Related papers: Towards $W_3$ classical blocks with semi-degenerat…
We construct modular linear differential equations (MLDEs) w.r.t. subgroups of the modular group whose solutions are Virasoro conformal blocks appearing in the expansion of a crossing symmetric 4-point correlator on the sphere. This uses a…
In this short note, we construct quasi-idempotent Rota-Baxter operators by quasi-idempotent elements and show that every finite dimensional Hopf algebra admits nontrivial Rota-Baxter algebra structures and tridendriform algebra structures.…
Nonclassical phenomena of quantum mechanics such as anticorrelation and photonic de Broglie waves (PBWs) have been recently understood as a special case of coherence optics with a particular phase relation between orthogonal bases composing…
The atomic third-order open-shell many-body perturbation theory is developed. Special attention is paid to the generation and algebraic analysis of terms of the wave operator and the effective Hamiltonian as well. Making use of…
In this paper, we are concerned with semiclassical states to the following Sobolev critical Dirac equation with degenerate potential, \begin{align*} -\textnormal{i} \eps \alpha \cdot \nabla u + a \beta u + V(x) u=|u|^{q-2} u + |u| u \quad…
We begin the study of PBW deformations of graded algebras relevant to the theory of Hopf algebras. One of our examples is the Fomin-Kirillov algebra FK3. Another one appeared in a paper of Garc\'ia Iglesias and Vay. As a consequence of our…
This series of papers is a contribution to the program of classifying $p$-blocks of finite groups up to source algebra equivalence, starting with the case of cyclic blocks. To any $p$-block $\mathbf{B}$ of a finite group with cyclic defect…
In this paper, we demonstrate an elementary method for constructing new solutions to Bochner's problem for matrix differential operators from known solutions. We then describe a large family of solutions to Bochner's problem, obtained from…
Semileptonic $\Lambda_b$ decays are investigated in the framework of the relativistic quark model based on the quasipotential approach and the quark-diquark picture of baryons. The decay form factors are expressed through the overlap…
We consider a class of pseudodifferential operators with a doubly characteristic point, where the quadratic part of the symbol fails to be elliptic but obeys an averaging assumption. Under suitable additional assumptions, semiclassical…
We study the ergodic problem for fully nonlinear operators which may be singular or degenerate when the gradient of solutions vanishes. We prove the convergence of both explosive solutions and solutions of Dirichlet problems for…
We provide a full classification scheme for exceptional Jacobi operators and polynomials. The classification contains six degeneracy classes according to whether $\alpha,\beta$ or $\alpha\pm\beta$ assume integer values. Exceptional Jacobi…
In this paper we continue the study (initiated in arXiv:2003.13584) of the semiclassical behavior of the scattering data of a non-self-adjoint Dirac operator with a real, positive, fairly smooth but not necessarily analytic potential…
Any homogeneous polynomial $P(x, y, z)$ of degree $d$, being restricted to a unit sphere $S^2$, admits essentially a unique representation of the form $\lambda_0 + \sum_{k = 1}^d \lambda_k [\prod_{j = 1}^k L_{kj}]$, where $L_{kj}$'s are…
In this article we establish an explicit link between the classical theory of deformations \`a la Gerstenhaber -- and a fortiori with the Hochschild cohomology-- and (weak) PBW-deformations of homogeneous algebras. Our point of view is of…
Classical Virasoro conformal blocks are believed to be directly related to accessory parameters of Floquet type in the Heun equation and some of its confluent versions. We extend this relation to another class of accessory parameter…
We study the semi-classical trace formula at a critical energy level for a $h$-pseudo-differential operator whose principal symbol has a unique non-degenerate critical point for that energy. This leads to the study of Hamiltonian systems…
We analyse the OPE of any two 1/2 BPS operators of (2,0) SCFT$_6$ by constructing all possible three-point functions that they can form with another, in general long operator. Such three-point functions are uniquely determined by…
A solution of the elliptic type PDE of the 4th order, being a reduction of the Eqs. of stress function corresponding to any case of plane anisotropy which is not equal to isotropy (proved by S.\,G.~Mikhlin), is described in terms of…
We study three point functions of half BPS operators in $\mathcal{N}=4$ super Yang-Mills theory focusing on correltors of two of the operators with dimension of order $\Delta\sim N^2$ and a light single trace operator. These describe vacuum…