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Applied Mathematics & Information Sciences
An International Journal



Computing the Median and Range for Power Function Distributions

Fahrettin Özbey,
Abstract :
Median and range of a random sample are measures based on order statistics which are descriptive of the central tendency and dispersion of the population, respectively. In this paper, I obtained the median and range for order statistics from non-identical standard power distributions functions. Then, the median and range for identical standard power functions distributions and uniform distributions functions are given. Finally numerical results of the median and range are presented.


The Solution of Quantum Kinetic Equation with Delta Potential and its Application for Information Technology

Mukhayo Rasulova,
Abstract :
The existence of the unique solution, in terms of initial data of the hierarchy of quantum kinetic equations with delta potential and application of kinetic equation for information technology, has been proven. The proof is based on the nonrelativistic quantum mechanics and application of semigroup theory methods.



Poornima R, Mahabub Basha A,
Abstract :
MIMO is a key technology to meet high data rate requirement for next generation communication system. It can efficiently use the spectrum to increase the communication throughput. Designing a low-complex, high performance detection algorithm for the MIMO system has been a vital issue. The efficient detection of MIMO signal using Modified Memetic Algorithm (MMA) with Quadrature Amplitude Modulation (QAM) varying constellation size is proposed in this paper. The performance of the proposed work is at far with the optimum Maximum Likelihood Detector (MLD) in terms of Bit Error Rate (BER) and computational complexity. Three stages are there in proposed work. In the first stage, using partial ML detections certain bits are detected. The undetected bits in the first stage are calculated in the second stage using soft values generation method. In the last stage, the undetected bits are detected by using MMA. The soft values obtained from second stage and the partial ML bits from the first stage are combined and used as the input for the last stage. In this stage, the best individuals are obtained. MMA uses hill climbing local search technique to obtain the high quality individuals as starting point. The simulation results demonstrate that MMA based MIMO detectors outperformed the state of art detectors for different antenna configurations. Also it gives reduced complexity as compared to the existing detectors. For a 4x4, 16-QAM MIMO system, the proposed work gives BER of 10-4 for 8dB SNR with the complexity value of 51.4.


New aspects and applications of entrepreneur’s critical success elements

Saad Darwish, Horiya AlDeeb, Atheela Al Azzawi, Atheer Al Rashid,
Abstract :
We investigate how critical success elements are perceived by the entrepreneurs. Determining unknown factors for small and medium businesses from an ensemble of identical systems is a fundamental, yet experimentally demanding, task in business. Here we study the critical success elements needed to fully characterize the success in business. We show this task can be achieved using new model, which yield a practical though non-universal set of projective measurements. An application has been given and it is shown that Bahrain is stepping up efforts to make small and medium businesses a major contributor to its growth.


A Hybrid Approach to Optimize Feature Selection Process Using iBPSO- BFPA for Review Spam Detection

SP. Rajamohana, K. Umamaheswari,
Abstract :
With the increase in the customer reviews, feedbacks, suggestions posted in the web forum, blogs led to the emergence of spam. Spam detection is important for both the customer and service providers to arrive at a proper decision while purchasing as well as marketing the product. Most of the research works has been developed only for sentiment classification for the past few decades which favors the spammers to write fake reviews. Hence it is important to detect the spam reviews but the major issues in spam review detection are the high dimensionality of feature space which contains redundant, noisy and irrelevant features. To resolve this, optimization method for selecting subset of features is necessary. Hence, this paper proposes Hybridization of Improved Binary Particle Swarm Optimization (iBPSO) and Binary Flower Pollination Algorithm (BFPA) utilized with Naive Bayes and k-NN for optimization process to improve the classification performance. Experimentation result proves that hybrid iBPSO BFPA outperformed the existing approach by obtaining the maximum accuracy of 94.43% for review spam dataset when compared with existing Cuckoo Search NB(CS) and Shuffled Frog Leaping Algorithm NB (SFLA) which achieved only 81.87% and 88.23%. The experimental result proves that the proposed hybrid method increases the classification accuracy.


