An Equivalence Between A Harmonic Form And A Closed Co-Closed Form In L^Q and Non-L^Q Spaces
An equivalent relation between a harmonic form and a closed co-closed form is established on a complete non-compact manifold. This equivalence has been generalized for a differential k-form ω from Lq spaces to non-Lq spaces when q=2 in the context of p-balanced growth where p=2. Especially for a simple differential k-form on a complete non-compact manifold, the equivalent relation has been verified with the extended scope of q for from finite q-energy in Lq spaces to infinite q-energy in non-Lq spaces when with 2-balanced growth. Generalized Hadamard Theorem, Cauchy-Schwarz Inequality, and Calculus skills including Integration by Parts as well as Convergent Series have been applied as estimation techniques to evaluate growth rates for a differential form. In particular, energy growth rates as indicated by an appropriate power range in a selected test function lead to a balance between a harmonic differential form and a closed co-closed differential form. Research ideas and computational methods in this paper could provide an innovative way in the study of broadening Lq spaces to non-Lq spaces with a wide variety of infinite energy growth for a differential form.
Generalized π-Armendariz Authentication Cryptosystem
Algebra is one of the important fields of mathematics. It concerns in the study and manipulates of mathematical symbols. It also concerns with study of abstractions such as groups, rings, and fields. Due to the development of these abstractions, it is extended to consider other structures such as, vectors, matrices, and polynomials, which are non-numerical objects. Computer algebra is the implementation of algebraic methods as algorithms and computer programs. Recently, many algebraic cryptosystem protocols based on non-commutative algebraic structures such as; authentication, key exchange, and encryption-decryption processes are adopted. Cryptography is the science that aimed of sending the information through public channels in such a way, that only an authorized recipient can read it. Ring theory is the most attractive category of algebra in the area of cryptography. In this paper, we employ the algebraic structure called skew π-Armendariz rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is established and illustrated through numerical example, and its soundness and completeness are proved.
Forecasting Performance Comparison of Autoregressive Fractional Integrated Moving Average and Jordan Recurrent Neural Network Models on the Turbidity of Stream Flows
In this study, the Autoregressive Fractional Integrated Moving Average (ARFIMA) and Jordan Recurrent Neural Network (JRNN) models were employed to model the forecasting performance of the daily turbidity flow of White Clay Creek (WCC). The two methods were applied to the log difference series of the daily turbidity flow series of WCC. The measurements of error employed to investigate the forecasting performance of the ARFIMA and JRNN models are the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE). The outcome of the investigation revealed that the forecasting performance of the JRNN technique is better than the forecasting performance of the ARFIMA technique in the mean square error sense. The results of the ARFIMA and JRNN models were obtained by the simulation of the models using MATLAB version 8.03. The significance of using the log difference series rather than the difference series is that the log difference series stabilizes the turbidity flow series than the difference series on the ARFIMA and JRNN.
Determining the Causality Variables in Female Genital Mutilation: A Factor Screening Approach
Female Genital Mutilation (FGM) is made up of three types namely: Clitoridectomy, Excision, and Infibulation. In this study, we examine the factors responsible for FGM in order to identify the causality variables in a logistic regression approach. From the result of the survey conducted by the Public Health Division, Nigeria Institute of Medical Research, Yaba, Lagos State, the tau statistic, τ was used to screen nine factors that causes FGM in order to select few of the predictors before multiple regression equations are obtained. The need for this may be that the sample size may not be able to sustain having a regression with all the predictors or to avoid multicollinearity. A total of 300 respondents, comprising 150 adult males and 150 adult females were selected for the household survey based on the multi-stage sampling procedure. The tau statistic,
Fuzzy Logic and Control Strategies on a Sump
Sump can be defined as a reservoir which contains slurry; a mixture of solid and liquid or water, in it. Sump system is an unsteady process owing to the level response. Sump level shall be monitored carefully by using a good controller to avoid overflow. As the current conventional controllers unable to solve problems with time delay and nonlinearities, Fuzzy Logic controller is tested to prove its ability in solving the listed problems of slurry sump. Therefore, in order to justify the effectiveness and reliability of these controllers, simulation of the sump system was created by using MATLAB and the results were compared. According to the result obtained, instead of Proprotional-Integral (PI) and Proportional-Integral and Derivative (PID), Fuzzy Logic controller showed the best result by offering quick response of 0.32s for step input and 5s for pulse generator, to the set point change as well as producing the minimal Integral Absolute Error (IAE) value that is 0.66 and 0.36.
