Search results for: differential pricing

Authors: Anuar Ishak

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The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, mixed convection, stability analysis

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Authors: Kajal K. Patel, M. N. Mehta, T. R. Singh

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When water is injected in oil formatted area in secondary oil recovery process the instability occurs near common interface due to viscosity difference of injected water and native oil. The governing equation gives rise to the non-linear partial differential equation and its solution has been obtained by Homotopy analysis method with appropriate guess value of the solution together with some conditions and standard relations. The solution gives the average cross-sectional area occupied by the schematic fingers during the occurs of instability phenomenon. The numerical and graphical presentation has developed by using Maple software.

Keywords: capillary pressure, homotopy analysis method, instability phenomenon, viscosity

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Authors: Daniel Panario, Daniel Santana de Freitas, Brett Stevens

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Almost Perfect Nonlinear (APN) permutations with optimal resistance against differential cryptanalysis can be found in several domains. The permutation used in the standard for symmetric cryptography (the AES), for example, is based on a special kind of inversion in GF(28). Although very close to APN (2-uniform), this permutation still contains one number 4 in its differential spectrum, which means that, rigorously, it must be classified as 4-uniform. This fact motivates the search for fully APN permutations in other domains of definition. The extremely high complexity associated to this kind of problem precludes an exhaustive search for an APN permutation with 256 elements to be performed without the support of a suitable mathematical structure. On the other hand, in principle, there is nothing to indicate which mathematically structured domains can effectively help the search, and it is necessary to test several domains. In this work, the search for APN permutations in rings ℤ2×ℤ2k is investigated. After a full, exhaustive search with k=2 and k=3, all possible APN permutations in those rings were recorded, together with their differential profiles. Some very promising heuristics in these cases were collected so that, when used as a basis to prune backtracking for the same search in ℤ2×ℤ8 (search space with size 16! ≅244), just a few tenths of a second were enough to produce an APN permutation in a single CPU. Those heuristics were empirically extrapolated so that they could be applied to a backtracking search for APNs over ℤ2×ℤ16 (search space with size 32! ≅2117). The best permutations found in this search were further refined through Simulated Annealing, with a definition of neighbors suitable to this domain. The best result produced with this scheme was a 3-uniform permutation over ℤ2×ℤ16 with only 24 values equal to 3 in the differential spectrum (all the other 968 values were less than or equal 2, as it should be the case for an APN permutation). Although far from being fully APN, this result is technically better than a 4-uniform permutation and demanded only a few seconds in a single CPU. This is a strong indication that the use of mathematically structured domains, like the rings described in this work, together with heuristics based on smaller cases, can lead to dramatic cuts in the computational resources involved in the complexity of the search for APN permutations in extremely large domains.

Keywords: APN permutations, heuristic searches, symmetric cryptography, S-box design

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Authors: Beata Jackowska-Zduniak

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We formulate and analyze a mathematical model describing dynamics of the hypothalamus-pituitary-thyroid homoeostatic mechanism in endocrine system. We introduce to this system two types of couplings and delay. In our model, feedback controls the secretion of thyroid hormones and delay reflects time lags required for transportation of the hormones. The influence of delayed feedback on the stability behaviour of the system is discussed. Analytical results are illustrated by numerical examples of the model dynamics. This system of equations describes normal activity of the thyroid and also a couple of types of malfunctions (e.g. hyperthyroidism).

Keywords: mathematical modeling, ordinary differential equations, endocrine system, delay differential equation

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Authors: P. W. Tsai, W. L. Hong, C. W. Chen, C. Y. Chen

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In this paper, we present a neural network (NN) based approach represent a nonlinear Tagagi-Sugeno (T-S) system. A linear differential inclusion (LDI) state-space representation is utilized to deal with the NN models. Taking advantage of the LDI representation, the stability conditions and controller design are derived for a class of nonlinear structural systems. Moreover, the concept of utilizing the Parallel Particle Swarm Optimization (PPSO) algorithm to solve the common P matrix under the stability criteria is given in this paper.