The impact of Arab Impact Factor (AIF) on Human Knowledge

Abd Elrazek Abd Elrazek, Abduh Elbanna, Hossam El Masry,
Abstract :
Inspiration driven activities and services are used more nowadays to raise a communication capacity for meeting such society demands. Arab impact factor (AIF) originally inspired by Arab Impact Factor Project, is highly needed to increase the attention towards Arabic journals regularly published. Important knowledge published in Arabic language can experience new products and services that improve Arab quality of life. Inspiration and innovation mainly achieved by mother tongue. Publications in Arabic language will increase the impact of Arab activity in a way may impact the human inspiration and innovation in different behaviors. Using data mining analyses can predict those Journals will be repeatedly cited in the future, other journals might not be highly cited, accordingly give advice to predictable high- cited journals and predictably not cited Journals to promote activities or change strategy respectively. AIF using data mining machine learning may predict success of every organization.


Magnetohydrodynamic Peristaltic Flow of Jeffry Nanofluid with Heat Transfer Through a Porous Medium in a Vertical Tube

Nabil T. M. El-dabe, Mohamed Y. Abou-zeid, Yasmeen M. Younis,
Abstract :
The present paper deals with the peristaltic motion of a non-Newtonian nanofluid with heat transfer through a porous medium inside a vertical tube. The system is stressed by a uniform magnetic field. The viscous dissipation, internal heat generation with radiation effects are considered. A Rung-Kutta-Merson method and a Newton iteration in a shooting and matching technique are used to find the solutions of the momentum, temperature and nanoparticles equations. The numerical formula of the axial velocity, temperature and nanoparticles are obtained as functions of the physical parameters of the problem. Numerical calculations are carried out for these formula. The effects of physical parameters of the problem on this formula are discussed numerically and illustrated graphically througth a set of figures.


Complete Tripartite Graph accepting Continuous Monotonic Decomposition theorem for evaluation routing of reaction mechanism of Piperdone Derivatives with different colour mobility of Graph labelling

V.Narayanan, J.B.VeeraMalini, G.Baskar,
Abstract :
This research paper has provided a new platform for the Graph labelling method of 3- isobutyl-2,6–bis(m-nitrophenyl)-piperidin-4-one semicarbazone. A futuristic approach for the synthesised compound has been developed in the graph theory and sequence of reaction mechanism of compound is done through Complete Tripartite Graph accepting Continuous Monotonic Decomposition concepts. In the same way we have desired functional illustration and acceptance of Graph Theory to chemistry dictionary. Thus the complex compound is enhanced in mathematical theory and to correlate the mode of arrangement of compound in graph labelling. The focus of this application is to bridge qualitative relationship and representation of research compound in graphical decomposition factors.


An Effective Approach for solving MHD Viscous Flow Due to A Shrinking Sheet

Mourad S. Semary, Hany N. Hassan,
Abstract :
In this paper, we present an effective technique combined between homotopy analysis method and traditional PadŽe approximation so-called (HAM PadŽe), the technique to obtain the analytic approximation solution of a certain type of nonlinear boundary value problem with one boundary condition at infinity. The analytic series solution obtained from the homotopy analysis method and the PadŽe diagonal approximation to handle the boundary condition at infinity. This technique apply to the boundary value problem resulting from the magnetohydrodynamic (MHD) viscous flow due to a shrinking sheet. The proposed technique success to obtain the two branches of solutions for important parameter. Comparison of the present solution is made with the existing solution and excellent agreement is noted.


Akaike Information Criterion and Fourth-Order Kernel Method for Line Transect Sampling (LTS)

Ali Algarni, Ahmad Almutlg,
Abstract :
Parametric and noparametric approaches were used to fit line transect data. Different parametric detection functions are suggested to compute the smoothing parameter of the nonparametric fourth-order kernel estimator. Among the different candidate parametric detection functions, the researcher suggests to use Akaike Information Criterion (AIC) to select the most appropriate one of them to fit line transect data. More specifically, four different parametric models are considered in this research. Where as two models were taken to satisfy the shoulder condition assumption, the other two do not. Once the appropriate model is determined, it can be used to select the smoothing parameter of the nonparametric fourth-order kernel estimator. As the researcher expected, this technique leads to improve the performances of the fourth-order kernel estimator. For a wide range of target densities, a simulation study is performed to study the properties of the proposed estimators which show the superiority of the resulting proposed fourth-order kernel estimator over the classical kernel estimator in most considered cases.


