In this paper, we construct a splitting of the metaplectic cover of the reductive dual pairs of orthogonal and symplectic groups or the reductive dual pairs of unitary groups over a nonarchimedean local field with respect to a generalized lattice model of the Weil representation. We also prove a result concerning the splitting that we construct and the theta dichotomy for unitary group. The spl...

The KP equation has a large family of quasiperiodic multiphase solutions. These solutions can be expressed in terms of Riemann-theta functions. In this paper, a finite-dimensional canonical Hamiltonian system depending on a finite number of parameters is given for the description of each such solution. The Hamiltonian systems are completely integrable in the sense of Liouville. In effect, this ...

OBJECTIVE Studies have suggested that non-phase-locked event-related oscillations (ERO) in target stimulus processing might provide biomarkers of alcoholism. This study investigates the discriminatory power of non-phase-locked oscillations in a group of long-term abstinent alcoholics (LTAAs) and non-alcoholic controls (NACs). METHODS EEGs were recorded from 48 LTAAs and 48 age and gender comp...

Ramanujan’s famous deathbed letter to G. H. Hardy concerns the asymptotic properties of modular forms and his so-called mock theta functions. For his mock theta function f(q), he asserts, as q approaches an even order 2k root of unity, that we have f(q)− (−1)(1− q)(1− q)(1− q) · · · ` 1− 2q + 2q − · · · ́ = O(1). We give two proofs of this claim by offering exact formulas for these limiting valu...

We study the low-lying spectrum of bilinear-biquadratic Heisenberg model in dimerized and Haldane phases using a tensor renormalization method. At critical point $\ensuremath{\theta}=\ensuremath{-}\ensuremath{\pi}/4$, finite-size predicted by Wess-Zumino-Witten (WZW) can only partly be confirmed. find singlet-singlet gap which does not fit into WZW systematics. The results obtained are compared...

The speed of theta brain oscillatory activity is thought to play a key role in determining working memory (WM) capacity. Individual differences in the length of a theta cycle (ranging between 4 and 7 Hz) might determine how many gamma cycles (>30 Hz) can be nested into a theta wave. Gamma cycles are thought to represent single memory items; therefore, this interplay could determine individual m...