Two Stages Segmentation Algorithm of Breast Tumor in DCE-MRI Based on Multi-Scale Feature and Boundary Attention Mechanism

Nuclearmagnetic resonance imaging of breasts often presents complex backgrounds.Breast tumors exhibit varying sizes,uneven intensity,and indistinct boundaries.These characteristics can lead to challenges such as low accuracy and incorrect segmentation during tumor segmentation.Thus,we propose a two-stage breast tumor segmentation method leveraging multi-scale features and boundary attention mechanisms.Initially,the breast region of interest is extracted to isolate the breast area from surrounding tissues and organs.Subsequently,we devise a fusion network incorporatingmulti-scale features and boundary attentionmechanisms for breast tumor segmentation.We incorporate multi-scale parallel dilated convolution modules into the network,enhancing its capability to segment tumors of various sizes through multi-scale convolution and novel fusion techniques.Additionally,attention and boundary detection modules are included to augment the network’s capacity to locate tumors by capturing nonlocal dependencies in both spatial and channel domains.Furthermore,a hybrid loss function with boundary weight is employed to address sample class imbalance issues and enhance the network’s boundary maintenance capability through additional loss.Themethod was evaluated using breast data from 207 patients at RuijinHospital,resulting in a 6.64%increase in Dice similarity coefficient compared to the benchmarkU-Net.Experimental results demonstrate the superiority of the method over other segmentation techniques,with fewer model parameters.

AN ANALYTICAL METHOD FOR A MIXED BOUNDARY VALUE PROBLEM OF CIRCULAR PLATES UNDER ARBITRARY LATERAL LOADS

In this paper by using the concept of mixed boundary funetions, an analytical method is proposed for a mixed boundary value problem of circular plates. The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system. Three examples are presented to show the stability and high convergence rate of the method.

SINGULARLY PERTURBED SEMI-LINEAR BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS FUNCTION

A class of singularly perturbed semi-linear boundary value problems with discontinuous functions is examined in this article. Using the boundary layer function method, the asymptotic solution of such a problem is given and shown to be uniformly effective. The existence and uniqueness of the solution for the system is also proved. Numerical result is presented as an illustration to the theoretical result.

Contrast structure for singular singularly perturbed boundary value problem

The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the step- type solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results.

A simplified two-dimensional boundary element method with arbitrary uniform mean flow

To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.

Singularly perturbed first-order differential equations with integral boundary condition

In this paper, a kind of singularly perturbed first-order differential equations with integral boundary condition are considered. With the method of boundary layer function and the Banach fixed-point theorem, the uniformly valid asymptotic solution of the original problem is obtained.

Stokes flow before plane boundary with mixed stick-slip boundary conditions

A general theorem for the Stokes flow over a plane boundary with mixed stick-slip boundary conditions is established. This is done by using a representation for the velocity and pressure fields in the three-dimensional Stokes flow in terms of a biharmonic function and a harmonic function. The earlier theorem for the Stokes flow due to fundamental singularities before a no-slip plane boundary is shown to be a special case of the present theorem. Furthermore, in terms of the Stokes stream function, a corollary of the theorem is also derived, providing a solution to the problem of the axisymmetric Stokes flow along a rigid plane with stick-slip boundary conditions. The formulae for the drag and torque exerted by the fluid on the boundary are established. An illustrative example is given.

MULTIPLE POSITIVE SOLUTIONS OF A SINGULAR (n-1,1) CONJUGATE BOUNDARY VALUE PROBLEM WITH DELAY

This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t<0), u (j) (0)=u(1)=0,(1≤j≤n-2).Effort is devoted to give some sufficient conditions for which the equation has at least two positive solutions.An example to illustrate the application of this theorem is given. [FQ(6*2。39,X-W]

A KIND OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM FOR NONLINEAR VOLTERRA FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper,a kind of boundary value problems for Volterra functional differential equation is studied.\$\$εx″(t)=f(t,x(t),\(t),x(t-τ),x′(t),ε),t∈(0,1), x(t)=φ(t,ε),t∈[-τ,0], ax(1)+bx′(1)=A(ε).\$\$\ \ By using the theory of differential inequality,the author proves the existence of the solutions and a uniformly valid asymptotic expansion of the solution is given as well.

An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems

This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

Numerical analysis of added mass and damping of floating production,storage and offloading system

An integral equation approach is utilized to in- vestigate the added mass and damping of floating produc- tion, storage and offloading system （FPSO system）. Finite water depth Green function and higher-order boundary ele- ment method are used to solve integral equation. Numeri- cal results about added mass and damping are presented for odd and even mode motions of FPSO. The results show ro- bust convergence in high frequency range and can be used in wave load analysis for FPSO designing and operation.

SOLUTION OF DIFFERENT HOLES SHAPE BORDERS OF FIBRE REINFORCED COMPOSITE PLATES BY INTEGRAL EQUATIONS

Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.

