Recently, a novel numerical computation on quantum mechanics by using bootstrap method was proposed Han, Hartnoll, and Kruthoff. We consider whether this works in systems with $\ensuremath{\theta}$-term, where the standard Monte-Carlo may fail due to sign problem. As starting point, we study of charged particle circle which constant gauge potential is counterpart $\ensuremath{\theta}$-term. fin...

Based on Spiridonov's analysis of elliptic generalizations of the Gauss hypergeomet-ric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions. In each case we derive the symmetries of the generalized hypergeometric function under the Weyl group of type E 7 (ellip-tic, hyperbolic) and of type E 6...

The hydrostatic equilibrium is a prominent topic in fluid dynamics and astrophysics. Understanding the stability of perturbations near Boussinesq systems helps gain insight into certain weather phenomena. 2D system focused here anisotropic involves only horizontal dissipation thermal diffusion. Due to lack vertical dissipation, precise large-time behavior problem difficult. When spatial domain ...

In this thesis, we formulate and partially prove conjectures à la MazurTate for two cases of L-functions. Suppose given a L-function L(M,K, s) attached to an arithmetic object M over a number field K (a “motive”) so that L can be twisted by characters of the Galois group G of an extension of K. To this pair (L,G), one may hope to associate a theta element Θ(L,G) ∈ A[G], where A is a well define...

Working memory (WM) is known to be associated with synchronization of the theta and alpha bands observed in electroencephalograms (EEGs). Although frontal-posterior global theta synchronization appears in modality-specific WM, local theta synchronization in frontal regions has been found in modality-independent WM. How frontal theta oscillations separately synchronize with task-relevant sensory...

The combined effect of mean and thermal particle motion on Doppler line shape is evaluated. Optical radiation transverse to the axis of a source flow with semi-angle theta(e) is considered in the limit theta(2)(e) <<1. Expressions for gain and anomalous index of refraction are deduced in terms of radiation frequency and a parameter X(e) which characterizes the ratio of mean to thermal motion in...

Let $(X, D)$ be a log variety with an effective holomorphic torus action, and $\Theta$ closed positive $(1,1)$-current. For any smooth function $g$ defined on the moment polytope of we study Monge-Amp\`{e}re equations that correspond to generalized twisted K\"{a}hler-Ricci $g$-solitons. We prove version Yau-Tian-Donaldson (YTD) conjecture for these general equations, showing existence solutions...

Impulsivity is a personality trait within the normal population, but also a feature of many psychiatric disorders that have been associated with poor inhibitory control. The aim of the present study was to examine the relation between subjective impulsivity, theta/beta EEG ratio, and inhibitory control in healthy individuals. In 15 high and 14 low impulsive healthy volunteers (as assessed by th...

Let Q(x) be a quadratic form over Rn. The Epstein zeta function associated to Q(x) is a well known function in number theory. We generalize the construction of the Epstein zeta function to a class of function φ(x) defined in Rn that we call A−homogeneous, where A is a real aquare matrix of order n having each eigenvalue in the left hal space Reλ > 0. Such a class includes all the homogeneous po...

We apply the Hecke operators T (p) and T̃j(p 2) (1 ≤ j ≤ n, p prime) to a degree n theta series attached to a rank 2k Z-lattice L, n ≤ k, equipped with a positive definite quadratic form in the case that L/pL is hyperbolic. We show that the image of the theta series under these Hecke operators can be realized as a sum of theta series attached to certain closely related lattices, thereby generali...