In this paper, a study on a basic fractional order epidemic model of dengue transmission is carried out using the SIR-SI model, including the aquatic phase of the vector. Many mathematical models have been established in the literature to study the mechanism of dengue transmission (Esteva. 3 The objectives of this study are to formulate a fractional order dengue epidemic model and to study the stability of the disease-free equilibrium point.
All parameters are assumed to be positive as the system monitors human population dynamics. This is the case when the disease is eradicated without action being taken to eradicate the mosquito population. After following Matignon's stability condition, we evaluated the Jacobian matrix of the system (2) at the equilibrium point E1.
Figures 4a, 4b and 5a, 5b revealed that the solution of the susceptible human population in fractional order does not decrease. However, we noticed that the order α, gives a significant effect on the results of the stability of the system. The memory of the mosquito and the human population represented by the order of the differential equation has a significant effect on the period of the disease elimination.
In this study, we can conclude that smaller value of α, provides a better approximation to reduce the intensity of dengue transmission.
STABILITY ANALYSIS OF A ROTATING FLOW TOWARD A SHRINKING PERMEABLE SURFACE IN NANOFLUID
This liquid is formed by dispersing part of the nanoparticles in the base liquid, namely water. However, to this day there are still only a few studies regarding a stability analysis of the double solutions for the boundary layer flow and heat transfer. The idea and procedure to determine the stability of the solutions obtained has been put forward by Merkin (1985).
The effect of the included parameter is numerically analyzed and has been specifically designed for fluid flow and heat transfer characteristics. PROBLEM FORMULATION In this study, a uniform three-dimensional rotating boundary layer flow in a nanofluid past a shrinking plate at z0 is considered by considering the effect of suction on the surface. We must take into account that for a certain value of Pr and, the stability of the steady flow solution f0( ), h0( ) and 0( ) is identified by the smallest eigenvalues.
Based on the previous study by Harris et al. 2009), they suggest that the range of possible eigenvalues can be calculated by relaxing a boundary condition on F0( ), H0( ) or. Figures 1 (a) to (c) present the effect of nanoparticle volume fraction on the variation of skin friction coefficient of x and y components, f(0) and h(0) and local Nusselt number (0) with absorption parameter for Cu-water nanofluid when 0.001. It is found that the magnitude of the skin friction coefficients for both components increases. with an increase in the value of
Figures 3 and 4 show the effects of different nanoparticles and the suction velocity of the x and y components. As we have observed, the thickness of the boundary layer for the solution of the lower branch is always thicker than that of the solution of the upper branch. a-c) Suction effect. 28 From this study, the stability of dual solutions is identified using bvp4c function in MATLAB software.
This analysis is performed to know which of the upper or lower branch solutions is linearly stable, depending on the sign of the smallest eigenvalues obtained. In this paper, the effect of volume fraction, rotation and suction parameters of nanoparticles on the fluid flow and heat transfer analysis of the rotational flow along a shrinking surface in nanofluid is investigated. Increasing the rotation parameter gives rise to the size of the skin friction coefficients and the local Nusselt number.
COMPARISONS OF HEINZ OPERATOR MEANS WITH DIFFERENT PARAMETERS
In this article, we will denote the space of all bounded linear operators on the Hilbert space by If we follow the definition in the scalar case, the Heinz mean is the arithmetic mean of two weighted geometric means. Thus, such a definition can be raised to the level of operators through operator means.
Subsequently (Kittaneh et al., 2012), the weighted arithmetic operator mean and geometric mean are defined as follows:. If , we write and to denote the arithmetic operator mean value and geometric operator mean value, respectively. It is well known that the Heinz operator mean lies between the arithmetic operator mean and geometric operator mean, i.e.
36 In this paper, we are concerned with finding new ordering relations between the mean of the Heinz operator with different parameters using appropriate scalar inequalities and the monotonicity principle for bounded self-adjoint operators on Hilbert space (see e.g. Pečarić et al., 2005) : Let be self-adjoint with a spectrum and let and be continuous real. The main purpose of this section is to derive new comparisons of Heinz means with different parameters for scalars and operators. Thus, our result in Theorem 2.1 is a converse of inequalities in (2) and (3) under the given conditions.
Now, on the basis of the monotonicity principle and on the basis of the inequality (6), we obtain our first equation of the Heinz operator means. Below we establish a refinement of the second inequality in (4) for the Hilbert-Schmidt norm under given circumstances. 40 In what follows we turn to another mean that lies between the geometric mean and the arithmetic mean.
