Search results for: Hamilton Cyprian Chinwenyi

Authors: Hussaini Doko Ibrahim, Hamilton Cyprian Chinwenyi, Henrietta Nkem Ude

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In this paper, efforts were made to examine and compare the algorithmic iterative solutions of the conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax=b, where A is a real n×n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3×3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi, and conjugate gradient methods), respectively. From the results obtained, we discovered that the conjugate gradient method converges faster to exact solutions in fewer iterative steps than the two other methods, which took many iterations, much time, and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, gauss-seidel, Jacobi, algorithm

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Authors: Khaled I. Nawafleh

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In this work, we apply the method of Hamilton-Jacobi to obtain solutions of Hamiltonian systems in classical mechanics with two certain structures: the first structure plays a central role in the theory of time-dependent Hamiltonians, whilst the second is used to treat classical Hamiltonians, including dissipation terms. It is proved that the generalization of problems from the calculus of variation methods in the nonstationary case can be obtained naturally in Hamilton-Jacobi formalism. Then, another expression of geometry of the Hamilton Jacobi equation is retrieved for Hamiltonians with time-dependent and frictional terms. Both approaches shall be applied to many physical examples.

Keywords: Hamilton-Jacobi, time dependent lagrangians, dissipative systems, variational principle

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Authors: Monty Vacura

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Hamilton’s Rule is a universal law of biology expressed in protists, plants and animals. When applied to human populations, this model explains: 1) Origin of religion in society as a biopsychological need selected to increase population size; 2) Instincts of racism expressed through intergroup competition; 3) Simultaneous selection for human cooperation and conflict, love and hate; 4) Connection between sporting events and instinctive social messaging for stimulating offensive and defensive responses; 5) Pathway to reduce human sacrifice. This chapter discusses the deep psychological influences of Hamilton’s Rule. Suggestions are provided to reduce human deaths via our instinctive sacrificial behavior, by consciously monitoring Hamilton’s Rule variables highlighted throughout our media outlets.

Keywords: psychology, Hamilton’s rule, evolution, human instincts

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Authors: Monty Vacura

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Hamilton’s Rule is a universal law of biology expressed in protists, plants and animals. When applied to human populations, this model explains: 1) Origin of religion in society as a biopsychological need naturally selected to increase population size; 2) Instincts of racism expressed through intergroup competition; 3) Simultaneous selection for human cooperation and conflict, love and hate; 4) Places Dawkins’s selfish gene as the r, relationship variable; 5) Flipping the equation variable themes (close relationship to distant relationship, and benefit to threat) the new equation can now be used to identify the offensive and defensive sides of conflict; 6) Connection between sporting events and instinctive social messaging for stimulating offensive and defensive responses; 6) Pathway to reduce human sacrifice through manipulation of variables. This paper discusses the deep psychological influences of Hamilton’s Rule. Suggestions are provided to reduce human deaths via our instinctive sacrificial behavior, by consciously monitoring Hamilton’s Rule variables highlighted throughout our media outlets.

Keywords: psychology, Hamilton’s rule, evolution, human instincts

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Authors: Mei-Jie Xu, Yang Zhong

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Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

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Authors: Weihua Ruan, Kuan-Chou Chen

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This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.

Keywords: Hamilton-Jacobi-Bellman equations, infinite-horizon differential games, continuous and discrete state variables, political-economy models

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Authors: Brian Ceh, Alison Jackson-Holland

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Food deserts are a reality in some cities. These deserts can be described as a shortage of healthy food options within close proximity of consumers. The shortage in this case is typically facilitated by a lack of stores in an urban area that provide adequate fruit and vegetable choices. This study explores new avenues to better understand food deserts by examining modes of transportation that are available to shoppers or consumers, e.g. walking, automobile, or public transit. Further, this study is unique in that it not only explores the location of large grocery stores, but small grocery and convenience stores too. In this study, the relationship between some socio-economic indicators, such as personal income, are also explored to determine any possible association with food deserts. In addition, to help facilitate our understanding of food deserts, complex network spatial models that are built on adequate algorithms are used to investigate the possibility of food deserts in the city of Hamilton, Canada. It is found that Hamilton, Canada is adequate serviced by retailers who provide healthy food choices and that the food desert phenomena is almost absent.

