Abstract: In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.
Abstract: The distribution of velocities of particles in plasma is a well understood discipline of plasma physics. Boltzmann’s law and the Maxwell-Boltzmann distribution describe the distribution of velocity of a particle in plasma as a function of mass and temperature. Particles with the same mass tend to have the same velocity. By expressing the same law in terms of energy alone, the author obtains a distribution independent of mass. In summary, for particles in plasma, the energies tend to equalize, independent of the masses of the individual particles. For high-energy plasma, the original law predicts velocities greater than the speed of light. If one uses Einstein’s formula for energy (E=mc2), then a relativistic correction is not required.
Abstract: This paper compared the efficiency of Simpson’s 1/3 and 3/8 rules for the numerical solution of first order Volterra integro-differential equations. In developing the solution, collocation approximation method was adopted using the shifted Legendre polynomial as basis function. A block method approach is preferred to the predictor corrector method for being self-starting. Experimental results confirmed that the Simpson’s 3/8 rule is more efficient than the Simpson’s 1/3 rule.
Abstract: Scientists are making attempts to solve proton radius puzzle. In this paper, the calculated value matches the experiment observation within 0.1%, compared to those obtained from CODATA, and muonic hydrogen scattering experiments of 4%. The calculation is made based on the assumption that the muonic hydrogen system has (Ep – Eµ) energy state (or frequency mix state of np –nµ), which interacts resonantly with the incoming photon of energy 206.2949(32) meV. A similar calculation is also made for muonic deuterium 2S-2P transition experiment with an accuracy of 1% from the experimental observation. The paper has also explored the theoretical as well as experimentation advancements that have led towards the development of results with lesser deviations.
Abstract: This paper employs the Jeffrey's prior technique in the
process of estimating the periodograms and frequency of sinusoidal
model for unknown noisy time variants or oscillating events (data) in
a Bayesian setting. The non-informative Jeffrey's prior was adopted
for the posterior trigonometric function of the sinusoidal model
such that Cramer-Rao Lower Bound (CRLB) inference was used
in carving-out the minimum variance needed to curb the invariance
structure effect for unknown noisy time observational and repeated
circular patterns. An average monthly oscillating temperature series
measured in degree Celsius (0C) from 1901 to 2014 was subjected to
the posterior solution of the unknown noisy events of the sinusoidal
model via Markov Chain Monte Carlo (MCMC). It was not only
deduced that two minutes period is required before completing a cycle
of changing temperature from one particular degree Celsius to another
but also that the sinusoidal model via the CRLB-Jeffrey's prior for
unknown noisy events produced a miniature posterior Maximum A
Posteriori (MAP) compare to a known noisy events.
Abstract: In this paper, we studied the effect of supplementary premium on the optimal portfolio policy in a defined contribution (DC) pension scheme with refund of premium clauses. This refund clause allows death members’ next of kin to withdraw their relative’s accumulated wealth during the accumulation period. The supplementary premium is to help sustain the scheme and is assumed to be stochastic. We considered cases when the remaining wealth is equally distributed and when it is not equally distributed among the remaining members. Next, we considered investments in cash and equity to help increase the remaining accumulated funds to meet up with the retirement needs of the remaining members and composed the problem as a continuous time mean-variance stochastic optimal control problem using the actuarial symbol and established an optimization problem from the extended Hamilton Jacobi Bellman equations. The optimal portfolio policy, the corresponding optimal fund size for the two assets and also the efficient frontier of the pension members for the two cases was obtained. Furthermore, the numerical simulations of the optimal portfolio policies with time were presented and the effect of the supplementary premium on the optimal portfolio policy was discussed and observed that the supplementary premium decreases the optimal portfolio policy of the risky asset (equity). Secondly we observed a disparity between the optimal policies for the two cases.
Abstract: In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity has been constructed. The resulting non-dimensional governing equations together with the Laplace and double Fourier transforms techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free in the directions of the principle co-ordinates. The inverses of double Fourier transforms, and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of the thermal conductivity has significant effects on the thermal and the mechanical waves.
Abstract: Harmonic functions are solutions to Laplace’s equation
that are known to have an advantage as a global approach in providing
the potential values for autonomous vehicle navigation. However,
the computation for obtaining harmonic functions is often too slow
particularly when it involves very large environment. This paper
presents a two-stage iterative method namely Modified Arithmetic
Mean (MAM) method for solving 2D Laplace’s equation. Once
the harmonic functions are obtained, the standard Gradient Descent
Search (GDS) is performed for path finding of an autonomous vehicle
from arbitrary initial position to the specified goal position. Details
of the MAM method are discussed. Several simulations of vehicle
navigation with path planning in a static known indoor environment
were conducted to verify the efficiency of the MAM method. The
generated paths obtained from the simulations are presented. The
performance of the MAM method in computing harmonic functions
in 2D environment to solve path planning problem for an autonomous
vehicle navigation is also provided.
