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The infrared (IR) spectra of different white copy paper types tend to appear indifferent. Discrimination between white copy papers could lead to the solution of forgery cases. In this preliminary study, three varieties of white paper were purchased from local stationery shops in Kuala Lumpur, Malaysia. The papers were classified according to their manufacturers using Partial Least Squares-Discriminant Analysis (PLS-DA) and sparse PLS-DA (sPLS-DA) models. The error rate for the two models on the training and the test data sets were estimated and compared. Results show that the performance of the two models are comparable. By including the first six latent variables in both models, classification accuracy as high as 100% can be achieved.

Selection of the most significant variables, i.e. the wavenumber, from an infrared (IR) spectrum is always difficult to be achieved. In this preliminary paper, the feasibility of genetic algorithms (GA) in identifying most informative wavenumbers from 150 IR spectra of papers was investigated. The list of selected wavenumbers was then employed in Linear Discriminant Analysis (LDA). GA procedure was repeated 30 times to get different lists of variables. Then the performances of LDA models were estimated via leave-one-out cross-validation. A total of six to eight wavenumbers were identified to be valuable variables in the GA procedures. All the 30 LDA models achieve correct classification rates between 97.3% to 100.0%. Therefore the GA-LDA model could be a suitable tool for differentiating white papers that appeared to be highly similar in their IR fingerprints.

Infrared (IR) spectral data are always influenced by undesired random and systematic variations. As such, pre-processing of spectral data is normally required before chemometric modeling. Two most widely used pre-processing techniques, i.e. scatter-correction methods and spectral derivatives, were used to pre-process 150 IR spectral data of paper. The algorithms investigated in this preliminary study are Standard Normal Variate (SNV), Multiplicative Scatter Correction (MSC), Savitzky-Golay (SG) and Gap-Segment (GS). The visual examination of the clustering among three studied varieties of paper, i.e. IK Yellow, One Paper and Save Pack, is accomplished via Principal Component Analysis (PCA). Overall, separation of the three varieties of paper is greatly enhanced after pre-processing. The most significant improvement is obtained with pre-processing via 1st derivative using SG algorithms.

Human immunodeficiency virus and acquired immune deficiency syndrome (HIV/AIDS) is pandemic. It has affected nearly 60 million people since the detection of the disease in 1981 to date. In this paper basic deterministic HIV/AIDS model with mass action incidence function are developed. Stability analysis is carried out. And the disease free equilibrium of the basic model was found to be locally asymptotically stable whenever the threshold parameter (RO) value is less than one, and unstable otherwise. The model is extended by introducing two optimal control strategies namely, CD4 counts and treatment for the infective using optimal control theory. Numerical simulation was carried out in order to illustrate the analytic results.

Vateria Indica is a multipurpose tree that is much used locally in India. It provides food, medicine and a range of other commodities. It is often planted along avenues in India. The use of vegetable oil as feedstock for biodiesel production is divisive as an outcome of the challenges of a food-fuel catastrophe linked with the use of fit to be eaten oils for biodiesel making. The present study is focused on the extraction of oil from vateria Indica seed using a solvent extraction method, evaluation of optimal conditions for oil extraction. A Box-Behnken design of response surface methodology (RSM) with 15 experimental runs is used to study the optimum environment for the withdrawal, and the variables of interest are effective solvent/seed ratio 1 ml/gm, 1.25 ml/gm and 1.5 ml/gm. extraction temperature 60°C, 65°C, 70°C, and extraction time 3 hr, 4 hr, 5 hr. From the current study it is observed that the optimized oil yield using the solvent extraction is found to be 22.85% at temperature of 66.6°C, extraction time of 4.41 hour keeping the solvent to seed ratio of 1.353 ml/g after adopting response optimization technique.

Pineapples are available all year round since they are unseasonal fruits. Due to the continuous harvesting of the fruit, the retailers and farmers had to find a solution such as the processing of pineapple into jam, to treat the unsuccessfully sold pineapples. The direct heating of pineapple puree during the production of pineapple jam can cause over degradation of quality of the fresh pineapple. Thus, this study aims to optimise the microwave-assisted processing conditions for producing pineapple jam which could reduce water activity and meets minimum requirement for pH and total soluble solids contents of fruit jam. The power and time of the microwave processing were chosen as the factors, while the water activity, pH and total soluble solids (TSS) content of the pineapple jam were determined as responses to be optimised. The microwave treatment on the pineapple jam was able to give significant effect on the water activity and TSS content of the pineapple jam. The optimum power and time for the microwav...

Color masterbatches are widely used in WPC production. As long as no product changes in terms of color will occur, the rheological behavior of color master batches as well as their influence on actual production conditions seems negligible. However, at short production runs or frequent color changes on the same product (within one shift), the rheological influence of color masterbatches to the WPC formulation is significant. Change of recorded production parameters are often observed and can also lead to production problems up to production stops. This presentation shows rheological analysis on color masterbatches, their influence to WPC formulations as well as their influence on WPC production in direct extrusion. Furthermore, possible strategies are discussed at the end.