Keywords: Canada, desert, food, Hamilton, store

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Authors: E. R. Swart, S. J. Gismondi, N. R. Swart, C. E. Bell

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We present an heuristic algorithm that decides graph non-Hamiltonicity. All graphs are directed, each undirected edge regarded as a pair of counter directed arcs. Each of the n! Hamilton cycles in a complete graph on n+1 vertices is mapped to an n-permutation matrix P where p(u,i)=1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n+1. We first create exclusion set E by noting all arcs (u, v) not in G, sufficient to code precisely all cycles excluded from G i.e. cycles not in G use at least one arc not in G. Members are pairs of components of P, {p(u,i),p(v,i+1)}, i=1, n-1. A doubly stochastic-like relaxed LP formulation of the Hamilton cycle decision problem is constructed. Each {p(u,i),p(v,i+1)} in E is coded as variable q(u,i,v,i+1)=0 i.e. shrinks the feasible region. We then implement the Weak Closure Algorithm (WCA) that tests necessary conditions of a matching, together with Boolean closure to decide 0/1 variable assignments. Each {p(u,i),p(v,j)} not in E is tested for membership in E, and if possible, added to E (q(u,i,v,j)=0) to iteratively maximize |E|. If the WCA constructs E to be maximal, the set of all {p(u,i),p(v,j)}, then G is decided non-Hamiltonian. Only non-Hamiltonian G share this maximal property. Ten non-Hamiltonian graphs (10 through 104 vertices) and 2000 randomized 31 vertex non-Hamiltonian graphs are tested and correctly decided non-Hamiltonian. For Hamiltonian G, the complement of E covers a matching, perhaps useful in searching for cycles. We also present an example where the WCA fails.

Keywords: Hamilton cycle decision problem, computational complexity theory, graph theory, theoretical computer science

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Authors: Ahmed A. Abd El Rahim, Andrew Anis Fakhrey Mosaad

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Background: An important psychological issue that has an impact on both mental and physical function is anxiety disorders. The general consensus is that aerobic exercise and physical activity are good for lowering anxiety and mood. Purpose: This study's goal was to look into how patients with anxiety disorders responded to aerobic exercise. Subjects: Anxiety disorders were identified in 30 individuals from the psychiatric hospital at Sohag University who were chosen based on inclusive criteria and had ages ranging from 25 to 45. Methods: Patients were split into two equal groups at random: For four weeks, three sessions per week, fifteen patients in group A (the study group), seven men and eight women, underwent medication therapy and aerobic exercise. Age (28.4 ± 2.11 years), weight (72.5 ± 10.06 kg), height (164.8 ± 9.64 cm), and BMI (26.65 ± 2.68 kg/m2) were all mean SD values. And in Group B (Control Group), only medication therapy was administered to 15 patients (9 males and 6 females). Age (29.6 ± 3.68), weight (75 ± 7.07 kg), height (166.9 ± 6.75) cm, and BMI (26.87 ± 1.11) kg/m2 were the mean SD values. Before and after the treatment, the Hamilton Anxiety Scale was used to gauge the patient's degree of anxiety. Results: Within the two groups, there were significant differences both before and after the treatment. Following therapy, there was a significant difference between the two groups; the study group displayed better improvement on the Hamilton Anxiety Scale. Conclusion: Patients with anxiety problems can benefit from aerobic activities and antianxiety drugs as effective treatments for lowering anxiety levels.

Keywords: aerobic exercises, anxiety disorders, antianxiety medications, Hamilton anxiety scale

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Authors: Khaled I. Nawafleh

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In this paper, it provide the canonical approach for studying dissipated oscillators based on the doubling of degrees of freedom. Clearly, expressions for Lagrangians of the elementary modes of the system are given, which ends with the familiar classical equations of motion for the dissipative oscillator. The equation for one variable is the time reversed of the motion of the second variable. it discuss in detail the extended Bateman Lagrangian specifically for a dual extended damped oscillator time-dependent. A Hamilton-Jacobi analysis showing the equivalence with the Lagrangian approach is also obtained. For that purpose, the techniques of separation of variables were applied, and the quantization process was achieved.