Keywords: Lyapunov stability, parallel particle swarm optimization, linear differential inclusion, artificial intelligence

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Authors: Abbes Lounis, Kahina Louadj, Mohamed Aidene

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This paper presents an optimal control problem applied to a robot; the problem is to determine a command which makes it possible to reach a final state from a given initial state in record time. The approach followed to solve this optimization problem with constraints on the control starts by presenting the equations of motion of the dynamic system then by applying Pontryagin's maximum principle (PMP) to determine the optimal control, and Picard's successive approximation method combined with the shooting method to solve the resulting differential system.

Keywords: robotics, Pontryagin's Maximum Principle, PMP, Picard's method, shooting method, non-linear differential systems

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Authors: Mohammad Azam

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This work is an endeavor to empirically investigate the Gross Domestic Product-Growth as mediating variable between various factors and portfolio returns using a broad sample of 522 financial and non-financial firms enlisted on Pakistan Stock Exchange between January-1993 and June-2022. The study employs the Structural Equation modeling and Ordinary Least Square regression to determine the findings before and during the Covid-19 epidemiological situation, which has not received due attention by researchers. The analysis reveals that market and investment factors are redundant, whereas size and value show significant results, whereas Gross Domestic Product-Growth performs significant mediating impact for the whole time frame. Using before Covid-19 period, the results reveal that market, value, and investment are redundant, but size, profitability, and Gross Domestic Product-Growth are significant. During the Covid-19, the statistics indicate that market and investment are redundant, though size and Gross Domestic Product-Growth are highly significant, but value and profitability are moderately significant. The Ordinary Least Square regression shows that market and investment are statistically insignificant, whereas size is highly significant but value and profitability are marginally significant. Using the Gross Domestic Product-Growth augmented model, a slight growth in R-square is observed. The size, value and profitability factors are recommended to the investors for Pakistan Stock Exchange. Conclusively, in the Pakistani market, the Gross Domestic Product-Growth indicates a feeble moderating effect between risk-premia and portfolio returns.

Keywords: asset pricing puzzle, mediating role of GDP-growth, structural equation modeling, COVID-19 pandemic, Pakistan stock exchange

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Authors: A. Azizi, M. Toubane, L. Chetibi

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Differential scanning calorimetry (DSC) is a widely used technique for the study of phase transformations, particularly in the study of precipitation. The kinetic of the precipitation and dissolution is always related to the concept of activation energy Ea. The determination of the activation energy gives important information about the kinetic of the precipitation reaction. In this work, we were interested in the study of the isothermal and non-isothermal treatments on the decomposition of the supersaturated solid solution in the alloy AZ91 (Mg-9 Al-Zn 1-0.2 Mn. mass fraction %), using Differential Calorimetric method. Through this method, the samples were heat treated up to 425° C, using different rates. To calculate the apparent activation energies associated with the formation of precipitated phases, we used different isoconversional methods. This study was supported by other analysis: X-ray diffraction and microhardness measurements.

Keywords: calorimetric, activation energy, AZ91 alloys, microstructural evolution

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Authors: Jingwen Shi, Qi Wu

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We study the role played interest rate risk in carry trade return in order to understand the forward premium puzzle. In this study, our goal is to investigate to what extent carry trade return is indeed due to compensation for risk taking and, more important, to reveal the nature of these risks. Using option data not only on exchange rates but also on interest rate swaps (swaptions), our first finding is that, besides the consensus currency risks, interest rate risks also contribute a non-negligible portion to the carry trade return. What strikes us is our second finding. We find that large downside risks of future exchange rate movements are, in fact, priced significantly in option market on interest rates. The role played by interest rate risk differs structurally from the currency risk. There is a unique premium associated with interest rate risk, though seemingly small in size, which compensates the tail risks, the left tail to be precise. On the technical front, our study relies on accurately retrieving implied distributions from currency options and interest rate swaptions simultaneously, especially the tail components of the two. For this purpose, our major modeling work is to build a new international asset pricing model where we use an orthogonal setup for pricing kernels and specify non-Gaussian dynamics in order to capture three sets of option skew accurately and consistently across currency options and interest rate swaptions, domestic and foreign, within one model. Our results open a door for studying forward premium anomaly through implied information from interest rate derivative market.

