The **modified** Kawahara (mKawahara) equation is a cubic non-linear equation with a fifth-order derivative term. The quadratic nonlinear form of the equation is suggested by Kawahara [12] with its steady solutions. Such solutions may exist due to the sign of the dispersive term and these solutions can be in a oscillatory form because of the dominant fifth-ordered term. The mKawahara equation has implicit doubly periodic solutions and they can be determined by using the **method** of auxiliary equation[13, 14]. Some soliton and periodic solutions are derived by using a set of forecasting methods having some trigonometric and hyperbolic functions inside[15]. The mKawahara equation has also non-constant meromorphic solutions in explicit form[16]. The existence of traveling wave type solutions in hyperbolic or trigonometric forms are discussed by Al-Ali[17]. Tanh and exp-function methods are also capable to derive the exact solutions to the mKawahara equation[18]. So far, some methods belonging to different categories have been proposed for the exact solutions of both integer or fractional ordered PDEs [19, 20, 21, 22]. In ths study ,The main aim is to derive some exact solutions to the three-dimensional conformable time fractional KP and the conformable time fractional mKawahara equations. The solutions are obtained explicitly by using **modified** **Kudryashov** **method**. The existence of the chain rule and other required properties in the defi- nition of the conformable derivative enable some wave transformations to generate the solutions.

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In this paper, the modiﬁed **Kudryashov** **method** is proposed to solve fractional diﬀerential equations, and Jumarie’s modiﬁed Riemann-Liouville derivative is used to convert nonlinear partial fractional diﬀerential equation to nonlinear ordinary diﬀerential equations. The modiﬁed **Kudryashov** **method** is applied to compute an approximation to the solutions of the space-time fractional modiﬁed

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The exact solutions of some conformable time fractional PDEs are pre- sented explicitly. The **modified** **Kudryashov** **method** is applied to construct the solutions to the conformable time fractional Regularized Long Wave- Burgers (RLW-Burgers, potential Korteweg-de Vries (KdV) and clannish random walker’s parabolic (CRWP) equations. Initially, the predicted so- lution in the finite series of a rational form of an exponential function is substituted to the ODE generated from the conformable time fractional PDE by using wave transformation. The coefficients used in the finite series are determined by solving the algebraic system derived from the coefficients of the powers of the predicted solution.

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To obtain the best execution time for a particular benchmark, all four synchronization methods should be executed by specifying the **method** at runtime. A program might benefit if we vary the synchronization mode between different regions of code. To incorporate such dynamic synchronization, the synchronization **method** should be able to be varied at every session. This result in a speedup when compared to the best execution time obtained from executing the four methods on an individual basis. But such aggressive switching might incur some overhead. Sliding-window **method** overcomes this problem by maintaining a particular **method** for a number of sessions before changing it to another synchronization **method**.

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Finding the edges of street-level fisheye images is even harder than satellite images due to the high variations of intensities, objects and distortion. Figure 5.3 (first and second rows) shows some sample street-level images that Otsu’s **method** did not work well for them. Also Figure 5.3 (third row) shows our effort to improve the results of Otsu’s **method** by adding an offset to the Otsu’s threshold (like what we did for the satellite images). However, this is not practical, because to get the best result we had to set the offset for each of the images of a chain individually. More importantly, in some of these images (like the 1st and 2nd column) it is impossible to separate the roads from the rest of the image even by carefully setting the offset. The reason is that the intensity histogram of these images is not separable at all into two modes (foreground and background).

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multistage procedure, the sequential recursive method, the modified. recursive method, and the recursive method under the simple linear[r]

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of a simulation problem to an initial value problem is then described. Sections 5 and 6 respec- tively contain reviews of two well-known methods for solving initial value problems; namely, Euler’s **method** and the **modified** midpoint **method**. The use of Richardson’s extrapolation is discussed in each case with the aid of a simple numerical example. Linear representations of a non-linear economic model are set out in section 7, where the practicalities of applying each of the foregoing methods are assessed in some detail. In the eighth and final section a tentative agenda for future research is sketched.

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where C Z is the set of real continuous functions on Z Keywords: Closed x-Filter; Open and Closed C*D-Filter Bases; Basic Open and Closed C*D-Filters; Compactification; Stone-Čec[r]

The steps to compare the estimation methods for missing data begun by step one by the selection of one station to represent station with the missing value. Step two comprises a pace to remove 5% of data from selected stations. Step three used the remaining data and data from neighboring stations to estimate the missing values using M **method**, NR **method**, MNR **method**, and CCW **method** followed. Step four was the performances of each estimation **method** are compared using the correlation coefficient (R), the similarity index (S-index), the root mean squared error (RMSE) and mean absolute error (MAE). Finally, step two and four repeated for 10% and 15% missing values.