Keywords: doubling of degrees of freedom, dissipated harmonic oscillator, Hamilton-Jacobi, time-dependent lagrangians, quantization

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Authors: Hosein Falahaty, Hitoshi Gotoh, Abbas Khayyer

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Performance of a Hamiltonian based particle method in simulation of nonlinear structural dynamics is subjected to investigation in terms of stability and accuracy. The governing equation of motion is derived based on Hamilton's principle of least action, while the deformation gradient is obtained according to Weighted Least Square method. The hyper-elasticity models of Saint Venant-Kirchhoff and a compressible version similar to Mooney- Rivlin are engaged for the calculation of second Piola-Kirchhoff stress tensor, respectively. Stability along with accuracy of numerical model is verified by reproducing critical stress fields in static and dynamic responses. As the results, although performance of Hamiltonian based model is evaluated as being acceptable in dealing with intense extensional stress fields, however kinds of instabilities reveal in the case of violent collision which can be most likely attributed to zero energy singular modes.

Keywords: Hamilton's principle of least action, particle-based method, hyper-elasticity, analysis of stability

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Authors: Mohammad Bukhari, Oumar Barry

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In order to reduce the Aeolian vibration of overhead transmission lines, the Stockbridge damper is usually attached. The efficiency of Stockbridge damper depends on its location on the conductor and its resonant frequencies. When the Stockbridge damper is located on a vibration node, it becomes inefficient. Hence, the static damper should be subrogated by a dynamic one. In the present study, a proposed dynamic absorber for transmission lines is studied. Hamilton’s principle is used to derive the governing equations, then the system of ordinary differential equations is solved numerically. Parametric studies are conducted to determine how certain parameters affect the performance of the absorber. The results demonstrate that replacing the static absorber by a dynamic one enhance the absorber performance for wider range of frequencies. The results also indicate that the maximum displacement decreases as the absorber speed and the forcing frequency increase. However, this reduction in maximum displacement is accompanying with increasing in the steady state vibration displacement. It is also indicated that the energy dissipation in moving absorber covers higher range of frequencies.

Keywords: absorber performance, Aeolian vibration, Hamilton’s principle, stockbridge damper

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Authors: Haofei Li

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To support academic growth and foster love of learning, MathMates has been introduced for grade 6-8 students at Andrew Hamilton public school in 2022. The program is targeted at students from diverse backgrounds, particularly those underperforming in Pennsylvania System of School Assessment (PSSA) exams. Then, this study aims to evaluate the efficacy of MathMates by comparing student performance on the PSSA test, before and after the intervention. Through a randomized control trial, the study will collect associated costs using the ingredients method and measure the effectiveness for cost-effectiveness analysis. Text messages will be sent to parents/guardians as a reminder of the program and to encourage student participation. The findings of this study will provide valuable insights for funding organizations seeking to understand the impact and costs of math tutoring interventions on student academic achievement, which also emphasizes the importance of the collaborative efforts between higher education and local public schools.

Keywords: mathematics education, mathematics tutoring, college-community initiative, middle schools, Philadelphia public schools, after-school program, PSSA

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Authors: Neeti Sharma, Harshika Pareek, Prerna Puri, Manika Mohan

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The present study is aimed at studying the significant relationship between anxiety and depression in chronic headache patients. Chronic Headache patients coming to the Neurology Unit-1 Outpatient Department of the Sawai Mansingh Hospital (SMS) Jaipur, Rajasthan, were included in this study. The sample consisted of 100 patients (N=100). Initially patients were examined by a physician and then they were assessed for Anxiety and Depression using the Hamilton Anxiety Rating Scale (HAM-A) and the Hamilton Rating Scale for Depression. The relevant information was recorded on a Performa designed for this purpose comprising of socio-demographic variables like age, gender and triggering factors. The correlation-coefficient indicated a significant positive relationship between the anxiety and depression in chronic headache patients. These findings implicate high prevalence of anxiety and depression in the general population, and also indicate an association between headache and psychological disorders. Many evidences support the anxiety-headache-depression syndrome as a distinct disorder, and the association of co-morbid psychiatric illness with headache intractability. This study highlights the importance of prospective research for studying the developmental course and consequences of headache syndromes. Also, various psychotherapies should be applied to the headache patients so as to treat them, at the onset level of anxiety and depression, with the help of medication.