Hmamiltonian Paths and Cycles Passing through Prescribed Edges in the Balanced Hypercubes
The n-dimensional balanced hypercube BHn (n ≥ 1) has been proved to be a bipartite graph. Let P be a set of edges whose induced subgraph consists of pairwise vertex-disjoint paths. For any two vertices u, v from different partite sets of V (BHn). In this paper, we prove that if |P| ≤ 2n − 2 and the subgraph induced by P has neither u nor v as internal vertices, or both of u and v as end-vertices, then BHn contains a Hamiltonian path joining u and v passing through P. As a corollary, if |P| ≤ 2n−1, then the BHn contains a Hamiltonian cycle passing through P.
Forecasting the Volatility of Geophysical TimeSeries with Stochastic Volatility Models
This work is devoted to the study of modeling geophysical time series. A stochastic technique with time-varying parameters is used to forecast the volatility of data arising in geophysics. In this study, the volatility is defined as a logarithmic first-order autoregressive process. We observe that the inclusion of log-volatility into the time-varying parameter estimation significantly improves forecasting which is facilitated via maximum likelihood estimation. This allows us to conclude that the estimation algorithm for the corresponding one-step-ahead suggested volatility (with ±2 standard prediction errors) is very feasible since it possesses good convergence properties.
Spatial Analysis of Misconception of HIV/AIDS among Ever-Married Women and Factor Associated with the Misconception: A Comparison of Non-Spatial Multilevel and Hierarchical Spatial Autoregressive Model
Combating HIV/AIDS is getting importance in the world health concerns as it increases with the passage of time. Pakistan is also under the attack of the HIV/AIDS virus, therefore, combating HIV is also the big health concern in Pakistan. Combating HIV is only possible by giving sufficient awareness to the general public especially women of child bearing age i.e. 15-49 years and the core hindrance of combating HIV is the misconception about HIV transmission. Therefore, combating HIV and misconception are associated with each other. Therefore, the present study aimed to identify the spatially distribution of the three type of misconception factors of HIV (i.e. transmitted by mosquito bite, supernatural means and sharing food with HIV positive person) and also to determine the core factors that may affect in reducing the misconception and increases the chances of combating HIV in Pakistan. Multilevel, Bayesian Multilevel and Hierarchical Spatial Autoregressive models were applied to the data and results from them revealed that the Hierarchical Spatial Autoregressive models is more appropriate. The results revealed that the condom use, women age, education of household head, hepatitis were the significant factors for all three types of misconception about HIV.
Comparison of the Logistic and the Gompertz Growth Functions Considering a Periodic Perturbation in the Model Parameters
Both the logistic growth model and the gompertz growth model are used to describe growth processes. Both models driven by perturbations in different cases are investigated using information theory as a useful measure of sustainability and the variability. Specifically, we study the effect of different oscillatory modulations in the system's parameters on the evolution of the system and Probability Density Function (PDF). We show the maintenance of the initial conditions for a long time. We offer Fisher information analysis in positive and/or negative feedback and explain its implications for the sustainability of population dynamics. We also display a finite amplitude solution due to the purely fluctuating growth rate whereas the periodic fluctuations in negative feedback can lead to break down the system's self-regulation with an exponentially growing solution. In the cases tested, the gompertz and logistic systems show similar behaviour in terms of information and sustainability although they develop differently in time.
Mathematics Model Approaching: Parameter Estimation of Transmission Dynamics of HIV and AIDS in Indonesia
Acquired Immunodeficiency Syndrome (AIDS) is one of the world's deadliest diseases caused by the Human Immunodeficiency Virus (HIV) that infects white blood cells and cause a decline in the immune system. AIDS quickly became a world epidemic disease that affects almost all countries. Therefore, mathematical modeling approach to the spread of HIV and AIDS is needed to anticipate the spread of HIV and AIDS which are widespread. The purpose of this study is to determine the parameter estimation on mathematical models of HIV transmission and AIDS using cumulative data of people with HIV and AIDS each year in Indonesia. In this model, there are parameters of r ∈ [0,1) which is the effectiveness of the treatment in patients with HIV. If the value of r is close to 1, the number of people with HIV and AIDS will decline toward zero. The estimation results indicate when the value of r is close to unity, there will be a significant decline in HIV patients, whereas in AIDS patients constantly decreases towards zero.