Median and Extreme Ranked Set Sampling for penalized spline estimation

Ali Algarni,
Abstract :
This paper improves and demonstrates two approaches of Ranked Set Sampling (RSS) method for penalized spline models which are Median and Extreme RSS. These improved methods increase the efficiency of the estimated parameters in the targeted model with comparing to usual RSS and Simple Random Sampling (SRS). Moreover, in practical studies, our improved methods can reduce sampling expenses dramatically. The paper approaches are illustrated using a simulation study as well as a practical example.


Control of Quantum and Classical Correlations in Werner-like States Under Dissipative Environments.

A.B. A. Mohamed.,
Abstract :
Quantum and classical correlations are studied for Werner-like state interacting with a thermal reservoir. Starting from Werner-like states, we have shown that entanglement sudden death and decay of both the quantum discord and classical correlation are accelerated by the different factors: thermal photons, cavity decay and the purity of the initial state. By these factors, the death-start points of the correlations can be controlled and the two-qubit states have no correlations that can be determined. There is no sudden death for quantum discord and classical correlation.


Visualisation of a Three-Dimensional (3D) Object’s Optimal Reality in a 3D Map on a Mobile Device

Adamu Abubakar, Akram M. Zeki, Haruna Chiroma, Sanah Abdullahi Muaz, Mueen Uddin, Nadeem Mahmood, Tutut Herawan,
Abstract :
Prior research on the subject of visualisation of three-dimensional (3D) objects by coordinate systems has proved that all objects are translated so that the eye is at the origin (eye space). The multiplication of a point in eye space leads to perspective space, and dividing perspective space leads to screen space. This paper utilised these findings and investigated the key factor(s) in the visualisation of 3D objects within 3D maps on mobile devices. The motivation of the study comes from the fact that there is a disparity between 3D objects within a 3D map on a mobile device and those on other devices; this difference might undermine the capabilities of a 3D map view on a mobile device. This concern arises while interacting with a 3D map view on a mobile device. It is unclear whether an increasing number of users will be able to identify the real world as the 3D map view on a mobile device becomes more realistic. We used regression analysis intended to rigorously explain the participants’ responses and the Decision Making Trial and Evaluation Laboratory method (DEMATEL) to select the key factor(s) that caused or were affected by 3D object views. The results of regression analyses revealed that eye space, perspective space and screen space were associated with 3D viewing of 3D objects in 3D maps on mobile devices and that eye space had the strongest impact. The results of DEMATEL using its original and revised version steps showed that the prolonged viewing of 3D objects in a 3D map on mobile devices was the most important factor for eye space and a long viewing distance was the most significant factor for perspective space, while large screen size was the most important factor for screen space. In conclusion, a 3D map view on a mobile device allows for the visualisation of a more realistic environment.


A bandwidth efficient video conferencing system for streaming gesture based video using a Pareto minimal approach to D-HOH-SI individuals

S. Swarna Parvathi, K.S.Easwarakumar, N. Devi, Raju Das,
Abstract :
Deaf, Hard-Of-Hearing and Speech-Impaired (D-HOH-SI) individuals have a specific interest in the development of affordable high-quality videoconferencing as a means of communicating with their family members and peers using sign language. Unlike Video Relay Service, which is intended to support communication between a caller using sign language and another party using spoken language, videoconferencing can directly be used either between two deaf signers or between a caller using sign language and the other using spoken language without the need of an interpreter. This paper proposes a Bandwidth Aware Gesture Based Layered (BAGBL) framework for sign language recognition based video conferencing application. Assuming a D-HOH-SI individual at the sender side, the proposed framework uses shape energy trajectory of hand sign gesture for video layering, a Multi-dimensional Multiplechoice Knapsack Problem (MMKP) based gradational hull pareto minimization heuristic called MMKP based Pareto Minimization Heuristic for Substream Scaling (MPMHSS) and a heuristic for substream scheduling which is based on Dynamic Multilevel Priority (DMP) called Modified DMP packet scheduling (MDMP) mechanism. At the receiving side, our framework includes an automatic sign language recognizer to recognize the sign language gesture and a speech synthesizer to convert the recognized words to speech. Our framework intelligently forms and selects video layers from a video sequence to maximize the video quality. Using extensive simulation and mathematical analysis we show that the proposed solution: (i) is efficient in terms of recognition rate (ii) achieves high radio resource utilization, (iii) maximizes the received video quality.


