相关论文: On a solution to display non-filled-in quaternioni…

Quantum computing promises substantial speedups by exploiting quantum mechanical phenomena such as superposition and entanglement. Corresponding design methods require efficient means of representation and manipulation of quantum…

Classical methods to simulate quantum systems are not only a key element of the physicist's toolkit for studying many-body models but are also increasingly important for verifying and challenging upcoming quantum computers. Pauli…

Dynamical phase transitions are defined as non-analytic points of the large deviation function of current fluctuations. We show that for boundary driven systems, many dynamical phase transitions can be identified using the geometrical…

Visualizing changes over time is fundamental to learning from the past and anticipating the future. However, temporal semantics can be complicated, and existing visualization tools often struggle to accurately represent these complexities.…

The Julia programming language has evolved into a modern alternative to fill existing gaps in scientific computing and data science applications. Julia leverages a unified and coordinated single-language and ecosystem paradigm and has a…

While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…

This paper presents a novel method for introducing time into discrete and continuous spatial representations used in mobile robotics, by modelling long-term, pseudo-periodic variations caused by human activities. Unlike previous approaches,…

We show that under the definition of computability which is natural from the point of view of applications, there exist non-computable quadratic Julia sets.

In a power system, the load demand considers two components such as the real power (P) because of resistive elements, and the reactive power (Q) because inductive or capacitive elements. This paper presents a graphical representation of the…

Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian…

This paper is a continuation of authors work: Fatou and Julia like sets,Ukranian J. Math., to appear/arXiv:2006.08308[math.CV](see [4]). Here, we introduce escaping like set and generalized escaping like set for a family of holomorphic…

A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…

On the basis of additive schemes (splitting schemes) we construct efficient numerical algorithms to solve approximately the initial-boundary value problems for systems of time-dependent partial differential equations (PDEs). In many applied…

The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…

The Fatou-Julia theory for rational functions has been extended both to transcendental meromorphic functions and more recently to several different types of quasiregular mappings in higher dimensions. We extend the iterative theory to…

Quasiclassical methods are used to define dynamical tunneling times in models of quantum cosmological bounces. These methods provide relevant new information compared with the traditional treatment of quantum tunneling by means of tunneling…

From the beginning of David Hestenes rediscovery of geometric algebra in the 1960s, outermorphisms have been a cornerstone in the mathematical development of GA. Many important mathematical formulations in GA can be expressed as…

Implementing and executing numerical algorithms to solve fractional differential equations has been less straightforward than using their integer-order counterparts, posing challenges for practitioners who wish to incorporate fractional…

We present a new time-stepping algorithm for nonlinear PDEs that exhibit scale separation in time. Our scheme combines asymptotic techniques (which are inexpensive but can have insufficient accuracy) with parallel-in-time methods (which,…

In this paper, a multiscale approach with partially explicit time discretization is proposed. The idea is to use a partially explicit time scheme, considering a filtration problem in a fractured medium, where the implicit scheme is used for…