Integral transforms such as the Elzaki, Aboodh, Sumudu, Natural, Sawi, and Shehu transforms have been developed to tackle some complex differential equations through the substantial advancements in the application of integral transforms. To seek the improvement of convergence, stability, and accuracy when solving differential equations, the Mamadu transform is developed and implemented. The Mamadu transform is an essential analytical tool built using a well-known kernel function that incorporates a polynomial and exponential-based terms. A major advantage of the Mamadu transform is the inclusion of a weight function to improve long-term behavior and singularities in differential equations. The method involves reducing a complex differential equation to an algebraic expression, making solution derivation and manipulation simpler. Also, the method offers a well-structured and efficient problem solving. Three examples are considered to illustrate the effectiveness and effectiveness of the Mamadu transform in the solution of different differential equations. Comparing with other traditional methods shows increased accuracy, faster convergence, and higher stability. The method is equally helpful in terms of computational efficiency and accuracy for the solution of fractional calculus, where other methods fail. Furthermore, the study reflects the relevance of Mamadu transform as a renowned analytical technique in applied sciences, particularly in fields such as mathematical modeling and engineering.

Random allocation models used in clinical trials can help reduce the between group bias which may occur when comparing multiple treatment groups to determine the preferred treatment method. Often however, this determination leaves researchers battling ethical issues of providing patients with unfavorable treatments. Many methods such as Play the Winner and Randomized Play the Winner Rule have historically been utilized to determine patient allocation, yet, these methods are prone to increased unfavorable assignments. Recently a new Bayesian Method using Decreasingly Informative Priors has been proposed but, this method can be time consuming when multiple individual Markov Chain Monte Carlo (MCMC) updating methods are required. We present an experimental design study via simulation using Dynamic Linear Models as an alternative method to increase allocation speed while also decreasing patient allocation samples necessary to identify the more favorable outcome and we illustrate the effectiveness of this new method. Furthermore, a sensitivity analysis is conducted on multiple parameters to demonstrate the method is robust. Finally, a Bayes Factor criterion is used to determine termination through decisive evidence in favor of the better treatment assignment.

The tourism sector is significantly and directly affected economically, due to the Covid-19 pandemic. This is a serious problem that requires immediate treatment. It is feared that the tourism industry will weaken further, as it is one of the foreign exchange earners with a large enough influence. The development of the tourism sector with the parameters of the current needs of the tourism society is, namely 4A, Amenity, Attractions, Accessibility, and Ancillary. The concept of the new normal destination to become a safe tourist destination during the Covid-19 pandemic was built by simulating a genetic algorithm that imitates the theory of evolution to get a solution that is close to optimal. Parameter 4A is achieved by adding 3M (Wearing masks, washing hands, and maintaining distance), and 3T (Testing, Tracing, and Treatment) as control of the spread of Covid-19. The main contribution of this research is to find a solution that is close to optimal with the parameters of the tourism society's needs through simulations of new normal destinations with 3M and 3T constraints to control the spread of Covid-19.

The aim of this paper is to establish some common fixed point results for two weakly subsequentially continuous and compatible of type (E) pairs of self mappings via implicit relation in modified intuitionistic fuzzy metric spaces, also we give an example to illustrate our results.

In this paper, we investigate how the Laplacian coefficients changed after some graph transformations. So, I express some results about Laplacian coefficients ordering of graphs, focusing our attention to the bicyclic graphs. Finally, as an application of these results, we discuss the ordering of graphs based on their Laplacian like energy.

Logistic mixtures, unlike normal mixtures, have not been studied for their topography. In this paper we discuss analogs of some of the multivariate normal mixture results for the multivariate logistic distribution. We focus on graphical techniques that are based on displaying the elevation of the density on the ridgeline. These techniques are quite elementary, and carry full information about the location and relative heights of the modes and saddle points. Moreover, we turn to a technique that names II-Plot which denotes that the first differentiation of the second component density ratios the difference between the first differentiations of the second component density and the first component density.

This paper's purpose is to provide a numerical scheme to approximate solutions of the nonlinear Klein-Gordon equation by applying the multiquadric quasi-interpolation scheme and the integrated radial basis function network scheme.Our scheme uses θ-weighted scheme for discretization of the temporal derivative and the integrated form of the multiquadric quasi-interpolation scheme for approximation of the unknown function and its spatial derivative.To confirm the accuracy and ability of the presented scheme, this scheme is applied on some test experiments and the numerical results have been compared with the exact solutions.Furthermore, it should be emphasized that with the presently available computing power, it has become possible to develop realistic mathematical models for the complicated problems in science and engineering.The mathematical description of various processes such as the nonlinear Klein-Gordon equation occurring in mathematical physics leads to a nonlinear partial differential equation.However, the mathematical model is only the first step towards the solution of the problem under consideration.The development of the well-documented, robust and reliable numerical technique for handing the mathematical model under consideration is the next step in the solution of the problem.This second step is at least as important as the first one.Therefore, the robustness, the efficiency and the reliability of the numerical technique have to be checked carefully.

Recently, a straightforward formula has been presented for evaluating singular integrals. Earlier extrapolation technique was used to guess the functional values at the singular points since most of the classical formulae contain both ends points. In this article a more accurate straightforward formula is presented for evaluating singular integrals. The new formula converges faster than others existing formulae. The Romberg integration scheme of this method also converges faster.

We prove a new inversion formula for Laplace transform in form SiCoLL(S(x))=c S(x),c=const., where Si is the sine-transform , Co is the cosine-transform of Fourier for not negative x , and L is the Laplace transform on real axis for not negative x .

In this article second Navier - Stokes (NSE) exact transformation to the simpler equations is covered. This transformation is executed by classical methods of Mathematical Analysis. It is shown that 3-D NSE can be conversed to a traditional vector form which looks like 2-D Vorticity Transport Equations. Second result, as well as first one, is very important for the solution of Navier-Stokes existence and smoothness one of seven Millennium Prize Problems that were stated by the Clay Mathematics Institute. The proof of solution' existence of such equations is simpler than traditional NSE. New equations will simplify the solutions of many other problems of Applied Mathematics in engineering, aeronautics, etc.