ALBERT

Description: With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree, easily verifiable criteria are established for the existence of multiple positive periodic solutions of delayed predator-prey systems with type IV functional responses on time scales. Our results not only unify the existing ones but also widen the range of applications.

Description: This paper deals with the investigation of the following more general rational difference equation: yn+1=αyn/(β+γ∑i=0kyn-(2i+1)p∏i=0kyn-(2i+1)), n=0,1,2,…, where α,β,γ,p∈(0,∞) with the initial conditions x0,x-1,…,x-2k,x-2k-1∈(0,∞). We investigate the existence of the equilibrium points of the considered equation and then study their local and global stability. Also, some results related to the oscillation and the permanence of the considered equation have been presented.

Description: Through analyzing the data about the releases, comment, and forwarding of 120,000 microblog messages in a year, this paper finds out that the intervals between information releases and comment follow a power law; besides, the analysis of data in each 24 hours reveals obvious differences between microblogging and website visit, email, instant communication, and the use of mobile phone, reflecting how people use fragments of time via mobile internet technology. The paper points out the significant influence of the user's activity on the intervals of information releases and thus demonstrates a positive correlation between the activity and the power exponent. The paper also points out that user's activity is influenced by social identity in a positive way. The simulation results based on the social identity mechanism fit well with the actual data, which indicates that this mechanism is a reasonable way to explain people's behavior in the mobile Internet.

Description: Two types of coronary artery system N-type and S-type, are investigated. The threshold conditions for the occurrence of Smale horseshoe chaos are obtained by using Melnikov method. Numerical simulations including phase portraits, potential diagram, homoclinic bifurcation curve diagrams, bifurcation diagrams, and Poincaré maps not only prove the correctness of theoretical analysis but also show the interesting bifurcation diagrams and the more new complex dynamical behaviors. Numerical simulations are used to investigate the nonlinear dynamical characteristics and complexity of the two systems, revealing bifurcation forms and the road leading to chaotic motion. Finally the chaotic states of the two systems are effectively controlled by two control methods: variable feedback control and coupled feedback control.

Description: In many applications, it is natural to use interval data to describe various kinds of uncertainties. This paper is concerned with an interval neural network with a hidden layer. For the original interval neural network, it might cause oscillation in the learning procedure as indicated in our numerical experiments. In this paper, a smoothing interval neural network is proposed to prevent the weights oscillation during the learning procedure. Here, by smoothing we mean that, in a neighborhood of the origin, we replace the absolute values of the weights by a smooth function of the weights in the hidden layer and output layer. The convergence of a gradient algorithm for training the smoothing interval neural network is proved. Supporting numerical experiments are provided.

Description: This paper deals with the problem of selective harvesting in a chemostat model. Here, we have taken the purifying effort as a dynamic variable and tax as a control instrument. The existence of the possible steady states along with their globally stable equilibrium is discussed. The optimal tax policy is also discussed with the help of Pontryagin's maximum principle. Finally, numerical examples are taken to illustrate some of the key results.

Description: In this paper we present a visual analytics approach for deriving spatio-temporal patterns of collective human mobility from a vast mobile network traffic data set. More than 88 million movements between pairs of radio cells—so-called handovers—served as a proxy for more than two months of mobility within four urban test areas in Northern Italy. In contrast to previous work, our approach relies entirely on visualization and mapping techniques, implemented in several software applications. We purposefully avoid statistical or probabilistic modeling and, nonetheless, reveal characteristic and exceptional mobility patterns. The results show, for example, surprising similarities and symmetries amongst the total mobility and people flows between the test areas. Moreover, the exceptional patterns detected can be associated to real-world events such as soccer matches. We conclude that the visual analytics approach presented can shed new light on large-scale collective urban mobility behavior and thus helps to better understand the “pulse” of dynamic urban systems.

Description: A planning support system for land consolidation has been developed that has, at its heart, an expert system called LandSpaCES (Land Spatial Consolidation Expert System) which contains a “design module” that generates alternative land redistributions under different scenarios and an “evaluation module” which integrates GIS with multi-criteria decision making for assessing these alternatives. This paper introduces the structural framework of the latter module which has been applied using a case study in Cyprus. Two new indices are introduced: the “parcel concentration coefficient” for measuring the dispersion of parcels; and the “landowner satisfaction rate” for predicting the acceptance of the land redistribution plan by the landowners in terms of the location of their new parcels. These two indices are used as criteria for the evaluation of the land redistribution alternatives and are transferable to any land consolidation project. Moreover, a modified version of the ratio estimation procedure, referred to as the “qualitative rating method” for assigning weights to the evaluation criteria, is presented, along with a set of non-linear value functions for standardizing the performance scores of the alternatives and incorporating expert knowledge for five evaluation criteria. The application of the module showed that it is a powerful new tool for the evaluation of alternative land redistribution plans that could be implemented in other countries after appropriate adjustments. A broader contribution has also been made to spatial planning processes, which might follow the methodology and innovations presented in this paper.

Description: Existing models of spatial relations do not consider that different concepts exist on different levels in a hierarchy and in turn that the spatial relations in a given scene are a function of the specific concepts considered. One approach to determining the existence of a particular spatial relation is to compute the corresponding high level concepts explicitly using map generalization before inferring the existence of the spatial relation in question. We explore this idea through the development of a model of the spatial relation “enters” that may exist between a road and a housing estate.

Description: Using functions in some function classes and a generalized Riccati technique, we establish interval oscillation criteria for second-order nonlinear dynamic equations on time scales of the form . The obtained interval oscillation criteria can be applied to equations with a forcing term. An example is included to show the significance of the results.

Description: Together with the Lyapunov-Krasovskii functional approach and an improved delay-partitioning idea, one novel sufficient condition is derived to guarantee a class of delayed neural networks to be asymptotically stable in the mean-square sense, in which the probabilistic variable delay and both of delay variation limits can be measured. Through combining the reciprocal convex technique and convex technique one, the criterion is presented via LMIs and its solvability heavily depends on the sizes of both time-delay range and its variations, which can become much less conservative than those present ones by thinning the delay intervals. Finally, it can be demonstrated by four numerical examples that our idea reduces the conservatism more effectively than some earlier reported ones.

Description: We discuss stochastic functional differential equation under regime switching . We obtain unique global solution of this system without the linear growth condition; furthermore, we prove its asymptotic ultimate boundedness. Using the ergodic property of the Markov chain, we give the sufficient condition of almost surely exponentially stable of this system.

