Related papers: The almost Einstein operator for $(2, 3, 5)$ distr…
In a recent re-analysis of the Standard Model (SM) beta-function for the effective neutrino mass operator, we found that the previous results were not entirely correct. Therefore, we consider the analogous dimension five operators in a…
This paper deals with the approximation of a magnetic Schr\"odinger operator with a singular $\delta$-potential that is formally given by $(i \nabla + A)^2 + Q + \alpha \delta_\Sigma$ by Schr\"odinger operators with regular potentials in…
The purpose of the article is to generalize the concept of approximate Birkhoff-James orthogonality, in the semi-Hilbertian structure. Given a positive operator $ A $ on a Hilbert space $ \mathbb{H}, $ we define $ (\epsilon,A)- $approximate…
In the framework of the semiclassical approach, we compute the normalized structure constants in three-point correlation functions, when two of the vertex operators correspond to heavy string states, while the third vertex corresponds to a…
The Schur-index of the $(A_1, X_n)$-Argyres-Douglas theory is conjecturally a character of a vertex operator algebra. Here such vertex algebras are found for the $A_{\text{odd}}$ and $D_{\text{even}}$-type Argyres-Douglas theories. The…
We solve for quantum-geometrically realised spectral triples or `Dirac operators' on the noncommutative torus $\Bbb C_\theta[T^2]$ and on the algebra $M_2(\Bbb C)$ of $2\times 2$ matrices with their standard quantum metrics and associated…
A Drazin invertible Hilbert space operator $T\in \B$, with Drazin inverse $T_d$, is $(n,m)$-power D-normal, $T\in [(n,m) DN]$, if $[T_d^n,T^{*m}]=T^n_dT^{*m}-T^{*m}T_d^n=0$; $T$ is $(n,m)$-power D-quasinormal, $T\in [(n,m) DQN]$, if…
In the first part of this thesis, we make use of representation theory of groups and algebras to perform an irreducible decomposition of tensors in the context of metric-affine gravity. In particular, we consider the action of the…
We obtain global pointwise estimates for kernels of the resolvents $(I-T)^{-1}$ of integral operators \[Tf(x) = \int_{\Omega} K(x, y) f(y) d \omega(y)\] on $L^2(\Omega, \omega)$ under the assumptions that $||T||_{L^2(\omega) \rightarrow L^2…
Let $M(\mathit{odd})\subset Z/2[[x]]$ be the space of odd mod~2 modular forms of level $\Gamma_{0}(3)$. It is known that the formal Hecke operators $T_{p}:Z/2[[x]]\rightarrow Z/2[[x]]$, $p$ an odd prime other than $3$, stabilize…
We derive superconformal partial waves for all scalar four-point functions on a super Grassmannian space Gr(m|n,2m|2n) for all m,n. This family of four-point functions includes those of all (arbitrary weight) half BPS operators in both N=4…
We compute some normalized structure constants in the $\eta$-deformed $AdS_5\times S^5$ in the framework of the semiclassical approach. This is done for the cases when the "heavy" string states are finite-size giant magnons carrying one…
We give an explicit formula for a quasi-isomorphism between the operads Hycomm (the homology of the moduli space of stable genus 0 curves) and BV/$\Delta$ (the homotopy quotient of Batalin-Vilkovisky operad by the BV-operator). In other…
We introduce a Bernoulli operator,let $\mathbf{B}$ denote the operator symbol,for n=0,1,2,3,... let ${\mathbf{B}^n}: = {B_n}$ (where ${B_n}$ are Bernoulli numbers,${B_0} = 1,B{}_1 = 1/2,{B_2} = 1/6,{B_3} = 0$...).We obtain some formulas for…
Thompson's partition of a cyclic subnormal operator into normal and completely non-normal components is combined with a non-commutative calculus for hyponormal operators for separating outliers from the cloud, in rather general point…
General Relativity in dimension $n = p + q$ can be formulated as a gauge theory for the conformal group $SO(p+1,q+1)$, along with an additional field reducing the structure group down to the Poincar\'e group $ISO(p,q)$. In this paper, we…
We classify $7$-dimensional Riemannian manifolds carrying a metric connection with parallel skew-symmetric torsion whose holonomy is contained in $\mathrm{G}_2$, up to naturally reductive homogeneous spaces and nearly parallel…
An operator $T$ in a separable factor $\mathcal{M}$ is said to be irreducible in $\mathcal{M}$ if the von Neumann subalgebra $W^*(T)$ generated by $T$ is an irreducible subfactor of $\mathcal{M}$, i.e., $W^*(T)'\cap\mathcal{M}=\mathbb{C}I$.…
We prove an inverse theorem for the Gowers $U^2$-norm for maps $G\to\mathcal M$ from an countable, discrete, amenable group $G$ into a von Neumann algebra $\mathcal M$ equipped with an ultraweakly lower semi-continuous, unitarily invariant…
We study operator semigroups in the Calkin algebra $\mathcal{Q}(\mathcal{H})$, represented as a subalgebra of the algebra of bounded linear operators on a Hilbert space via one of `canonical' Calkin's representations. Using the BDF theory,…