A Mathematical Analysis of Behavioural Epidemiology: Drugs Users Transmission Dynamics Based on Level Education for Susceptible Population
The spread of drug users is one kind of behavioral epidemiology that becomes a threat to every country in the world. This problem caused various crisis simultaneously, including financial or economic crisis, social, health, until human crisis. Most drug users are teenagers at school age. A new deterministic model would be constructed to determine the dynamics of the spread of drug users by considering level of education in a susceptible population. Based on the analytical model, two equilibria points were obtained; there were E₀ (zero user) and E₁ (endemic equilibrium). Existence of equilibrium and local stability of equilibria depended on the Basic Reproduction Ratio (R₀). This parameter was defined as the expected rate of secondary prevalence and primary prevalence in virgin population along spreading primary prevalence. The zero-victim equilibrium would be locally asymptotically stable if R₀ < 1 while if R₀ > 1 the endemic equilibrium would be locally asymptotically stable. The result showed that R₀ was proportional to the rate of interaction of each susceptible population based on educational level with the users' population. It is concluded that there was a need to be given a control in interaction, so that drug users population could be minimized. Numerical simulations were also provided to support analytical results.
Application of Mathematical Sciences to Farm Management
Agriculture has been the mainstay of the nation’s economy in Nigeria. It provides food for the ever rapidly increasing population and raw materials for the industries. People especially the rural dwellers are gainfully employed on their crop farms and small-scale livestock farms for income earning. In farming, availability of funds and time management are one of the major factors that influence the system of farming in Nigeria in which mathematical science knowledge was highly required in order for farms to be managed effectively. Farmers often applied mathematics, almost every day for a variety of tasks, ranging from measuring and weighing, to land marking. This paper, therefore, explores some of the ways math is used in farming. For instance, farmers use arithmetic variety of farm activities such as seed planting, harvesting crop, cultivation and mulching. It is also important in helping farmers to know how much their livestock weighs, how much milk their cows produce and crop yield per acres, among others.
Flow and Heat Transfer Analysis of Copper-Water Nanofluid with Temperature Dependent Viscosity past a Riga Plate
Flow of electrically conducting nanofluids is of pivotal importance in countless industrial and medical appliances. Fluctuations in thermophysical properties of such fluids due to variations in temperature have not received due attention in the available literature. Present investigation aims to fill this void by analyzing the flow of copper-water nanofluid with temperature dependent viscosity past a Riga plate. Strong wall suction and viscous dissipation have also been taken into account. Numerical solutions for the resulting nonlinear system have been obtained. Results are presented in the graphical and tabular format in order to facilitate the physical analysis. An estimated expression for skin friction coefficient and Nusselt number are obtained by performing linear regression on numerical data for embedded parameters. Results indicate that the temperature dependent viscosity alters the velocity, as well as the temperature of the nanofluid and, is of considerable importance in the processes where high accuracy is desired. Addition of copper nanoparticles makes the momentum boundary layer thinner whereas viscosity parameter does not affect the boundary layer thickness. Moreover, the regression expressions indicate that magnitude of rate of change in effective skin friction coefficient and Nusselt number with respect to nanoparticles volume fraction is prominent when compared with the rate of change with variable viscosity parameter and modified Hartmann number.
The Valuation of Employees Provident Fund on Long Term Care Cost among Elderly in Malaysia
Nowadays, financing long-term care for elderly people is a crucial issue, either towards the family members or the care institution. Corresponding with the growing number of ageing population in Malaysia, there’s a need of concern on the uncertaintiness of future family care and the need for long-term care services. Moreover, with the increasing cost of living, children feels the urge of needing to work and receive a fixed monthly income that results to sending their elderly parents to care institutions. Currently, in Malaysia, the rates for private nursing homes can amount up to RM 4,000 per month excluding medical treatments and other recurring expenses. These costs are expected to be paid using their Employees Provident Fund (EPF) savings that they accumulate during their working years, especially for those working under private sectors. Hence, this study identifies the adequacy of EPF in funding the cost of long-term care service during old age. This study used a hypothetical simulation model to simulate different scenarios. The findings of this study could be used for individuals to prepare on the importance of planning for retirement, especially with the increasing cost of long-term care services.
