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) ...
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Background Burn injuries present a significant global health challenge. Among the most severe long-term consequences are contractures , which can lead to functional impairments and disfigurement. Understanding and pre...
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Background Burn injuries present a significant global health challenge. Among the most severe long-term consequences are contractures , which can lead to functional impairments and disfigurement. Understanding and predicting the evolution of post-burn wounds is essential for developing effective treatment strategies. Traditional mathematical models, while accurate, are often computationally expensive and time-consuming, limiting their practical application. Recent advancements in machine learning, particularly in deep learning, offer promising alternatives for accelerating these predictions. Methods This study explores the use of a deep operator network , a type of neural operator, as a surrogate model for finite element simulations aimed at predicting post-burn contraction across multiple wound shapes. A deep operator network was trained on three distinct initial wound shapes, with enhancements made to the architecture by incorporating initial wound shape information and applying sine augmentation to enforce boundary conditions. Findings The performance of the trained deep operator network was evaluated on a test set including finite element simulations based on convex combinations of the three basic wound shapes. The model achieved an R 2 score of 0.99 , indicating strong predictive accuracy and generalization. Moreover, the model provided reliable predictions over an extended period of up to one year, with speedups of up to 128-fold on the Central Processing Unit and 235-fold on the Graphical Processing Unit, compared to the numerical model. Interpretation These findings suggest that deep operator networks can effectively serve as a surrogate for traditional finite element methods in simulating post-burn wound evolution, with potential applications in medical treatment planning.
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.
Many organisms employ reversible dormancy, or seedbank, in response to environmental fluctuations. This life-history strategy alters fundamental ecoevolutionary forces, leading to distinct patterns of genetic diversit...
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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...
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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...
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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.
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...
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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.
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