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voice, were recorded alternately on the right and left channels of the tape recorder.. Play- back volume is adjusted so that the reproduced sounds are not as loud as the original noise m[r]

We present cyclic models for systems with two renewable resources. In modelling, the interactions and the reciprocal influences between these two resources are taken into ac- count. Analysis of the models is carried out in weighted Holder spaces. A **method** for the solution of the balance system of equations is proposed. The equilibrium state of the system is found.

5. Recognition – The recognition engine will take data from either a newly captured subject via the feature extraction module, or a previously stored signature, and perform recognition based on a database of test subjects. The **modified** CPN model did not require training parameters because it is not an iterative **method** like back- propagation architecture which took a long time for learning. Rather, a minimum error value is specified initially and the weights are estimated based on the specified error value and this is what accounts for higher convergence rate of the model since one set of weights are estimated directly.

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so presented combined preconditioners, which are given by combinations of R with any upper preconditioner, and showed that the convergence rate of the combined meth- ods are better than those of the Gauss-Seidel **method** ap- plied with other upper preconditioners [7]. In [14], Niki et al. considered the preconditioner P SR = I S R .

processing of a wide range of materials, both living and fos- sil. It involves two main chemicals, kerosene and kitchen drain cleaner fluid, both of which are cheap, easy to obtain, and easy to discard afterwards. Kerosene, used here as a sub- stitute for naphtha in the Oda and Sato **method** (2013), is a familiar fuel oil for room heaters or hot water supply systems in Japan, while the kitchen drain cleaning fluid can be bought at a reasonable cost at supermarkets, drug stores, or do-it- yourself or daily grocery shops in Japan. Similar nonacidic products are also available in other countries. However, if acidic products are used the calcareous microfossils includ- ing coccoliths will be dissolved, so care must be taken when choosing the kitchen drain cleaner fluid.

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Next, the controlled solutions at times 0.2 ms, 1 ms and 2 ms using the MDY **method** are shown in Figure 6. Observe that the excitation wavefront is unable to be dampened out by the applied current, and the excitation wavefront continue to spread to the computational do- main. This phenomenon happens because the MDY me- thod failed to converge to the optimal solution during the optimization process.

Routing **method** accuracy and application depends on basic assumptions inherent in the **method**. Researchers have performed studies trying to determine which routing **method** is best suited to a certain routing situation. Strelkoff (1980) compared the kinematic model, diffusion model, and **modified** Puls **method** with the complete Saint Venant equations as a basis for comparison. Floodplains, simple channels, and downstream boundary conditions were considered in the study. He found that the diffusion model produced results most comparable to the Saint Venant equations. The other methods produce acceptable results under certain conditions, as described in the

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This paper proposes a **modified** synchronization approach to make the synchronization practicable in the situation when the direct signal is unsatisfactory, and the parameters of the transmitted signal are even unknown. Both the experiment results of imaging and BiInSAR results verified the effectiveness of the proposed approach.

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In this paper, the Black-Scholes equation is solved by using the Adomian’s decomposition **method** , **modified** Adomian’s decomposition **method** , variational iteration **method** , **modified** variational iteration **method**, ho- motopy perturbation **method**, **modified** homotopy perturbation **method** and homotopy analysis **method**. The existence and uniqueness of the solution and convergence of the proposed methods are proved in details. A numerical example is studied to demonstrate the accuracy of the presented methods.

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An alternative **method** is a test-centered **method** whereby the pass mark is based on item or station char- acteristics, such as the **modified** Angoff standard setting **method**. In the **modified** Angoff methods, judges reviewed each question after defining a borderline candi- date, and decided whether the borderline examinee will respond correctly [2, 6, 13, 14]. The main advantage of such a **method** is that the pass/fail standard can be reliably set before the OSCE is undertaken, which would be useful in the setting of CBME [2, 15, 16]. Furthermore, a modi- fied Angoff could potentially be used to set different pass marks for junior and senior residents, eliminating the need for two end of rotation OSCEs.

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I t namic problems in physics and other fields has been shown that many important dy- are usually characterized by nonlinear evolution equations which are often called governing equa- tions [3, 42, 36, 27]. To understand the physical mechanism of these problems one has to study the solutions to the associated governing equations. Searching for the exact solutions of the nonlin- ear physical models has been a major concern for both mathematicians and physicists since they can provide much physical information and more insight into the physical aspects of the problems and thus maybe lead to further applications. Re- cently, some mathematician have studied the nu- merical solution of the Degasperis-Procesi equa- tion by numerical **method** [28, 21, 12, 29, 32, 20].

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