Dirac type operators for spin manifolds associated to congruence subgroups of generalized modular groups

Fundamental solutions of Dirac type operators are introduced for a class of conformally. at spin manifolds. This class consists of manifolds obtained by factoring out the upper half-space of R-n by congruence subgroups of generalized modular groups. Basic properties of these fundamental solutions are presented together with associated Eisenstein and Poincare type series

Reciprocal Relations Between Kinetic Curves

We study coupled irreversible processes. For linear or linearized kinetics with microreversibility, $\dot{x}=Kx$, the kinetic operator $K$ is symmetric in the entropic inner product. This form of Onsager's reciprocal relations implies that the shift in time, $\exp (Kt)$, is also a symmetric operator. This generates the reciprocity relations between the kinetic curves. For example, for the Master equation, if we start the process from the $i$th pure state and measure the probability $p_j(t)$ of the $j$th state ($j\neq i$), and, similarly, measure $p_i(t)$ for the process, which starts at the $j$th pure state, then the ratio of these two probabilities $p_j(t)/p_i(t)$ is constant in time and coincides with the ratio of the equilibrium probabilities. We study similar and more general reciprocal relations between the kinetic curves. The experimental evidence provided as an example is from the reversible water gas shift reaction over iron oxide catalyst. The experimental data are obtained using Temporal Analysis of Products (TAP) pulse-response studies. These offer excellent confirmation within the experimental error.Comment: 6 pages, 1 figure, the final versio

Riemann-Hilbert problems for poly-Hardy space on the unit ball

In this paper, we focus on a Riemann–Hilbert boundary value problem (BVP) with a constant coefficients for the poly-Hardy space on the real unit ball in higher dimensions. We first discuss the boundary behaviour of functions in the poly-Hardy class. Then we construct the Schwarz kernel and the higher order Schwarz operator to study Riemann–Hilbert BVPs over the unit ball for the poly- Hardy class. Finally, we obtain explicit integral expressions for their solutions. As a special case, monogenic signals as elements in the Hardy space over the unit sphere will be reconstructed in the case of boundary data given in terms of functions having values in a Clifford subalgebra. Such monogenic signals represent the generalization of analytic signals as elements of the Hardy space over the unit circle of the complex plane

O\u27Hair, James (SC 1538)

Finding aid and scan (Click on Additional Files below) for Manuscripts Small Collection 1538. Notecard featuring silk painting of a sailboat sent from James O\u27Hair in Vietnam to John W. Breeding of Rineyville, Kentucky, wishing him a happy New Year