Description: The operator on sequence space on is defined , where , and and are two convergent sequences of nonzero real numbers satisfying certain conditions, where . The main purpose of this paper is to determine the fine spectrum with respect to the Goldberg's classification of the operator defined by a double sequential band matrix over the sequence space . Additionally, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator over the space .

Description: We will prove some new Opial dynamic inequalities involving higher order derivatives on time scales. The results will be proved by making use of Hölder's inequality, a simple consequence of Keller's chain rule and Taylor monomials on time scales. Some continuous and discrete inequalities will be derived from our results as special cases.

Description: A discrete two species predator-prey captured system is studied. Firstly, a sufficient condition of a positive equilibrium point for this system is obtained. Secondly, we observe that the two nonnegative equilibriums of the system are unstable through the eigenvalue discriminant method, and the positive equilibrium point is asymptotically stable by Jury criterion. Lastly, we obtain the optimal capture strategy of the system from the maximum principle by constructing a discrete Hamiltonian function. To show the feasibility of the main results, a suitable example together with its numerical simulations is illustrated in the last part of the paper. The example with certain practical significance might give an optimal scheme of the greatest economic benefits for the captors.

Description: We investigate the global dynamics of an HIV infection model with two classes of target cells and multiple distributed intracellular delays. The model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, CD4+ T cells and macrophages. The incidence rate of infection is given by saturation functional response. The model has two types of distributed time delays describing time needed for infection of target cell and virus replication. This model can be seen as a generalization of several models given in the literature describing the interaction of the HIV with one class of target cells, CD4+ T cells. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states of the model. We have proven that if the basic reproduction number

Description: We investigate value distribution and uniqueness problems of meromorphic functions with their -shift. We obtain that if is a transcendental meromorphic (or entire) function of zero order, and is a polynomial, then has infinitely many zeros, where , is nonzero constant, and (or ). We also obtain that zero-order meromorphic function share is three distinct values IM with its -difference polynomial , and if , then .

Description: This paper investigates the optimal control and MLE (maximum likelihood estimation) for a single-species system subject to random perturbation. With the help of the techniques of stochastic analysis and mathematical statistics, sufficient conditions for the optimal control threshold value, the optimal control moment, and the maximum likelihood estimation of parameters are established, respectively. An example is presented to illustrate the feasibility of our theoretical results.

Description: Let n be a fixed integer greater than 3 and let λ be a real number with λ≠(n2-n+4)/2. We investigate the Hyers-Ulam stability of derivations on Banach algebras related to the following generalized Cauchy functional inequality ‖∑1≤i<j≤n1≤kl≠i,j≤nf((xi+xj)/2+∑l=1n-2xkl)+f(∑i=2nxi)+f(x1)‖≤‖λf(∑i=1nxi)‖.

Description: By using continuation theorem of coincidence degree theory, sufficient conditions of the existence of positive periodic solutions are obtained for a generalized predator-prey system with diffusion and delays. In this paper, we construct a V-function to make the prior estimation for periodic solutions, which makes the discussion more concise. Moreover, to compute the mapping's topological degree, a polynomial function matrix is constructed straightforwardly as a homotopic mapping for the generalized one, which improves the methods of computation on topological degree for a generalized mapping.

Description: Based on soft sets and N-structures, the notion of (closed) N-ideal over a BCI-algebra is introduced, and related properties are investigated. Relations between N-BCI-algebras and N-ideals are established. Characterizations of a (closed) N-ideal over a BCI-algebra are provided. Conditions for an N-ideal to be an N-BCI-algebra are considered.

Description: At first we find the solution of the functional equation Df(x1,…,xm):=∑k=2m(∑i1=2k∑i2=i1+1k+1⋯∑im-k+1=im-k+1m)f(∑i=1,i≠i1,…,im-k+1mxi-∑r=1m-k+1xir)+f(∑i=1mxi)-2m-1f(x1)=0, where m≥2 is an integer number. Then, we obtain the generalized Hyers-Ulam-Rassias stability in random normed spaces via the fixed point method for the above functional equation.

Description: A novel deterministic SEIS model for the transmission of email viruses in growing communication networks is formulated. Interestingly, the model is different from classical SEIS models not only in the form, but also in the dynamical features. We study the equilibria and their stability and analyse the bifurcation dynamics of the model. In particular, we find that the virus-free equilibrium is locally asymptotically stable for any parameter values, which may attribute to the absence of the basic reproduction number. It is shown that the model undergoes a saddle-node bifurcation and admits the bistable phenomenon. Moreover, on the basis of the Lyapunov function, the domains of attraction of equilibria are estimated by solving an LMI optimization problem. Based on the above theoretical results, some effective strategies are also provided to control the propagation of the email viruses. Additionally, our results are confirmed by numerical simulations.

Description: Crowdsourced geodata has been proven to be a rich and major data source for environmental simulations and analysis, as well as the visualization of spatial phenomena. With the increasing size and complexity of public buildings, such as universities or hotels, there is also an increasing demand for information about indoor spaces. Trying to stimulate this growing demand, both researchers and Volunteered Geographic Information (VGI) communities envision to extend established communities towards indoors. It has already been showcased that VGI from OpenStreetMap (OSM) can be utilized for different applications in Spatial Data Infrastructures (SDIs) as well as for simple shortest path computations inside buildings. The here presented research now tries to utilize crowdsourced indoor geodata for more complex indoor routing scenarios of multiple users. Essentially, it will be investigated if, and to what extent, the available data can be utilized for performing indoor evacuation simulations with the simulation framework MATSim. That is, this paper investigates the suitability of crowdsourced indoor information from OSM (IndoorOSM) for evacuation simulations. Additionally, the applicability of MATSim for agent-based indoor evacuation simulations is conducted. The paper discusses the automatic generation simulation-related data, and provides experimental results for two different evacuation scenarios. Furthermore, limitations of the IndoorOSM data and the MATSim framework for indoor evacuation simulations are elaborated and discussed.

Description: A new method for approximate analytic series solution called multistep Laplace Adomian Decomposition Method (MLADM) has been proposed for solving the model for HIV infection of CD4+T cells. The proposed method is modification of the classical Laplace Adomian Decomposition Method (LADM) with multistep approach. Fourth-order Runge-Kutta method (RK4) is used to evaluate the effectiveness of the proposed algorithm. When we do not know the exact solution of a given problem, generally we use the RK4 method for comparison since it is widely used and accepted. Comparison of the results with RK4 method is confirmed that MLADM performs with very high accuracy. Results show that MLADM is a very promising method for obtaining approximate solutions to the model for HIV infection of CD4+T cells. Some plots and tables are presented to show the reliability and simplicity of the methods. All computations have been made with the aid of a computer code written in Mathematica 7.