We describe the results of an expert system applied to the evaluation of samples of kaolin for industrial use in paper or ceramic manufacture. Different machine learning techniques—classification trees, support vector machines and Bayesian networks—were applied with the aim of evaluating and comparing their interpretability and prediction capacities. The predictive capacity of these models for the samples analyzed was highly satisfactory, both for ceramic quality and paper quality. However, Bayesian networks generally proved to be the most useful technique for our study, as this approach combines good predictive capacity with excellent interpretability of the kaolin quality structure, as it graphically represents relationships between variables and facilitates what‐if analyses.

The main purpose of this short paper is to present the Chernoff product formula from which we derive the exponential formula and the Lie-Trotter formula for C0-semigroups of linear operators on L∞.

The main purpose of this short paper is to introduce the evolution semigroup associated with an evolutionary process with exponential growth on L∞.

In this short paper, we present a Kato’s type inequality for symmetric diffusion operators.

In this short paper we present a necessary and sufficient condition for that the one‐dimensional mass transport equation has one unique L1 weak solution.

Neutralizing pH value of sugar cane juice is the important craft in the control process in the clarifying process of sugar cane juice, which is the important factor to influence output and the quality of white sugar. On the one hand, it is an important content to control the neutralized pH value within a required range, which has the vital significance for acquiring high quality purified juice, reducing energy consumption and raising sucrose recovery. On the other hand, it is a complicated physical‐chemistry process, which has the characteristics of strong non‐linearity, time‐varying, large time‐delay, and multi‐input. Therefore, there has not been a very good solution to control the neutralized pH value. Firstly, in this chapter, a neural network model for the clarifying process of sugar juice is established based on gathering 1200 groups of real‐time sample data in a sugar factory. Then, the HDP (Heuristic Dynamic Programming) method is used to optimize and control the neutralized pH value in the clarifying process of sugar juice. Simulation results indicate that this method has good control effect. This will build a good foundation for stabilizing the clarifying process and enhancing the quality of the purified juice and lastly enhancing the quality of white sugar.

In the noiseless context, it has long been known that the average encoded word length of an instantaneous or uniquely decipherable code can be made to lie between the source entropy and that value plus unity. We address the question of finding sufficient conditions on the code–word probabilities for it to be possible to make the average code–word length approximate the entropy by a smaller prescribed amount.

Modeling survival data depends on the shape of the hazard rate. In this paper, a distribution called the Extended Inverse Lindley distribution, will be introduced. Extended Inverse Lindley distribution is a distribution that is formed from the transformation of the two-parameter Lindley distribution. The transformations used are power transformation and inverse transformation. Thus, the Extended Inverse Lindley distribution can model heavy-tailed data with an upside-down bathtub hazard rate. In this essay, we discuss how to construct Extended Inverse Lindley distribution and characteristics of these distributions. These include the probability density function, cumulative distribution function, survival function, hazard rate, r-th moment, and mode. The parameters of the Extended Inverse Lindley distribution were estimated using the maximum likelihood method. At the end of this paper, the Extended Inverse Lindley distribution is used to illustrate the repairing time data (in hours) for 46 failures of an airborne communications receiver and shown that the Extended Inverse Lindley distribution is more suitable for modeling data than other distributions.

Modeling the data with a standard distribution is usually difficult to do because of the different characteristics of the body and tail in data. For example, Gamma distribution that has the right-skewing and light tail characteristics is considered unable to model the amount of claim that has a heavy tail. However, the correct fit of the model in the body data and tail data is important in analyzing the risk. Therefore, the splicing distribution is introduced at a threshold value that separates the body and the tail of data. In this paper, splicing distribution at a threshold value is used to model the amount of claim that has heavy tails. The splicing distribution in this paper links a light-tailed distribution for the body data and heavy-tailed distribution for the tail data. In this paper, the splicing distribution of the Truncated Gamma is used to model the data of Phoenix City claim below the threshold value and the Truncated Weibull distribution to model the data above the threshold value. By considering the result of the Kolmogorov-Smirnov test, it can be concluded that this distribution is suitable for modeling Phoenix City claim dataset.

In this paper, we produced n-points quadrature method which is a Derivative-based Quadrature method on the compact interval [-1,1] with a constant weight function. This n-point Quadrature method looks like as Taylor series and includes up to n - 1 derivatives of a given function. This quadrature rule is the exact result to the polynomials of degree 2n-1 or less by the best values of the points and weights. We will show rules and errors up to n=5 on this paper.

Fractional calculus appears to be a powerful tool of solid mechanics. In recent years several papers have been published including various forms of non-localities. Two basic fields can be distinguished, there are non-locality in space and in time. When term non-locality is used in its original meaning the value of some quantity in an internal point of the body is determined by the values of other quantities in a whole region around that location. The second one means to include hereditary effects like non-classical viscosity and study fractional visco-elasticity or visco-plasticity. In non-linear stability investigation the way of the loss of stability is studied and classified as a generic static or dynamic bifurcation. To do that step some kind of regular condition is necessary. This condition is connected with non-locality. Generally such behaviour is a result of viscous (time derivative) and gradient dependent terms in the constitutive equations. Such derivatives are not always of first order. There are materials where tests justify models with fractional order derivatives. Moreover, there are (for example Riemann-Liouville) type of fractional derivatives which are non-local itself. Thus by defining strain by fractional derivation of the displacement field a non-local quantity appears instead of the conventional (local) strain. In such a way various versions of non-localities are obtained by using various types of fractional derivatives. The paper studies how the selection of that fractional derivative effects the way of the loss of stability. Basically the study aims constitutive modelling via instability phenomena, that is, by observing the way of loss of stability of some material we can be informed about the form of fractional derivative in its mathematical model.