Free Convection from a Perforated Spinning Cone with Heat Generation, Temperature-Dependent Viscosity and Partial Slip
The problem of free convection from a perforated spinning cone with viscous dissipation, temperature-dependent viscosity, and partial slip was studied. The boundary layer velocity and temperature profiles were numerically computed for different values of the spin, viscosity variation, inertia drag force, Eckert, suction/blowing parameters. The partial differential equations were transformed into a system of ordinary differential equations which were solved using the fourth-order Runge-Kutta method. This paper considered the effect of partial slip and spin parameters on the swirling velocity profiles which are rarely reported in the literature. The results obtained by this method was compared to those in the literature and found to be in agreement. Increasing the viscosity variation parameter, spin, partial slip, Eckert number, Darcian drag force parameters reduce swirling velocity profiles.
Investigating the Dynamics of Knowledge Acquisition in Learning Using Differential Equations
A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates the effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the Department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.
Computation of Reliability and Probability Weighted Moment Estimation for Three Parameter Mukherjee-Islam Failure Model
The Mukherjee-Islam Model is commonly used as a simple life time distribution to assess system reliability. The model exhibits a better fit for failure information and provides more appropriate information about hazard rate and other reliability measures as shown by various authors. We have introduced a location parameter at a time α (i.e. a time before which failure can’t occur) which makes it a more useful failure distribution than the existing ones. Even after shifting the location of the distribution, it represents a decreasing, constant and increasing failure rate. It has been shown to represent appropriate lower tail of the distribution of random variables having fixed lower bound. This study presents the reliability computations and probability weighted moment estimation of three parameter model. A comparative analysis is carried out between three parameters finite range model and some existing bathtub shaped curve fitting models. The results obtained in the study may be applied to semiconductor devices. Since probability weighted moment method is used, the results obtained can also be applied to small sample cases. Maximum likelihood estimation method is also applied in this study.
A Filtering Algorithm for a Nonlinear State-Space Model
Kalman filter is a famous algorithm that utilizes to estimate the state in the linear systems. It has numerous applications in technology and science. Since of the most of applications in real life can be described by nonlinear systems. So, Kalman filter does not work with the nonlinear systems because it is suitable to linear systems only. In this work, a nonlinear filtering algorithm is presented which is suitable to use with the special kinds of nonlinear systems. This filter generalizes the Kalman filter. This means that this filter also can be used for the linear systems. Our algorithm depends on a special linearization of the second degree. We introduced the nonlinear algorithm with a bilinear state-space model. A simulation example is presented to illustrate the efficiency of the algorithm.
A Study of Algebraic Structure Involving Banach Space through Q-Analogue
The aim of the present paper is to study the Banach Space and Combinatorial Algebraic Structure of R. It is further aimed to study algebraic structure of set of all q-extension of classical formula and function for 0 < q < 1.
Deep Learning for Recommender System: Principles, Methods and Evaluation
Recommender systems have become increasingly popular in recent years, and are utilized in numerous areas. Nowadays many web services provide several information for users and recommender systems have been developed as critical element of these web applications to predict choice of preference and provide significant recommendations. With the help of the advantage of deep learning in modeling different types of data and due to the dynamic change of user preference, building a deep model can better understand users demand and further improve quality of recommendation. In this paper, deep neural network models for recommender system are evaluated. Most of deep neural network models in recommender system focus on the classical collaborative filtering user-item setting. Deep learning models demonstrated high level features of complex data can be learned instead of using metadata which can significantly improve accuracy of recommendation. Even though deep learning poses a great impact in various areas, applying the model to a recommender system have not been fully exploited and still a lot of improvements can be done both in collaborative and content-based approach while considering different contextual factors.
Science, Technology, Engineering And Math Approach on Playing Video Games
This STEM project is to demonstrate how to play Video Game through STEM approach and learning science and statistics. Kids are playing video games too long and parents do not want kids to play video games since most video games are not developing critical thinking. Hill Climb Car Racing game was chosen not based on commercial rating but on potential of applying statistical data-driven methodology. The author took STEM approach: Science (Physics, Mechanics), Technology (Car Upgrading), Engineering (Failure Mode), and Math (Geometry, Trigonometry and Statistics). Based on the engineering failure mode analysis and scientific understanding, author can develop a systematic car upgrading system through statistical modeling to optimize car performance. Simple linear regression was conducted to quantify the Performance Index (ROI) return (car travelling distance) of investment (car grading cost). The regression model accuracy has been improved from original 66% (random playing mode) to 92% (systematic playing mode). The ROI slope has been improved from 147.2 to 512.4 meter/upgrade unit. The clustering analysis grouped the similar field stages with common challenges and science which has helped upgrade car to support multiple stages. The best car of each stage has matched well with literature research. It’s a very successful STEM project on playing video games.