First-Principles Study of the High-Temperature Behaviors of the Willemite-Ⅱ and Post-Phenacite Phases of Silicon Nitride

The structural and elastic properties of the recently-discovered wⅡ- and δ-Si3N4 are investigated through the plane-wave pseudo-potential method within ultrasoft pseudopotentials.The elastic constants show that wⅡ- and δ-Si3N4 are mechanically stable in the pressure ranges of 0-50 GPa and 40-50 GPa,respectively.The α→wⅡ phase transition can be observed at 18.6 GPa and 300 K.The β→δ phase transformation occurs at pressures of 29.6,32.1,35.9,39.6,41.8,and 44.1 GPa when the temperatures are100,200,300,400,500,and 600 K,respectively.The results show that the interactions among the N-2s,Si-3s,3p bands（lower valence band） and the Si-3p,N-2p bands（upper valence band） play an important role in the stabilities of the wⅡ and S phases.Moreover,several thermodynamic parameters（thermal expansion,free energy,bulk modulus and heat capacity） of δ-Si3N4 are also obtained.Some interesting features are found in these properties.δ-Si3N4 is predicted to be a negative thermal expansion material.The adiabatic bulk modulus decreases with applied pressure,but a majority of materials show the opposite trend.Further experimental investigations with higher precisions may be required to determine the fundamental properties of wⅡ- andδ-Si3N4.

STABILITY ANALYSIS FOR LINEAR DELAY DIFFERENTIAL EQUATIONS AND NUMERICAL EXAMPLES

The asymptotic stability of delay differential equation x′(t)=Ax(t)+Bx(t τ) is concerned with,where A,B∈C d×d are constant complex matrices, x(t τ)=(x 1(t-τ 1),x 2(t-τ 2),...,x d(t-τ d))T,τ k>0(k=1,...,d) stand for constant delays. Two criteria through evaluation of a harmonic function on the boundary of a certain region are obtained. The similar results for neutral delay differential equation x′(t)=Lx(t)+Mx(t-τ)+Nx′(t-τ) are also obtained,where L,M and N∈C d×d are constant complex matrices and τ>0 stands for constant delay. Numerical examples are showed to check the results which are more general than those already reported.

A Meshless Method for Retrieving Nonlinear Large External Forces on Euler-Bernoulli Beams

We retrieve unknown nonlinear large space-time dependent forces burdened with the vibrating nonlinear Euler-Bernoulli beams under varied boundary data,comprising two-end fixed,cantilevered,clamped-hinged,and simply supported conditions in this study.Even though some researchers used several schemes to overcome these forward problems of Euler-Bernoulli beams;however,an effective numerical algorithm to solve these inverse problems is still not available.We cope with the homogeneous boundary conditions,initial data,and final time datum for each type of nonlinear beam by employing a variety of boundary shape functions.The unknown nonlinear large external force can be recuperated via back-substitution of the solution into the nonlinear Euler-Bernoulli beam equation when we acquire the solution by utilizing the boundary shape function scheme and deal with a smallscale linear system to gratify an additional right-side boundary data.For the robustness and accuracy,we reveal that the current schemes are substantiated by comparing the recuperated numerical results of four instances to the exact forces,even though a large level of noise up to 50%is burdened with the overspecified conditions.The current method can be employed in the online real-time computation of unknown force functions in space-time for varied boundary supports of the vibrating nonlinear beam.

APPLICATION OF TREFFTZ BEM TO ANTI-PLANE PIEZOELECTRIC PROBLEM

Anti-plane electroelastic problems are studied by the Trefftz boundary element method （BEM） in this paper. The Trefftz BEM is based on a weighted residual formulation and indirect boundary approach. In particular the point-collocation and Galerkin techniques, in which the basic unknowns are the retained expansion coefficients in the system of complete equations, are considered. Furthermore, special Trefftz functions and auxiliary functions which satisfy exactly the specified boundary conditions along the slit boundaries are also used to derive a special purpose element with local defects. The path-independent integral is evaluated at the tip of a crack to determine the energy release rate for a mode Ⅲ fracture problem. In final, the accuracy and efficiency of the Trefftz boundary element method are illustrated by an example and the comparison is made with other methods.

Fundamental Solution for Welding Problem by Two Dissimilar Isotropic Semi－Planes

A fundamental solution was obtained for an infinite plane bonded by two dissimilar isotropic semi-planes by employing plane elastic complex variable method and theory of boundary value problems for analytic functions.Fundamental solution was prepared for solving these types of problems with boundary element method.

Free Vibration and Stbaility of Moderate-Thick Cantilever Plates

By means of the constitution of the two displacement functions and theapplication of the least square method and the energy method this paper gives theReissner approximate solutions of the free vibration and the stability for the moderate-thick cantilever rectangular plate.

Domain boundaries in silicene:Density functional theory calculations on electronic properties

By using density functional theory(DFT)-based first-principles calculations, the structural stability and electronic properties for two kinds of silicene domain boundaries, forming along armchair edge and zigzag edge, have been investigated. The results indicate that a linkage of tetragonal and octagonal rings(4|8) appears along the armchair edge, while a linkage of paired pentagonal and octagonal rings(5|5|8) appears along the zigzag edge. Different from graphene, the buckling properties of silicene lead to two mirror symmetrical edges of silicene line-defect. The formation energies indicate that the 5|5|8 domain boundary is more stable than the 4|8 domain boundary. Similar to graphene, the calculated electronic properties show that the 5|5|8 domain boundaries exhibit metallic properties and the 4|8 domain boundaries are half-metal.Both domain boundaries create the perfect one-dimensional(1D) metallic wires. Due to the metallic properties, these two kinds of nanowires can be used to build the silicene-based devices.

Existence and Uniqueness of Positive Solutions for Some Singular Boundary Value Problems with Linear Functional Boundary Conditions

By using the upper and lower solution method and fixed point theory, we investigate some nonlinear singular second-order differential equations with linear functional boundary conditions. The nonlinear term f（t, u） is nonincreasing with respect to u, and only possesses some integrability. We obtain the existence and uniqueness of the C[0, 1] positive solutions as well as the C1 [0, 1] positive solutions.