Keywords: anxiety, chronic headaches, depression, HAM-A, HAM

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Authors: Sherwan Kher Alden Yakub Alsofy

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In this paper, we consider the relativistic Hamilton-Jacobi (HJ) equation and study the Hawking radiation (HR) of scalar particles from uncharged Grumiller black hole (GBH) which is affordable for testing in astrophysics. GBH is also known as Rindler modified Schwarzschild BH. Our aim is not only to investigate the effect of the Rindler parameter A on the Hawking temperature (TH ), but to examine whether there is any discrepancy between the computed horizon temperature and the standard TH as well. For this purpose, in addition to its naive coordinate system, we study on the three regular coordinate systems which are Painlev´-Gullstrand (PG), ingoing Eddington- Finkelstein (IEF) and Kruskal-Szekeres (KS) coordinates. In all coordinate systems, we calculate the tunneling probabilities of incoming and outgoing scalar particles from the event horizon by using the HJ equation. It has been shown in detail that the considered HJ method is concluded with the conventional TH in all these coordinate systems without giving rise to the famous factor- 2 problem. Furthermore, in the PG coordinates Parikh-Wilczek’s tunneling (PWT) method is employed in order to show how one can integrate the quantum gravity (QG) corrections to the semiclassical tunneling rate by including the effects of self-gravitation and back reaction. We then show how these corrections yield a modification in the TH.

Keywords: ingoing Eddington, Finkelstein, coordinates Parikh-Wilczek’s, Hamilton-Jacobi equation

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Authors: Farnaz Farhangi

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Many people in New Zealand believe that the access to water is inexhaustible, and it comes from a history of virtually unrestricted access to it. For the region like Hamilton which is one of New Zealand’s fastest growing cities, it is crucial for policy makers to know about the future water consumption and implementation of rules and regulation such as universal water metering. Hamilton residents use water freely and they do not have any idea about how much water they use. Hence, one of proposed objectives of this research is focusing on forecasting water consumption using different methods. Residential water consumption time series exhibits seasonal and trend variations. Seasonality is the pattern caused by repeating events such as weather conditions in summer and winter, public holidays, etc. The problem with this seasonal fluctuation is that, it dominates other time series components and makes difficulties in determining other variations (such as educational campaign’s effect, regulation, etc.) in time series. Apart from seasonality, a stochastic trend is also combined with seasonality and makes different effects on results of forecasting. According to the forecasting literature, preprocessing (de-trending and de-seasonalization) is essential to have more performed forecasting results, while some other researchers mention that seasonally non-adjusted data should be used. Hence, I answer the question that is pre-processing essential? A wide range of forecasting methods exists with different pros and cons. In this research, I apply double seasonal ARIMA and Artificial Neural Network (ANN), considering diverse elements such as seasonality and calendar effects (public and school holidays) and combine their results to find the best predicted values. My hypothesis is the examination the results of combined method (hybrid model) and individual methods and comparing the accuracy and robustness. In order to use ARIMA, the data should be stationary. Also, ANN has successful forecasting applications in terms of forecasting seasonal and trend time series. Using a hybrid model is a way to improve the accuracy of the methods. Due to the fact that water demand is dominated by different seasonality, in order to find their sensitivity to weather conditions or calendar effects or other seasonal patterns, I combine different methods. The advantage of this combination is reduction of errors by averaging of each individual model. It is also useful when we are not sure about the accuracy of each forecasting model and it can ease the problem of model selection. Using daily residential water consumption data from January 2000 to July 2015 in Hamilton, I indicate how prediction by different methods varies. ANN has more accurate forecasting results than other method and preprocessing is essential when we use seasonal time series. Using hybrid model reduces forecasting average errors and increases the performance.