Abstract: Efficiency of the cooling process for cryogenic
propellant boiling in engine cooling channels on space applications is
relentlessly affected by the phase change occurs during the boiling.
The effectiveness of the cooling process strongly pertains to the
type of the boiling regime such as nucleate and film. Geometric
constraints like a non-transparent cooling channel unable to use
any of visualization methods. The ultrasonic (US) technique as a
non-destructive method (NDT) has therefore been applied almost
in every engineering field for different purposes. Basically, the
discontinuities emerge between mediums like boundaries among
different phases. The sound wave emitted by the US transducer is
both transmitted and reflected through a gas-liquid interface which
makes able to detect different phases. Due to the thermal and
structural concerns, it is impractical to sustain a direct contact
between the US transducer and working fluid. Hence the transducer
should be located outside of the cooling channel which results in
additional interfaces and creates ambiguities on the applicability
of the present method. In this work, an exploratory research is
prompted so as to determine detection ability and applicability of
the US technique on the cryogenic boiling process for a cooling
cycle where the US transducer is taken place outside of the channel.
Boiling of the cryogenics is a complex phenomenon which mainly
brings several hindrances for experimental protocol because of
thermal properties. Thus substitute materials are purposefully selected
based on such parameters to simplify experiments. Aside from
that, nucleate and film boiling regimes emerging during the boiling
process are simply simulated using non-deformable stainless steel
balls, air-bubble injection apparatuses and air clearances instead
of conducting a real-time boiling process. A versatile detection
algorithm is perennially developed concerning exploratory studies
afterward. According to the algorithm developed, the phases can be
distinguished 99% as no-phase, air-bubble, and air-film presences.
The results show the detection ability and applicability of the US
technique for an exploratory purpose.
Abstract: Lenstra’s attack uses Chinese remainder theorem as a tool and requires a faulty signature to be successful. This paper reports on the security responses of fourth and sixth order Lucas based (LUC4,6) cryptosystem under the Lenstra’s attack as compared to the other two Lucas based cryptosystems such as LUC and LUC3 cryptosystems. All the Lucas based cryptosystems were exposed mathematically to the Lenstra’s attack using Chinese Remainder Theorem and Dickson polynomial. Result shows that the possibility for successful Lenstra’s attack is less against LUC4,6 cryptosystem than LUC3 and LUC cryptosystems. Current study concludes that LUC4,6 cryptosystem is more secure than LUC and LUC3 cryptosystems in sustaining against Lenstra’s attack.
Abstract: Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.
Abstract: The incubation period is defined as the time from infection with a microorganism to development of symptoms. In this research, two disease models: one with incubation period and another without incubation period were studied. The study involves the use of a mathematical model with a single incubation period. The test for the existence and stability of the disease free and the endemic equilibrium states for both models were carried out. The fourth order Runge-Kutta method was used to solve both models numerically. Finally, a computer program in MATLAB was developed to run the numerical experiments. From the results, we are able to show that the endemic equilibrium state of the model with incubation period is locally asymptotically stable whereas the endemic equilibrium state of the model without incubation period is unstable under certain conditions on the given model parameters. It was also established that the disease free equilibrium states of the model with and without incubation period are locally asymptotically stable. Furthermore, results from numerical experiments using empirical data obtained from Nigeria Centre for Disease Control (NCDC) showed that the overall population of the infected people for the model with incubation period is higher than that without incubation period. We also established from the results obtained that as the transmission rate from susceptible to infected population increases, the peak values of the infected population for the model with incubation period decrease and are always less than those for the model without incubation period.
Abstract: It can be frequently observed that the data arising in our environment have a hierarchical or a nested structure attached with the data. Multilevel modelling is a modern approach to handle this kind of data. When multilevel modelling is combined with a binary response, the estimation methods get complex in nature and the usual techniques are derived from quasi-likelihood method. The estimation methods which are compared in this study are, marginal quasi-likelihood (order 1 & order 2) (MQL1, MQL2) and penalized quasi-likelihood (order 1 & order 2) (PQL1, PQL2). A statistical model is of no use if it does not reflect the given dataset. Therefore, checking the adequacy of the fitted model through a goodness-of-fit (GOF) test is an essential stage in any modelling procedure. However, prior to usage, it is also equally important to confirm that the GOF test performs well and is suitable for the given model. This study assesses the suitability of the GOF test developed for binary response multilevel models with respect to the method used in model estimation. An extensive set of simulations was conducted using MLwiN (v 2.19) with varying number of clusters, cluster sizes and intra cluster correlations. The test maintained the desirable Type-I error for models estimated using PQL2 and it failed for almost all the combinations of MQL. Power of the test was adequate for most of the combinations in all estimation methods except MQL1. Moreover, models were fitted using the four methods to a real-life dataset and performance of the test was compared for each model.