Keywords: carry trade, forward premium anomaly, FX option, interest rate swaption, implied volatility skew, uncovered interest rate parity

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Authors: Raj Nandkeolyar, Precious Sibanda

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The flow of a viscous, incompressible, and electrically conducting fluid under the influence of aligned magnetic field acting along the direction of fluid flow over an exponentially stretching sheet is investigated numerically. The nonlinear partial differential equations governing the flow model is transformed to a set of nonlinear ordinary differential equations using suitable similarity transformation and the solution is obtained using a local linearization method followed by the Chebyshev spectral collocation method. The effects of various parameters affecting the flow and heat transfer as well as the induced magnetic field are discussed using suitable graphs and tables.

Keywords: aligned magnetic field, exponentially stretching sheet, induced magnetic field, magnetohydrodynamic flow

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Authors: Mohammad Besharatloo

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Intrusion detection is an important research topic in network security because of increasing growth in the use of computer network services. Intrusion detection is done with the aim of detecting the unauthorized use or abuse in the networks and systems by the intruders. Therefore, the intrusion detection system is an efficient tool to control the user's access through some predefined regulations. Since, the data used in intrusion detection system has high dimension, a proper representation is required to show the basis structure of this data. Therefore, it is necessary to eliminate the redundant features to create the best representation subset. In the proposed method, a hybrid model of differential evolution and firefly algorithms was employed to choose the best subset of properties. In addition, decision tree and support vector machine (SVM) are adopted to determine the quality of the selected properties. In the first, the sorted population is divided into two sub-populations. These optimization algorithms were implemented on these sub-populations, respectively. Then, these sub-populations are merged to create next repetition population. The performance evaluation of the proposed method is done based on KDD Cup99. The simulation results show that the proposed method has better performance than the other methods in this context.

Keywords: intrusion detection system, differential evolution, firefly algorithm, support vector machine, decision tree

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Authors: M. Y. Malika, Farzana, Abdul Rehman

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The study deals with the steady, 3D MHD boundary layer flow of a non-Newtonian Maxwell fluid flow due to a horizontal surface stretched exponentially in two lateral directions. The temperature at the boundary is assumed to be distributed exponentially and possesses convective boundary conditions. The governing nonlinear system of partial differential equations along with associated boundary conditions is simplified using a suitable transformation and the obtained set of ordinary differential equations is solved through numerical techniques. The effects of important involved parameters associated with fluid flow and heat flux are shown through graphs.

Keywords: boundary layer flow, exponentially stretched surface, Maxwell fluid, numerical solution

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Authors: Angelis P. Barlampas

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Theoretical background Disorders of fixation and rotation of the large intestine, result in the existence of its parts in ectopic anatomical positions. In case of symptomatology, the clinical picture is complicated by the possible symptomatology of the neighboring anatomical structures and a differential diagnostic problem arises. Target The purpose of this work is to demonstrate the difficulty of revealing the real cause of abdominal pain, in cases of anatomical variants and the decisive contribution of imaging and especially that of computed tomography. Methods A patient came to the emergency room, because of acute pain in the right hypochondrium. Clinical examination revealed tenderness in the gallbladder area and a positive Murphy's sign. An ultrasound exam depicted a normal gallbladder and the patient was referred for a CT scan. Results Flexible, unfixed ascending colon and cecum, located in the anatomical region of the right mesentery. Opacities of the surrounding peritoneal fat and a small linear concentration of fluid can be seen. There was an appendix of normal anteroposterior diameter with the presence of air in its lumen and without clear signs of inflammation. There was an impression of possible inflammatory swelling at the base of the appendix, (DD phenomenon of partial volume; e.t.c.). Linear opacities of the peritoneal fat in the region of the second loop of the duodenum. Multiple diverticula throughout the colon. Differential Diagnosis The differential diagnosis includes the following: Inflammation of the base of the appendix, diverticulitis of the cecum-ascending colon, a rare case of second duodenal loop ulcer, tuberculosis, terminal ileitis, pancreatitis, torsion of unfixed cecum-ascending colon, embolism or thrombosis of a vascular intestinal branch. Final Diagnosis There is an unfixed cecum-ascending colon, which is exhibiting diverticulitis.