Keywords: artificial neural network (ANN), double seasonal ARIMA, forecasting, hybrid model

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Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma

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An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Black-Scholes partial differential equations, Ito process, option price valuation, partial differential equations

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Authors: Adele Pierre, Nadia Amoroso

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Changing climate patterns are resulting in increased in storm severity, challenging traditional methods of managing stormwater runoff. This research compares a system of bioswales to existing curb and gutter infrastructure in a post-industrial streetscape of Hamilton, Ontario. Using the geodesign process, including rule-based set parameters and an integrated approach combining geospatial information with stakeholder input, a section of Ottawa St. North was modelled to show how green infrastructure can ease the burden on aging, combined sewer systems. Qualitative data was gathered from residents of the neighbourhood through field notes, and quantitative geospatial data through GIS and site analysis. Parametric modelling was used to generate multiple design scenarios, each visualizing resulting impacts on stormwater runoff along with their calculations. The selected design scenarios offered both an aesthetically pleasing urban bioswale street-scape system while minimizing and controlling stormwater runoff. Interactive maps, videos and the 3D model were presented for stakeholder comment via ESRI’s (Environmental System Research Institute) web-scene. The results of the study demonstrate powerful tools that can assist landscape architects in designing, collaborating and communicating stormwater strategies.

Keywords: bioswale, geodesign, data-driven and rule-based design, geodesign, GIS, stormwater management

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Authors: Cyprian M. Mostert

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This paper investigates the effectiveness of tobacco control policy (TCP) in averting cancer mortalities in both educated and uneducated segments of the South African population. A two-stage least squares model (2SLS) was used covering the period 2009-2013. The results show that the TCP caused a 26 percent average decrease in cancer mortalities in both educated and uneducated segment of the population. However, limiting the sales of cheap and illegal tobacco cigarettes is necessary for advancing the effectiveness of TCP in averting cancer mortalities in the uneducated population — as the paper noted an insignificant decrease in cancer mortalities in 2012-2013 due to the presence of cheaper cigarettes. The paper also discovered evidence of persisting tobacco purchases of branded cigarettes in the educated population group which limited the effectiveness of TCP in 2009-2011. Hikes in real tobacco tax to a 0.8 USD price level in 2012 limited tobacco consumption in the educated group resulting in a 29 percent decrease in cancer mortalities. Other developing countries may learn from the South African case and strive to limit the sales of cheap illegal cigarettes while hiking real tobacco tax of branded cigarettes as a key strategy to improve cancer deaths across educated and uneducated population groups.

Keywords: cancer, health policy, health system, tobacco tax

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Authors: H. C. Chinwenyi, H. D. Ibrahim, F. A. Ahmed

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In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.

Keywords: equivalent martingale measure, European put option, girsanov theorem, martingales, monte carlo method, option price valuation formula

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Authors: H. C. Chinwenyi, H. D. Ibrahim, J. O. Adekunle

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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.

Keywords: asymptotic stability, Hartman-Grobman stability criterion, incubation period, Routh-Hurwitz criterion, Runge-Kutta method

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Authors: Hossein Kheiri, Bashir Naderi, Mohamad Reza Niknam

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In this paper we study the optimal synchronization of chaotic T-system with complete uncertain parameter. Optimal control laws and parameter estimation rules are obtained by using Hamilton-Jacobi-Bellman (HJB) technique and Lyapunov stability theorem. The derived control laws are optimal adaptive control and make the states of drive and response systems asymptotically synchronized. Numerical simulation shows the effectiveness and feasibility of the proposed method.

Keywords: Lyapunov stability, synchronization, chaos, optimal control, adaptive control

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Authors: Guy Joseph Eyebe, Gambo Betchewe, Alidou Mohamadou, Timoleon Crepin Kofane

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In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that appearance of chaos in the system depends strongly on the fractional order parameter.

