Evaluation of 5G Core Slicing on User Plane Function

Network slicing is one of the most important features in 5G which enables a large variety of services with diverse performance requirements by network virtualization. Traditionally, the network can be viewed as a one-size-fits-all slice and its services are bundled with proprietary hardware supported by telecom equipment providers. Now with the network virtualization technology in 5G, open networking software can be deployed flexibly on commodity hardware to offer a multi-slice network where each slice can offer a different set of network services. In this research, we propose a multi-slice 5G core architecture by provisioning its User Plane Functions (UPFs) with different QoS requirements. We compare the performance of such a multi-slice system with that of one-size-fits-all single slice architecture under the same resource assignment. Our research objective is to compare the performance of a network slicing architecture with that of a “one-size-fits-all” architecture and validate that the former can achieve better performance with the same underlying infrastructure. The results validate that our proposed system can achieve better performance by slicing one UPF into three with proper resource allocation.

NUMERICAL COMPARISON OF TWO BOUNDARY ELEMENT METHODS FOR PLANE HARMONIC FUNCTIONS

A direct boundary element method (BEM) has been studied in the paper based on a set of sufficient and necessary boundary integral equations (BIE) for the plane harmonic functions. The new sufficient and necessary BEM leads to accurate results while the conventional insufficient BEM will lead to inaccurate results when the conventional BIE has multiple solutions. Theoretical and numerical analyses show that it is beneficial to use the sufficient and necessary BEM, to avoid hidden dangers due to non-unique solution of the conventional BIE.

CHARACTERISTIC FUNCTION AND DEFICIENCY OF MEROMORPHIC FUNCTIONS IN THE PUNCTURED PLANE

In this article, some facts of the value distribution theory for meromorphic func- tions with maximal deficiency sum in the plane will be considered in the punctured plane, and also the relationship between the deficiency of meromorphic function in the punctured plane and that of their derivatives is studied.

Comments on “General solutions of plane problem for power function curved cracks”

An error has been found in Ref. [1]. In the case of n = 2, authors of Ref. [1] suggested the following conformal mapping function：

Dissipation function in turbulent plane Poiseuille and Couette flows subject to spanwise rotations

The dissipation function in turbulent plane Poiseuille flows(PPFs) and plane Couette flows(PCFs) subject to spanwise rotations is analyzed. It is found that, in the PCFs without system rotations, the mean part is constant while the fluctuation part follows a logarithmic law, resulting in a similar logarithmic skin friction law as PPFs.However, if the flow system rotates in the spanwise direction, no obvious dependence on the rotation number can be evaluated. In the PPFs with rotations, the dissipation function shows an increase with the rotation number, while in the PCFs with rotations,when the rotation number increases, the dissipation function first decreases and then increases.

Reduced Partition Function Ratio in the Frequency Complex Plane: A Mathematical Approach

This paper gives a mathematical approach to calculate the fractionation factor of isotopes in a general cluster (also known as?super-molecule), which composes of necessary chemical effect within three bonds outside the interested atom(s). The cluster might have imaginary frequencies after being optimized in quantum softwares. The approach includes the contribution of the difference, which is resulted from the substitution of heavy and light isotopes in the cluster, of vibrations of imaginary frequencies to give precise prediction of isotope fractionation factor. We call the new mathematical approximation “reduced partition function ratio in the frequency complex plane (RPFRC)”. If there is no imaginary frequency for a cluster, RPFRC?is simplified to be Urey (1947) or Bigeleisen and Mayer (1947) formula. Final results of this new algorithm are in good agreement with those in earlier studies.

ANTI-PLANE FRACTURE ANALYSIS OF FUNCTIONALLY GRADIENT MATERIAL INFINITE STRIP WITH FINITE WIDTH

The special case of a crack under mode Ⅲ conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor （SIF） results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter.

A High-Elasticity Router Architecture with Software Data Plane and Flow Switching Plane Separation

Routers have traditionally been architected as two elements: forwarding plane and control plane through For CES or other protocols. Each forwarding plane aggregates a fixed amount of computing, memory, and network interface resources to forward packets. Unfortunately, the tight coupling of packet-processing tasks with network interfaces has severely restricted service innovation and hardware upgrade. In this context, we explore the insightful prospect of functional separation in forwarding plane to propose a next-generation router architecture, which, if realized, can provide promises both for various packet-processing tasks and for flexible deployment while solving concerns related to the above problems. Thus, we put forward an alternative construction in which functional resources within a forwarding plane are disaggregated. A forwarding plane is instead separated into two planes: software data plane(SDP) and flow switching plane(FSP), and each plane can be viewed as a collection of "building blocks". SDP is responsible for packet-processing tasks without its expansibility restricted with the amount and kinds of network interfaces. FSP is in charge of packet receiving/transmitting tasks and can incrementally add switching elements, such as general switches, or even specialized switches, to provide network interfaces for SDP. Besides, our proposed router architecture uses network fabrics to achievethe best connectivity among building blocks,which can support for network topology reconfiguration within one device.At last,we make an experiment on our platform in terms of bandwidth utilization rate,configuration delay,system throughput and execution time.