Description: The new type rural social endowment insurance system is one of the important policy arrangements in public welfare field in China. Quantitative research is theoretically and practically important for studying the new type rural social endowment insurance system. In this paper, based on the modern control theory, the linear control model for the new type rural social endowment insurance system is set up, and then the robust stability for the new type rural social endowment insurance system of China with minor fluctuations is discussed by using the linear control model.

Description: We generalize the unbounded upper and lower solution method to a third-order ordinary differential equation on the half line subject to the Sturm-Liouville boundary conditions. By using such techniques and the Schäuder fixed point theorem, some criteria are presented for the existence of solutions and positive ones to the problem discussed.

Description: This paper explores the patterns of human activities within a geographical space by adopting the taxicab static points which refer to the locations with zero speed along the tracking trajectory. We report the findings from both aggregated and individual aspects. Results from the aggregated level indicate the following: (1) Human activities exhibit an obvious regularity in time, for example, there is a burst of activity during weekend nights and a lull during the week. (2) They show a remarkable spatial drifting pattern, which strengthens our understanding of the activities in any given place. (3) Activities are heterogeneous in space irrespective of their drifting with time. These aggregated results not only help in city planning, but also facilitate traffic control and management. On the other hand, investigations on an individual level suggest that (4) activities witnessed by one taxicab will have different temporal regularity to another, and (5) each regularity implies a high level of prediction with low entropy by applying the Lempel-Ziv algorithm.

Description: Let {Si}i=1l be a weakly conformal iterated function system on Rd with attractor K. Let π be the canonical projection. In this paper we define a new concept called “projection pressure” Pπ(φ) for φ∈C(Σ) and show the variational principle about the projection pressure under AWSC. Furthermore, we check that the zero of “projection pressure” still satisfies Bowen's equation. Using the root of Bowen's equation, we can get the Hausdorff dimension of the attractor K.

Description: We consider the nonlinear dynamic system xΔ(t)=a(t)g(y(t)),  yΔ(t)=-f(t,xσ(t)). We establish some necessary and sufficient conditions for the existence of oscillatory and nonoscillatory solutions with special asymptotic properties for the system. We generalize the known results in the literature. Some examples are included to illustrate the results.

Description: This paper studies the dynamics of the traveler's day-to-day route adjustment process in the general transportation network with fixed or elastic demand and homogeneous or heterogeneous users. Each traveler is assumed to adjust his/her route choice according to the excess travel cost between the instantaneous experienced travel cost and a certain referred level, which induces an aggregate path flow dynamics. We call the path flow dynamics the excess travel cost dynamics, which corresponds to the excess payoff dynamics in evolutionary games and serves a general framework of modeling the homogeneous or heterogeneous route choice behavior of travelers.

Description: Based on linear feedback control technique, a projective synchronization scheme of N-dimensional chaotic fractional-order systems is proposed, which consists of master and slave fractional-order financial systems coupled by linear state error variables. It is shown that the slave system can be projectively synchronized with the master system constructed by state transformation. Based on the stability theory of linear fractional order systems, a suitable controller for achieving synchronization is designed. The given scheme is applied to achieve projective synchronization of chaotic fractional-order financial systems. Numerical simulations are given to verify the effectiveness of the proposed projective synchronization scheme.

Description: We discuss the existence of weak solutions for a nonlinear boundary value problem of fractional differential equations in Banach space. Our analysis relies on the Mönch's fixed point theorem combined with the technique of measures of weak noncompactness.

Description: Several tasks in urban and architectural design are today undertaken in a geospatial context. Building Information Models (BIM) and geospatial technologies offer 3D data models that provide information about buildings and the surrounding environment. The Industry Foundation Classes (IFC) and CityGML are today the two most prominent semantic models for representation of BIM and geospatial models respectively. CityGML has emerged as a standard for modeling city models while IFC has been developed as a reference model for building objects and sites. Current CAD and geospatial software provide tools that allow the conversion of information from one format to the other. These tools are however fairly limited in their capabilities, often resulting in data and information losses in the transformations. This paper describes a new approach for data integration based on a unified building model (UBM) which encapsulates both the CityGML and IFC models, thus avoiding translations between the models and loss of information. To build the UBM, all classes and related concepts were initially collected from both models, overlapping concepts were merged, new objects were created to ensure the capturing of both indoor and outdoor objects, and finally, spatial relationships between the objects were redefined. Unified Modeling Language (UML) notations were used for representing its objects and relationships between them. There are two use-case scenarios, both set in a hospital: “evacuation” and “allocating spaces for patient wards” were developed to validate and test the proposed UBM data model. Based on these two scenarios, four validation queries were defined in order to validate the appropriateness of the proposed unified building model. It has been validated, through the case scenarios and four queries, that the UBM being developed is able to integrate CityGML data as well as IFC data in an apparently seamless way. Constraints and enrichment functions are used for populating empty database tables and fields. The motivation scenarios also show the needs and benefits of having an integrated approach to the modeling of indoor and outdoor spatial features.

Description: We investigate the dynamics of a delayed stochastic mathematical model to understand the evolution of the alcohol consumption in Spain. Sufficient condition for stability in probability of the equilibrium point of the dynamic model with aftereffect and stochastic perturbations is obtained via Kolmanovskii and Shaikhet general method of Lyapunov functionals construction. We conclude that alcohol consumption in Spain will be constant (with stability) in time with around 36.47% of nonconsumers, 62.94% of nonrisk consumers, and 0.59% of risk consumers. This approach allows us to emphasize the possibilities of the dynamical models in order to study human behaviour.

