1- Introduction

2- Weak Galerkin finite element schemes

3- Well posedness

4- Error estimates in energy norm

5- Error estimates in L 2 norm

6- Numerical experiments

References

Abstract 

A stabilizing/penalty term is often used in finite element methods with discontinuous approximations to enforce connection of discontinuous functions across element boundaries. Removing stabilizers from discontinuous Galerkin finite element methods will simplify formulations and reduce programming complexity significantly. The goal of this paper is to introduce a stabilizer free weak Galerkin (WG) finite element method for second order elliptic equations on polytopal meshes. This new WG method keeps a simple symmetric positive definite form and can work on polygonal/polyhedral meshes. Optimal order error estimates are established for the corresponding WG approximations in both a discrete H 1 norm and the L 2 norm. Numerical results are presented verifying the theorem.

6. Numerical experiments

We solve the following Poisson equation on the unit square:
− ∆u = 2π 2 sin πx sin πy, (x, y) ∈ Ω = (0, 1)2 , (6.1)
with the boundary condition u = 0 on ∂Ω. In the first computation, the level one grid consists of two unit right triangles cutting from the unit square by a forward slash. The high level grids are the half-size refinements of the previous grid. The first three levels of grids are plotted in Fig. 6.1. The error and the order of convergence are shown in Table 6.1. The numerical results confirm the convergence theory. In Fig. 6.2, we plot the finite element solution and the discretization errors on triangular and on polygonal grids. We can see, with same number of unknowns, the solutions on triangular grids are more accurate than those on polygonal grids. This can also be seen from the two data tables. In the next computation, we use a family of polygonal grids (with 12-side polygons) shown in Fig. 6.3. The numerical results in Table 6.2 indicate that the polynomial degree j for the weak gradient needs to be larger, which confirms the theory: j depending on the number of edges of a polygon. The convergence history confirms the theory.

1- Introduction

2- Related study

3- Methodology

4- Experimental result

5- Discussion

6- Conclusion and future work

References

Abstract

Diabetes causes a large number of deaths each year and a large number of people living with the disease do not realize their health condition early enough. In this study, we propose a data mining based model for early diagnosis and prediction of diabetes using the Pima Indians Diabetes dataset. Although K-means is simple and can be used for a wide variety of data types, it is quite sensitive to initial positions of cluster centers which determine the final cluster result, which either provides a sufficient and efficiently clustered dataset for the logistic regression model, or gives a lesser amount of data as a result of incorrect clustering of the original dataset, thereby limiting the performance of the logistic regression model. Our main goal was to determine ways of improving the k-means clustering and logistic regression accuracy result. Our model comprises of PCA (principal component analysis), k-means and logistic regression algorithm. Experimental results show that PCA enhanced the k-means clustering algorithm and logistic regression classifier accuracy versus the result of other published studies, with a k-means output of 25 more correctly classified data, and a logistic regression accuracy of 1.98% higher. As such, the model is shown to be useful for automatically predicting diabetes using patient electronic health records data. A further experiment with a new dataset showed the applicability of our model for the predication of diabetes.

