We obtain a formula relating the Fourier coefficients of a modular form of half-integral weight (that is constructed as a theta lift from an indefinite quaternion algebra B over Q) to the special values of L-functions. This formula has applications to proving the nonvanishing of a certain explicit theta lift and to an explicit version of the Rallis inner product formula for the dual pair (S̃L2, ...

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...

Abstract This paper focuses on the most prominent theta roles used in the Sindhi language. The study attempts to answer to the research question, ‘How are theta roles prominently used in the Sindhi language?’ The data come from the young native Sindhi speakers. Each verb phrase in the data is examined with the help of Carnie’s (2007) ‘Theta Roles and Thematic Relations’ in order to find the pro...

Abstract This paper focuses on the most prominent theta roles used in the Sindhi language. The study attempts to answer to the research question, ‘How are theta roles prominently used in the Sindhi language?’ The data come from the young native Sindhi speakers. Each verb phrase in the data is examined with the help of Carnie’s (2007) ‘Theta Roles and Thematic Relations’ in order to find the pro...

The first phase of experiments on beat wave acceleration have been completed at UCLA. Here we examined the suitability of a theta pinch as a plasma source. The beatwave was excited to amplitudes providing GeV/m-scale accelerating fields. However, trapped magnetic fields within the theta-pinch plasma hindered the injection of test particles. Optical diagnostics were developed to measure the acce...

The current applications of non-Hermitian but ${\cal PT}-$symmetric Hamiltonians $H$ cover several, mutually not too closely connected subdomains quantum physics. Mathematically, the split between open and closed systems can be characterized by respective triviality non-triviality an auxiliary inner-product metric $\Theta=\Theta(H)$. With our attention restricted to latter, mathematically more ...

The propionate (Pro), decanoate (Dec) and laurate (Lau) esters of 5-(4-hydroxy-3,5-dimethoxyphenylmethylene)-2-thioxothiazoline++ +-3-acetic acid were assessed as substrates for lipase and esterase. On hydrolysis these substrates yield an intensely red coloured phenol which could be assayed at 505 nm. The Pro ester was an effective substrate for porcine esterase and was hydrolysed at a rate 20 ...

In the popular ${\cal PT}-$symmetry-based formulation of quantum mechanics closed systems one can build unitary models using non-Hermitian Hamiltonians (i.e., $H \neq H^\dagger$) which are Hermitizable (so that write, simultaneously, = H^\ddagger$). The essence trick is reference Hilbert space $\cal R$ (in we use conventional inner product $\langle \psi_a|\psi_b\rangle$ and write declared unphy...

Abstract Given an inner function $$\theta $$ θ on the unit disk, let $$K^p_\theta :=H^p\cap \theta {\overline{z}}\overline{H^p}$$ K p : = H ∩ <mm...