Description: The dynamics of online content popularity has attracted more and more researches in recent years. In this paper, we provide a quantitative, temporal analysis about the dynamics of online content popularity in a massive system: Sina Microblog. We use time-stamped data to investigate the impact of bursty human comment patterns on the popularity of online microblog news. Statistical results indicate that the number of news and comments exhibits an exponential growth. The strength of forwarding and comment is characterized by bursts, displaying fat-tailed distribution. In order to characterize the dynamics of popularity, we explore the distribution of the time interval Δ

Description: In Brazil, plantations of exotic species such as Eucalyptus have expanded substantially in recent years, due in large part to the great demand for cellulose and wood. The combination of the steep slopes in some of these regions, such as the municipalities located close to the Serra do Mar and Serra da Mantiqueira, and the soil exposure that occurs in some stages in the Eucalyptus cultivation cycle, can cause landslides. The use of a geographic information system (GIS) assists with the identification of areas that are susceptible to landslides, and one of the GIS tools used is the spatial inference technique. In this work, the landslide susceptibility of areas occupied by Eucalyptus plantations in different stages of development in municipalities in the state of São Paulo was examined. Eight thematic maps were used, and, the fuzzy gamma technique was used for data integration and the generation of susceptibility maps, in which scenarios were created with different gamma values for the dry and rainy seasons. The results for areas planted with Eucalyptus were compared with those obtained for other land uses and covers. In the moderate and high susceptibility classes, the pasture is the land use type that presented the greatest susceptibility, followed by new Eucalyptus plantations and urban areas.

Description: This paper is concerned with exponential estimates and stabilization of a class of discrete-time singular systems with time-varying state delays and saturating actuators. By constructing a decay-rate-dependent Lyapunov-Krasovskii function and utilizing the slow-fast decomposition technique, an exponential admissibility condition, which not only guarantees the regularity, causality, and exponential stability of the unforced system but also gives the corresponding estimates of decay rate and decay coefficient, is derived in terms of linear matrix inequalities (LMIs). Under the proposed condition, the exponential stabilization problem of discrete-time singular time-delay systems subject actuator saturation is solved by designing a stabilizing state feedback controller and determining an associated set of safe initial conditions, for which the local exponential stability of the saturated closed-loop system is guaranteed. Two numerical examples are provided to illustrate the effectiveness of the proposed results.

Description: We investigate some identities on the Bernoulli and the Hermite polynomials arising from the orthogonality of Jacobi polynomials in the inner product space Pn.

Description: By coincidence degree theory for k-set-contractive mapping, this paper establishes a new criterion for the existence of at least two positive periodic solutions for a neutral delay model of single-species population growth with harvesting. An example is given to illustrate the effectiveness of the result.

Description: We study the life behavior of a system which is subjected to shocks of random magnitudes over discrete time periods. We obtain the survival function and mean time to failure of the system assuming that the sizes of the shocks follow a discrete probability distribution under cumulative and mixed shock models.

Description: Local polynomial regression (LPR) is applied to solve the partial differential equations (PDEs). Usually, the solutions of the problems are separation of variables and eigenfunction expansion methods, so we are rarely able to find analytical solutions. Consequently, we must try to find numerical solutions. In this paper, two test problems are considered for the numerical illustration of the method. Comparisons are made between the exact solutions and the results of the LPR. The results of applying this theory to the PDEs reveal that LPR method possesses very high accuracy, adaptability, and efficiency; more importantly, numerical illustrations indicate that the new method is much more efficient than B-splines and AGE methods derived for the same purpose.

Description: This paper investigates the robust finite-time ℋ∞ controller design problem of discrete-time systems with intermittent measurements. It is assumed that the system is subject to the norm-bounded uncertainties and the measurements are intermittent. The Bernoulli process is used to describe the phenomenon of intermittent measurements. By substituting the state-feedback controller into the system, a stochastic closed-loop system is obtained. Based on the analysis of the robust stochastic finite-time stability and the ℋ∞ performance, the controller design method is proposed. The controller gain can be calculated by solving a sequence of linear matrix inequalities. Finally, a numerical example is used to show the design procedure and the effectiveness of the proposed design methodology.

Description: We solve the bi-additive functional equation f(x+y,z−w)+f(x−y,z+w)=2f(x,z)−2f(y,w) and prove that every bi-additive Borel function is bilinear. And we investigate the stability of a bi-additive functional equation in Banach modules over a unital C⋆-algebra.

Description: We study the predator-prey model proposed by Aziz-Alaoui and Okiye (Appl. Math. Lett. 16 (2003) 1069–1075) First, the structure of equilibria and their linearized stability is investigated. Then, we provide two sufficient conditions on the global asymptotic stability of a positive equilibrium by employing the Fluctuation Lemma and Lyapunov direct method, respectively. The obtained results not only improve but also supplement existing ones.

Description: This paper deals with the robust filtering problem for linear discrete-time constrained systems. The purpose is the design of a linear filter such that the resulting error system is bounded. An orthogonal factorization is used to decompose the original robust filtering problem into stochastic and deterministic parts, which are then solved separately. Finally, a numerical example is presented to demonstrate the applicability of the proposed method.

Description: This paper is devoted to the existence of periodic solutions for a semi-ratio-dependent predator-prey system with time delays on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish necessary and sufficient conditions for the existence of periodic solutions. Our results show that for the most monotonic prey growth such as the logistic, the Gilpin, and the Smith growth, and the most celebrated functional responses such as the Holling type, the sigmoidal type, the Ivlev type, the Monod-Haldane type, and the Beddington-DeAngelis type, the system always has at least one periodic solution. Some known results are shown to be special cases of the present paper.

Description: We develop a simple behavioral macromodel to study interactions between the real economy and the stock market. The real economy is represented by a Keynesian-type goods market approach while the setup for the stock market includes heterogeneous speculators. Using a mixture of analytical and numerical tools we find, for instance, that speculators may create endogenous boom-bust dynamics in the stock market which, by spilling over into the real economy, can cause lasting fluctuations in economic activity. However, fluctuations in economic activity may, by shaping the firms' fundamental values, also have an impact on the dynamics of the stock market.

Description: This paper is devoted to investigate the global behavior of the following rational difference equation: yn+1=αyn-t/(β+γ∑i=0kyn-(2i+1)p∏i=0kyn-(2i+1)q),  n=0,1,2,…, where α,β,γ,p,q∈(0,∞) and k,t∈{0,1,2,…} with the initial conditions x0,  x-1,…,  x-2k,  x-2max {k,t}-1∈ (0,∞). We will find and classify the equilibrium points of the equations under studying and then investigate their local and global stability. Also, we will study the oscillation and the permanence of the considered equations.

Description: We prove the existence of a compact random attractor for the random dynamical system generated by stochastic three-component reversible Gray-Scott system with a multiplicative white noise on infinite lattices.