3D scattering of obliquely incident plane SV waves by an alluvial valley embedded in a fluid-saturated, poroelastic layered half-space

The indirect boundary element method is used to study the 3D dynamic response of an infinitely long alluvial valley embedded in a saturated layered half-space for obli- quely incident SV waves. A wave-number transform is first applied along the valley＇s axis to reduce a 3D problem to a 2D plane strain problem. The problem is then solved in the section perpendicular to the axis of the valley. Finally, the 3D dynamic responses of the valley are obtained by an inverse wave-number transform. The validity of the method is con- firmed by comparison with relevant results. The differences between the responses around the valley embedded in dry and in saturated poroelastic medium are studied, and the effects of drainage conditions, porosity, soil layer stiffness, and soil layer thickness on the dynamic response are dis- cussed in detail resulting in some conclusions.

Crack tip field in functionally gradient material with exponential variation of elastic constants in two directions

This paper presents an exact solution of the crack tip field in functionally gradient material with exponential variation of elastic constants. The dimensionless Poisson＇s ratios v0 of the engineering materials （iron, glass …… ） are far less than one; therefore, neglecting them, one can simplify the basic equation and the exact solution is easy to obtain. Although the exact solution for the case v0 ≠ 0 is also obtained, it is very complicated and the main result is the same with the case v0 = 0 （it will be dealt with in Appendix VII）. It has been found that the exponential term exp（ax ＋ by） in the constitutive equations becomes exp（ ax /2 ＋ by/2- kr /2 ） in the exact solution.

Analytical solution for functionally graded anisotropic cantilever beam subjected to linearly distributed load

The bending problem of a functionally graded anisotropic cantilever beam subjected to a linearly distributed load is investigated. The analysis is based on the exact elasticity equations for the plane stress problem. The stress function is introduced and assumed in the form of a polynomial of the longitudinal coordinate. The expressions for stress components are then educed from the stress function by simple differentiation. The stress function is determined from the compatibility equation as well as the boundary conditions by a skilful deduction. The analytical solution is compared with FEM calculation, indicating a good agreement.

Assignment of terahertz vibrational modes of L-glutamine using density functional theory within generalized-gradient approximation

The crystal structure of L-glutamine is stabilized by a three-dimensional network of intermolecular hydrogen bonds.We utilize plane-wave density functional theory lattice-dynamics calculations within the generalized-gradient approximation（GGA）, Perdew–Burke–Ernzerhof（PBE）, PBE for solids（PBEsol）, PBE with Wu–Cohen exchange（WC）, and dispersion-corrected PBE, to investigate the effect of these intermolecular contacts on the absorption spectra of glutamine in the terahertz frequency range. Among these calculations, the solid-state simulated results obtained using the WC method exhibit a good agreement with the measured absorption spectra, and the absorption features are assigned with the help of WC. This indicates that the vibrational modes of glutamine were related to the combination of intramolecular and intermolecular motions, the intramolecular modes were dominated by rocking or torsion involving functional groups; the intermolecular modes mainly result from the translational motions of individual molecules, and the rocking of the hydrogenbonded functional groups.

Evaluation of Right Ventricular Volume and Systolic Function by Real-time Three-dimensional Echocardiography

The optimal plane for measurement of the right ventricular (RV) volumes by real-time three-dimensional echocardiography (RT3DE) was determined and the feasibility and accuracy of RT3DE in studying RV systolic function was assessed. RV “Full volume” images were acquired by RT3DE in 22 healthy subjects. RV end-diastolic volumes (RVEDV) and end-systolic volumes (RVESV) were outlined using apical biplane, 4-plane, 8-plane, 16-plane offline separately. RVSV and RVEF were calculated. Meanwhile tricuspid annual systolic excursion (TASE) was measured by M-mode echo. LVSV was outlined by 2-D echo according to the biplane Simpson's rule. The results showed: (1) There was a good correlation between RVSV measured from series planes and LVSV from 2-D echo (r=0.73; r=0.69; r=0.63; r=0.66, P<0.25—0.0025); (2) There were significant differences between RVEDV in biplane and those in 4-, 8-, 16-plane (P<0.001). There was also difference between RV volume in 4-plane and that in 8-plane (P<0.05), but there was no significant difference between RV volume in 8-plane and that in 16-plane (P>0.05); (3) Inter-observers and intro-observers variability analysis showed that there were close agreements and relations for RV volumes (r=0.986, P<0.001; r=0.93, P<0.001); (4) There was a significantly positive correlation of TASE to RVSV and RVEF from RT3DE (r=0.83; r=0.90). So RV volume measures with RT3DE are rapid, accurate and reproducible. In view of RV's complex shape, apical 8-plane method is better in clinical use. It may allow early detection of RV systolic function.