Keywords: unfixed cecum-ascending colon, abdominal pain, malrotation, abdominal CT, congenital anomalies

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Authors: Tahseen Saad, Halim Ceylan, Jonathan Weaver, Osman Nuri Çelik, Onur Gungor Sahin

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A new concept of uniform delay offset dependent mathematical optimization problem is derived as the main objective for this study using a differential evolution algorithm. To control the coordination problem, which depends on offset selection and to estimate uniform delay based on the offset choice in a traffic signal network. The assumption is the periodic sinusoidal function for arrival and departure patterns. The cycle time is optimized at the entry links and the optimized value is used in the non-entry links as a common cycle time. The offset optimization algorithm is used to calculate the uniform delay at each link. The results are illustrated by using a case study and are compared with the canonical uniform delay model derived by Webster and the highway capacity manual’s model. The findings show new model minimizes the total uniform delay to almost half compared to conventional models. The mathematical objective function is robust. The algorithm convergence time is fast.

Keywords: area traffic control, traffic flow, differential evolution, sinusoidal periodic function, uniform delay, offset variable

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Authors: Z. B. Ibrahim, N. Ismail, K. I. Othman

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Fuzzy Differential Equations (FDEs) play an important role in modelling many real life phenomena. The FDEs are used to model the behaviour of the problems that are subjected to uncertainty, vague or imprecise information that constantly arise in mathematical models in various branches of science and engineering. These uncertainties have to be taken into account in order to obtain a more realistic model and many of these models are often difficult and sometimes impossible to obtain the analytic solutions. Thus, many authors have attempted to extend or modified the existing numerical methods developed for solving Ordinary Differential Equations (ODEs) into fuzzy version in order to suit for solving the FDEs. Therefore, in this paper, we proposed the development of a fuzzy version of three-point block method based on Block Backward Differentiation Formulas (FBBDF) for the numerical solution of first order FDEs. The three-point block FBBDF method are implemented in uniform step size produces three new approximations simultaneously at each integration step using the same back values. Newton iteration of the FBBDF is formulated and the implementation is based on the predictor and corrector formulas in the PECE mode. For greater efficiency of the block method, the coefficients of the FBBDF are stored at the start of the program. The proposed FBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing fuzzy version of the Modified Simpson and Euler methods in terms of the accuracy of the approximated solutions. The numerical results show that the FBBDF method performs better in terms of accuracy when compared to the Euler method when solving the FDEs.

Keywords: block, backward differentiation formulas, first order, fuzzy differential equations

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Authors: Pranitha Janapatla, Venkata Suman Gontla

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The present paper investigates the effects of MHD, double dispersion and variable properties on mixed convection flow from a vertical surface in a power-law fluid saturated non-Darcy porous medium. The governing non-linear partial differential equations are reduced to a system of ordinary differential equations by using a special form of Lie group transformations viz. scaling group of transformations. These ordinary differential equations are solved numerically by using Shooting technique. The influence of relevant parameters on the non-dimensional velocity, temperature, concentration for pseudo-plastic fluid, Newtonian and dilatant fluid are discussed and displayed graphically. The behavior of heat and mass transfer coefficients are shown in tabular form. Comparisons with the published works are performed and are found to be in very good agreement. From this analysis, it is observed that an increase in variable viscosity causes to decrease in velocity profile and increase the temperature and concentration distributions. It is also concluded that increase in the solutal dispersion decreases the velocity and concentration but raises the temperature profile.

Keywords: power-law fluid, thermal conductivity, thermal dispersion, solutal dispersion, variable viscosity

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Authors: Anandhi Santhosh

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In order to describe various real-world problems in physical and engineering sciences subject to abrupt changes at certain instants during the evolution process, impulsive differential equations has been used to describe the system model. In this article, the problem of approximate controllability for nonlinear impulsive integrodifferential equations with state-dependent delay is investigated. We study the approximate controllability for nonlinear impulsive integrodifferential system under the assumption that the corresponding linear control system is approximately controllable. Using methods of functional analysis and semigroup theory, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the proposed theory.

