A metric graph is a pair (G, d), where G and $$d:E(G) \rightarrow \mathbb {R}_{\ge 0}$$ distance function. Let $$p \in [1,\infty ]$$ be fixed. An isometric embedding of the d) in $$\ell _p^k = (\mathbb {R}^k, d_p)$$ map $$\phi :V(G) {R}^k$$ such that $$d_p(\phi (v), \phi (w)) d(vw)$$ for all edges $$vw\in E(G)$$ . The _p$$ -dimension least integer k there exists an _p^k$$ functions d has _p^K$$...

Canonical threefold singularities in M-theory and Type IIB string theory give rise to superconformal field theories (SCFTs) 5d 4d, respectively. In this paper, we study canonical hypersurface whose resolutions contain residual terminal and/or 3-cycles. We focus on a certain class of `trinion' which exhibit these properties. IIB, they 4d $\mathcal{N}=2$ SCFTs that call $D_p^b(G)$-trinions, are m...

A 1-form symmetry and a 0-form may combine to form an extension known as the 2-group symmetry. We find presence of latter in class Argyres-Douglas theories, called $D_p($USp$(2N))$, which can be realized by $\mathbb{Z}_2$-twisted compactification 6d $\mathcal{N}=(2,0)$ $D$-type on sphere with irregular twisted puncture regular full puncture. propose $3$d mirror theories general $D_p($USp$(2N))$...

In this article we introduce a family of valuative invariants defined in terms the p-th moment expected vanishing order. These lie between $$\alpha $$ and $$\delta -invariants. They vary continuously big cone semi-continuously families. Most importantly, they give sufficient conditions for K-stability Fano varieties, which generalizes -criterions literature. are also related to $$d_p$$ -geometr...

Argyres-Douglas theories constitute an important class of superconformal field in $4$d. The main focus this paper is on two infinite families such theories, known as $D^b_p(\mathrm{SO}(2N))$ and $(A_m, D_n)$. We analyze depth their conformal manifolds. In doing so we encounter several $\mathcal{S}$ twisted $A_{\text{odd}}$, $A_{\text{even}}$ $D$ types associated with a sphere one irregular punc...

In this paper, we will discuss the concept of almost sure convergence for specic groups of fuzzyrandom variables. For this purpose, we use the type of generalized Chebyshev inequalities.Moreover, we show the concept of almost sure convergence of weighted average pairwise NQDof fuzzy random variables.

We evaluate the contribution of CP violating gluon chromo-electric dipole moment (the so-called Weinberg operator, denoted as $w$) to electric (EDM) nucleons in nonrelativistic quark model. The CP-odd interquark potential is modeled by perturbative one-loop level exchange generated operator with massive quarks and gluons. nucleon EDM obtained solving Schr\"{o}dinger equation three-quark system ...

We demonstrate the presence of non-invertible symmetries in an infinite family superconformal Argyres-Douglas theories. This class theories arises from diagonal gauging flavor symmetry a collection multiple copies $D_p(\mathrm{SU}(N))$ The same set that we study can also be realized 6d $\mathcal{N}=(1,0)$ compactification on torus. main example this is $(A_2, D_4)$ theory. show detail specific ...