Introduction

Diabetes stands among the top 10 causes of death for 2016. Diabetes killed 1.6 million people in 2016, up from less than 1 million in 2000. With this figure diabetes replaced HIV/AIDS as the seventh top cause of death [1]. The number of people with diabetes has risen from 108 million in 1980 to 422 million in 2014, with the global prevalence of diabetes among adults over 18 years of age rising from 4.7% in 1980 to 8.5% in 2014 [2]. By 2040, 642 million adults (1 in 10 adults) are expected to have diabetes. Also, 46.5% of those with diabetes have not been diagnosed [3]. In order to reduce the number of deaths attributable to diabetes, it is essential that methods and techniques that will aid in early diagnosis of diabetes be devised, because a large number of deaths in diabetic patients are due to late diagnosis. In order to achieve cutting-edge techniques for the early diagnosis of diabetes, we need to utilize advanced information technology, and data mining is a suitable field for this. Data mining offers the ability to extract and discover previously unknown, hidden, but interesting patterns from a large database repository. These patterns can aid medical diagnosis and decision-making. Various techniques and algorithms have been designed for application in extracting knowledge and information in the diagnosis and treatment of disease from medical databases. PCA is a simple, nonparametric method for extracting relevant information from confusing data sets [4]. When a large dataset is to be clustered into a user specified number of clusters (k), which are represented by their centroids, k-means will cluster the data by minimizing the squared error function [5], and often misclassifies some data due to outliers; also the time complexity will be greater. To overcome these problems, principal components analysis (PCA) can be used to reduce the dataset to a lower dimension, while ensuring that the least information is lost, and providing a better centroid point for clustering. K-means clustering partitions a dataset into different groups of similar objects. Clusters that are highly dissimilar from the others are regarded as outliers and discarded. Logistic regression is an efficient regression predictive analysis algorithm. Its application is efficient when the dependent variable of a dataset is dichotomous (binary).

1- Introduction

2- Preliminary results

3- Existence and uniqueness theorems

4- Stability analysis for the logistic models

5- Numerical discussion

6- Conclusion

References

Abstract

In this article, we study different types of fractional-order logistic models in the frame of Caputo type fractional operators generated by conformable derivatives (Caputo CFDs). We present the existence and uniqueness theorems to solutions of these models and discuss their stability by perturbing the equilibrium points. Finally, we furniture our results by illustrative numerical examples for the studied models.

Introduction

Fractional calculus is a branch of mathematical analysis that takes into consideration the integration and differentiation of real or complex order. In spite of the fact that this kind of calculus is old, it gained popularity and started to catch the interest of scientists only in the last 20 or 30 years because important results were reported when fractional derivatives and integrals were applied to describe many real world phenomena [1–10]. A big virtue of the fractional calculus is that there are many different fractional derivatives or integrals. This virtue gives the opportunity to choose the most appropriate derivative or integral in order to describe complex systems of real world problems eligibly. Nevertheless, in order to have better mathematical models of real world problems, scientists started to disclose some new types of fractional integrals and consequently fractional derivatives using two main methods. The first method is the traditional method based on iterating to find the nth order integral and then replacing n by any number α. Hadamard, generalized fractional operators and the fractional operators generated from conformable derivatives, can be considered as examples of fractional operators obtained using this approach [11–17]. These operators usually have singular kernels. The second method is subject to the limiting process and using some properties of the Dirac-Delta functions.

1- Introduction

2- Topological indices

3- Models

4- Conclusions

References

INTRODUCTION

Chemical graph theory applies this branch of mathematics to model molecules in order to study their various physical properties. A graph G = (V, E) consists of a set V of vertices (or nodes) and a set E of unordered pairs of distinct elements of V, which are the edges. In chemistry, the atoms of a molecule are represented by the vertices and the chemical bonds are represented by the edges. The resulting graph is often called a chemical graph. When studying alkanes which have the chemical formula CnH2n+2, the hydrogen atoms are removed from the graph resulting in what is known as a hydrogen-depleted molecular graph or a carbon tree. Since each carbon has four bonds and each hydrogen has one bond, no information about the molecule is lost by removing the hydrogen atoms. The resulting graph is in fact easier to study since the geometric structure of the alkane is more apparent. For example, a rendering of 2,2,4-trimethylpentane is given in Fig. 1. The chemical graph of 2,2,4- trimethylpentane is given in Fig. 2. The vertex set of the graph in Fig. 2 is V = {a, b, c, d, e, f , g, h}, and the edge set of this graph is given by E = {ab, bc, cd, de, bf , bg, dh}. The degree of a vertex v is the number of edges attached to vertex v and is denoted deg(v). In a molecular compound, this is the number of bonds an atom has and is defined as the valency of an atom. In Fig. 2, deg(a)= deg(f)=deg(g)=deg(h)=deg(e)=1, deg(b)=4, deg(c)=2, and deg(d)=3. Given a graph G with vertices u, v ∈ V(G), we define a u–v path as a sequence of edges from G of the form uv1, v1v2, v2v3, … , vnv where each vertex vi ∈ V(G) for 1 ≤ i ≤ n is distinct. The length of the given u–v path is n, the number of edges in the path. The shortest path from vertex u to v is the path for which n, the number of edges in the path, is minimal. A path from vertex g to h in Fig. 2 is given by gb, bc, cd, dh and has length four. This is also the shortest path from g to h since this is the only g–h path. Given that 2,2,4-trimethylpentane is an acyclic hydrocarbon, its chemical graph contains no cycles.

