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The number of high-voltage parallel cables is rapidly increasing. The alternating magnetic field generated by the working current of power cable cores induces voltage in the adjacent metal sheath; if the sheath and earth form a circuit, the metal sheath will create a circulating current, resulting in a reduction in the load capacity of power cable and the life of cable insulation. This paper uses MATLAB to construct a model for calculating the circulating current of cables connected in parallel in the same phase, and the effects of cable arrangement, phase sequence, and loop distance of cables connected in parallel on the sheath circulating current are investigated. The induced voltage in power cable sheaths is decomposed into two components, i.e., the component resulting from the core current and the component resulting from the metal sheath. Two new sheath connection methods are proposed to suppress the sheath circulating current. Compared with traditional cross-connection grounding, the proposed methods can reduce the coupling degree between loops, thus decreasing the induced voltage and circulating current. The different grounding methods of the sheath are modeled in the environment of an electromagnetic transient program (EMTP), and the sheath circulating current is simulated and compared with the conventional cross-connection grounding method. In the asymmetric arrangement, the proposed series connection method can reduce the sheath circulating current by at least 50%; however, its increases the sheath circulating current in the symmetric arrangement. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence and regularity of solutions of the homogeneous Dirichlet initial-boundary value problem for a class of degenerate elliptic equations with lower order terms. The results we obtained here, extend some existing ones of [2, 9, 11] in some sense. [ABSTRACT FROM AUTHOR]

In this paper, we study the Dirichlet problem for degenerate parabolic equations of the form ∂ u ∂ t − div ( a ( x , t , u , ∇ u ) ) − div ϕ ( u ) = f − div g , where the main operator a ( x , t , u , ∇ u ) is allowed to degenerate with respect to the unknown u . Under suitable conditions on a and ϕ , we prove that there exists an unique solution u of this problem. [ABSTRACT FROM AUTHOR]

In this paper we study a class of nonlinear parabolic problems with $p(x,t)$ growth conditions. We prove the existence and uniqueness of bounded solutions to such a problem, with less constraint to $p(x,t)$. Our results are generalizations of the corresponding results in the constant exponent case. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of nonlinear obstacle problems with nonstandard growth. We obtain the L∞ estimate on the solutions and prove the existence and uniqueness of solutions to such problems. Our results are generalizations of the corresponding results in the constant exponent case. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper deals with a class of degenerate quasilinear elliptic equations of the form $-\operatorname{div}(a(x,u,\nabla u))+F(x,u,\nabla u)=f $, where $a(x,u,\nabla u)$ is allowed to degenerate with the unknown u. Under some hypothesis on a, F, and f, we obtain the existence of bounded solutions $u\in W_{0}^{1,p}(\Omega)\cap L^{\infty}(\Omega)$. For the case $f\in L^{1}(\Omega)$, we also prove that there exists at least one renormalized solution. [ABSTRACT FROM AUTHOR]

This paper deals with a class of doubly degenerate parabolic equations of the type ∂ b ( u ) ∂ t − div ( a ( x , t , u , ∇ u ) ) + F ( x , t , u , ∇ u ) = f , where b is a strictly increasing C 1 -function. Under some suitable hypothesis, we prove that there exists at least a bounded solution to this problem in standard weak sense. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study a class of degenerate parabolic equations of porous medium-type with a lower order term and data, i.e. , where the principal part of the operator is degenerate in . Under some hypothesis on and , we prove that the problem admits at least a renormalized solution. [Copyright &y& Elsevier]

Abstract: This paper deals with a nonlocal problem arising in plasma physics. This problem involves the terms and , which are neither local, nor continuous and monotone. By using the Galerkin approximate method and the topological degree theory, the existence of solutions will be proved. [Copyright &y& Elsevier]

The paper deals with a nonlocal problem related to the equilibrium of a confined plasma in a Tokamak machine. This problem involves terms u′ (| u > u( x)|) and | u > u( x)|, which are neither local, nor continuous, nor monotone. By using the Galerkin approximate method and establishing some properties of the decreasing rearrangement, we prove the existence of solutions to such problem. [ABSTRACT FROM AUTHOR]

This paper deals with a nonlocal free boundary problem arising in the study of the dynamics of the confinement of a plasma in a Stellarator device. The free boundary represents the separation between the plasma and vacuum regions, and the nonlocal term involves the notions of relative rearrangement and monotone rearrangement. We establish some new properties on the decreasing rearrangement that can be used to prove the convergence of the approximate problem, and then prove the existence of solutions by Galerkin method. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with a class of degenerate quasilinear elliptic equations of the form , where is allowed to be degenerate with the unknown . We prove existence of bounded solutions under some hypothesis on and . Moreover we prove that there exists a renormalized solution in the case where and . [ABSTRACT FROM AUTHOR]

Considering current problems in the identifying, locating, and supervising of construction waste, it is difficult to achieve real-time target judgement and identification in the short term. This study proposes a deep learning-based construction waste identification and classification system, named IUNet-IF, developed using unmanned aerial vehicle (UAV) images. High-resolution UAV aerial images were used to establish a sample database and train U-Net models. The U-Net model, which exhibited the highest overall performance and identification accuracy, was enhanced to develop an IUNet model. Subsequently, the texture and colour features of UAV images were extracted and input to the IUNet model to build a novel IUNet-IF model. The proposed method uses the optimal model and an input combination of texture features, colour features, and original images, which improves the segmentation results compared to those when only the original image is used. The experimental results indicate that the system can achieve a maximum pixel accuracy index, mean intersection over union (mIoU), and mean pixel accuracy (MPA) of 98.98%, 93.78%, and 97.26%, respectively. These results verify the feasibility of extracting construction waste covered by a dust-proof net from UAV remote sensing images and can provide reference information for the automatic extraction of construction waste. [ABSTRACT FROM AUTHOR]

In this article we study a class of nonlinear elliptic equations with variable exponents. We obtain anL∞estimate on the solutions and prove the existence of weak solutions to such problems. [ABSTRACT FROM AUTHOR]