In this paper, the existence and uniqueness of time-periodic generalized solutions and time-periodic classical solutions to a class of parabolic type equation of higher order are proved by Galerkin method.
In this paper, the existence and uniqueness of time-periodic generalized solutions and time-periodic classical solutions to a class of parabolic type equation of higher order are proved by Galerkin method.
Quantum computing offers new opportunities for addressing complex classification tasks in biomedical applications. This study investigates two quantum machine learning models-the Quantum Support Vector Machine (QSVM) ...
详细信息
Two-point Green's function is measured on the manifolds of a 2-dimensional quantum gravity. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to hundred thousand trian...
Two-point Green's function is measured on the manifolds of a 2-dimensional quantum gravity. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to hundred thousand triangles. The grid Laplacian was inverted by means of the algebraic multi-grid solver. The free field model of the Quantum Gravity assumes the Gaussian behavior of Liouville field and curvature. We measured histograms as well as six momenta of these fields. Our results support the Gaussian assumption.
Waves occurring in a polytropic gas which is rotating in the form of a Rankine vortex with a vacuum funnel about the axial region are considered. The solutions constructed are extensions of those relating to the unfun...
Waves occurring in a polytropic gas which is rotating in the form of a Rankine vortex with a vacuum funnel about the axial region are considered. The solutions constructed are extensions of those relating to the unfunnelled configuration. In particular it is shown that for a given non-zero harmonicmthere is an infinite set of unstable transverse waves. This complements the work of another author who did not report waves form= 1, and for|$m \geqslant 2$|found just two waves. The situation is a little more complicated when the waves have an axial component. In that case form= 0 there is an acoustic wave and an infinite set of stable waves, whereas for|$m \geqslant 1$|there are one or two infinite sets of helical waves, depending onm, the axial wave number and the Mach number at the periphery of the core of the vortex.
A formulation for selecting operator and control inputs to a high fidelity dynamics model, governed by differential-algebraic equations, is presented to minimize deviation in its response relative to that of a lower f...
详细信息
A formulation for selecting operator and control inputs to a high fidelity dynamics model, governed by differential-algebraic equations, is presented to minimize deviation in its response relative to that of a lower fidelity model that is also governed by differential-algebraic equations of motion. An adjoint variable method for computing sensitivity of the error measure defined is derived and implemented in a nonlinear programming formulation that is suitable for iterative minimization of the error functional. A numerical example using a multibody mechanism is presented to demonstrate effectiveness of the method and provide insights into means for effectively formulating problems of model correlation and strategies for their solution.
We consider several synchronous and asynchronous multisplitting iteration schemes for solving a class of nonlinear complementarity problems with the system matrix being an H-matrix. We establish the convergence theore...
详细信息
We consider several synchronous and asynchronous multisplitting iteration schemes for solving a class of nonlinear complementarity problems with the system matrix being an H-matrix. We establish the convergence theorems for the schemes. The numerical experiments show that the schemes are efficient for solving the class of nonlinear complementarity problems.
Convection-dominated singularly perturbed problems are a special type of differential equations that arise in various natural phenomena such as fluid dynamics. Hence, these problems need special consideration in the l...
Convection-dominated singularly perturbed problems are a special type of differential equations that arise in various natural phenomena such as fluid dynamics. Hence, these problems need special consideration in the literature due to their singular characteristics. Solving these problems involves various challenges, including layer resolution and non-linear mesh formation. However, this paper introduces a novel algorithm for generating optimal adaptive meshes using a modified particle swarm optimization technique to solve convection-dominated singularly perturbed problems. Our proposed algorithm uses an entropy-like adaptation parameter to locate the layer positions (singular regions). Unlike the other meshes (gradient-based), the proposed algorithm requires no priori knowledge of the number of mesh points required. Hence, it works as an arbitrary method to solve the problem. Once the layer positions are known, the particle swarm optimization algorithm is implemented to find out the required adaptive mesh using parameters ( N , θ ) . Various test problems (linear and non-linear) have been solved numerically, and the results have been discussed and compared with the previously existing algorithm. The results turn out to be better than the existing algorithm as the proposed algorithm results are more accurate, along with a lesser number of required points. This paper brings a novel and robust method to find a non-linear adaptive mesh for convection-dominated singularly perturbed problems. Also, this research bridges the literature gap by merging the capabilities of metaheuristic algorithms with the challenges of singularly perturbed problems, opening up avenues for further exploration and application in similar domains.
We consider a class of non-linear time-lag optimal control problems. The class of admissible controls are taken to be the class of piecewise smooth functions. A control parameterization technique is used to approximat...
详细信息
We consider a class of non-linear time-lag optimal control problems. The class of admissible controls are taken to be the class of piecewise smooth functions. A control parameterization technique is used to approximate the optimal control problem by a sequence of optimal parameter selection problems. The solution of each of these approximate problems gives rise to a sub-optimal solution to the true optimal control problem in an obvious way. The error bound is derived for the sub-optimal costs and the true optimal cost.
The transformer architecture, known for capturing long-range dependencies and intricate patterns, has extended beyond natural language processing. Recently, it has attracted significant attention in quantum informatio...
详细信息
暂无评论