The Development of a Prototype of the Campus Guide Mobile Application

Jaegeol Yim, Jaehun Joo, Gyeyoung Lee, Kyubark Shim,
Abstract :
We have developed a so-called campus guide mobile application running on Android smart phones. Nowadays, a smart phone is equipped with many sensors - some of them are pretty accurate, a powerful processor, and large capacity secondary memory devices. Making use of these features of smart phones, we have made the campus guide a location-based service in that it determines where the user is located, which building the user is interested in, and plays the video which is related to the building. Our implementation of the application is briefly described in this paper.


A completely monotonic function involving the gamma and tri-gamma functions

Feng Qi,
Abstract :
In this paper we provide necessary and sufficient conditions on $a$ for the function $ \frac{1}{2}\ln(2\pi)-x+\bigl(x-\frac{1}{2}\bigr)\ln x-\ln\Gamma(x)+\frac1{12}{\psi(x+a)} $ and its negative to be completely monotonic on $(0,\infty)$, where $a\ge0$ is a real number, $\Gamma(x)$ is the classical gamma function, and $\psi(x)=\frac{\Gamma(x)}{\Gamma(x)}$ is the di-gamma function. As applications, some known results and new inequalities are derived.


Quantum information of two three-level trapped ions irradiated by laser beams

M. Abdel-Aty, F. N. M. Al-Showaikh,
Abstract :
Quantum information of two particles taking into account the time-dependent laser field is discussed. Considering the initial pure state of the ions, we discuss the properties of the entanglement due to the concurrence and quasi-probability distribution via Wigner function. Although, the results are presented in a general framework, we have realized controllable coupling between the qubit and field by inserting an additional factors between them.


An On-line Analytical Data Mining (OLAM) Prototype for Telecommunication Data Mining International Calls

A. Darwish and Sapna Tyagi,
Abstract :
In Nowadays, the telecommunication market is rapidly expanding and becoming highly competitive especially in international calls. The telecommunication companies have several millions of daily international call records. The huge corpus of database could be used to study the trend of customer. The main objective of this paper is to develop a model to decision system support. One of the main problems addressed in this paper is the shortage of quickly and accurate tool to process these data using data mining techniques. In this paper we designed an Online Analysis Data Mining (OLAM) prototype to help in the analysis of telecommunication data to support decision makers using Microsoft SQL server 2005 and SSAS 2005. We have also used association rules, clustering, Naïve Bayes, decision tree, and linear regression which have given us different views to the same data.


A new triangulation algorithm from 3D unorganized dense point cloud

xiaopeng wei,
Abstract :
This paper presents an algorithm for triangular mesh generation from unorganized points based on 3D Delaunay tetrahedralization and mesh-growing method. This algorithm requires the point density to meet the well-sampled condition in smooth regions and dense sampling in sections of a great curvature and two close opposite surfaces. The principle of the algorithm is as follows. It begins with 3D Delaunay tetrahedralization of all sampling points. Then extract part of triangles belonging to the surface as the seed facets according to the rough separation characteristics which based on the angle formed by the circumscribing balls of incident tetrahedrons. Finally, the algorithm grows the seed facets from front triangles to all triangles of the surface. This paper shows several experimental results which explain this approach is general and applicable to various object topologies.


Numerical Investigations of Turbulent Liquid Flows through a Centrifugal Impeller by Using Structural-Function LES

Zhuq-ing Liu, Xue-lin Tang, Fu-jun Wang, Yao-jun Li, Yu-lin Wu,
Abstract :
Based on second-order structural functions, a sub-grid eddy viscosity model is proposed for Large Eddy Simulation (LES) of turbulent flows through a centrifugal impeller in a rotating coordinate system. The current model is based on the modified Karman-Howarth equation of resolved scale turbulence of LES and allows energy transfer between resolved and unresolved scale turbulence, but the sub-grid eddy viscosity model is a function of structural functions and measures the ratio of cascade energy to the dissipation. During the simulation, the finite volume method is used to discretize the filtered governing equations, the SIMPLEC algorithm is used to solve the discretized equations and body-fitted coordinates are used to simulate turbulent flows in complex geometries. The computational results of turbulent flows in a centrifugal impeller are used to illustrate the effectiveness of the model and the predicted relative velocity distributions follow the practical rules of turbulent flows inside an impeller. The simulated pressure is in good agreement with experimental data.


