THE CAUCHY INTEGRAL OF MANY COMPLEX VARIABLES PASSIVE OPERATORS AND MULTIDIMENSIONAL DISPERSION RELATIONS

This note illustrates the multidimensional dispersion relations that connect the real and imaginary parts of the matrixwhere z(p)) is the boundary value of the impedance

The Calculation of Parameters for DNA Kinetic Structure Based on Monte-Carlo Multiple Integrals

Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA structure statistical mechanical model,and time complexity and precision were analyzed on the calculated results.

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.

COMPLEX WIENER-ITO CHAOS DECOMPOSITION REVISITED

In this article, some properties of complex Wiener-It? multiple integrals and complex Ornstein-Uhlenbeck operators and semigroups are obtained. Those include Stroock’s formula, Hu-Meyer formula, Clark-Ocone formula, and the hypercontractivity of complex Ornstein-Uhlenbeck semigroups. As an application, several expansions of the fourth moments of complex Wiener-It? multiple integrals are given.

PARALLEL INFORMATION-BASED COMPLEXITY OF NUMERICAL INTEGRATION ON SOBOLEV CLASS W_q^s(Ω)

This paper deals with the parallel information-based complexity of numerical integration on Sobolev class. We obtain tight bounds on the complexity, considered as a function of two variables simultaneously:the number of processors, the rquired precision. This result seems to be new even in serial case.

MEASURING OF COMPLEX STRUCTURE TRANSFER FUNCTION AND CALCULATING OF INNER SOUND FIELD

In order to measure complex structure transfer function and calculate inner sound field, transfer function of integration is mentioned. By establishing virtual system, transfer function of integration can be measured and the inner sound field can also be calculated. In the experiment, automobile body transfer function of integration is measured and experimental method of establishing virtual system is very valid.

Software Metric Analysis of Open-Source Business Software

Over the past decade, open-source software use has grown. Today, many companies including Google, Microsoft, Meta, RedHat, MongoDB, and Apache are major participants of open-source contributions. With the increased use of open-source software or integration of open-source software into custom-developed software, the quality of this software component increases in importance. This study examined a sample of open-source applications from GitHub. Static software analytics were conducted, and each application was classified for its risk level. In the analyzed applications, it was found that 90% of the applications were classified as low risk or moderate low risk indicating a high level of quality for open-source applications.

Quasi-Z Source Inverter Control of PV Grid-Connected Based on Fuzzy PCI

The photovoltaic grid-connected inverter is an important interface between the photovoltaic power generation system and power grid.Its high-quality operation is directly related to the output power quality of the power grid.In order to further optimize the control effect of the quasi-Z source grid-connected photovoltaic inverter,a fuzzy proportional complex integral control(PCI)method is proposed for the current internal loop control.This method can eliminate the steady-state error,and has the characteristic of zero steady-state error adjustment for the AC disturbance signal of a specific frequency.The inductance-capacitance-inductance(LCL)filter is adopted in the grid-connected circuit,and the feedback capacitive current is taken as the control variable of the inner loop to form the active damping control method,which can not only effectively suppress the resonance of the LCL circuit,but also significantly inhibit the high-order harmonics in the grid-connected current.Finally,a system simulation model is built in MATLAB/Simulink to verify the superiority and effectiveness of the proposed method.

New transformation of Wigner operator in phase space quantum mechanics for the two-mode entangled case

As a natural and important extension of Fan＇s paper （Fan Hong-Yi 2010 Chin. Phys. B 19 040305） by employing the formula of operators＇ Weyl ordering expansion and the bipartite entangled state representation this paper finds a new two-fold complex integration transformation about the Wigner operator A （#, ~） （in its entangled form） in phase space quantum mechanics, and its inverse transformation. In this way, some operator ordering problems regarding to （a1-a2） and （a1＋a2） can be solved and the contents of phase space quantum mechanics can be enriched, where ai,ai are bosonic creation and annihilation operators, respectively.