Keywords: approximate controllability, impulsive differential system, fixed point theorem, state-dependent delay

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Authors: Ebru Dural, M. Zulfu Asık

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Laminated glass is a kind of safety glass, which is made by 'sandwiching' two glass sheets and a polyvinyl butyral (PVB) interlayer in between them. When the glass is broken, the interlayer in between the glass sheets can stick them together. Because of this property, the hazards of sharp projectiles during natural and man-made disasters reduces. They can be widely applied in building, architecture, automotive, transport industries. Laminated glass can easily undergo large displacements even under their own weight. In order to explain their true behavior, they should be analyzed by using large deflection theory to represent nonlinear behavior. In this study, a nonlinear mathematical model is developed for the analysis of laminated glass cylindrical shell which is free in radial directions and restrained in axial directions. The results will be verified by using the results of the experiment, carried out on laminated glass cylindrical shells. The behavior of laminated composite cylindrical shell can be represented by five partial differential equations. Four of the five equations are used to represent axial displacements and radial displacements and the fifth one for the transverse deflection of the unit. Governing partial differential equations are derived by employing variational principles and minimum potential energy concept. Finite difference method is employed to solve the coupled differential equations. First, they are converted into a system of matrix equations and then iterative procedure is employed. Iterative procedure is necessary since equations are coupled. Problems occurred in getting convergent sequence generated by the employed procedure are overcome by employing variable underrelaxation factor. The procedure developed to solve the differential equations provides not only less storage but also less calculation time, which is a substantial advantage in computational mechanics problems.

Keywords: laminated glass, mathematical model, nonlinear behavior, PVB

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Authors: Marcelo Jesus Kato Avila, Joao Da Costa Pantoja

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Differential settlement of foundations is a serious pathology in buildings that put at risk lives and property. A common reason for the occurrence of this specific pathology in central Brazil is the presence of collapsible clay, a typical soil in the region. In this study, the foundation of a condemned building erected above this soil is analyzed. The aim is to prevent problems in new constructions, to predict which buildings may be subjected to damages, and to make possible a more precise treatment in less advanced differential settlements observed in the buildings of the vicinity, which includes a hospital, a Military School, an indoor sporting arena, the Police Academy, and the Military Police Headquarters. The methodology consists of visual inspection, photographic report of the main pathologies, analysis of the existing foundations, determination of the soil properties, the study of the cracking level and assessment of structural failure risk of the building. The findings show that the presence of water weaken the soil structure on which the foundation rest, being the main cause of the pathologic settlement, indicating that even in a one store building it was necessary to consider deeper digging, other categories of foundations, and more elaborated and detailed foundation plans when the soil presents this behavior.

Keywords: building cracks, collapsible clay, differential settlement, structural failure risk

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Authors: Evans Iyamu

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Genes encoding hydrophobins play distinct roles at different stages of the life cycle of fungi, and they foster hyphal attachment to surfaces. The hydrophobin Sc4 is known to provide a hydrophobic membrane lining of the gas channels within Schizophyllum commune fruiting bodies. Here, we cultivated non-fruiting, monokaryotic S. commune 12-43 on glass surfaces that could be verified by micrography. Differential gene expression profiling of nine hydrophobin genes and the hydrophobin-like sc15 gene by quantitative PCR showed significant up-regulation of sc4 when S. commune was attached to glass surfaces, also confirmed with RNA-Seq data analysis. Another silicate, namely quartz sand, was investigated, and induction of sc4 was seen as well. The up-regulation of the hydrophobin gene sc4 may indicate involvement in S. commune hyphal attachment to glass as well as quartz surfaces. We propose that the covering of hyphae by Sc4 allows for direct interaction with the hydrophobic surfaces of silicates and that differential functions of specific hydrophobin genes depend on the surface interface involved. This study could help with the clarification of the biological functions of hydrophobins in natural surroundings, including hydrophobic surface attachment. Therefore, the analysis of growth on glass serves as a basis for understanding S. commune interaction with glass surfaces while providing the possibility to visualize the interaction microscopically.