This paper presents application of the equilibrated residual method (ERM) of a posteriori error estimation to the elliptic problems of elasticity (elastostatics) and dielectricity (electrostatics), and to the coupled problem of (stationary) piezoelectricity as well. It has been shown in numerous works that the direct application of the method based on the linear equilibration may lead to unacceptable overestimation of the errors. In this preliminary work, we show how to tune the estimators in order to obtain reasonable results of the estimation. We address the approximation and total error estimation within the mentioned two uncoupled and one coupled problem. The modeling error is defined as a difference between the previous two errors for each of three problems. We focus on three issues in the paper. The first one is comparison of the existing methods of liner equilibration. The second one is the assessment of the application of the higher order equilibration. Finally, the third one is the effectivity assessment of the estimation for some chosen promising variants of the equilibration, which leads to the equilibrated residual methods tuned for particular applications.

Friction is a phenomenon which occurs commonly in the nature and in mechanical constructions. One can find numerous mathematical models describing friction as a one-dimensional process. On the other hand, the number of models which take into account second dimension is significantly smaller. The paper in hand introduce two-dimensional, dynamical model for orthotropic dry friction. Proposed model obeys maximum dissipation power principle by means of non-linear two-dimensional bristle stiffness. Numerical studies show influence of orthotropic friction on planar oscillator and 2D stick-slip system trajectories. Model is also verified against experimental results. Frictional pair with orthotropic properties have been prepared for laboratory rig which is a spherical pendulum with frictional contact. Comparison between experimental and simulation results shows good similarity, although further validation is required.Friction is a phenomenon which occurs commonly in the nature and in mechanical constructions. One can find numerous mathematical models describing friction as a one-dimensional process. On the other hand, the number of models which take into account second dimension is significantly smaller. The paper in hand introduce two-dimensional, dynamical model for orthotropic dry friction. Proposed model obeys maximum dissipation power principle by means of non-linear two-dimensional bristle stiffness. Numerical studies show influence of orthotropic friction on planar oscillator and 2D stick-slip system trajectories. Model is also verified against experimental results. Frictional pair with orthotropic properties have been prepared for laboratory rig which is a spherical pendulum with frictional contact. Comparison between experimental and simulation results shows good similarity, although further validation is required.

In this paper, we define soft D− metric spaces and give some fundamental definitions. In addition to this, we define a soft Δ− distance on a complete soft D− metric.In this paper, we define soft D− metric spaces and give some fundamental definitions. In addition to this, we define a soft Δ− distance on a complete soft D− metric.

In this paper derived the mathematical formulas of the Reliability for Special (2+1) cascade model, expression for model reliability are found when strength and stress distributions are generalized inverse Rayleigh random variables. The estimation for the reliability function (R) of model is done by Sixth different methods (ML, Mo, LS, WLS, Rg and Pr) and make the compare between them in simulation study with the program made by (MATLAB 2016) using two statistical criteria MSE and MAPE, where it found that best estimator between the six estimators is ML.In this paper derived the mathematical formulas of the Reliability for Special (2+1) cascade model, expression for model reliability are found when strength and stress distributions are generalized inverse Rayleigh random variables. The estimation for the reliability function (R) of model is done by Sixth different methods (ML, Mo, LS, WLS, Rg and Pr) and make the compare between them in simulation study with the program made by (MATLAB 2016) using two statistical criteria MSE and MAPE, where it found that best estimator between the six estimators is ML.

Holomorphic functions are the key tool to construct representation formulae for the solutions for a manifold of plane problems, especially for the flow of a viscous fluid modelled by the Stokes system. Three-dimensional representation formulae can be constructed by tools of hypercomplex analysis, i.e. by working with monogenic functions playing the role of a three-dimensional analogue of holomorphic functions. However, several alternative constructions in hypercomplex setting are possible. In this paper, the three-dimensional representation of a general solution for the Stokes system, based on the functions of a reduced quaternionic variable, is presented. Moreover, an ill-posed Cauchy problem for the Stokes system, consisting in reconstruction of the velocity field in the interior from overdetermined boundary conditions given on a part of the boundary, is considered. It is shown, that if the domain is star-shaped, then the Cauchy problem can be reduced to the problem of the regular extension for a quaternionic function from the boundary conditions given on a part of its boundary.Holomorphic functions are the key tool to construct representation formulae for the solutions for a manifold of plane problems, especially for the flow of a viscous fluid modelled by the Stokes system. Three-dimensional representation formulae can be constructed by tools of hypercomplex analysis, i.e. by working with monogenic functions playing the role of a three-dimensional analogue of holomorphic functions. However, several alternative constructions in hypercomplex setting are possible. In this paper, the three-dimensional representation of a general solution for the Stokes system, based on the functions of a reduced quaternionic variable, is presented. Moreover, an ill-posed Cauchy problem for the Stokes system, consisting in reconstruction of the velocity field in the interior from overdetermined boundary conditions given on a part of the boundary, is considered. It is shown, that if the domain is star-shaped, then the Cauchy problem can be reduced to the problem of the regular extension for a quater...