8-1- Introduction

8-2- Nash Equilibrium for Perov Contractions

8-3- Nash Equilibrium for Systems of Variational Inequalities

8-4- Nash Equilibrium of Nonvariational Systems

8-5- Applications to Periodic Problems

NASH EQUILIBRIUM OF NONVARIATIONAL SYSTEMS

Many systems arising in mathematical modeling require positive solutions as acceptable states of the investigated real processes. Mathematically, finding positive solutions means to work in the positive cone of the space of all possible states. However, a cone is an unbounded set and, in many cases, nonlinear problems have several positive solutions. That is why it is important to localize solutions in bounded subsets of a cone. This problem becomes even more interesting in the case of nonlinear systems that do not have a variational structure, but each of its component equations has, namely there exist real “energy” functionals E1 and E2 such that the system is equivalent to the equations E11 (u,v) = 0 E22 (u,v) = 0. We recall that E11 (u,v) is the partial derivative of E1 with respect to u, and E22 (u,v) is the partial derivative of E2 with respect to v.

Introduction

Literature review

Methodology

Case study: information security RA for corrugated cardboard sector

Conclusion

References

Abstract

Risk analysis (RA) contains several methodologies that object to ensure the protection and safety of occupational stakeholders. Multi attribute decision-making (MADM) is one of the most important RA methodologies that is applied to several areas from manufacturing to information technology.With the widespread use of computer networks and the Internet, information security has become very important. Information security is vital as institutions are mostly dependent on information, technology, and systems. This requires a comprehensive and effective implementation of information security RA. Analytic hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS) are commonly used MADM methods and recently used for RA. In this study, a new RA methodology is proposed based on AHP–TOPSIS integration extended with Pythagorean fuzzy sets. AHP strengthened by interval-valued Pythagorean fuzzy numbers is used to weigh risk parameters with expert judgment. Then, TOPSIS with Pythagorean fuzzy numbers is used to prioritize previously identified risks. A comparison of the proposed approach with three approaches (classical RA method, Pythagorean fuzzy VIKOR and Pythagorean fuzzy MOORA) is also provided. To illustrate the feasibility and practicality of the proposed approach, a case study for information security RA in corrugated cardboard sector is executed.

Introduction

Information is a tool that people use to communicate among themselves from the moment they start living together. The nature and type of information technology have changed dramatically over the past decade. Simple and single batch applications are transformed into distributed computing environments including multitasking real-time control, and distributed processing. It is at least as important as the information itself to determine that information is valuable or worthless, or to measure the value carried by it. The most general definition of information security is that our own information is not passed on to anyone else. It is a combination of three main elements called “privacy”, “integrity”, and “accessibility”. Information is protected from unauthorized access which is called privacy. Integrity defined as information that is not altered by unauthorized persons. Information is available when authorized people are needed. Information is reachable and available when authorized people are needed which is called accessibility. If any of these three basic security elements are damaged, a security weakness occurs. Information security RA is essential for any corporate organizational system. It is essential to ensure that controls and expenditures are in full compliance with the risks that the organization is experiencing or experienced before. Organizations’ heavy dependence on information systems necessitates managing risks related to them [1]. One of the most important aspects of information security is technical measures. Given better access control policy models, better tools for system assessment and assurance should be resolved, including better ways to detect cryptographic formal evidence, protocols, approved firewalls, intrusions and malicious codes [2].