Description: Under some simple conditions, by using some techniques such as truncated method for random variables (see e.g., Gut (2005)) and properties of martingale differences, we studied the moving process based on martingale differences and obtained complete convergence and complete moment convergence for this moving process. Our results extend some related ones.

Description: Power law (PL) and fractional calculus are two faces of phenomena with long memory behavior. This paper applies PL description to analyze different periods of the business cycle. With such purpose the evolution of ten important stock market indices (DAX, Dow Jones, NASDAQ, Nikkei, NYSE, S&P500, SSEC, HSI, TWII, and BSE) over time is studied. An evolutionary algorithm is used for the fitting of the PL parameters. It is observed that the PL curve fitting constitutes a good tool for revealing the signal main characteristics leading to the emergence of the global financial dynamic evolution.

Description: This paper investigates the existence of solutions for fractional-order neutral impulsive differential inclusions with nonlocal conditions. Utilizing the fractional calculus and fixed point theorem for multivalued maps, new sufficient conditions are derived for ensuring the existence of solutions. The obtained results improve and generalize some existed results. Finally, an illustrative example is given to show the effectiveness of theoretical results.

Description: This paper presents a 2D convergence density criterion for minimizing the total junction delay at isolated junctions in the lane-based optimization framework. The lane-based method integrates the design of lane markings and signal settings for traffic movements in a unified framework. The problem of delay minimization is formulated as a Binary Mix Integer Non Linear Program (BMINLP). A cutting plane algorithm can be applied to solve this difficult BMINLP problem by adding hyperplanes sequentially until sufficient numbers of planes are created in the form of solution constraints to replicate the original nonlinear surface in the solution space. A set of constraints is set up to ensure the feasibility and safety of the resultant optimized lane markings and signal settings. The main difficulty to solve this high-dimension nonlinear nonconvex delay minimization problem using cutting plane algorithm is the requirement of substantial computational efforts to reach a good-quality solution while approximating the nonlinear solution space. A new stopping criterion is proposed by monitoring a 2D convergence density to obtain a converged solution. A numerical example is given to demonstrate the effectiveness of the proposed methodology. The cutting-plane algorithm producing an effective signal design will become more computationally attractive with adopting the proposed stopping criterion.

Description: The stability problem is proposed for a new class of stochastic Markovian jump reaction-diffusion neural networks with partial information on transition probability and mixed time delays. The new stability conditions are established in terms of linear matrix inequalities (LMIs). To reduce the conservatism of the stability conditions, an improved Lyapunov-Krasovskii functional and free-connection weighting matrices are introduced. The obtained results are dependent on delays and the measure of the space AND, therefore, have less conservativeness than delay-independent and space-independent ones. An example is given to show the effectiveness of the obtained results.

Description: According to the different effects of biological and chemical control, we propose a model for Holling I functional response predator-prey system concerning pest control which adopts different control methods at different thresholds. By using differential equation geometry theory and the method of successor functions, we prove that the existence of order one periodic solution of such system and the attractiveness of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results which show that our method used in this paper is more efficient and easier than the existing ones for proving the existence of order one periodic solution.

Description: We study of warped product submanifolds, especially warped product hemi-slant submanifolds of LP-Sasakian manifolds. We obtain the results on the nonexistance or existence of warped product hemi-slant submanifolds and give some examples of LP-Sasakian manifolds. The existence of warped product hemi-slant submanifolds of an LP-Sasakian manifold is also ensured by an interesting example.

Description: Given high urbanization rates and increasing spatio-temporal variability in many present-day cities, exposure information is often out-of-date, highly aggregated or spatially fragmented, increasing the uncertainties associated with seismic risk assessments. This work therefore aims at using space-based technologies to estimate, complement and extend exposure data at multiple scales, over large areas and at a comparatively low cost for the case of the city of Bishkek, Kyrgyzstan. At a neighborhood scale, an analysis of urban structures using medium-resolution optical satellite images is performed. Applying image classification and change-detection analysis to a time-series of Landsat images, the urban environment can be delineated into areas of relatively homogeneous urban structure types, which can provide a first estimate of an exposed building stock (e.g., approximate age of structures, composition and distribution of predominant building types). At a building-by-building scale, a more detailed analysis of the exposed building stock is carried out using a high-resolution Quickbird image. Furthermore, the multi-resolution datasets are combined with census data to disaggregate population statistics. The tools used within this study are being developed on a free- and open-source basis and aim at being transparent, usable and transferable.

Description: A predator-prey system with disease in the predator is investigated, where the discrete delay τ is regarded as a parameter. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when τ crosses some critical values. Using the normal form theory and center manifold argument, the explicit formulae which determine the stability, direction, and other properties of bifurcating periodic solutions are derived.

Description: An epidemiological model of TB with infectivity in latent period and imperfect treatment is introduced. As presented, sustained oscillations are not possible and the endemic proportions either approach the disease-free equilibrium or an endemic equilibrium. The expanded model that stratified the infectious individuals according to their time-since-infection θ is also carried out. The global asymptotic stability of the infection-free state is established as well as local asymptotic stability of the endemic equilibrium. At the end, numerical simulations are presented to illustrate the results.

Description: The generalized projective synchronization (GPS) between two different neural networks with nonlinear coupling and mixed time delays is considered. Several kinds of nonlinear feedback controllers are designed to achieve GPS between two different such neural networks. Some results for GPS of these neural networks are proved theoretically by using the Lyapunov stability theory and the LaSalle invariance principle. Moreover, by comparison, we determine an optimal nonlinear controller from several ones and provide an adaptive update law for it. Computer simulations are provided to show the effectiveness and feasibility of the proposed methods.

Description: We consider a weakly nonlinear system of the form (I+φ(x)A)x=p, where φ(x) is a real function of the unknown vector x, and (I+φ(x)A) is an M-matrix. We propose to solve it by means of a sequence of linear systems defined by the iteration procedure (I+φ(xr)A)xr+1=p, r=0,1,…. The global convergence is proved by considering a related fixed-point problem.

Description: This paper studies multispecies nonautonomous Lotka-Volterra competitive systems with delays and fixed-time impulsive effects. The sufficient conditions of integrable form on the permanence of species are established.