We discussed the vector style delay of SI model with immigration. Thus, we have to obtain the unique solutions of Equilibrium of SI model with delay. Also, this paper we derive the solutions of local and global stability for asymptotically stable.We discussed the vector style delay of SI model with immigration. Thus, we have to obtain the unique solutions of Equilibrium of SI model with delay. Also, this paper we derive the solutions of local and global stability for asymptotically stable.

In this paper we propose new methods of interpretation and verification of interval solutions obtained using interval parametric integral equations systems (interval PIES). These strategies concern the examples with the analytical solutions as well as more sophisticated examples. To obtain errors of precisely defined solutions (for comparison with interval ones), we base on well known methods of errors calculation. All of considered boundary value problems examples are described by Laplace’s equation. For modeling the uncertainty of boundary value problems we propose the modified directed interval arithmetic, which was previously applied in mentioned interval PIES method.In this paper we propose new methods of interpretation and verification of interval solutions obtained using interval parametric integral equations systems (interval PIES). These strategies concern the examples with the analytical solutions as well as more sophisticated examples. To obtain errors of precisely defined solutions (for comparison with interval ones), we base on well known methods of errors calculation. All of considered boundary value problems examples are described by Laplace’s equation. For modeling the uncertainty of boundary value problems we propose the modified directed interval arithmetic, which was previously applied in mentioned interval PIES method.

The main goal of this paper is to establish a criterion on the exponential ergodicity in the bounded Lipschitz distance, the strong law of large numbers (SLLN) and the central limit theorem (CLT) for a certain class of Markov chains, taking values in a Polish space. The examined dynamical systems provide a mathematical framework for modelling the stochastic dynamics of single-gene autoregulation in bacterium.The main goal of this paper is to establish a criterion on the exponential ergodicity in the bounded Lipschitz distance, the strong law of large numbers (SLLN) and the central limit theorem (CLT) for a certain class of Markov chains, taking values in a Polish space. The examined dynamical systems provide a mathematical framework for modelling the stochastic dynamics of single-gene autoregulation in bacterium.

The most systems in our environment contain components that interact through competition or cooperation, which can lead to system adaptation. Recently, it is especially important to study the behavior of such systems, and to develop and apply new appropriate mathematical methods for studying the processes in these systems. Such approaches have many applications in economy and sociology and are successfully used in mathematics, physics, ecology, biology and technical sciences. In the last decades non–linear models are intensively used to model economic and social systems. In many cases the main features of such complex systems can be explained by a relatively small number of non–linear differential equations. Examples of such systems are some economic organizations. In this paper we model the behavior of a socio-economic system by partial differential equations. The model describes dynamics of populations competing for limited resources. In the model, migration is treated as a advection–diffusion process influenced by changing of the growth rates and the interactions among population individuals. The model describes several novel features of the interacting populations compared to the well-known classic models in population dynamics. Using the modified method of simplest equation and one of its extended versions, we obtain new wave solutions of the model system.The most systems in our environment contain components that interact through competition or cooperation, which can lead to system adaptation. Recently, it is especially important to study the behavior of such systems, and to develop and apply new appropriate mathematical methods for studying the processes in these systems. Such approaches have many applications in economy and sociology and are successfully used in mathematics, physics, ecology, biology and technical sciences. In the last decades non–linear models are intensively used to model economic and social systems. In many cases the main features of such complex systems can be explained by a relatively small number of non–linear differential equations. Examples of such systems are some economic organizations. In this paper we model the behavior of a socio-economic system by partial differential equations. The model describes dynamics of populations competing for limited resources. In the model, migration is treated as a advection–diffusion process i...

This paper presents a method for quantitatively calculating the responsibility of harmonic energy loss. First, we establish a Norton equivalent circuit at the PCC to obtain a harmonic loss calculation formula for the user and the background under the condition that the circuit equivalent parameters are known. For the background side of the PCC, the background fluctuation harmonic method is used to calculate the background equivalent harmonic impedance. For the user side of the PCC, the user equivalent harmonic impedance is estimated by calculating the fundamental impedance. Under the premise of accurately calculating the equivalent circuit parameters, by measuring the voltage and current data of the PCC during the analysis period, the user’s responsibility for harmonic energy loss can be quantitatively calculated. Through the IEEE14 node system simulation test, the calculation results show that our error control is within a small range, and the calculation method is accurate and easy to implement.This paper presents a method for quantitatively calculating the responsibility of harmonic energy loss. First, we establish a Norton equivalent circuit at the PCC to obtain a harmonic loss calculation formula for the user and the background under the condition that the circuit equivalent parameters are known. For the background side of the PCC, the background fluctuation harmonic method is used to calculate the background equivalent harmonic impedance. For the user side of the PCC, the user equivalent harmonic impedance is estimated by calculating the fundamental impedance. Under the premise of accurately calculating the equivalent circuit parameters, by measuring the voltage and current data of the PCC during the analysis period, the user’s responsibility for harmonic energy loss can be quantitatively calculated. Through the IEEE14 node system simulation test, the calculation results show that our error control is within a small range, and the calculation method is accurate and easy to implement.

