for any lacunary sequence $theta = (k_{r})$, we define the concepts of $s_{theta}-$limit point and $s_{theta}-$cluster point of a sequence of fuzzy numbers $x = (x_{k})$. we introduce the new sets  $lambda^{f}_{s_{theta}}(x)$, $gamma^{f}_{s_{theta}}(x)$ and prove some inclusion relaions between these and the sets $lambda^{f}_{s}(x)$, $gamma^{f}_{s}(x)$ introduced in ~cite{ayt:slpsfn} by aytar [...

We consider (3+1)-dimensional SU(N)/ZN Yang-Mills theory on a space-time with a compact spatial direction, and prove the following result: Under a continuous increase of the theta angle θ → θ+2π, a ’t Hooft operator T (γ) associated with a closed spatial curve γ that winds around the compact direction undergoes a monodromy T (γ) → T (γ). The new ’t Hooft operator T (γ) transforms under large ga...

It is well known that an (in general, non-commutative) set of non-Hermitian operators $\Lambda_j$ with real eigenvalues need not necessarily represent observables. We describe a specific class quantum models in which these plus the underlying physical Hilbert-space metric $\Theta$ are all represented terms auxiliary operator $(N+1)-$plet $Z_k$, $k=0,1,\ldots,N$. Our formalism degenerates to ${\...

We present a detailed study of the electric dipole moment of the neutron induced by a vacuum theta angle within the framework of QCD sum rules. At next-to-next-to leading order in the operator product expansion, we find the result dn(θ) = 1.2 × 10 −16θ̄e · cm, to approximately 40% precision. With the current experimental bound this translates into a limit on the theta parameter of |θ̄| < 6 × 10−1...

Using Krattenthaler’s operator method, we give a new proof of Warnaar’s recent elliptic extension of Krattenthaler’s matrix inversion. Further, using a theta function identity closely related to Warnaar’s inversion, we derive summation and transformation formulas for elliptic hypergeometric series of Karlsson–Minton-type. A special case yields a particular summation that was used by Warnaar to ...

In this work, we aim to prove the theta dichotomy conjecture for dual dual pairs of type ( ̃ Sp(W ),O(V )) with dim(V ) odd. The crux of the proof relies on the analysis the reducibility of a certain a degenerate principal series representation of the group ̃ Sp(W ′) having double the rank of ̃ Sp(W ). This analysis is carried out by way of a normalized standard intertwining operator which is al...

Let $$\mathcal {H}$$ be a complex Hilbert space with inner product $$\langle \cdot , \rangle $$ and let A non-zero bounded positive linear operator on {H}.$$ $$\mathbb {B}_A(\mathcal {H})$$ denote the algebra of all operators which admit A-adjoint, $$N_A(\cdot )$$ seminorm . The generalized A-numerical radius $$T\in \mathbb is defined as $$\begin{aligned} \omega _{N_A}(T)=\displaystyle {\sup _{...

The focus of this paper is on Ahlfors Q-regular compact sets $$E\subset \mathbb {R}^n$$ such that, for each $$Q-2<\alpha \le 0$$ , the weighted measure $$\mu _{\alpha }$$ given by integrating density $$\omega (x)=\text {dist}(x, E)^\alpha $$ yields a Muckenhoupt $$\mathcal {A}_p$$ -weight in ball B containing E. For E we show existence bounded linear trace operator acting from $$W^{1,p}(B,...