The process of substituting variables in a polynomial with other polynomials is dubbed polynomial *** behaviour of Gröbner bases and Sagbi bases under composition is well *** this paper,the authors provide a suff...
详细信息
The process of substituting variables in a polynomial with other polynomials is dubbed polynomial *** behaviour of Gröbner bases and Sagbi bases under composition is well *** this paper,the authors provide a sufficient and necessary condition on a setΘof polynomials under which the Sagbi-Gröbner basis computation commutes with *** has natural applications to the computations of Sagbi-Gröbner bases for subsets of composed polynomials of subalgebra.
Modeling and controlling aircraft can be particularly challenging when the system is highly nonlinear or only partially understood. While data-driven approaches can be promising in this regard, they are often bottlene...
详细信息
Cardiac arrhythmias pose a significant health risk, underscoring the critical need for precise detection. This paper introduces 'VATML: Ventricular Arrhythmia Detection using TinyML' demonstrating TinyML's...
详细信息
A novel idea, physics informed neural networks introduced a few years back to solve forward and inverse problems for differential equations using the physics information that lies inside them. The central pillar of th...
详细信息
A novel idea, physics informed neural networks introduced a few years back to solve forward and inverse problems for differential equations using the physics information that lies inside them. The central pillar of the physics informed neural networks is automatic differentiation, which is based on the chain rule of differentiation. Automatic differentiation is not applicable to non-local operators because the standard chain rule of differentiation is not valid for non-local operators. Therefore, this work presents non-local physics informed neural networks, which use standard approximation methods for non-local operators and automatic differentiation for local operators to solve differential equations containing non-local operators (forward problems) as well as learn differential equations involving non-local operators (inverse problems). In this work, we consider the Caputo fractional derivative, Volterra integral, and Itô integral as non-local operators. Moreover, we demonstrate the efficiency of the non-local physics informed neural networks with different test examples like the time-fractional diffusion equation in one and two dimensions, the time-fractional Burgers’ equation (both equations involving Caputo fractional derivative as non-local operators), the fractional integro-differential equation (Caputo fractional derivative and Volterra integral as non-local operators), and the stochastic fractional integro-differential equation (Caputo fractional derivative, Itô integral, and Volterra integral as non-local operators). Furthermore, for the non-smooth solution, we use the approximation method on non-uniform mesh for non-local operators and compare the results with the approximation method on uniform mesh. We also discuss the error analysis and convergence of the proposed non-local physics informed neural networks. Finally, we take real-world data, which is described by the differential equation containing non-local operators, and show the effectiveness of no
Enzymatic Reaction feasibility prediction is used to determine whether the reaction generated by computational methods can actually occur, which can effectively reduce the complexity of synthetic pathway design. Exist...
详细信息
We present a faithful geometric picture for genuine tripartite entanglement of discrete, continuous, and hybrid quantum systems. We first find that the triangle relation Ei|jkα≤Ej|ikα+Ek|ijα holds for all subaddit...
详细信息
We present a faithful geometric picture for genuine tripartite entanglement of discrete, continuous, and hybrid quantum systems. We first find that the triangle relation Ei|jkα≤Ej|ikα+Ek|ijα holds for all subadditive bipartite entanglement measure E, all permutations under parties i,j,k, all α∈[0,1], and all pure tripartite states. Then, we rigorously prove that the nonobtuse triangle area, enclosed by side Eα with 0<α≤1/2, is a measure for genuine tripartite entanglement. Finally, it is significantly strengthened for qubits that given a set of subadditive and nonsubadditive measures, some state is always found to violate the triangle relation for any α>1, and the triangle area is not a measure for any α>1/2. Our results pave the way to study discrete and continuous multipartite entanglement within a unified framework.
Non-destructive testing of composites is an important issue in the modern aircraft *** are susceptible to the barely visible impact damage which can affect the residual strength of the material and occurs both during ...
详细信息
Non-destructive testing of composites is an important issue in the modern aircraft *** are susceptible to the barely visible impact damage which can affect the residual strength of the material and occurs both during production and *** continuum model for describing the damaged zone is *** slip theory relations used for a continuous distribution of slip planes are *** the initial stage,the isotropic background model is *** model allows the material slippage along the fractures based on the Coulomb friction law with the small viscous *** this regime,the govern system of equations becomes *** overcome this difficulty,the explicit-implicit grid-characteristic scheme is *** standard ultrasound diagnostic procedure of damaged composite materials is successfully *** with the trivial free-surface fracture model,different reactions on the compression and stretch waves are *** approach provided an effective way for the simulation of complex dynamic behavior of damage zones.
Content analysis of pilot speech is a key tool for improving flight safety as it allows to identify potential problems in communication between pilots, dispatchers and crew. The development of efficient algorithms for...
详细信息
Physics-based optical flow models have been successful in capturing the deformities in fluid motion arising from digital imagery. However, a common theoretical framework analyzing several physics-based models is missi...
详细信息
We establish a pointwise property for homogeneous fractional Sobolev spaces in domains with non-empty boundary,extending a similar result of Koskela–Yang–*** use this to show that a conformal map from the unit disk ...
详细信息
We establish a pointwise property for homogeneous fractional Sobolev spaces in domains with non-empty boundary,extending a similar result of Koskela–Yang–*** use this to show that a conformal map from the unit disk onto a simply connected planar domain induces a bounded composition operator from the borderline homogeneous fractional Sobolev space of the domain into the corresponding space of the unit disk.
暂无评论