Blades on the wind turbine are moving due to the lift and drag force. During the conversion process of wind energy into electrical energy arise energy loss naturally. One of the optimization techniques of power harvesting in wind turbine is pitch angle control on the turbine blades hence, the wind turbine power output lies on optimum condition. The wind turbine control system in this paper is composed of turbine blades, servo motor as actuator, rotational connector and rotary encoder as transmitter. The best result of wind turbine prototype test shows that Power Coefficient (CP) up to 0.57510. To obtain adaptive control conform to the existing wind speed, pitch angle adjustment is controlled using PID control, with each parameters value of Kp, Ki, and Kd are equal to 0,0239069, 0.0001382, 0,053518, respectively. The parameters value are achieved by implementing PSO optimization method. According to the result of the test, the set points are 40, 60, 80 and 100 rpm, which is the system is able to reach the set point with maximum overshoot attains 26.25% and the rise time in 181 seconds. Therefore, the PID-PSO produces a better response than uncontrolled and fuzzy-based controller.Blades on the wind turbine are moving due to the lift and drag force. During the conversion process of wind energy into electrical energy arise energy loss naturally. One of the optimization techniques of power harvesting in wind turbine is pitch angle control on the turbine blades hence, the wind turbine power output lies on optimum condition. The wind turbine control system in this paper is composed of turbine blades, servo motor as actuator, rotational connector and rotary encoder as transmitter. The best result of wind turbine prototype test shows that Power Coefficient (CP) up to 0.57510. To obtain adaptive control conform to the existing wind speed, pitch angle adjustment is controlled using PID control, with each parameters value of Kp, Ki, and Kd are equal to 0,0239069, 0.0001382, 0,053518, respectively. The parameters value are achieved by implementing PSO optimization method. According to the result of the test, the set points are 40, 60, 80 and 100 rpm, which is the system is able to reach the ...

This paper is a part of the results of my study on lattice topology on some algebraic structures; for examples on Rn (the collection of all n-tuples of real numbers), S (R) (the collection of all sequences of real numbers), C[a, b] (the collection of all continuous functions on [a, b]), and M[a, b] (the collection of all measurable functions on [a, b]). Each of them is a lattice topological algebra (See [6]) and each of them can be considered as a generalization of the system of real numbers.This paper is a part of the results of my study on lattice topology on some algebraic structures; for examples on Rn (the collection of all n-tuples of real numbers), S (R) (the collection of all sequences of real numbers), C[a, b] (the collection of all continuous functions on [a, b]), and M[a, b] (the collection of all measurable functions on [a, b]). Each of them is a lattice topological algebra (See [6]) and each of them can be considered as a generalization of the system of real numbers.

In this paper, we solve the fractional Bagley-Torvik equation by using discrete cubic spline and a fourth order approxi-mation based on weighted shifted Grunwald-Letnikov difference operator. By matrix analysis, the numerical scheme is proved to be uniquely solvable and third order accurate. An example is presented to verify the efficiency of the numerical scheme and to compare with other methods in the literature.In this paper, we solve the fractional Bagley-Torvik equation by using discrete cubic spline and a fourth order approxi-mation based on weighted shifted Grunwald-Letnikov difference operator. By matrix analysis, the numerical scheme is proved to be uniquely solvable and third order accurate. An example is presented to verify the efficiency of the numerical scheme and to compare with other methods in the literature.

We have recently proved Tauberian conditions (for single sequences) relating to statistical convergence following statistical summability by weighted means in non-archimedean fields. In this paper, statistically summable double sequences by weighted means for which the necessary and sufficient Tauberian conditions over non-archimedean fields are discussed.We have recently proved Tauberian conditions (for single sequences) relating to statistical convergence following statistical summability by weighted means in non-archimedean fields. In this paper, statistically summable double sequences by weighted means for which the necessary and sufficient Tauberian conditions over non-archimedean fields are discussed.

In the paper, a system of two linear discrete equations is considered. Numerous sufficient conditions are derived for the existence of solutions to such systems with prescribed asymptotic behavior of solutions. In the literature, not many recommendations are given as to how to detect the initial data generating such solutions. For the case of a system of two linear equations, this gap is filled in this paper. Using the limits of special convergent sequences, sets of initial data are constructed generating the desired solutions.In the paper, a system of two linear discrete equations is considered. Numerous sufficient conditions are derived for the existence of solutions to such systems with prescribed asymptotic behavior of solutions. In the literature, not many recommendations are given as to how to detect the initial data generating such solutions. For the case of a system of two linear equations, this gap is filled in this paper. Using the limits of special convergent sequences, sets of initial data are constructed generating the desired solutions.

In this paper, a class of second-order Hamiltonian systems with impulsive effects are considered. By using critical point theory, we obtain some new existence theorems of periodic solutions generated by impulses. Here, a solution of the Second-order Hamiltonian System with the impulsive condition is said to be generated by impulses if the System does not possess any solution without the impulsive condition. To the best of the authors’ knowledge, there are still few results in the literature to consider periodic solutions generated by impulses. Based on the facts mentioned above, in this paper we study the existence of periodic solutions generated by impulses with convexity potential.

