Related papers: Construction of coupled Harry Dym hierarchy and it…
We show that the system of the standard one-component KP hierarchy endowed with a special infinite set of abelian additional symmetries, generated by squared eigenfunction potentials, is equivalent to the two-component KP hierarchy.
We construct the limiting mixed Hodge structure of a degeneration of compact K\"ahler manifolds over the unit disk with a possibly non-reduced simple normal crossing singular central fiber via holonomic $\mathscr D$-modules, generalizing…
In this paper, we study decoupled mixed element schemes for fourth order problems. A general process is designed such that an elliptic problem on high-regularity space is transformed to a decoupled system with spaces of low order involved…
We construct spectral decomposition of 1D Fokker - Planck differential operator. This reveal solution of Cauchy problem. We develop fundamental solution of Cauchy problem and compare it with one obtained by other means in our former work…
In this paper, we introduce a new concept so called harmonic complex structure by using harmonic theory for vector bundle-valued differential forms. It is a new structure intermediates between complex structure and K\"ahler structure. From…
Controlling complex dynamical systems to satisfy sophisticated specifications remains a significant challenge in modern engineering. A promising approach to this problem is the approximate simulation-based hierarchical control (ASHC)…
This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial heterogeneity, which incorporate temperature-dependent…
We investigate numerical solutions of high order curl problems with various formulations and finite elements. We show that several classical conforming finite elements lead to spurious solutions, while mixed formulations with finite…
Clustered solutions in oscillator networks provide an important insight into how a system might diversify from a synchronous solution into spatiotemporal complex solutions. They can therefore form a link between fully synchronized and…
We introduce a formalism for derived moduli functors on differential graded associative algebras, which leads to non-commutative enhancements of derived moduli stacks and naturally gives rise to structures such as Hall algebras. Descent…
Supercompact extender based forcings are used to construct models with HOD cardinal structure different from those of V. In particular, a model with all regular uncountable cardinals measurable in HOD is constructed.
Autonomous systems typically leverage layered control architectures with a combination of discrete and continuous models operating at different timescales. As a result, layered systems form a new class of hybrid systems composed of systems…
Motivated by the recent work of Batkam-Tcheka on pointed multiplicative operads, we construct in this paper new chain complex algebras and two distinct bicomplex algebra structures on a free symmetric connected multiplicative differential…
We derive some rational solutions for the multicomponent and matrix KP hierarchies generalising an approach by Wilson. Connections with the multicomponent version of the KP/CM correspondence are discussed.
We show that every sheaf on the site of smooth manifolds with values in a stable (infinity,1)-category (like spectra or chain complexes) gives rise to a differential cohomology diagram and a homotopy formula, which are common features of…
In this paper, we establish Liouville correspondences for the integrable two-component Camassa-Holm hierarchy, the two-component Novikov (Geng-Xue) hierarchy, and the two-component dual dispersive water wave hierarchy by means of the…
Separability theory of one-Casimir Poisson pencils, written down in arbitrary coordinates, is presented. Separation of variables for stationary Harry-Dym and the KdV dressing chain illustrates the theory.
It is known that $Q$-conditional symmetries of the classical Burgers' equation express in terms of three functions satisfying a coupled system of Burgers-like equations. The search of conditional symmetries of this system leads to a system…
In mixed finite element approximations of Hodge Laplace problems associated with the de Rham complex, the exterior derivative operators are computed exactly, so the spatial locality is preserved. However, the numerical approximations of the…
A method is developed here for building differentiable three-dimensional manifolds on multicube structures. This method constructs a sequence of reference metrics that determine differentiable structures on the cubic regions that serve as…