Description: Hierarchy of cities reflects the ubiquitous structure frequently observed in the natural world and social institutions. Where there is a hierarchy with cascade structure, there is a Zipf's rank-size distribution, and vice versa. However, we have no theory to explain the spatial dynamics associated with Zipf's law of cities. In this paper, a new angle of view is proposed to find the simple rules dominating complex systems and regular patterns behind random distribution of cities. The hierarchical structure can be described with a set of exponential functions that are identical in form to Horton-Strahler's laws on rivers and Gutenberg-Richter's laws on earthquake energy. From the exponential models, we can derive four power laws including Zipf's law indicative of fractals and scaling symmetry. A card-shuffling model is built to interpret the relation between Zipf's law and hierarchy of cities. This model can be expanded to illuminate the general empirical power-law distributions across the individual physical and social sciences, which are hard to be comprehended within the specific scientific domains. This research is useful for us to understand how complex systems such as networks of cities are self-organized.

Description: Spatial cluster analysis is an important data-mining task. Typical techniques include CLARANS, density- and gravity-based clustering, and other algorithms based on traditional von Neumann’s computing architecture. The purpose of this paper is to propose a technique for spatial cluster analysis based on DNA computing and a grid technique. We will adopt the Adleman-Lipton model and then design a flexible grid algorithm. Examples are given to show the effect of the algorithm. The new clustering technique provides an alternative for traditional cluster analysis.

Description: We investigate the problem of existence of positive solutions for the nonlinear third-order three-point boundary value problem u‴(t)+λa(t)f(u(t))=0, 0<t<1, u(0)=u′(0)=0, u″(1)=∝u″(η), where λ is a positive parameter, ∝∈(0,1), η∈(0,1), f:(0,∞)→(0,∞), a:(0,1)→(0,∞) are continuous. Using a specially constructed cone, the fixed point index theorems and Leray-Schauder degree, this work shows the existence and multiplicities of positive solutions for the nonlinear third-order boundary value problem. Some examples are given to demonstrate the main results.

Description: Using fixed point methods, we prove the generalized Hyers-Ulam stability of homomorphisms in C∗-algebras and Lie C∗-algebras and of derivations on non-Archimedean C∗-algebras and Non-Archimedean Lie C∗-algebras for an m-variable additive functional equation.

Description: We define the incomplete bivariate Fibonacci and Lucas p-polynomials. In the case x=1, y=1, we obtain the incomplete Fibonacci and Lucas p-numbers. If x=2, y=1, we have the incomplete Pell and Pell-Lucas p-numbers. On choosing x=1, y=2, we get the incomplete generalized Jacobsthal number and besides for p=1 the incomplete generalized Jacobsthal-Lucas numbers. In the case x=1, y=1, p=1, we have the incomplete Fibonacci and Lucas numbers. If x=1, y=1, p=1, k=⌊(n-1)/(p+1)⌋, we obtain the Fibonacci and Lucas numbers. Also generating function and properties of the incomplete bivariate Fibonacci and Lucas p-polynomials are given.

Description: This paper considers a rumor transmission model with incubation that incorporates constant recruitment and has infectious force in the latent period and infected period. By carrying out a global analysis of the model and studying the stability of the rumor-free equilibrium and the rumor-endemic equilibrium, we use the geometric approach for ordinary differential equations which is based on the use of higher-order generalization of Bendixson’s criterion. It shows that either the number of rumor infective individuals tends to zero as time evolves or the rumor persists. We prove that the transcritical bifurcation occurs at R0 crosses the bifurcation threshold R0=1 by projecting the flow onto the extended center manifold. Since the rumor endemic level at the equilibrium is a continuous function of R0, as a consequence for successful eradication of the rumor, one should simply reduce R0 continuously below the threshold value 1. Finally, the obtained results are numerically validated and then discussed from both the mathematical and the sociological perspectives.

Description: Differential transform method is adopted, for the first time, for solving linear singularly perturbed two-point boundary value problems. Four numerical examples are given to demonstrate the effectiveness of the present method. Results show that the numerical scheme is very effective and convenient for solving a large number of linear singularly perturbed two-point boundary value problems with high accuracy.

Description: Defined in the early 1990s for use with gridded satellite passive microwave data, the Equal-Area Scalable Earth Grid (EASE-Grid) was quickly adopted and used for distribution of a variety of satellite and in situ data sets. Conceptually easy to understand, EASE-Grid suffers from limitations that make it impossible to format in the widely popular GeoTIFF convention without reprojection. Importing EASE-Grid data into standard mapping software packages is nontrivial and error-prone. This article defines a standard for an improved EASE-Grid 2.0 definition, addressing how the changes rectify issues with the original grid definition. Data distributed using the EASE-Grid 2.0 standard will be easier for users to import into standard software packages and will minimize common reprojection errors that users had encountered with the original EASE-Grid definition.

Description: The existence and uniqueness of the solutions to the Dirichlet boundary value problem in the Banach spaces is discussed by using the fixed point theory of condensing mapping, doing precise computation of measure of noncompactness, and calculating the spectral radius of linear operator.

Description: The dynamic complexities of a prey-predator system in the presence of alternative prey with impulsive state feedback control are studied analytically and numerically. By using the analogue of the Poincaré criterion, sufficient conditions for the existence and stability of semitrivial periodic solutions can be obtained. Furthermore, the corresponding bifurcation diagrams and phase diagrams are investigated by means of numerical simulations which illustrate the feasibility of the main results.

Description: This paper investigates the guaranteed cost control of chaos problem in 4D Lorenz-Stenflo (LS) system via Takagi-Sugeno (T-S) fuzzy method approach. Based on Lyapunov stability theory and linear matrix inequality (LMI) technique, a state feedback controller is proposed to stabilize the 4D Lorenz-Stenflo chaotic system. An illustrative example is provided to verify the validity of the results developed in this paper.

Description: All things in our world are related to some location in space and time, and according to Tobler’s first law of geography “everything is related to everything else, but near things are more related than distant things” [1]. Since humans exist they have been contemplating about space and time and have tried to depict and manage the geographic space they live in. We know graphic representations of the land from various regions of the world dating back several thousands of years. The processing and analysis of spatial data has a long history in the disciplines that deal with spatial data such as geography, surveying engineering, cartography, photogrammetry, and remote sensing. Until recently, all these activities have been analog in nature; only since the invention of the computer in the second half of the 20th century and the use of computers for the acquisition, storage, analysis, and display of spatial data starting in the 1960s we speak of geo-information and geo-information systems. [...]

