A singularly perturbed second-order semilinear differential equation with integral boundary conditions is considered. By the method of boundary functions, the conditions under which there exists an internal transition...
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A singularly perturbed second-order semilinear differential equation with integral boundary conditions is considered. By the method of boundary functions, the conditions under which there exists an internal transition layer for the original problem are established. The existence of spike-type solution is obtained by smoothly connecting the solutions of left and right associated problems, and the asymptotic expansion of the spike-type solution is also presented.
Using Banach fixed point theorem and a priori estimate,the existence of periodic and almost periodic solutions of Ca massa-Holm type equation with a nonlinear boundary condition are respectively proved when g(x,t)is p...
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Using Banach fixed point theorem and a priori estimate,the existence of periodic and almost periodic solutions of Ca massa-Holm type equation with a nonlinear boundary condition are respectively proved when g(x,t)is periodic or almost periodic function of time t.
Combining first-principles accuracy and empirical-potential efficiency for the description of the potential energy surface(PES)is the philosopher's stone for unraveling the nature of matter via atomistic *** has b...
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Combining first-principles accuracy and empirical-potential efficiency for the description of the potential energy surface(PES)is the philosopher's stone for unraveling the nature of matter via atomistic *** has been particularly challenging for multi-component alloy systems due to the complex and non-linear nature of the associated *** this work,we develop an accurate PES model for the Al-Cu-Mg system by employing deep potential(DP),a neural network based representation of the PES,and DP generator(DP-GEN),a concurrent-learning scheme that generates a compact set of ab initio data for *** resulting DP model gives predictions consistent with first-principles calculations for various binary and ternary systems on their fundamental energetic and mechanical properties,including formation energy,equilibrium volume,equation of state,interstitial energy,vacancy and surface formation energy,as well as elastic *** benchmark shows that the DP model is ready and will be useful for atomistic modeling of the Al-Cu-Mg system within the full range of concentration.
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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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.
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.
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.
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