1- Introduction

2- Local existence of classical solutions

3- Global boundedness

References

Introduction

Cancer invasion is associated with the degradation of the extracellular matrix (ECM), which is degraded by matrix degrading enzymes (MDEs) such as the urokinase-type plasminogen activator (uPA) secreted by cancer cells. The degradation provides space for cancer cells to proliferate and invade into the surrounding tissue. In addition to random diffusion, the migration of cancer cells is biased towards a gradient of the diffusible MDEs by chemotaxis which as a significant mechanism of directional migration of cells is the movement of cells in response to concentration gradients of a chemical signal emitted by the cells themselves in many biological process, and towards a gradient of the nondiffusible ECM through detecting the ECM material vitronectin VN adhered therein by haptotaxis (see [1]). In addition, the cancer cells undergo birth and death in a logistic manner, competing for space with the ECM. The MDE is assumed to be produced by cancer cells, and to diffuse and decay, whereas the ECM is assumed to be degraded up contact with MDE. The combination of these two cell migration mechanisms forms the core of the modeling approach pursued by Chaplain and Lolas to describe cancer cell invasion into surrounding healthy tissue. Except for the model [2], a variety of mathematical models describing the different stages of cancer invasion and metastasis have been developed before (see [1–10]).

Abstract

In order to perform medical surgeries, hospitals keep large inventories of surgical instruments. These instruments need to be sterilized before each surgery. Typically the instruments are kept in trays. Multiple trays may be required for a single surgery, while a single tray may contain instruments that are required for multiple surgical procedures. The tray optimization problem (TOP) consists of three main decisions: (i) the assignment of instruments to trays, (ii) the assignment of trays to surgeries, and (iii) the number of trays to keep in inventory. The TOP decisions have to be made such that total operating costs are minimized and such that for every surgery sufficient instruments are available. This paper presents and evaluates several exact and heuristic solution methods for the TOP. We compare solution methods on computation time and solution quality. Moreover, we conduct simulations to evaluate the performance of the solutions in the long run. The novel methods that are provided are the first methods that are capable of solving instances of realistic size. The most promising method consists of a highly scalable advanced greedy algorithm. Our results indicate that the outcomes of this method are, on average, very close to the outcomes of the other methods investigated, while it may be easily applied by (large) hospitals. The findings are robust with respect to fluctuations in long term OR schedules.

Introduction

Throughout the developed world, health care costs have shown a tremendous increase over the last decades. Since 1970 the inflation adjusted government spending on health care has risen by nearly 5 percent per year (Hagist and Kotlikoff [2005]), currently averaging 9 percent of gross domestic product (OECD [2014]). At the same time, patient waiting lists have become longer and are nowadays a major problem (Worthington [1991]). Managerial efforts to control the steeply rising health care costs and long patient waiting lists have not only placed attention on main health care processes, but have focused especially on efficiency management of various, priorly neglected, side processes. One such side process which has received recent attention is hospital sterilization logistics.

The main goal of the study was to analyze vibration of pumping aggregate. There are fourth position which could be very harmful for the total working operation of the pumping aggregate. The pumping aggregated should have smooth continuous operations without any mistake. Vibration could affect different parts or segments of the pumping aggregate and therefore it is need to analyze the vibrating. Analyzing of the vibration could be highly nonlinear task since many different parameters are involved in the model. To avoid the analytical model in this article soft computing approach was used since the soft computing approach does not require internal knowledge of the vibration model. For the soft computing model there is enough to collect the input output data pairs through experimental measurement procedure. Based on the input/output data pairs the model will be created. The approach should rank the influence of the measuring positions vibration on the pumping aggregate. Finally three different soft computing methods were compared and results were reported.

