Introduction: There have been multiple explorations for the finding of biological markers of suicide. Some studies indicated the association of neurophysiological markers with suicidal ideation (SI). In previous studies, antidepressant treatment-emergent SI was associated with theta value in midline right frontal region, and pretreatment assessment of frontal quantitative EEG (QEEG) may be asso...

Introduction: There have been multiple explorations for the finding of biological markers of suicide. Some studies indicated the association of neurophysiological markers with suicidal ideation (SI). In previous studies, antidepressant treatment-emergent SI was associated with theta value in midline right frontal region, and pretreatment assessment of frontal quantitative EEG (QEEG) may be asso...

Theta characteristics appeared for the first time in the context of characteristic theory of odd and even theta functions in the papers of Göpel [Go] and Rosenhain [Ro] on Jacobi’s inversion formula for genus 2. They were initially considered in connection with Riemann’s bilinear addition relation between the degree two monomials in theta functions with characteristics. Later, in order to syste...

2014 We study a direct renormalization method for polymer chains near the theta-tricritical point, which we have introduced previously for explicit tricritical calculations. With the help of the dimensional renormalization of field theory in the limit n = 0, we prove that this latter dimensional renormalization as well as the direct one yield a finite renormalized polymer theory to all orders i...

Let Σg,r be a compact oriented surface of genus g with r boundary components. We determine the abelianization of the symmetric mapping class group M̂(g,r)(p2) of a double unbranched cover p2 : Σ2g−1,2r → Σg,r using the Riemann constant, Schottky theta constant, and the theta multiplier. We also give lower bounds of the abelianizations of some finite index subgroups of the mapping class group.

We degenerate the finite gap solutions of KdV equation from general formulation given in terms abelian functions when gaps tend to points, get Fredholm determinants and wronskians. For this we establish a link between Riemann theta functions, This gives bridge algebro-geometric approach Darboux dressing method. construct also multi-parametric rational equation.

Over a perfect field k of characteristic p > 0, we construct a “Witt vector cohomology with compact supports” for separated k-schemes of finite type, extending (after tensorisation with Q) the classical theory for proper k-schemes. We define a canonical morphism from rigid cohomology with compact supports to Witt vector cohomology with compact supports, and we prove that it provides an identifi...

For an action of a finite cyclic group $F$ on $n$-dimensional noncommutative torus $A\_\theta$, we give sufficient conditions when the fundamental projective modules over which determine range canonical trace extend to crossed product $C^\*$-algebra $A\_\theta \rtimes F$. Our results allow us understand F$, and it completely for several examples including products 2-dimensional tori with groups...