We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate *** some suitable a...
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We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate *** some suitable assumptions,we prove the existence of a ground state solution of the ***,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.
This paper investigate the possibility of UAV-interaction through the API of the implementation of Natural Language Processing (LLM) and Large Language Models (LLMs) implemented of form of quadrone. The aim of the art...
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In this article,we consider the long-time behavior of extensible beams with nonlocal weak damping:ε(t)u_(tt)+Δ^(2)u-m(‖▽u‖^(2))Δu+‖u_(t)‖^(p_(u_(t)))+f(u)=h,whereε(t)is a decreasing function vanishing at *** ...
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In this article,we consider the long-time behavior of extensible beams with nonlocal weak damping:ε(t)u_(tt)+Δ^(2)u-m(‖▽u‖^(2))Δu+‖u_(t)‖^(p_(u_(t)))+f(u)=h,whereε(t)is a decreasing function vanishing at *** the theory of process on time-dependent spaces,we investigate the existence of the time-dependent attractor by using the Condition(C_(t))method and more detailed *** results obtained essentially improve and complete some previous works.
The existence and stability of stationary solutions for a reaction-diffusion-ODE system are investigated in this *** first show that there exist both continuous and discontinuous stationary *** a good understanding of...
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The existence and stability of stationary solutions for a reaction-diffusion-ODE system are investigated in this *** first show that there exist both continuous and discontinuous stationary *** a good understanding of the stability of discontinuous stationary solutions is gained under an appropriate *** addition,we demonstrate the influences of the diffusion coefficient on stationary *** results we obtained are based on the super-/sub-solution method and the generalized mountain pass ***,some numerical simulations are given to illustrate the theoretical results.
Wireless sensor networks (WSN) are networks consisting of a collection of sensors with the functions of collecting, processing, and transmitting data on the state of the environment. In the article, using the example ...
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This paper reviews deep learning architectures used in continuous authentication, emphasizing on sensor-based or implicit device authentication methods such as motion patterns and keystroke dynamics. We review fundame...
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Let g be a finite dimensional complex simple Lie algebra with Cartan subalgebraη.Then C[η]has a g-module structure if and only if g is of type A or of type C;this is called the polynomial module of rank one,In the q...
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Let g be a finite dimensional complex simple Lie algebra with Cartan subalgebraη.Then C[η]has a g-module structure if and only if g is of type A or of type C;this is called the polynomial module of rank one,In the quantum version,the rank one polynomial modules over U_(q)(sl_(2))have been *** this paper,we prove that the quantum group U_(q)(sl_(3))has no rank one polynomial module.
Analytic Hierarchy Process (AHP) is one of the most widely applied multicriteria methods for solving many real-world decision-making problems, including the prioritization. The paper deals with the pairwise comparison...
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The paper provides a survey of the fractal theory, focusing on applications to the study of cities. Cities are especially interesting because they can be considered fractal systems with self-affinity or self-similarit...
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Abstract: A simplified model system of governing equations describing the motion of an ensemble of solid fine-grained particles arising in the continual description of two-phase dispersed media is considered. The spec...
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