COMPLEX HOPF BIFURCATION OF INTEGRAL SURFACES

The existence of the Hopf bifurcation of a complex ordinary differential equation system in the complex domain is studied in this paper by using the complex qualitative theory.In the complex domain,we conclude that the Hopf bifurcation appears for both directions of the parameter μ. The formulae of the Hopf bifurcation are also given in this paper.

Amended influence matrix method for removal of rigid motion in the interior BVP for plane elasticity

A conventional complex variable boundary integral equation （CVBIE） in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an additional integral equality is obtained. By adding both sides of this integral equality to both sides of the conventional CVBIE, the amended boundary integral equation （BIE） is obtained. The method based on the discretization of the amended BIE is called the amended influence matrix method. With this method, for the Neumann boundary value problem （BVP） of an interior region, a unique solution for the displacement can be obtained. Several numerical examples are provided to prove the efficiency of the suggested method.

Software Analytics of Open Source Business Software

This paper applies software analytics to open source code. Open-source software gives both individuals and businesses the flexibility to work with different parts of available code to modify it or incorporate it into their own project. The open source software market is growing. Major companies such as AWS, Facebook, Google, IBM, Microsoft, Netflix, SAP, Cisco, Intel, and Tesla have joined the open source software community. In this study, a sample of 40 open source applications was selected. Traditional McCabe software metrics including cyclomatic and essential complexities were examined. An analytical comparison of this set of metrics and derived metrics for high risk software was utilized as a basis for addressing risk management in the adoption and integration decisions of open source software. From this comparison, refinements were added, and contemporary concepts of design and data metrics derived from cyclomatic complexity were integrated into a classification scheme for software quality. It was found that 84% of the sample open source applications were classified as moderate low risk or low risk indicating that open source software exhibits low risk characteristics. The 40 open source applications were the base data for the model resulting in a technique which is applicable to any open source code regardless of functionality, language, or size.

How does the improved DB mode degrade the complex integrity of infrastructure mega-projects？ Evidence from the Hong Kong-Zhuhai-Macao Bridge project in China

Complex integrity is one of the main characteristics of infrastructure mega-projects(IMPs). Cost,technology, risk, duration, environmental impact, and other uncertain complexities are interrelated and constitute a challenging and complex management problem. At present, there is no unified understanding of or solutions to these complex integrity problems. This study analyzes the complex integrity of the island-tunnel subproject of the Hong Kong-Zhuhai-Macao Bridge(HZMB) project and proposes an improved design-build(DB) mode in which the owner provides a preliminary design and has the right to form and manage consortium. This improved DB mode creatively degrades the special complexities that arise from multiple dimensions. On this basis, it is an efficacious way to grasp the main contradictions, integrate the effective resources, and degrade the complex integrity in multiple dimensions and at multiple levels so as to effectively deal with the complexity management of IMPs.

Recent developments in plastic forming technology of titanium alloys

Titanium alloys have been used extensively in industry fields including aviation,aerospace and automobile due to their excellent comprehensive properties.Research and development of advanced plastic forming technology are of great importance to manufacturing titanium products of high performance and lightweight with low cost and short cycle.This paper analyzes the development tendencies of titanium alloy forming technology.Recent achievements in precision forming,microstructure control and multi-scale simulation of titanium alloys are reviewed.The forming techniques of large-sale integral complex components are presented.

An Explicit Formula for Szeg? Kernels on the Heisenberg Group

In this paper, we give an explicit formula for the Szego kernel for （0, q） forms on the Heisenberg group Hn＋1.

ON THE FUNDAMENTAL PROBLEM FOR AN INFINITE ELASTIC PLANE BONDED BY DIFFERENT ANISOTROPIC MATERIALS WITH CRACKS

In this paper, the first fundamental problem for an infinite elastic plane bonded by different anisotropic materials with cracks of arbitrary shape is discussed. The problem is reduced to a certain system of singular integral equations with several undetermined constants, which is proved to be uniquely solvable when these constants are suitably and uniquely chosen.