Introduction

The development of non-invasive methods of monitoring of the machine conditions are important in order to predict maintenance of the machines. There are various indicators for machine condition; however, the method of use vibration monitoring for determination of machine operating conditions was proved the most important. Vibration monitoring is one among many methods of technical diagnostics which has been continuously monitoring a technical state of a device by observing the level of a mechanical oscillation in a real time [1]. The mechanical oscillation is the manifestation of a device during its operation [2]. Certain parts become vibration exciters, others, depending on excitation, react specifically [3]. Therefore the vibration monitoring is one of the most important methods used in technical diagnostics for identifying a technical state [4]. With the use of vibration diagnostics we are able to detect an incipient failure, locate the place of an incipient failure and predict the length of time during which a device is going to work before a failure occurs or a preventive action is performed [5-8]. For example in article [9] the vibration behavior of microscale beams and plates was studied based on micropolar theory (MPT). Presented in paperr [10, 11] was a size-dependent analysis of the surface stress and nonlocal influences on the free vibration characteristics of rectangular and circular nanoplates. Maintenance and repair of pumping units requires a lot of high material costs and time. Therefore, control of vibration and parametric characteristics of pumping units in real time allows to identify defect of pumping units at an early stage [12]. The condition monitoring of a rotating machine is efficient, but often it is difficult and labour intensive task for maintenance crew to troubleshoot the machine and vibration analysis is a method used for condition monitoring of the machine [13]. Measured signals are usually fed into filters or signal decomposers to extract useful features to assist making identification in state monitoring or fault diagnosis. But what is routinely ignored is that an experienced expert can realize what is happening just by watching the signals presented on the oscilloscope even without the analyzing report [14]. Vibration-based condition monitoring is an important approach to ensure the reliability of industrial machines [15].

In this paper we present the extraproximal method for computing the Stackelberg/Nash equilibria in a class of ergodic controlled finite Markov chains games. We exemplify the original game formulation in terms of coupled nonlinear programming problems implementing the Lagrange principle. In addition, Tikhonov’s regularization method is employed to ensure the convergence of the cost-functions to a Stackelberg/Nash equilibrium point. Then, we transform the problem into a system of equations in the proximal format. We present a two-step iterated procedure for solving the extraproximal method: (a) the first step (the extra-proximal step) consists of a “prediction” which calculates the preliminary position approximation to the equilibrium point, and (b) the second step is designed to find a “basic adjustment” of the previous prediction. The procedure is called the  extraproximal method” because of the use of an extrapolation. Each equation in this system is an optimization problem for which the necessary and efficient condition for a minimum is solved using a quadratic programming method. This solution approach provides a drastically quicker rate of convergence to the equilibrium point. We present the analysis of the convergence as well the rate of convergence of the method, which is one of the main results of this paper. Additionally, the extraproximal method is developed in terms of Markov chains for Stackelberg games. Our goal is to analyze completely a three-player Stackelberg game consisting of a leader and two followers. We provide all the details needed to implement the extraproximal method in an efficient and numerically stable way. For instance, a numerical technique is presented for computing the first step parameter (λ) of the extraproximal method. The usefulness of the approach is successfully demonstrated by a numerical example related to a pricing oligopoly model for airlines companies.

Introduction
The extraproximal approach (Antipin, 2005) can be considered a natural extension of the proximal and gradient optimization methods used for solving the more difficult problems of finding an equilibrium point in game theory. The simplest and most natural approach to implement the proximal method is to use a simple iteration by omitting the prediction step. However, as shown by Antipin (2005), this approach fails. A more versatile procedure   would be to perform an “ex- ∗Corresponding author traproximal step” i.e., gathering certain information on the future development of the process. Using this information, it is possible to execute the “principle step” based on the preliminary position. It seems natural to call this procedure an “extraproximal method” (because of the use of extrapolation (Antipin, 2005)). Along with the extra-gradient technique (Poznyak, 2009), the extraproximal method can be considered a natural extension of the proximal and gradient optimization approaches to resolve more complicated game problems, such as the Stackelberg–Nash game.