Keywords: chaos, fractional-order, Melnikov method, nanobeam

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Authors: Yasmeen Jamal Alabdallat, Almutazballlah Bassam Qablan, Obada Ahmad Al Jayyousi, Ihdaa Mahmoud Bani Khalaf, Eman E. Alshial

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Background: Bipolar disorder, formerly known as manic depression, is a mental health status that leads to extreme mood swings that include emotional lows (depression) and highs (mania or hypomania). This systematic review and meta-analysis aimed to assess the safety and efficacy of lithium versus valproate among bipolar patients. Methods: A computer literature search of PubMed, Scopus, Web of Science, and Cochrane Central Register of Controlled Trials was conducted from inception until June 2022. Studies comparing lithium versus valproate among bipolar patients were selected for the analysis, and all relevant outcomes were pooled in the meta-analysis using Review Manager Software. Results: 11 Randomized Clinical Trials were included in this meta-analysis with a total of 4159 patients. Our meta showed that lithium was superior to valproate in terms of Young Mania Rating Scale (YMRS) (MD = 0.00 with 95% CI, (-0.55 – 0.55; I2 = 0%), P = 1.00). The results of the Hamilton Depression Rating Scale (HDRS) showed that the overall effect favored the valproate treated group (MD = 1.41 with 95% CI, (-0.15 – 2.67; I2 = 0%), P = 0.03). Concerning the results of the Montgomery-Asberg Depression Rating Scale (MADRS), the results showed that the lithium was superior to valproate (MD = 0.03 with 95% CI, (-0.80 to 0.87; I2 = 40%), P = 0.94). In terms of the sexual side effect, we found that the valproate was superior to lithium (RR 1.19 with 95% CI, (0.74 to 1.91; I2 = 0%), P = 0.47). The lithium-treated group was superior in comparison to valproate treated group in terms of Abnormal Involuntary Movement Scale (AIMS) (MD = -0.03 with 95% CI (-0.38 to 0.32; I2 = 0%), P = 0.87). The lithium was more favorable in terms of Simpson-Agnes scale (MD = -0.40 with 95% CI, (-0.86 to 0.06; I2 = 0%), P = 0.09). The results of the Barnes akathisia scale showed that the overall effect of the valproate was more favorable in comparison to lithium (MD = 0.05 with 95% CI, (-0.12 to 0.22; I2 = 0%), P = 0.57). Conclusion: Our study revealed that on the scales of efficacy Lithium treated group surpassed Valproate treated group in terms of Young Mania Rating Scale (YMRS), Abnormal Involuntary Movement Scale (AIMS) and Simpson-Agnes scale, but valproate surpassed it in Barnes Akathisia scale. Furthermore, on the scales of depression Hamilton Depression Rating Scale (HDRS) showed that the overall effect favored Valproate treated group, but Lithium surpassed valproate in terms of Montgomery-Asberg Depression Rating Scale (MADRS). Valproate surpassed Lithium in terms of sexual side effects.

Keywords: bipolar, mania, bipolar-depression, sexual dysfunction, sexual side effects, treatment

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Authors: K. Vigneshwaran, Manoj Pandey

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In this paper, breathing crack is considered for the non linear dynamic analysis. The stiffness of the cracked beam is found out by using influence coefficients. The influence coefficients are calculated by using Castigliano’s theorem and strain energy release rate (SERR). The equation of motion of the beam was derived by using Hamilton’s principle. The stiffness and natural frequencies for the cracked beam has been calculated using XFEM and Eigen approach. It is seen that due to presence of cracks, the stiffness and natural frequency changes. The mode shapes and the FRF for the uncracked and breathing cracked cantilever beam also obtained and compared.