Description: We develop an optimization model for risk management in a virtual enterprise environment based on a novel multiswarm particle swarm optimizer called PS2O. The main idea of PS2O is to extend the single population PSO to the interacting multiswarms model by constructing hierarchical interaction topology and enhanced dynamical update equations. With the hierarchical interaction topology, a suitable diversity in the whole population can be maintained. At the same time, the enhanced dynamical update rule significantly speeds up the multiswarm to converge to the global optimum. With five mathematical benchmark functions, PS2O is proved to have considerable potential for solving complex optimization problems. PS2O is then applied to risk management in a virtual enterprise environment. Simulation results demonstrate that the PS2O algorithm is more feasible and efficient than the PSO algorithm in solving this real-world problem.

Description: Analysis of spatial and temporal changes of vegetation cover using remote sensing (RS) technology, in conjunction with Geographic Information Systems (GIS), is becoming increasingly important in environmental conservation. The objective of this study was to use RS data and GIS techniques to assess the vegetation cover in 1989 and 2009, in the barangays (smallest administrative units) of the city of San Fernando, La Union, the Philippines, for planning vegetation rehabilitation. Landsat images were used to prepare both the 1989 and 2009 land cover maps, which were then used to detect changes in the vegetation cover for the barangays. In addition to conventional accuracy assessment parameters such as; proportion correct, and standard Kappa index of agreement, two other parameters; quantity, and allocation disagreements were used to assess the accuracy of the land cover classification. Results revealed that there were gains and losses of vegetation cover in most of the barangays, but overall vegetation cover increased by 11% (around 625 ha) based on the original extent of 1989. Those barangays that showed substantial net losses in vegetation cover need to be prioritised for rehabilitation planning. As exemplified in this study, the collection, processing and analysis of relevant RS and GIS information, can facilitate priority-setting in the planning of environmental rehabilitation and conservation by the local government at both city and barangay levels.

Description: The primary objective of this research is to predict and analyze the future urban growth of Dhaka City using the Landsat satellite images of 1989, 1999 and 2009. Dhaka City Corporation (DCC) and its surrounding impact areas have been selected as the study area. At the beginning, a fisher supervised classification method has been applied to prepare the base maps with five land cover classes. In the next stage, three different models have been implemented to simulate the land cover map of Dhaka city of 2009. These have been named as “Stochastic Markov (St_Markov)” Model, “Cellular Automata Markov (CA_Markov)” Model and “Multi Layer Perceptron Markov (MLP_Markov)” Model. Then the best-fitted model has been selected by implementing a method to compare land cover categories in three maps: a reference map of time 1, a reference map of time 2 and a simulation map of time 2. This is how the “Multi Layer Perceptron Markov (MLP_Markov)” Model has been qualified as the most appropriate model for this research. Later, using the MLP_Markov model, the land cover map of 2019 has been predicted. The MLP_Markov model extrapolates that built-up area increases from 46% to 58% of the total study area during 2009–2019.

Description: In this paper, a novel digital image denoising algorithm called generalized fractional integral filter is introduced based on the generalized Srivastava-Owa fractional integral operator. The structures of n×n fractional masks of this algorithm are constructed. The denoising performance is measured by employing experiments according to visual perception and PSNR values. The results demonstrate that apart from enhancing the quality of filtered image, the proposed algorithm also reserves the textures and edges present in the image. Experiments also prove that the improvements achieved are competent with the Gaussian smoothing filter.

Description: A class of Beddington-DeAngelis functional response predator-prey model is considered. The conditions for the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are derived. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using the normal form theory and center manifold theory. Some numerical simulations for justifying the theoretical analysis are also provided. Finally, main conclusions are given.

Description: The Painlevé property and Bäcklund transformation for the KdV equation with a self-consistent source are presented. By testing the equation, it is shown that the equation has the Painlevé property. In order to further prove its integrality, we give its bilinear form and construct its bilinear Bäcklund transformation by the Hirota's bilinear operator. And then the soliton solution of the equation is obtained, based on the proposed bilinear form.

Description: This paper deals with the convergence and stability of linear multistep methods for impulsive differential equations. Numerical experiments demonstrate that both the mid-point rule and two-step BDF method are of order p=0 when applied to impulsive differential equations. An improved linear multistep method is proposed. Convergence and stability conditions of the improved methods are given in the paper. Numerical experiments are given in the end to illustrate the conclusion.

Description: We investigate the stability property for the predator-free equilibrium point of predator-prey systems with a class of functional response and prey refuges by using the analytical approach. Under some very weakly assumption, we show that conditions that ensure the locally asymptotically stable of the predator-free equilibrium point are consistent with that of the globally asymptotically stable ones. Our result supplements the corresponding result of Ma et al., 2009.

Description: This work concerns the modeling of evolvement of trading behavior in stock markets which can cause significant impact on the movements of prices and volatilities. Based on the assumption of the investors' limited rationality, the evolution mechanism of trading behavior is modeled according to peer effect in network, that investors are prone to imitate their neighbors' activity through comprehensive analysis on the neighboring preferred degree, self-psychological preference, and the network topology of the relationship among them. We investigate by mean-field analysis and extensive simulations the evolution of investors' trading behavior in various typical networks under different characteristics of peer effect. Our results indicate that the evolution of investors' behavior is affected by the network structure of stock market and the effect of neighboring preferred degree; the stability of equilibrium states of investors' behavior dynamics is directly related with the concavity and convexity of the peer effect function; connectivity and heterogeneity of the network play an important role in the evolution of the investment behavior in stock market.

Description: This paper furnishes a guide for the study of 2-dimensional evolutionary games in discrete time. Evolutionarily stable strategies are identified and nonlinear outcomes are explored. Besides the baseline payoffs of the established strategic interaction, the following elements are also vital to determine the dynamic outcome of a game: the initial fitness of each agent and the rule of motion that describes how individuals switch between strategies. In addition to the dynamic rule commonly used in evolutionary games, the replicator dynamics, we propose another rule, which acknowledges the role of expectations and sophisticates the replicator mechanism.

Description: We consider the existence for eventually positive solutions of high-order nonlinear neutral differential equations with distributed delay. We use Lebesgue's dominated convergence theorem to obtain new necessary and sufficient condition for the existence of eventually positive solutions.

Description: The dynamic behaviors in a droop model for phytoplankton growth in a chemostat with nutrient periodically pulsed input are studied. A series of new criteria on the boundedness, permanence, extinction, existence of positive periodic solution, and global attractivity for the model are established. Finally, an example is given to demonstrate the effectiveness of the results in this paper.