Rotation-Invariant Texture Image Retrieval Based on Multiscale Geometric Analysis and WARD

Zhengli Zhu, Chunxia Zhao, Yingkun Hou,
Abstract :
In this paper, we present an effective approach for rotation-invariant texture image retrieval based on multiscale geometric analysis and weighted average relative distance(WARD). The anisotropy of nonsubsampled contourlet transform (NSCT) can help us to represent the texture in image more effectively than traditional orthogonal wavelet transforms. We achieve rotation-invariant features by combining average energy with average standard deviation of all subbands at each NSCT scale. We propose an effective similarity measure, and this measure need not calculate the statistics of the entire image database in advance, so it has much wider application situation, e.g., internet. Experimental results demonstrate that the proposed approach improves retrieval accuracy from 73.3% to 77.6% on the rotated database, compared with Dual-Tree-Complex Wavelet Transform (DT-CWT)- based approach.


Doubly Constrained Robust Constant Modulus Algorithm

Xin Song, Jinkuan Wang, Qiuming Li, Han Wang,
Abstract :
The constant modulus algorithm (CMA) has been known as blind adaptive beamforming because it requires no knowledge about the signal except that the transmitted signal waveform has a constant envelope. But in practical applications, the performance of the linearly constrained CMA is known to degrade severely in the presence of even slight signal steering vector mismatches. To account for the mismatches, a novel robust CMA algorithm based on double constraints is proposed via oblique projection of signal steering vector and worst-case performance optimization. To improve robustness, the weight vector is optimized to involve minimization of a constant modulus algorithm objective function with penalty for the worst-case signal steering vector by the Lagrange multiplier method, in which the parameters can be precisely derived at each iterative step. Moreover, the online implementation of the proposed algorithm has a low computational load. A theoretical analysis for our proposed algorithm in terms of the choice of step size, convergence perforamnce and SINR performance is presented in this paper. The proposed robust constrained CMA suffers the least distortion from the directions near the desired steering angle, provides a significantly improved robustness against the signal steering vector mismatches, yields better signal capture performance and improves the mean output array SINR as compared with the conventional constrained CMA. The numerical experiments have been carried out to demonstrate the superiority of the proposed algorithm on beampattern control and output SINR enhancement.


Global Exponential Stability for Hopfield Neural Networks with Varying Delays

Gao Yuan,
Abstract :
The main purpose of this paper is to study the global exponential stability of the equilibrium point for a class of Hopfield neural networks with varying delays. A new sufficient condition for the global exponential stability of neural networks is obtained by using M-matrix analysis. The condition is easy to check in practice. A numerical example is worked out by using the results obtained to illustrate it


The Evolution of Communication Network Architecture

Jinxin Zhang, Mangui Liang, Aqun Zhao,
Abstract :
Communication network architecture has experienced tremendous improvement from the ARPANET to IP with the number and traffic forms of users. Although IP is widely considered as the platform for future network, unfortunately, it is burdened by its her- itage of several decades. Nowadays, the bottleneck of bandwidth mainly lies in IP router not links. In this paper, we argue that one of the principal reasons for this is routing and forwarding planes are coupled together by analyzing the evolution of com- munication network architecture. Then we proposed a new network architecture to pro- vide faster forwarding speed. Simulation scenery shows this architecture is practical. Furthermore, we compared performance metrics (forwarding speed, length of address and total cost) with today’s IP network, our results indicate that forwarding speed is increased 72% of IP, the length of address is much less than IPv4 address and the total cost can be decreased 76% of the current network. Finally, we discuss several impor- tant issues of the new network architecture including address, network connection and end-to-end QoS as well as architecture extension.


Quaternion Encryption Scheme Modification Resistant to Known Plaintext- Ciphertext Attack and its Hardware-Oriented Implementation

Evgueni Doukhnitch, Alexander G. Chefranov, Ahmed Y. Mahmoud,
Abstract :
Quaternion encryption scheme (QES) is shown to be susceptible to the known plaintext-ciphertext attack (KPCA) due to not proper choice of the frame size and the procedure of secret quaternion updating. In this paper, we propose a modification of the QES (M-QES) which is resistant to the KPCA. The M-QES is based on adjusting the frame size and the quaternion update procedure. An approach for effective hardware (HW-QES) implementation of the proposed algorithm is discussed. The HW-QES uses mainly addition and shift operations. Experimental results show that the proposed M-QES and HW-QES are six-eight times more effective in the encryption quality of signals than the original QES. Additionally, M-QES is shown to be significantly more effective in the encryption quality of images than the original QES. Our results show that, the performance of the HW-QES is only 10% worse than that of QES.