Study on a Family of Optimal Fourth-Order Multiple-Root Solver
In this paper,we develop the complex dynamics of a family of optimal fourth-order multiple-root solvers and plot their basins of attraction. Mobius conjugacy maps and extraneous fixed points applied to a prototype quadratic polynomial raised to the power of the known integer multiplicity m are investigated. A 300 x 300 uniform grid centered at the origin covering 3 x 3 square region is chosen to visualize the initial values on each basin of attraction in accordance with a coloring scheme based on their dynamical behavior. The illustrative basins of attractions applied to various test polynomials and the corresponding statistical data for convergence are shown to confirm the theoretical convergence.
A Class of Third Derivative Four-Step Exponential Fitting Numerical Integrator for Stiff Differential Equations
In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.
Modelling the Spread of HIV/AIDS Epidemic with Condom Campaign and Treatment
This paper considers a deterministic model for the transmission dynamics of HIV/AIDS in which condom campaign and treatment are both important for the disease management. In modelling of the spread of AIDS, the population is divided into six subpopulations, namely susceptible population, susceptible population who change their behavior due to education condom campaign, infected population, pre-AIDS population, treated population and full-blown AIDS population. We calculate the effective reproduction number using the next generation matrix method and investigate the existence and stability of the equilibrium points. A sensitivity analysis discovers parameters that have a high impact on effective reproduction number and should be targeted by intervention strategies. Numerical simulations are given to illustrate and verify our analytic results.
Equity Investment Restrictions and Pension Replacement Rates in Nigeria: A Ruin-Risk Analysis
Pension funds are pooled assets which are established to provide income for retirees. The funds are usually regulated to check excessive risk taking by fund managers. In Nigeria, the current defined contribution (DC) pension scheme appears to contain some overly stringent restrictions which might be hampering its successful implementation. Notable among these restrictions is the 25 percent maximum limit on investment in ordinary shares of quoted companies. This paper examines the extent to which these restrictions affect pension replacement rates at retirement. The study made use of both simulated and historical asset return distributions using mean-variance, regression analysis and ruin-risk analyses, the study found that the current equity investment restriction policy in Nigeria reduces replacement rates at retirement.
Numerical Approach to a Mathematical Modelling of Bioconvection Due to Gyrotactic Micro-Organisms over a Nonlinear Inclined Stretching Sheet Numerical Approach
The term bioconvection refers to the phenomenon of macroscopic convective motion of fluid caused by the density gradient and is created by collective swimming of motile micro-organisms. The density of base fluid increases as these self-propelled motile micro-organisms swim in a particular direction, thus causing bioconvection. It has many applications in biological systems and biotechnology. The present work represents the study of water-based nanofluid bioconvection due to gyrotactic micro-organisms over a nonlinear inclined stretching sheet. The model of the problem considers the effects of Brownian motion and thermophoresis. Boussinesq approximation is used to determine the variation of density in the buoyancy term. The governing partial differential equations are reduced to nonlinear ordinary differential equations using similarity transformations. For computational purpose, Finite Element Method is used. The numerical results for velocity, temperature, nanoparticles concentration and density of motile micro-organism are expressed graphically. The local Skin friction coefficient, the local Nusselt number, the Sherwood number and the local density number of the motile micro-organisms are also calculated.
Analysis of Financial Time Series by Using Ornstein-Uhlenbeck Type Models
In the present work, we develop a technique for estimating the volatility of financial time series by using stochastic differential equation. Taking the daily closing prices from developed and emergent stock markets as the basis, we argue that the incorporation of stochastic volatility into the time-varying parameter estimation significantly improves the forecasting performance via Maximum Likelihood Estimation. While using the technique, we see the long-memory behavior of data sets and one-step-ahead-predicted log-volatility with 2 standard errors despite the variation of the observed noise from a Normal mixture distribution, because the financial data studied is not fully Gaussian. Also, the Ornstein-Uhlenbeck process followed in this work simulates well the financial time series, which aligns our estimation algorithm with large data sets due to the fact that this algorithm has good convergence properties.
