Related papers: On flexes associated with higher-order flexible ba…
We provide a rigorous mathematical analysis of a coupled system consisting of a floating platform in a fluid of finite depth, clamped to a flexible Euler-Bernoulli beam. The superstructure supports a rigid tip mass at its free end,…
In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…
We define higher quantum Airy structures as generalizations of the Kontsevich-Soibelman quantum Airy structures by allowing differential operators of arbitrary order (instead of only quadratic). We construct many classes of examples of…
A formalism for the study of highly interacting electronic systems is presented. The proposed scheme is based on two key concepts: composite operators and algebra constraints. Composite field operators, that naturally appear as a…
We give properties of strict pseudocontractions and demicontractions defined on a Hilbert space, which constitute wide classes of operators that arise in iterative methods for solving fixed point problems. In particular, we give necessary…
We investigate the connections between max-weight approaches and dual subgradient methods for convex optimisation. We find that strong connections exist and we establish a clean, unifying theoretical framework that includes both max-weight…
We show that universal rigidity of a generic bar and joint framework (G,p) in the line depends on more than the ordering of the vertices. In particular, we construct examples of one-dimensional generic frameworks with the same graph and…
A bar-joint framework $(G,p)$ is the combination of a graph $G$ and a map $p$ assigning positions, in some space, to the vertices of $G$. The framework is rigid if every edge-length-preserving continuous motion of the vertices arises from…
A relationship between two old mathematical subjects is observed: the theory of hypergeometric functions and the separability in classical mechanics. Separable potential perturbations of the integrable billiard systems and the Jacobi…
We explore the relation between the singleton and adjoint modules of higher-spin algebras via so(2,d) characters. In order to relate the tensor product of the singleton and its dual to the adjoint module, we consider a heuristic formula…
We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…
We present a brief survey of fluctuations and large deviations of particle systems with subextensive growth of the variance. These are called hyperuniform (or superhomogeneous) systems. We then discuss the relation between hyperuniformity…
We define higher categorical invariants (gerbes) of codimension two algebraic cycles and provide a categorical interpretation of the intersection of divisors on a smooth proper algebraic variety. This generalization of the classical…
We study higher-order elliptic operators on one-dimensional ramified structures (networks). We introduce a general variational framework for fourth-order operators that allows us to study features of both hyperbolic and parabolic equations…
Highest weight categories are described in terms of standard objects and recollements of abelian categories, working over an arbitrary commutative base ring. Then the highest weight structure for categories of strict polynomial functors is…
The paper extends the formulation of a 2D geometrically exact beam element proposed in our previous paper [1] to curved elastic beams. This formulation is based on equilibrium equations in their integrated form, combined with the kinematic…
An effective way to design structured coherent wave interference patterns that builds on the theory of coherent lattices, is presented. The technique combines prime number factorization in the complex plane with moir\'e theory to provide a…
We consider weighted double Hurwitz numbers, with the weight given by arbitrary rational function times an exponent of the completed cycles. Both special singularities are arbitrary, with the lengths of cycles controlled by formal…
In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…
This work studies two-dimensional fixed-flux Rayleigh-B\'enard convection with periodic boundary conditions in both horizontal and vertical directions and analyzes its dynamics using numerical continuation, secondary instability analysis…