Description: Let n>1 be an integer, let A be an algebra, and X be an A-module. A quadratic function D:A→X is called a quadratic n-derivation if D(∏i=1nai)=D(a1)a22⋯an2+a12D(a2)a32⋯an2+⋯+a12a22⋯an−12D(an) for all a1,...,an∈A. We investigate the Hyers-Ulam stability of quadratic n-derivations from non-Archimedean Banach algebras into non-Archimedean Banach modules by using the Banach fixed point theorem.

Description: Managing multiple project is a complex task involving the unrelenting pressures of time and cost. Many studies have proposed various tools and techniques for single-project scheduling; however, the literature further considering multimode or multiproject issues occurring in the real world is rather scarce. In this paper, design structure matrix (DSM) and an improved artificial immune network algorithm (aiNet) are developed to solve a multi-mode resource-constrained scheduling problem. Firstly, the DSM is used to simplify the mathematic model of multi-project scheduling problem. Subsequently, aiNet algorithm comprised of clonal selection, negative selection, and network suppression is adopted to realize the local searching and global searching, which will assure that it has a powerful searching ability and also avoids the possible combinatorial explosion. Finally, the approach is tested on a set of randomly cases generated from ProGen. The computational results validate the effectiveness of the proposed algorithm comparing with other famous metaheuristic algorithms such as genetic algorithm (GA), simulated annealing algorithm (SA), and ant colony optimization (ACO).

Description: This paper investigates the blow-up and global existence of nonnegative solutions for a class of nonlocal degenerate parabolic system. By using the super- and subsolution techniques, the critical exponent of the system is determined. That is, if Pc=p1q1−(m−p2)(n−q2)<0, then every nonnegative solution is global, whereas if Pc>0, there are solutions that blowup and others that are global according to the size of initial values u0(x) and v0(x). When Pc=0, we show that if the domain is sufficiently small, every nonnegative solution is global while if the domain large enough that is, if it contains a sufficiently large ball, there is no global solution.

Description: The cohomology groups of tiling spaces with three-fold and nine-fold symmetries are obtained. The substitution tilings are characterized by the fact that they have vanishing first cohomology group in the space of tilings modulo a rotation. The rank of the rational first cohomology, in the tiling space formed by the closure of a translational orbit, equals the Euler totient function evaluated at N if the underlying rotation group is ZN. When the symmetries are of crystallographic type, the cohomologies are infinitely generated.

Description: A metaheuristic algorithm for global optimization called the collective animal behavior (CAB) is introduced. Animal groups, such as schools of fish, flocks of birds, swarms of locusts, and herds of wildebeest, exhibit a variety of behaviors including swarming about a food source, milling around a central locations, or migrating over large distances in aligned groups. These collective behaviors are often advantageous to groups, allowing them to increase their harvesting efficiency, to follow better migration routes, to improve their aerodynamic, and to avoid predation. In the proposed algorithm, the searcher agents emulate a group of animals which interact with each other based on the biological laws of collective motion. The proposed method has been compared to other well-known optimization algorithms. The results show good performance of the proposed method when searching for a global optimum of several benchmark functions.

Description: Let (X,d) be a metric space and a sequence of continuous maps fn:X→X that converges uniformly to a map f. We investigate the transitive subsets of fn whether they can be inherited by f or not. We give sufficient conditions such that the limit map f has a transitive subset. In particular, we show the transitive subsets of fn that can be inherited by f if fn converges uniformly strongly to f.

Description: Using fixed point method and direct method, we prove the Hyers-Ulam stability of the following additive-quadratic functional equation r2f((x+y+z)/r)+r2f((x-y+z)/r)+r2f((x+y-z)/r)+r2f((-x+y+z)/r)=4f(x)+4f(y)+4f(z), where r is a positive real number, in non-Archimedean normed spaces.

Description: Recently, Kim introduced the fermionic p-adic integral on Zp. By using the equations of the fermionic and bosonic p-adic integral on Zp, we give some interesting identities on Bernoulli and Euler numbers.

Description: This paper presents a subband approach to financial time series prediction. Multivariate empirical mode decomposition (MEMD) is employed here for multiband representation of multichannel financial time series together. Autoregressive moving average (ARMA) model is used in prediction of individual subband of any time series data. Then all the predicted subband signals are summed up to obtain the overall prediction. The ARMA model works better for stationary signal. With multiband representation, each subband becomes a band-limited (narrow band) signal and hence better prediction is achieved. The performance of the proposed MEMD-ARMA model is compared with classical EMD, discrete wavelet transform (DWT), and with full band ARMA model in terms of signal-to-noise ratio (SNR) and mean square error (MSE) between the original and predicted time series. The simulation results show that the MEMD-ARMA-based method performs better than the other methods.

Description: We present some new multiplicity of positive solutions results for nonlinear semipositone fractional boundary value problem D0+αu(t)=p(t)f(t,u(t))-q(t),0<t<1,u(0)=u(1)=u'(1)=0, where 2<α≤3 is a real number and D0+α is the standard Riemann-Liouville differentiation. One example is also given to illustrate the main result.

Description: Numerical solution of differential-algebraic equations with Hessenberg index-3 is considered by variational iteration method. We applied this method to two examples, and solutions have been compared with those obtained by exact solutions.

Description: Cho et al. [Comput. Math. Appl. 61(2011), 1254–1260] studied common fixed point theorems on cone metric spaces by using the concept of c-distance. In this paper, we prove some coupled fixed point theorems in ordered cone metric spaces by using the concept of c-distance in cone metric spaces.

Description: The primary objective of this research is to predict and analyze the future urban growth of Dhaka City using the Landsat satellite images of 1989, 1999 and 2009. Dhaka City Corporation (DCC) and its surrounding impact areas have been selected as the study area. At the beginning, a fisher supervised classification method has been applied to prepare the base maps with five land cover classes. In the next stage, three different models have been implemented to simulate the land cover map of Dhaka city of 2009. These have been named as “Stochastic Markov (St_Markov)” Model, “Cellular Automata Markov (CA_Markov)” Model and “Multi Layer Perceptron Markov (MLP_Markov)” Model. Then the best-fitted model has been selected by implementing a method to compare land cover categories in three maps: a reference map of time 1, a reference map of time 2 and a simulation map of time 2. This is how the “Multi Layer Perceptron Markov (MLP_Markov)” Model has been qualified as the most appropriate model for this research. Later, using the MLP_Markov model, the land cover map of 2019 has been predicted. The MLP_Markov model extrapolates that built-up area increases from 46% to 58% of the total study area during 2009–2019.