Keywords: hydrophobin, structured glass surfaces, differential gene expression, quartz sand

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Authors: Olanrewaju Aladeitan, Obiageli Phina Anaghara-Uzor

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Despite the abundance of natural gas deposits in Nigeria and the immense potential, this presents both for the domestic and export oriented revenue, there exists an imbalance in the preference for export as against the development and optimal utilization of natural gas for the domestic industry. Considerable amounts of gas are still being wasted by flaring in the country to this day. Although the government has set in place initiatives to harness gas at the flare and thereby reduce volumes flared, the gas producers would rather direct the gas produced to the export market whereas gas apportioned to the domestic market is often marred by the low domestic gas price which is often discouraging to the gas producers. The exported fraction of gas production no doubt yields healthy revenues for the government and an encouraging return on investment for the gas producers and for this reason export sales remain enticing and preferable to the domestic sale of gas. This export pull impacts negatively if left unchecked, on the domestic market which is in no position to match the price at the international markets. The issue of gas price remains critical to the optimal development of the domestic gas industry, in that it comprises the basis for investment decisions of the producers on the allocation of their scarce resources and to what project to channel their output in order to maximize profit. In order then to rebalance the domestic industry and streamline the market for gas, the Gas Aggregation Company of Nigeria, also known as the Strategic Aggregator was proposed under the Nigerian Gas Master Plan of 2008 and then established pursuant to the National Gas Supply and Pricing Regulations of 2008 to implement the domestic gas supply obligation which focuses on ramping-up gas volumes for domestic utilization by mandatorily requiring each gas producer to dedicate a portion of its gas production for domestic utilization before having recourse to the export market. The 2008 Regulations further stipulate penalties in the event of non-compliance. This study, in the main, assesses the adequacy of the legal framework for the Nigerian Gas Industry, given that the operational laws are structured more for oil than its gas counterpart; examine the legal basis for the Strategic Aggregator in the light of the Domestic Gas Supply and Pricing Policy 2008 and the National Domestic Gas Supply and Pricing Regulations 2008 and makes a case for a review of the pivotal role of the Aggregator in the Nigerian Gas market. In undertaking this assessment, the doctrinal research methodology was adopted. Findings from research conducted reveal the reawakening of the Federal Government to the immense potential of its gas industry as a critical sector of its economy and the need for a sustainable domestic natural gas market. A case for the review of the ownership structure of the Aggregator to comprise a balanced mix of the Federal Government, gas producers and other key stakeholders in order to ensure the effective implementation of the domestic supply obligations becomes all the more imperative.

Keywords: domestic supply obligations, natural gas, Nigerian gas sector, strategic gas aggregator

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Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

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The physics-informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on a strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary conditions to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of the Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful in studying various optical phenomena.

Keywords: deep learning, optical soliton, physics informed neural network, partial differential equation

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Authors: Muslim Malik, Avadhesh Kumar

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A stronger concept of exact controllability which is called Total Controllability is introduced in this manuscript. Sufficient conditions have been established for the total controllability of a control problem, governed by second order nonlinear differential equation with delay and non-instantaneous impulses in a Banach space X. The results are obtained using the strongly continuous cosine family and Banach fixed point theorem. Also, the total controllability of an integrodifferential problem is investigated. At the end, some numerical examples are provided to illustrate the analytical findings.

Keywords: Banach fixed point theorem, non-instantaneous impulses, strongly continuous cosine family, total controllability

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Authors: Debajyoti Choudhuri, Ratan Kumar Giri, Shesadev Pradhan

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The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed.

Keywords: p-Laplacian, p-biharmonic, elliptic PDEs, Concentration lemma, Sobolev space

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Authors: Kobamelo Mashaba

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The molten slag has a high substantial temperatures range between 1723-1923, carrying a huge amount of useful energy for reducing energy consumption and CO₂ emissions under the heat recovery process. Therefore in this study, we investigated the performance of the modified crank Nicolson method for a delayed partial differential equation on the heat recovery of molten slag in the metallurgical mining environment. It was proved that the proposed method converges quickly compared to the classic method with the existence of a unique solution. It was inferred from numerical result that the proposed methodology is more viable and profitable for the mining industry.