Let K be a complete, non-trivially valued non-archimedean field. In this paper, Generalized weighted statistical convergence and statistical summabilityof double sequences over K are studied. Also (SN¯)λ,μ and (N¯2λμ,p,q,α,β) - summability inclusion relations have been discussed in such fields K. Weighted Statistical Convergence of order α are analysed in fields K.Let K be a complete, non-trivially valued non-archimedean field. In this paper, Generalized weighted statistical convergence and statistical summabilityof double sequences over K are studied. Also (SN¯)λ,μ and (N¯2λμ,p,q,α,β) - summability inclusion relations have been discussed in such fields K. Weighted Statistical Convergence of order α are analysed in fields K.

This paper gives a detailed study of cordial labeling of double duplication of all vertices by edges, of a circulant graph C[n : (±a, ±b)] by fixing various values as generators has been verified.This paper gives a detailed study of cordial labeling of double duplication of all vertices by edges, of a circulant graph C[n : (±a, ±b)] by fixing various values as generators has been verified.

In this paper, new results of domination in graphs called bi-domination are determined. Some properties for bi-dominating set are presented. The bi-domination number of G is the minimum cardinality of a bi-dominating set of G. In this paper, we investigate the bi-domination number for web graph, tadpole graph, lollipop graph, daisy graph, Dutch windmill graph, windmill graph, dumbbell graph, barbell graph, grid graph, product of two path, and the corona H ⊙ K2 and H + K2.

This paper considers the underlying group theoretic properties of a system of two linear second-order stochastic ordi- nary differential equations (SODEs) with constant coefficients. The approach involves obtaining the corresponding determining equations of the system of equations and their corresponding equivalent transformations which assist with further classifying the system for selected cases. It is postulated that the approach used here can be applied to all other cases that should help obtain the full classification of the system.This paper considers the underlying group theoretic properties of a system of two linear second-order stochastic ordi- nary differential equations (SODEs) with constant coefficients. The approach involves obtaining the corresponding determining equations of the system of equations and their corresponding equivalent transformations which assist with further classifying the system for selected cases. It is postulated that the approach used here can be applied to all other cases that should help obtain the full classification of the system.

In this paper, we propose and study a time-delay compartmental model for human immunodeficiency virus (HIV) transmission, a disease which may lead to an advanced stage of infection called acquired immunodeficiency syndrome (AIDS), in a sexually active population with the presence of media coverage. The inclusion of vertical transmission in the recruitment of infected individuals is also considered. Moreover, two time delays are incorporated in the model. One delay τ1 covers the period from the time of gathering statistical data on the total number of infections in the community up to the time that these information are reported to the public through media. The other delay τ2 corresponds to the period that an infected newborn baby reaches the age of sexual maturity. If the threshold value R0 < 1, then the only equilibrium point is the disease-free equilibrium which is globally asymptotically stable. If the threshold values R0 and R00 are both greater than 1, then a unique endemic equilibrium exists, which is globally asymptotically stable when media coverage is not considered. When there is no vertical transmission but media coverage is considered, the system undergoes a Hopf bifurcation at some critical value of the media delay. Numerical simulations are presented to illustrate theoretical results.In this paper, we propose and study a time-delay compartmental model for human immunodeficiency virus (HIV) transmission, a disease which may lead to an advanced stage of infection called acquired immunodeficiency syndrome (AIDS), in a sexually active population with the presence of media coverage. The inclusion of vertical transmission in the recruitment of infected individuals is also considered. Moreover, two time delays are incorporated in the model. One delay τ1 covers the period from the time of gathering statistical data on the total number of infections in the community up to the time that these information are reported to the public through media. The other delay τ2 corresponds to the period that an infected newborn baby reaches the age of sexual maturity. If the threshold value R0 < 1, then the only equilibrium point is the disease-free equilibrium which is globally asymptotically stable. If the threshold values R0 and R00 are both greater than 1, then a unique endemic equilibrium exists, which ...

The movement of data changes in time series often cannot be seen as a single model throughout the time the serial data is recorded. The occurrence of model structure changes often must be accommodated in time series data modeling. This paper aims to study the Markov Switching models in capturing the structural changes the closing price stocks data of three companies (PT. Indofood Sukses Makmur Tbk. (INDF.JK), PT. Indofood CBP Sukses Makmur Tbk. (ICBP.JK), and PT. Mustika Ratu Tbk. (MRAT.JK)) from the member and not members of LQ45, estimating the run-length for each model structure, and forecasting the one-step-ahead of stocks. The parameters in the Markov Switching models are estimated using the Expectation Maximization (EM). The result shows that the three companies had more than one structural model. The best stock for investment is IDNF.JK share which have the longest Average Run Length (ARL) that provides the bigger probability of the forecasting regime and the stock values.The movement of data changes in time series often cannot be seen as a single model throughout the time the serial data is recorded. The occurrence of model structure changes often must be accommodated in time series data modeling. This paper aims to study the Markov Switching models in capturing the structural changes the closing price stocks data of three companies (PT. Indofood Sukses Makmur Tbk. (INDF.JK), PT. Indofood CBP Sukses Makmur Tbk. (ICBP.JK), and PT. Mustika Ratu Tbk. (MRAT.JK)) from the member and not members of LQ45, estimating the run-length for each model structure, and forecasting the one-step-ahead of stocks. The parameters in the Markov Switching models are estimated using the Expectation Maximization (EM). The result shows that the three companies had more than one structural model. The best stock for investment is IDNF.JK share which have the longest Average Run Length (ARL) that provides the bigger probability of the forecasting regime and the stock values.