To establish a number of adjustments to Heinz inequalities, Kittaneh and Krnić (2013) considered. Finally, an operator version of the inequality (9) is obtained by applying the monotonicity principle in the same way as in the proof of Theorem 2.2.
The strategy of pursuer is defined as a function
- Show that pursuit is completed. Using (11) and (14), we obtain
We study the following control problem for the infinite system of differential equations (3): find an instant such that In this paper, a pursuit differential game problem described by an infinite system of 2-systems of 1st order differential equations has been studied in Hilbert space l2. We have solved a control problem to transfer the state of system (3) from the given initial state z0 to another given state z1 in finite time.
We also obtained sufficient conditions for the completion of the game, gave an equation for the guaranteed pursuit time, and constructed a strategy for the pursuer to complete the pursuit in game (2). A theoretical approach-avoidance problem for a linear system with integral constraints imposed on player control.
PERFORMANCE ANALYSIS OF FOUR-POINT EGAOR ITERATIVE METHOD APPLIED TO POISSON IMAGE BLENDING PROBLEM
4-EGAOR iterative method i. Select desired region from source
To verify the power of the proposed methods, three sets of images with different sizes are chosen. Each set of images consists of source and target images, taken from Public Domain Pictures.net, see Figure 4. The performance evaluation of SOR, AOR, and 4-EGAOR in terms of the number of iterations used is shown in Figure 5 and the values of ω and r used are optimal.
According to Figure 5 , the number of iterations used by 4-EGAOR is reduced compared to the iterative methods of SOR and AOR. It decreased approximately compared to the iterative numerical result of SOR for comparison in the iterative AOR method. Compared to the iterative SOR method, the assembly time of 4-EGAOR is reduced by approx., while compared to the iterative AOR method it is reduced by approx.
The images generated by the SOR method are used as a reference image and then compared to the images generated by the AOR and 4-EGAOR methods. In this study, pointwise and blockwise iterative methods are used to solve the Poisson image unmixing problem. From the obtained numerical results, 4-EGAOR performed best compared to the iterative methods SOR and AOR both in terms of number of iterations and assembly time.
Finally, the new blended images generated from the three proposed iterative methods showed excellent quality as evaluated using the SSIM index. Numerical assessment of the poisson image mixing problem using MSOR iteration via a five-point laplacian operator. Performance analysis of the explicit decoupled group iteration via a five-point rotated laplacian operator in solving the poisson image mixing problem.
Robot path planning using four-point explicit group via nine-point Laplacian (4EG9L) iterative method. Simulation of path planning using harmonic potential fields with the four-point EDGSOR method via the 9-point Laplacian. Using harmonic functions using a modified SOR (MSOR) method for robot path planning in an indoor structured environment.
ANOTHER PROOF OF WIENER'S SHORT SECRET EXPONENT
Theorem 2.2 (Legendre's Theorem) Suppose 𝑥 is written in its continued fraction
The integer 𝑘 and 𝑑 can be obtained from the convergent 𝑘 and 𝑑 can be obtained from the convergent of the continued fraction of 𝑁𝑒, if 𝑑 < √6√26 𝑁14. Thus, by making the secret value 𝑑 as subject and filling in the condition of Lemma 3.1, we get the following result. The result, as shown in Table 1, indicates that regarding the attack and finding the secret parameter 𝑑, our result significantly improves on the previous bound, extending Wiener's theorem by 16.7%.
Algorithm for factoring finding 𝑑 and 𝑘 based on Theorem 3.2
72 Let us compare the integers 𝑑 and 𝑘 with the upper bound of 𝑑 obtained by applying Wiener's Theorem and Nitaj's Theorem attacks to the same problem. Referring to Example 4.2, the attack presented in this example uses a much larger value of 𝑑 but our attack still finds such a secret integer 𝑑. Note that, our attack works with the maximum value 𝑑 less than for the corresponding 𝑁 in both examples.
Thus, it is in good agreement with our theoretical result, which is proved mathematically in Theorem 3.2 and as reported in Table 1. Note that Wiener's attack works efficiently on RSA with the condition that the secret exponent 𝑑 <13𝑁14, which has a use Diophantine's method called continued fractions. In this work, we present another proof using continued fraction method which shows a way to obtain the secret exponent 𝑑 efficiently, satisfying 𝑑 <12𝑁14.
Comparative analysis of three asymmetric encryption schemes based on the persistence of square roots Modulo 𝑁 = 𝑝2𝑞. 2016a) Analysis of the AA 𝛽 Cryptosystem.
