A bstract In this paper, we study the general form of three-point functions conserved current multiplets S ? ( k ) = 1… ?k arbitrary rank in four-dimensional $$ \mathcal{N} N 1 superconformal theory. We find that correlation function three such operators \left\langle {\overline{S}}_{\dot{\alpha}(k)}\left({z}_...

We consider the periodic problem for Korteweg–de Vries–Burgers (KdVB) equation with pumping v t − x + α 3 = ∂ 2 , ∈ Ω > 0 ( ) \begin{equation*} {\left\lbrace \def\eqcellsep{&}\begin{array}{c}v_{t}-v_{xx}+\frac{\alpha }{3}v_{xxx}=v+\partial _{x}{\left(v^{2}\right)} ,\text{ }x\in \Omega ,t>0,\\ v(0,x)=v_{0}{\left(x\right)} \end{array} \right.} \end{equation*} where [ π ] $\Omega =[ -\pi ,\pi ]$ R...

Let μ $$ \mu be a finite Borel measure on [ 0,1 ) \left[0,1\right) . In this paper, we consider the generalized integral type Hilbert operator I α + 1 ( f z = ∫ 0 t − d > {\mathcal{I}}_{\mu_{\alpha +1}}(f)(z)={\int}_0^1\frac{f(t)}{{\left(1- tz\right)}^{\alpha +1}} d\mu (t)\kern0.30em \left(\alpha >-1\right). ...

Abstract We show that for any $\varepsilon>0$, $\alpha \in [0,\frac {1}{2})$, as $g\to \infty $ a generic finite-area genus $g$ hyperbolic surface with $n=O\left (g^{\alpha }\right )$ cusps, sampled probability arising from the Weil–Petersson metric on moduli space, has no non-zero eigenvalue of Laplacian below $\frac {1}{4}-\left (\frac {2\alpha +1}{4}\right )^{2}-\varepsilon $. For =0$...

We consider the Dirac operators with singular potentials 1 $$\begin{aligned} D_{\varvec{A},\Phi ,m,\Gamma \delta _{\Sigma }}=\mathfrak {D}_{\varvec{A},\Phi ,m}+\Gamma } \end{aligned}$$ where 2 \mathfrak ,m}= \sum \limits _{j=1}^{n} \alpha _{j}\left( -i\partial _{x_{j}}+A_{j}\right) +\alpha _{n+1}m+\Phi I_{N} is a operator on $$\mathbb {R}^{n}$$ variable magnetic and electrostatic $$\varvec{A=}(...

We show that for a model complete strongly minimal theory whose pregeometry is flat, the recursive spectrum (SRM($T$)) either of form $[0,\alpha )$ $\alpha \in \omega +2$ or $[0,n]\cup \left \{\omega \right \}$ $n\in \omega$, $\{\omega \}$, contained in $\left \{0,1,2\right \}$. Combined with previous results, this leaves precisely 4 sets which it not yet determined whether each flat pregeometry.