Parallel Evaluation of Sommerfeld Integrals for Multilayer Dyadic Green's Function
Sommerfeld-integrals (SIs) are commonly encountered in electromagnetics problems involving analysis of antennas and scatterers embedded in planar multilayered media. Generally speaking, the analytical solution of SIs is unavailable, and it is well known that numerical evaluation of SIs is very time consuming and computationally expensive due to the highly oscillating and slowly decaying nature of the integrands. Therefore, fast computation of SIs has a paramount importance. In this paper, a parallel code has been developed to speed up the computation of SI in the framework of calculation of dyadic Green’s function in multilayered media. OpenMP shared memory approach is used to parallelize the SI algorithm and resulted in significant time savings. Moreover accelerating the computation of dyadic Green’s function is discussed based on the parallel SI algorithm developed.
Susceptible-Vaccinated-Infected-Recovery Model for Analyzing Tax Amnesty in Indonesia
Tax amnesty is an opportunity for a particular group of taxpayers to disclose incomplete or unreported information about previous tax periods. Tax amnesty requires specific group of taxpayers to pay certain amount relating to previous tax liability including penalties and interest without fear of criminal prosecution. This research will discuss how effective the tax amnesty using the Susceptible-Vaccinated-Infected-Recovery (SVIR) model with the population of taxpayers (S), the population in the tax amnesty program (V), the population that does not want to pay the tax (I), and the population that has revealed tax (R). The assumption used in this research is the population who does not want to pay taxes can affect people who still have responsibility to pay tax, so there is interaction between Susceptible and Infected. The tax amnesty program is a vaccine for a population of taxpayers so the population of the vaccinated taxpayers can be incorporated into population that has disclosed the tax. In addition, there is also the possibility of vaccine failure so that there is population incorporated into population that does not want to pay taxes. This SVIR model equation used differential equation system to know the effectiveness level of tax amnesty program.
Improved Elastoplastic Bounding Surface Model for the Mathematical Modeling of Geomaterials
The nature of most engineering materials is quite complex. It is, therefore, difficult to devise a general mathematical model that will simulate all possible ranges and types of excitation and behavior of a given material. As a result, the development of mathematical models is based upon simplifying assumptions regarding material behavior. Such simplifications result in some material idealization; for example, one of the simplest material idealizations is to assume that the material is elastic. However, geomaterials are nonhomogeneous, anisotropic, path-dependent materials that exhibit nonlinear stress-strain response, changes in volume under shear, dilatancy, as well as time-, rate- and temperature-dependent behavior. Over the years, many constitutive models, possessing different levels of sophistication, have been developed to simulate the behavior of geomaterials. Early in the development of constitutive models, it became evident that elastic or standard elastoplastic formulations, employing purely isotropic hardening and predicated in the existence of a yield surface surrounding a purely elastic domain, were incapable of realistically simulating the behavior of geomaterials in general, and cohesive soils in particular. Accordingly, more sophisticated constitutive models classes have been developed; one such class includes models based on the bounding surface concept. The essence of this concept is the hypothesis that inelastic deformations can occur for stress states either within or on the bounding surface. Thus, unlike classical yield surface elastoplasticity, the inelastic states are not restricted only to those lying on a surface. Elastoplastic bounding surface models have been progressively improved. Recently, the Generalized Bounding Surface Model (GBSM) for cohesive soils was been developed in an effort to conveniently unify and further improve upon past models in this class. The GBSM is a fully three-dimensional, time- and rate-dependent model that accounts for both inherent and stress induced anisotropy employing either an associative or non-associative flow rule. The GBSM includes an improved rotational hardening rule that better simulates the response of cohesive soils, particularly in extension. The GBSM is numerically implemented through a series of modular subroutines that facilitate its inclusion into new and existing research and commercial finite element computer programs. This implementation includes an adaptive multistep integration scheme in conjunction with local iteration and radial return. The one-step trapezoidal rule was used to compute the tangential stiffness matrix that defines the relationship between the stress increment and the strain increment. In verifying the predictive capabilities of the GBSM, it has been shown to successfully simulate the response of various cohesive soils, including Cardiff Kaolin, Spestone Kaolin, and Lower Cromer Till. The simulated undrained stress paths, stress-strain response, and excess pore pressures were found to be in very good agreement with the experimental values, for both compression and extension and under both drained and undrained conditions.