Keywords: delayed partial differential equation, modified Crank-Nicolson Method, molten slag, heat recovery, parabolic equation

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Authors: Xuezhang Hou

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A control problem of a flexible Lamina formulated by partial differential equations with viscoelastic boundary conditions is studied in this paper. The problem is written in standard form of linear infinite dimensional system in an appropriate energy Hilbert space. The semigroup approach of linear operators is adopted in investigating wellposedness of the closed loop system. A variable structural control for the system is proposed, and meanwhile an equivalent control method is applied to the thin plate system. A significant result on control theory that the thin plate can be approximated by ideal sliding mode in any accuracy in terms of semigroup approach is obtained.

Keywords: partial differential equations, flexible lamina, variable structural control, semigroup of linear operators

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Authors: Haowen Xi

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We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function.

Keywords: bubble, crash, finite-time-singular, numerical simulation, price dynamics, stochastic differential equations

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Authors: Somnath Karmakar, S. Chakraverty

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This work investigates the vibration of nonhomogeneous Timoshenko nanobeam resting on the Winkler-Pasternak foundation. Eringen’s nonlocal theory has been used to investigate small-scale effects. The Differential Quadrature method is used to obtain the frequency parameters with various classical boundary conditions. The nonhomogeneous beam model has been considered, where Young’s modulus and density of the beam material vary linearly and quadratically. Convergence of frequency parameters is also discussed. The influence of mechanical properties and scaling parameters on vibration frequencies are investigated for different boundary conditions.

Keywords: Timoshenko beam, Eringen's nonlocal theory, differential quadrature method, nonhomogeneous nanobeam

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Authors: M. Salmanzadeh

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In paper, we will deal with incompressible Couette flow, which represents an exact analytical solution of the Navier-Stokes equations. Couette flow is perhaps the simplest of all viscous flows, while at the same time retaining much of the same physical characteristics of a more complicated boundary-layer flow. The numerical technique that we will employ for the solution of the Couette flow is the Crank-Nicolson implicit method. Parabolic partial differential equations lend themselves to a marching solution; in addition, the use of an implicit technique allows a much larger marching step size than would be the case for an explicit solution. Hence, in the present paper we will have the opportunity to explore some aspects of CFD different from those discussed in the other papers.

Keywords: incompressible couette flow, numerical method, partial differential equation, Crank-Nicolson implicit

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Authors: Benniche Omar

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We are concerned with abstract fully nonlinear differential equations having the form y’(t)=Ay(t)+f(t,y(t)) where A is an m—dissipative operator (possibly multi—valued) defined on a subset D(A) of a Banach space X with values in X and f is a given function defined on I×X with values in X. We consider a graph K in I×X. We recall that K is said to be viable with respect to the above abstract differential equation if for each initial data in K there exists at least one trajectory starting from that initial data and remaining in K at least for a short time. The viability problem has been studied by many authors by using various techniques and frames. If K is closed, it is shown that a tangency condition, which is mainly linked to the dynamic, is crucial for viability. In the case when X is infinite dimensional, compactness and convexity assumptions are needed. In this paper, we are concerned with the notion of near viability for a given graph K with respect to y’(t)=Ay(t)+f(t,y(t)). Roughly speaking, the graph K is said to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)), if for each initial data in K there exists at least one trajectory remaining arbitrary close to K at least for short time. It is interesting to note that the near viability is equivalent to an appropriate tangency condition under mild assumptions on the dynamic. Adding natural convexity and compactness assumptions on the dynamic, we may recover the (exact) viability. Here we investigate near viability for a graph K in I×X with respect to y’(t)=Ay(t)+f(t,y(t)) where A and f are as above. We emphasis that the t—dependence on the perturbation f leads us to introduce a new tangency concept. In the base of a tangency conditions expressed in terms of that tangency concept, we formulate criteria for K to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)). As application, an abstract null—controllability theorem is given.

Keywords: abstract differential equation, graph, tangency condition, viability

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