Keywords: breathing crack, XFEM, mode shape, FRF, non linear analysis

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Authors: Xiao Wang, Qinge Zhang

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Background: This randomized, open-label study examined the therapeutic effects of computerized cognitive training (CCT) combined with selective serotonin reuptake inhibitors (SSRIs) on cognitive impairment among patients with late-life depression (LLD). Method: Study data were collected from May 5, 2021, to April 21, 2023. Outpatients who met diagnostic criteria for major depressive disorder according to the fifth revision of the Diagnostic and Statistical Manual of Mental Disorders (DSM-5) criteria (i.e., a total score on the 17-item Hamilton Depression Rating Scale (HAMD-17) ≥ 18 and a total score on the Montreal Cognitive Assessment scale (MOCA) <26) were randomly assigned to receive up to 12 weeks of CCT and SSRIs treatment (n=57) or SSRIs and Control treatment (n=61). The primary outcome was the change in Alzheimer's Disease Assessment Scale-Cognitive Subscale (ADAS-Cog) scores from baseline to week 12 between the two groups. The secondary outcomes included changes in the HAMD-17 score, Hamilton Anxiety Scale (HAMA) score and Neuropsychiatric Inventory (NPI) score. Mixed model repeated measures (MMRM) analysis was performed on modified intention-to-treat (mITT) and completer populations. Results: The full analysis set (FAS) included 118 patients (CCT and SSRIs group, n=57; SSRIs and Control group, n =61). Over the 12-week study period, the reduction in the ADAS-cog total score was significant (P < 0.001) in both groups, while MMRM analysis revealed a significantly greater reduction in cognitive function (ADAS-cog total scores) from baseline to posttreatment in the CCT and SSRIs group than in the SSRI and Control group [(F (1,115) =13.65, least-squares mean difference [95% CI]: −2.77 [−3.73, −1.81], p<0.001)]. There were significantly greater improvements in depression symptoms (measured by the HAMD-17) in the CCT and SSRIs group than in the control group [MMRM, estimated mean difference (SE) between groups −3.59 [−5.02, −2.15], p < 0.001]. The least-squares mean changes in the HAMA scores and NPI scores between baseline and week 8 were greater in the CCT and SSRIs group than in the control group (all P < 0.05). There was no significant difference between groups on response rates and remission rates by using the last-observation-carried-forward (LOCF) method (all P > 0.05). The most frequent adverse events (AEs) in both groups were dry mouth, somnolence, and constipation. There was no significant difference in the incidence of adverse events between the two groups. Conclusions: CCT combined with SSRIs was efficacious and well tolerated in LLD patients with cognitive impairment.

Keywords: late-life depression, cognitive function, computerized cognitive training, SSRIs

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Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun

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The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model

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Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun

Abstract:

The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model

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Authors: Min Dai, Hong Liu, Shuaijie Qian

Abstract:

We study a portfolio selection problem of an investor who faces constraints on rebalancing frequency, which is common in pension fund investment. We formulate it as a multiple optimal stopping problem and utilize the dynamic programming principle. By numerically solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation, we find a series of free boundaries characterizing optimal strategy, and the constraints significantly impact the optimal strategy. Even in the absence of transaction costs, there is a no-trading region, depending on the number of the remaining trading chances. We also find that the equivalent wealth loss caused by the constraints is large. In conclusion, our model clarifies the impact of the constraints on transaction frequency on the optimal strategy.

Keywords: portfolio selection, rebalancing frequency, optimal strategy, free boundary, optimal stopping

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Authors: Robert Christopher Hamilton

Abstract:

This research examined the effects of reflexive cosmopolitanism on the competition for sexual territoriality. By adopting Michel De Certeau’s (1984) spatial didactic model, the article maps out the key elements at play and the dynamics explaining how gays gay place in the backdrop of rapid modernization. It found that heterosexual space and heteronormative assumptions helped to create temporal and spatial opportunities that allow for sexual performativity of gay males. Moreover, using data collected from multiple semi-controlled one-on-one interviews over 13 months, this article illustrates how spatial competition culminates in non-zero sum game outcomes and particularly to compromise of sexual territoriality while further demonstrating the need to understand the sexual coping tactics used in cultures with similar backgrounds. The findings enable researchers to better understand how gay men gay space, and how space performatively embodies gay men.

Keywords: South Korea, coffee bean, sexual territoriality, reflexive cosmopolitanism

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