In recent years, there has been significant uptake of meditation and related relaxation techniques, as a means of alleviating stress and fostering an attentive mind. Several electroencephalogram (EEG) studies have reported changes in spectral band frequencies during Qigong meditation indicating a relaxed state. Much less is reported on effects of brain activation patterns induced by Qigong tech...

The partial theta function is the sum of series \medskip\centerline{$\displaystyle\theta (q,x):=\sum\nolimits _{j=0}^{\infty}q^{j(j+1)/2}x^j$,}\medskip\noi where $q$is a real or complex parameter ($|q|<1$). Its name due to similaritieswith formula for Jacobi function$\Theta (q,x):=\sum _{j=-\infty}^{\infty}q^{j^2}x^j$. $\theta$ has been considered in Ramanujan's lost notebook. Itfinds applic...

Although the authors do not emphasize the point, there appears to be more theta from the temporal lobe electrodes than from the others. Because surface electrodes were used, the present study could not identify the generator for this activity, much less localize it to the hippocampal formation. Furthermore the authors did not comment on the relationship between theta activity in different areas...

We use Jacobi theta functions to construct examples of Jacobi forms over number fields. We determine the behavior under modular transformations by regarding certain coefficients of the Jacobi theta functions as specializations of symplectic theta functions. In addition, we show how sums of those Jacobi theta functions appear as a single coefficient of a symplectic theta function. 2000 Mathemati...

In this paper, we deal to obtain some new complexity results for solving semidefinite optimization (SDO) problem by interior-point methods (IPMs). We define a new proximity function for the SDO by a new kernel function. Furthermore we formulate an algorithm for a primal dual interior-point method (IPM) for the SDO by using the proximity function and give its complexity analysis, and then we sho...

We give a local deformation theoretic proof of Farkas’ conjecture that a principally polarized complex abelian variety of dimension 4 whose theta divisor has an isolated double point of rank 3 at a point of order two is a Jacobian. The argument yields an explicit local normal form for the theta function near such a point. The proof depends only on the facts that the theta function is even, a ge...