In [17] (A. Yardimci and Y. Simsek, Identities for Korobov-type polynomials arising from functional equations and p-adic integrals, J. Nonlinear Sci. Appl., 10(5), 2767–2777 (2017)), by using functional equations and p-adic integrals method, Yardimci and Simsek derived various identities and relations on the Korobov-type polynomials. The aim of this paper is to derive some other new and important identities and formulas on these polynomials with their comments and observation on molecular dynamic model.In [17] (A. Yardimci and Y. Simsek, Identities for Korobov-type polynomials arising from functional equations and p-adic integrals, J. Nonlinear Sci. Appl., 10(5), 2767–2777 (2017)), by using functional equations and p-adic integrals method, Yardimci and Simsek derived various identities and relations on the Korobov-type polynomials. The aim of this paper is to derive some other new and important identities and formulas on these polynomials with their comments and observation on molecular dynamic model.

In this paper, we give the generating function of the Euler and Bernoulli polynomials. Then, by using the generating function of these polynomials, we obtain two convolution formulae for some special cases of Euler and Bernoulli polynomials.In this paper, we give the generating function of the Euler and Bernoulli polynomials. Then, by using the generating function of these polynomials, we obtain two convolution formulae for some special cases of Euler and Bernoulli polynomials.

Motivated by the recent physicists’ interest in contact geometry, this review paper is devoted to some modern geometric insights upon the contact structures. In view of this, we start from the initial perspective on contact manifolds, namely that of an odd-dimensional orientable manifold whose volume form is generated by a 1-form θ and its differential dθ. This naturally arises from a coorientable maximally non-integrable hyperplane distribution. In this picture, we establish a one-to-one correspondence between the transitive Jacobi pairs over odd-dimensional manifolds and the coorientable contact structures over the same manifolds. Then, we introduce the geometric perspective on contact manifolds by omitting the coorientability of the maximally non-integrable hyperplane distribution, and we define the contact structure via an L-valued 1-form [with (L, π, M) a line bundle over an odd-dimensional manifold] with non-degenerate curvature. In this realm, it is shown that there exists a one-to-one correspondence between the transitive Jacobi line bundles over odd-dimensional manifolds and the contact structures over the same manifolds. This faithful ‘representation’ of contact structures brings them nearer to symplectic-like ones through the canonical [bracket] structures inherited from the corresponding Jacobi structures.Motivated by the recent physicists’ interest in contact geometry, this review paper is devoted to some modern geometric insights upon the contact structures. In view of this, we start from the initial perspective on contact manifolds, namely that of an odd-dimensional orientable manifold whose volume form is generated by a 1-form θ and its differential dθ. This naturally arises from a coorientable maximally non-integrable hyperplane distribution. In this picture, we establish a one-to-one correspondence between the transitive Jacobi pairs over odd-dimensional manifolds and the coorientable contact structures over the same manifolds. Then, we introduce the geometric perspective on contact manifolds by omitting the coorientability of the maximally non-integrable hyperplane distribution, and we define the contact structure via an L-valued 1-form [with (L, π, M) a line bundle over an odd-dimensional manifold] with non-degenerate curvature. In this realm, it is shown that there exists a one-to-one corresponden...

The recent paper (DOI: 10.1007/s10898-017-0537-6) suggests various practical tests (sufficient conditions) for checking pseudoconvexity of a twice differentiable function on an interval domain. The tests were implemented using interval extensions of the gradient and the Hessian of the function considered. In this paper, we present an alternative approach which is based on the use of linear interval parametric enclosures of the gradient and the Hessian. It is shown that the new approach results in more efficient tests for checking pseudoconvexity.

The main purpose of this paper is to increase accuracy of modeling uncertainly defined boundary shape in parametric integral equations systems method (PIES), by inclusion of interval NURBS curves into mathematical formalism of the method. We model the uncertainty of the boundary shape by interval control points and examine such strategy on examples of 2D elasticity problems. Accuracy improvement of the boundary shape modeling affects the solutions accuracy. Additionally using interval NURBS we make the modeling process much easier and ensure the continuity of the shape.The main purpose of this paper is to increase accuracy of modeling uncertainly defined boundary shape in parametric integral equations systems method (PIES), by inclusion of interval NURBS curves into mathematical formalism of the method. We model the uncertainty of the boundary shape by interval control points and examine such strategy on examples of 2D elasticity problems. Accuracy improvement of the boundary shape modeling affects the solutions accuracy. Additionally using interval NURBS we make the modeling process much easier and ensure the continuity of the shape.

In this paper the objectivity in science, the Riemann-Liouville and the Caputo fractional order derivatives are presented shortly. This is followed by the presentation of some recent papers which propose the use of these fractional order derivatives, instead of the integer order derivatives, in the description of some physical phenomena. The objectivity of the new mathematical concepts, constitutive equations, evolution equations in these papers is not considered. In the present paper it is shown that in classical mechanics when Riemann-Liouville or Caputo fractional derivatives are used, the objectivity of the new concepts, constitutive relations, evolution equations, is lost. With this aim this study was undertaken.