Previous works on adding hedges to logical systems of mathematical fuzzy logic (MFL) [9] include those by Hájek [18], Vychodil [37], and Esteva et al. [14]. In MFL, hedges are called truth-stressing or truth-depressing depending on whether they strengthen or weaken the meaning of the proposition. The intuitive interpretation of a truth-stressing (resp., truth-depressing) hedge on a chain of truth values is a subdiagonal (resp., superdiagonal) non-decreasing function preserving 0 and 1. Such functions are called hedge functions. Hájek [18] introduces an axiomatization of a truth-stressing hedge vt as an expansion of Basic Logic (BL) [17], and the resulting logic is called BLvt . Vychodil [37] extends BLvt to a logic BLvt,st with a truth-depressing hedge st dual to vt. The logics are shown to be algebraizable and enjoy completeness w.r.t. the classes of their chains, but are not proved to enjoy standard completeness in general. Moreover, Hájek and Vychodil’s axiomatizations do not cover a large class of hedge functions [14]. Hence, Esteva et al. [14] propose weaker axiomatizations over any core fuzzy logic for a truth-stressing hedge or/and a truthdepressing one, which do not impose any more constraints on hedge functions, and the axiomatizations are proved to enjoy standard completeness. This work proposes two axiomatizations over any propositional core fuzzy logic for multiple truth-stressing and truth-depressing hedges, one for non-dual hedges and the other for dual ones. The axiomatizations not only cover a large class of hedge functions but also have all completeness properties of the underlying core fuzzy logic w.r.t. the class of their chains and distinguished subclasses of their chains, including standard completeness. The axiomatizations are also extended to the first-order level. Moreover, we show how to build linguistic fuzzy logics based on the axiomatizations and hedge algebras [32,33] for representing and reasoning with linguistically-expressed human knowledge. The remainder of the paper is organized as follows. Section 2 gives an overview of MFL, previous axiomatizations for hedges, linguistic truth domains and operations on them. Section 3 presents an axiomatization for multiple non-dual hedges while Section 4 provides an axiomatization for multiple dual ones. Section 5 shows how to build linguistic fuzzy logics. Section 6 extends the axiomatizations to the first-order level. Section 7 discuses related work. Finally, Section 8 concludes the paper.

Active scientific research on heat transfer from a rotating disk has been underway for several decades. The main results of these studies can be found in a number of papers and monographs [1-4]. This increased interest in the problem is due to the fact that the rotation of the flow initiated by the rotation of the mechanical system can be found in a variety of engineering applications and industrial installations. Systems containing rotating discs are used in gas-turbine and electrochemical plants, chemical reactors, in brake systems of transport, etc. For today, interest in this issue is not decreasing, as evidenced by the materials of many relevant scientific and technical conferences and articles. In a limited number of cases, the flow above the rotating surface can be viewed as a modified flow above a fixed surface, provided that the observer is on a rotating surface, that is, moves along with it. However, in most cases, the action of centrifugal forces or the nature of the spatial boundary layer causes the formation of significant additional flows, which can not be neglected. In this case, the description of the resultant flow can be very complex and, according to [5], “practically any rotating system releases new and unexpected flow characteristics in the case of a complete stability analysis or in experimental studies due to the widest variation of the hydrodynamic variables”. Due to the fact that in convective heat transfer in the rotating systems the strongest and most complicated way is connected with the flow, these two phenomena in the complex are also the subject of scientific and practical interest.

II. FORMULATION OF THE PROBLEM

Based on the description of the reactor unit for the installation of gas-phase epitaxy, cited in [2], in order to optimize the epitaxy process taking place in it, it is also necessary to investigate the processes of heat transfer and the motion of an external forced flow for the case of a rotating disc whose rotation plane, in general, is at an angle to the main flow.