Selfish Game-Theoretic Approach for Dynamic Spectrum Sharing with Software Defined Radio Networks

Desheng Li,
Abstract :
To analyze the dynamic spectrum access of Cognitive Radio Networks (CRN), this paper proposes the selfish game-theoretic model for multi-hop networking with wireless nodes, which matches well with the physical administrative structure in real-life situations. User communication session is investigated via a cross-layer optimization approach, with joint consideration of power control, scheduling, and routing. Both the channel quality and the spectrum substitutability are discussed. A utility function is built, for the secondary user to obtain the spectrum demand function. In addition, in terms of spectrum access opportunities, an equilibrium pricing scheme is presented to shows that it is close to optimal in most scenarios. The proposed Game-theoretic End-to-end Spectrum Sharing algorithm (GE2SS) highlights the trend of spectrum pricing design that it is not necessarily bad for the network users to behave selfishly. Simulation and experimental results are presented as verifications.


High Variability Resilient in Nano-Scaled Technologies for Low power 7T-SRAM Design

Shyam Akashe, Sanjay Sharma,
Abstract :
High variability in nano-scaled technologies can easily disturb the stability of a carefully designed standard 6TSRAM cell, causing access failures during a read/write operation. We propose a 7T-SRAM cell to increase the read/write stability under large variations. The proposed design uses a low overhead read/write assist circuitry to increase the noise immunity. Use of an additional transistor and a floating ground allows read disturb free operation. While the write assist circuitry provides a floating ground during a write operation that weakens cell storage by turning off the supply voltage to ground path of the cross-coupled inverter pair. This allows a high speed/low power write operation. Monte Carlo simulations indicate a 200% increase in the read stability and a boost of 124% in write stability compared to a conventional 6T-SRAM design, when subjected to random dopant fluctuations, line edge roughness, and poly-granularity variations. HSPICE simulations of a 45nm 64x32 bit SRAM array designed using standard 6T and proposed 7T SRAM cells indicate a 31% improvement in write speed, 30% decrease in write power, read power decreases by 60%, and a 44% reduction in the total average power consumption is achieved with the proposed design.


Numerical Simulations of Circular Anchor Plates under Pull-out in Sand

Khairul Anuar Kassim, Ramli Nazir,
Abstract :
This research presents the studies conducted on a type of soil anchor, a circular anchor plate, and its pullout capacity. Soil anchors are used as foundation system for the soil structures that needs to pull-out load. Experimental and numerical analysis investing the pullout test of 0.1m diameter of circular horizontal anchor plates in cohesion less soil show that maximum pullout increase with embedment ratio in sand. This paper investigated the ultimate pullout capacity of circular horizontal anchor plate in cohesion less soils subjected to pullout test in loose sand. An agreement between pullout loads from chamber box and finite element modeling using PLAXIS based on 0.4m analyzed maximum displacements for circular horizontal anchor plates to embedment ratio of 4. In the research, The Hardening Soil Model is using in PLAXIS. The numerical analysis based on PLAXIS predicted higher pullout load in loose sand due to experimental results but in final showed a good agreement with physical results.


Numerical Analysis of Buried Pipe under Wheel Loads by Three Dimensional at Finite Difference Method (FDM)

Khairul Anuar Kassim, Ramli Nazir,
Abstract :
The behavior of steel pipe during wheel load was studied in this paper by FLAC 3D. A steel pipe is buried at a shallow depth beneath a roadway. An analysis is needed to evaluate the effect of wheel loading on the road surface deflection and pipe deformation. The top of the pipe is 1.5m beneath the road surface. The pipe has an outer diameter of 4m and is 0.12m thick. The pipe excavation is 15m wide and 6m depth. The steel pipe is placed on a 0.4m thick layer of soil backfill, and then soil is compacted around the steel pipe. The wheel load is increased during failure occurs in the soil. Soil backfill behavior has been considered with Mohr-Coulomb Model in analysis. The analysis defines the failure load and the resulting soil and pipe displacement.

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