SEMI-WEIGHT FUNCTION METHOD ON COMPUTATION OF STRESS INTENSITY FACTORS IN DISSIMILAR MATERIALS

Semi_weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi_weight functions were obtained as virtual displacement and stress fields with eigenvalue?_lambda. Integral expression of fracture parameters, K Ⅰ and K Ⅱ, were obtained from reciprocal work theorem with semi_weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi_weight function method is a simple, convenient and high precision calculation method.

Design of Novel S-plane Controller of Autonomous Underwater Vehicle Established on Sliding Mode Control

Based on the deep analysis of the mathematical model of an autonomous underwater vehicle( AUV),comprehensive considerations are given to the coupling effect of AUV's longitudinal velocity on the other degrees of freedom. In the meantime,discussions are made on the influence of residual buoyancy and restoring moment.A novel S-plane controller established on sliding mode control( SMC) is hereby proposed in this study. The strengths of traditional S-plane controller including simple structure and easily adjustable parameters are maintained in the improved design while the weakness of unsatisfactory control effect at the time of high-speed operation is also overcome. Lyapunov function is introduced to make the stability analysis of the controller before it is successfully applied to the basic motion control of AUV-X. Then the comparative experiment test is carried out between the traditional S-plane controller and the novel S-plane controller. The effectiveness and feasibility of the novel S-plane controller established on sliding mode control in the AUV basic motion control is verified by the comparative analysis of experiment results.

ELASTIC ANALYSIS OF ORTHOTROPIC PLANE PROBLEMS BY THE SPLINE FICTITIOUS BOUNDARY ELEMENT METHOD

Non-singular fictitious boundary integral equations for orthotropic elastic plane problems were deduced according to boundary conditions by the techniques of singular-points-outside-domain. Then the unknown fictitious load functions along the fictitious boundary were expressed in terms of basic spline functions, and the boundary-segment-least-squares method was proposed to eliminate the boundary residues obtained. By the above steps, numerical solutions to the integral equations can be achieved. Numerical examples are given to show the accuracy and efficiency of the proposed method.

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.

COMPLETE EIGEN-SOLUTIONS FOR ANTI-PLANE NOTCHES WITH MULTI-MATERIALS BY SUPER-INVERSE ITERATION

Ln this paper, the super-inverse iterative method is proposed to compute the accurate and complete eigen-solutions for anti-plane cracks/notches with multi-materials, arbitrary opening angles and various surface conditions. Taking the advantage of the knowledge of the variation forms of the eigen-functions, a series of numerical techniques are proposed to simplify the computation and speed up the convergence rare of the inverse iteration. A number of numerical examples are given to demonstrate the excellent accuracy, efficiency and reliability of the proposed approach.

SOME IDENTITY RELATIONS BETWEEN PLANE PROBLEMS FOR VISCO-AND ELASTICITY

In this paper.the boundary value problems of plane problems with a simply-ormultiply-connected domain for isotropic linear visca-elosticity are first established byterms of Airy stress function F(Xu t). Secondly some identity relations betweendisplacements and stresses for plane problems of sisco-and elasticity are discussed indetait and some meaningful conclusions are obtained As an example the deformationresponse for viscoelastic plate with a small circular hote at the center is analyzed undera uniasial uniform extension.

缆线在铅垂面内弯曲的大变形曲线微分方程及其数值解法

针对民用与工业应用中经常用到的自然弯曲的软管和柔缆,归纳出5个共同特点,作为本文研究缆线的基本假设。从这些假设出发,根据受力和应力分析,首次推导了缆线在铅垂面内弯曲的大变形曲线方程。列出了多种端部约束条件下相对应的求解大变形曲线的方程组。证明了悬链线与纯弯曲线都是本文的特例。提出了获得数值解的递进法,并针对两端夹持约束的情形给出了具体算例。说明了存在多解的原因以及比较不同解稳定性的方法。