In [T. K. Samanta, S. Mohinta and I. H. Jebril, On fixed point theorems in intuitionistic fuzzy metric spaces:int. J. Open problems compt. Math, Vol.5, No2, (2012), 15–27] the authors raise an open problem that Kannan’s and Chatterjee’sfixed point theorems can be established with the help of (TS − IFλ) contractive mapping. In this paper we not only gave the answer to this problem but also obtain generalization of Kannan’s and Chatterjee’s fixed point theorem in intuitionistic fuzzy metric spaces with new contractive mapping IFCα. We also obtained generalization of Banach fixed point theorem of (TS-IF) contractive mapping. An example is also given to convince our results.In [T. K. Samanta, S. Mohinta and I. H. Jebril, On fixed point theorems in intuitionistic fuzzy metric spaces:int. J. Open problems compt. Math, Vol.5, No2, (2012), 15–27] the authors raise an open problem that Kannan’s and Chatterjee’sfixed point theorems can be established with the help of (TS − IFλ) contractive mapping. In this paper we not only gave the answer to this problem but also obtain generalization of Kannan’s and Chatterjee’s fixed point theorem in intuitionistic fuzzy metric spaces with new contractive mapping IFCα. We also obtained generalization of Banach fixed point theorem of (TS-IF) contractive mapping. An example is also given to convince our results.

Since the real structure is not perfect, the geometric imperfections are present. In this case, the bifurcation buckling load overestimates the buckling load. This problem is particularly interesting in experimental studies, because the amplitude of imperfection and its mode can differ for each sample. In this paper, a methodology for determination of the lowest buckling load of a thin-walled plate structure with imperfection using a load–axial shortening plot was presented. The proposed approach can be applied, when the post-buckling path is stable, only. It was shown that the load corresponding to an alternation in rigidity of the real structure on the load-axial shortening plot determines the buckling load with high accuracy. The P-w2 method and the inflection point method were applied, as well, to verify the obtained results. First, numerical calculations were performed by the finite element method and Koiter's method using Byskov-Hutchinson's formulation. The imperfections were defined explicitly. Other parameters of the system, such as boundary conditions, loads, geometrical dimensions were free from inaccuracies. A plate model of the thin-walled structure was applied. An eigenvalue buckling problem of perfect structures was solved to determine bifurcation loads and their eigenmodes. Then nonlinear problem of buckling was solved by Koiter's perturbation method for one mode approach or the finite element method employing Newton-Rawson's method. The load - axial shortening plots were made to analyse an influence of the imperfection amplitude on an approximate value of the lowest buckling load. The uncoupled local buckling was considered. Detailed computations were conducted for short Z-column made of general carbon-epoxy laminate under uniform compression. The Z-column was simply supported on both ends. Finally, the numerical results were verified in experimental tests using Aramis system. A static compression test was performed on a universal testing machine. Tests were performed at a constant velocity of the cross-bar equal to 2 mm/min. The compressive load was less than 150% of the bifurcation load. A very good agreement between the results attained with both the methods for solving the nonlinear problem was obtained.Since the real structure is not perfect, the geometric imperfections are present. In this case, the bifurcation buckling load overestimates the buckling load. This problem is particularly interesting in experimental studies, because the amplitude of imperfection and its mode can differ for each sample. In this paper, a methodology for determination of the lowest buckling load of a thin-walled plate structure with imperfection using a load–axial shortening plot was presented. The proposed approach can be applied, when the post-buckling path is stable, only. It was shown that the load corresponding to an alternation in rigidity of the real structure on the load-axial shortening plot determines the buckling load with high accuracy. The P-w2 method and the inflection point method were applied, as well, to verify the obtained results. First, numerical calculations were performed by the finite element method and Koiter's method using Byskov-Hutchinson's formulation. The imperfections were defined explicitly. Ot...

Measuring risk of a portfolio comprising of multi assets such as option and stock by Value at Risk (VaR) will become more challenging because unlike stock price, value of an option has a nonlinear dependence on market risk factor. This paper considered to utilize Delta Normal and Delta Gamma Normal as a linear approach of the factor determining price of the assets. The methods use consecutively the expansion of first and second-order Taylor Series to approximate the profit loss, which is prominent to develop VaR of a multi-asset portfolio. As an application of these methods, this paper analyzed a portfolio comprising of one stock (Exxon Mobile Corporation (XOM)) and two options from two different enterprises, namely JD.com, Inc. (JD), and Eni. S.p. A (E). According to Kupiec Backtesting, it can be concluded that in this case, VaR Delta Normal and VaR Delta Gamma Normal Models provide a good risk measurement at some different confidence levels (90, 95, and 99 percent).

A numerical solution of the Fredholm integral equations can be obtained by many methods. Most of them lead to a solution of a system of linear equations with fully populated matrices. In the case of collocation or product integration methods, each element of the matrix is an integral, which needs to be calculated. It causes high computing time in multidimensional problems. Computing time can be reduced by the Nystrom method. It is based on substitution of the integral by a numerical integration rule. It has the advantage that only diagonal elements of the matrix are integrals. When the kernel function is singular, a singularity subtraction is needed. However it can not be used for every kernel function and every integration rule. The main point of this paper is the convergence conditions of the Nystrom method as applied to a special multidimensional integral equation. The paper includes an illustrative example.