D'Atri spaces by commuting mean value operators.     

A timeon model of quark and lepton mass matrices

It is proposed that T violation in physics, as well as the masses of electron and quarks, arise from a pseudoscalar interaction with a new spin 0 field τ(x), odd in P and T, but even in C. This interaction contains a factor iγ₅ in the quark and lepton Dirac algebra, so that the full Hamiltonian is conserving; but by spontaneous symmetry breaking, the new field τ(x) has a nonzero expectation value τ≠0 that breaks P and T symmetry. Oscillations of τ(x) about its expectation value produce a new particle, the “timeon”. The mass of timeon is expected to be high because of its flavor-changing properties.The main body of the paper is on the low energy phenomenology of the timeon model. As we shall show, for the quark system the model gives a compact three-dimensional geometric picture consisting of two elliptic plates and one needle, which embodies the 10 observables: six quark masses, three Eulerian angles and the Jarlskog invariant of the CKM matrix.For leptons, we assume that the neutrinos do not have a direct timeon interaction; therefore, the lowest neutrino mass is zero. The timeon interaction with charged leptons yields the observed nonzero electron mass, analogous to the up and down quark masses. Furthermore, the timeon model for leptons contains two fewer theoretical parameters than observables. Thus, there are two testable relations between the three angles and the Jarlskog invariant of the neutrino mapping matrix.     

Evaluation of Light Fluence Distribution Using an IR Navigation System for HPPH-mediated Pleural Photodynamic Therapy (pPDT)

Uniform light fluence distribution for patients undergoing photodynamic therapy (PDT) is critical to ensure predictable PDT outcomes. However, current practice when delivering intrapleural PDT uses a point source to deliver light that is monitored by seven isotropic detectors placed within the pleural cavity to assess its uniformity. We have developed a real-time infrared (IR) tracking camera to follow the movement of the light point source and the surface contour of the treatment area. The calculated light fluence rates were matched with isotropic detectors using a two-correction factor method and an empirical model that includes both direct and scattered light components. Our clinical trial demonstrated that we can successfully implement the IR navigation system in 75% (15/20) of the patients. Data were successfully analyzed in 80% (12/15) patients because detector locations were not available for three patients. We conclude that it is feasible to use an IR camera-based system to track the motion of the light source during PDT and demonstrate its use to quantify the uniformity of light distribution, which deviated by a standard deviation of 18% from the prescribed light dose. The navigation system will fail when insufficient percentage of light source positions is obtained (<30%) during PDT.     

Model with strong γ4T-violation

We extend the T violating model of the paper on "Hidden symmetry of the CKM and neutrino mapping matrices" by assuming its T-violating phases X↑ and X↓ to be large and the same,with X = X↑= X↓.In this case,the model has 9 real parameters:α↑,β↑T,ξ↑,η↑ for the ↑-quark sector,α↑,β↑T,ξ↑,η↑ for the ↓sector and a common X.We examine whether these nine parameters are compatible with ten observables:the six quark masses and the four real parameters that characterize the CKM matrix (i.e.,the Jarlskog invariant J and three Eulerian angles).We find that this is possible only if the T violating phase X is large,between -120° to -135°.In this strong T violating model,the smallness of the Jarlskog invariant J ≌ 3 × 10-5 is mainly accounted for by the large heavy quark masses,with mc/mt＜ ms/mb≈ 0.02,as well as the near complete overlap of t and b quark,with (c|b)=-0.04.