In this article, we give necessary and sufficient conditions under which the Leavitt path algebra $$L_K(\mathcal {G})$$ of an ultragraph $$\mathcal {G}$$ over a field K is purely infinite simple that it von Neumann regular. Consequently, obtain every graded either locally matricial algebra, or full matrix ring $$K[x, x^{-1}]$$ , algebra.

In this paper, we compute exactly the average density of a harmonically confined Riesz gas $N$ particles for large in presence hard wall. gas, repel each other via pairwise interaction that behaves as $|x_i - x_j|^{-k}$ $k>-2$, with $x_i$ denoting position $i^{\rm th}$ particle. This can be classified into three different regimes $k$. For $k \geq 1$, where interactions are effectively short-ran...

we study connected orientable spacelike hypersurfaces $x:m^{n}rightarrowm_q^{n+1}(c)$, isometrically immersed into the riemannian or lorentzian space form of curvature $c=-1,0,1$, and index $q=0,1$, satisfying the condition $~l_kx=ax+b$,~ where $l_k$ is the $textit{linearized operator}$ of the $(k+1)$-th mean curvature $h_{k+1}$ of the hypersurface for a fixed integer $0leq k

Let G be a simple graph with order n and size m. The quantity $$M_1(G)=\sum _{i=1}^{n}d^2_{v_i}$$ is called the first Zagreb index of G, where $$d_{v_i}$$ degree vertex $$v_i$$ , for all $$i=1,2,\dots ,n$$ . signless Laplacian matrix $$Q(G)=D(G)+A(G)$$ A(G) D(G) denote, respectively, adjacency diagonal degrees G. $$q_1\ge q_2\ge \dots \ge q_n\ge 0$$ eigenvalues largest eigenvalue $$q_1$$ spectr...

We investigate how a combination of nonmagnetic-impurity scattering rate $\gamma$ and finite subgap states parametrized by Dynes $\Gamma$ affects various physical quantities relevant to superconducting devices: kinetic inductance $L_k$, complex conductivity $\sigma$, surface resistance $R_s$, quality factor $Q$, depairing current density $J_d$. All the calculations are based on Eilenberger form...

We consider L-functions \(L_1,\ldots ,L_k\) from the Selberg class which have polynomial Euler product and satisfy Selberg’s orthonormality condition. show that on every vertical line \(s=\sigma +it\) with \(\sigma \in (1/2,1)\), these simultaneously take large values of size \(\exp \left( c\frac{(\log t)^{1-\sigma }}{\log \log t}\right) \) inside a small neighborhood. Our method extends to =1\...

Let $\mathbf L_k$ be the holomorphic line bundle of degree $k \in \mathbb Z$ on projective line. Here, tuples $(k_1 k_2 k_3 k_4)$ for which there does not exists homogeneous non-split supermanifolds $CP^{1|4}_{k_1 k_4}$ associated with vector L_{−k_1} \oplus \mathbf L _{−k_2} L_{−k_3} L_{−k_4}$ are classified. \\For many types remaining tuples, listed cocycles that determine supermanifolds. \\P...

We present a basis of eigenvectors for the graph building operators acting along mirror channel planar fishnet Feynman integrals in $d$-dimensions. The lattice length $L$ depend on set quantum numbers $(u_k,l_k)$, each associated with rapidity and bound-state index excitation. Each excitation is particle $(1+1)$-dimensions $O(d)$ internal symmetry, wave-functions are formally constructed creati...