Abstract: Networks can be utilized to represent project planning problems, using nodes for activities and arcs to indicate precedence relationship between them. For fixed activity duration, a simple algorithm calculates the amount of time required to complete a project, followed by the activities that comprise the critical path. Program Evaluation and Review Technique (PERT) generalizes the above model by incorporating uncertainty, allowing activity durations to be random variables, producing nevertheless a relatively crude solution in planning problems. In this paper, based on the findings of the relevant literature, which strongly suggests that a Beta distribution can be employed to model earthmoving activities, we utilize Monte Carlo simulation, to estimate the project completion time distribution and measure the influence of skewness, an element inherent in activities of modern technical projects. We also extract the activity criticality index, with an ultimate goal to produce more accurate planning estimations.
Abstract: Back propagation algorithm (BP) is a widely used
technique in artificial neural network and has been used as a tool
for solving the time series problems, such as decreasing training
time, maximizing the ability to fall into local minima, and optimizing
sensitivity of the initial weights and bias. This paper proposes an
improvement of a BP technique which is called IM-COH algorithm
(IM-COH). By combining IM-COH algorithm with cuckoo search
algorithm (CS), the result is cuckoo search improved control output
hidden layer algorithm (CS-IM-COH). This new algorithm has a
better ability in optimizing sensitivity of the initial weights and bias
than the original BP algorithm. In this research, the algorithm of
CS-IM-COH is compared with the original BP, the IM-COH, and the
original BP with CS (CS-BP). Furthermore, the selected benchmarks,
four time series samples, are shown in this research for illustration.
The research shows that the CS-IM-COH algorithm give the best
forecasting results compared with the selected samples.
Abstract: In the field of quantum secure communication, there
is no evaluation that characterizes quantum secure communication
(QSC) protocols in a complete, general manner. The current paper
addresses the problem concerning the lack of such an evaluation
for QSC protocols by introducing an optimality evaluation, which
is expressed as the average over the three main parameters of QSC
protocols: efficiency, security, and practicality. For the efficiency
evaluation, the common expression of this parameter is used, which
incorporates all the classical and quantum resources (bits and qubits)
utilized for transferring a certain amount of information (bits) in a
secure manner. By using criteria approach whether or not certain
criteria are met, an expression for the practicality evaluation is
presented, which accounts for the complexity of the QSC practical
realization. Based on the error rates that the common quantum attacks
(Measurement and resend, Intercept and resend, probe attack, and
entanglement swapping attack) induce, the security evaluation for
a QSC protocol is proposed as the minimum function taken over
the error rates of the mentioned quantum attacks. For the sake of
clarity, an example is presented in order to show how the optimality
Abstract: In the present work, we consider one category of curves
denoted by L(p, k, r, n). These curves are continuous arcs which are
trajectories of roots of the trinomial equation zn = αzk + (1 − α),
where z is a complex number, n and k are two integers such that
1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting
by L the union of all trinomial curves L(p, k, r, n) and using the
box counting dimension as fractal dimension, we will prove that the
dimension of L is equal to 3/2.
Abstract: In this paper, we deal with the optimal I/O point location in an automated parking system. In this system, the S/R machine (storage and retrieve machine) travels independently in vertical and horizontal directions. Based on the characteristics of the parking system and the basic principle of AS/RS system (Automated Storage and Retrieval System), we obtain the continuous model in units of time. For the single command cycle using the randomized storage policy, we calculate the probability density function for the system travel time and thus we develop the travel time model. And we confirm that the travel time model shows a good performance by comparing with discrete case. Finally in this part, we establish the optimal model by minimizing the expected travel time model and it is shown that the optimal location of the I/O point is located at the middle of the left-hand above corner.
Abstract: A Banach space operator T obeys property (gm) if the
isolated points of the spectrum σ(T) of T which are eigenvalues
are exactly those points λ of the spectrum for which T − λI is
a left Drazin invertible. In this article, we study the stability of
property (gm), for a bounded operator acting on a Banach space,
under perturbation by finite rank operators, by nilpotent operators,
by quasi-nilpotent operators, or more generally by algebraic operators
commuting with T.
Abstract: Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.