3-dimensional Graph Research Articles

Analysis of Fractional Advection Equation with Improved Homotopy Analysis Method

The enhanced homotopy analysis method was employed to solve the nonlinear time-fractional advection equation, resulting in the derivation of a series of solutions. The objective of this study is to minimize the absolute error by identifying the ideal value for a certain parameter, indicated as h, by the utilization of the residual error (RE) function associated with that parameter. The 3-dimensional graphs illustrating the absolute discrepancies between the solutions obtained from the exact approach and the modified homotopy analysis method have been made using the MAPLE software. Hence, the proposed approach demonstrates efficacy and appropriateness in tackling fractional partial differential equations.

SEMI-DOMAIN SOLUTIONS TO THE FRACTAL (3+1)-DIMENSIONAL JIMBO–MIWA EQUATION

In this work, the variational direct method (VDM) based on the variational theory and Ritz-like method, combined with the fractal two-scale transformation, is employed to construct the semi-domain solutions of the (3+1)-dimensional fractal Jimbo–Miwa (JM) equation, which is derived by He’s fractal derivative. The applicability and effectiveness of the acquired solutions on the Cantor sets are presented through the numerical results in the form of 3-dimensional graphs. In addition, as a comparison, the exact solutions of the classic (3+1)-dimensional JM equation for [Formula: see text] are also illustrated. The obtained results in this work are expected to open new perspectives for the traveling wave theory.

DTester: Diversity-Driven Test Case Generation for Web Applications

Search-based Test Case Generation (TCG) for web applications suffers from unstable performance and suboptimal test suite problems due to diversity loss. However, previous diversity metrics mainly only focus on client-side models or server-side code, which are prone to low robustness and poor generalization in practical applications. We propose a diversity-driven TCG method DTester, which can maximize behavior exploration and minimize the test suite size while covering more server-side vulnerable paths. Three diversity metrics (i.e. phenotypic coupling, intent coupling and competitiveness) are proposed to measure the underlying relationship between test cases from user behavior, code logic and test execution history. Moreover, a 3-dimensional weight graph is designed to model association among metrics, which provides fine-grained guidance for the genetic algorithm to generate diverse test cases from the client-side behavior model. Our empirical evaluation on five web applications shows that DTester can efficiently and robustly generate better test suites than the state-of-the-art TCG method. The maximum improvement is [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in efficiency, test suite size, diversity and robustness.

Cyanide effluent treatment by electrocoagulation using airlift reactor: Modeling and optimization by response surface methodology

The extraction processes of gold, silver, and various metals from ores consume 13% of 1.1 million metric tons of hydrogen cyanide produced worldwide annually. Therefore, developing efficient processes to treat the issuing effluents before releasing them into the environment is imperative. In this context, the present study aims to evaluate the effect of three factors: inter-electrodes distance (d), current density (J) and electrolysis time (t) on the cyanide removal efficiency by a combination between Electro-Coagulation process and Internal Loop Airlift Reactor. Employing an airlift reactor enables an effective dispersion of the coagulant without the need for additional stirring. The optimization of the process was conducted using Response Surface Methodology in conjunction with Box–Behnken Design. The statistical analysis results reveal that electrolysis time(t)and current density (J) have significant effects on reactor performance to reduce cyanide with a confidence level of 99%, and 97.5%, respectively. The multiple regression analysis method demonstrates the model's overall predictability as the coefficient of determination was 98 % for the cyanide removal efficiency. The investigation inside the RSM 2 and 3-dimensional graphs allowed us to define the optimal domains of the variables to reduce cyanide. At a current density of 68 A.m−2 and an inter-electrodes distance of 13mm during 57.5min of electrolysis time, 98.27% of cyanide removal is achieved. The knowledge obtained through this study using the airlift reactor operating in batch mode and the EC process for the treatment of cyanide effluent confirms EC's ability to successfully remove cyanide and might be useful for the transposition from batch to continuous mode.

Laplace Homotopy Perturbation Method (Lhpm) For Solving Systems Of N-Dimensional Non-Linear Partial Differential Equation

In this research, we proposed coupling the Laplace transform method and the homotopy Perturbation Method (LHPM). We employed the fusion of the Laplace method to make up for the shortcomings of other semi-analytical approaches like the homotopy perturbation method, variation iteration method, and the Adomian decomposition method. We aim to obtain an approximate and semi-analytic solution of the n-dimensional system of nonlinear partial differential equations. N-dimensional partial differential equations with nonlinear terms are known as nonlinear partial differential equations. They have been used to solve mathematical problems like the Poincaré conjecture and the Calabi-Yau conjecture and describe physical systems, from gravity to fluid dynamics. Therefore, we proffer a semi-analytic solution in the form of a Taylor multivariate series of displacements x, y, and time t using the proposed method. A side-by-side comparison was carried out to compare the exact solution with the new solution using 3-dimensional graphs, and thus the graph analysis followed. Results show excellent agreement, and the emergence of this method as a viable alternative demonstrates its viability by requiring fewer computations and being much easier and more convenient than others, making it suitable for widespread use in engineering as well.

Jaulent–Miodek evolution equation: Analytical methods and various solutions

In this study, the m+1G′-expansion technique and the extended rational sine–cosine approach are applied to investigate the (2+1)-dimensional integrodifferential equation, namely the Jaulent–Miodek evolution equation (JMEE). Via these powerful approaches, some wave solutions to the JMEE evolution equation are successfully constructed. Using suitable values of the parameters, we plot the 2- and 3-dimensional graphs of the reported solutions. The two utilized approaches are powerful and efficient mathematical tools that secure important wave solutions. The reported solutions in this study may be used in explaining the physical features of various nonlinear physical models.

Multiple lump solutions and their interactions for an integrable nonlinear dispersionless PDE in vector fields

In this article, lump solutions, lump with I-kink, lump with II- kink, periodic, multiwaves, rogue waves and several other interactions such as lump interaction with II-kink, interaction between lump, lump with I-kink and periodic, interaction between lump, lump with II-kink and periodic are derived for Pavlov equation by using appropriate transformations. Additionally, we also present 3-dimensional, 2-dimensional and contour graphs for our solutions.

Modification in Two-Connected Graph with Gallai’s Property in 2-Dimensional and 3-Dimensional Graph Containing 19 Vertices

The graph theory plays an important role in the network analysis, social networking as well as in many engineering fields such as electrical circuits, artificial intelligence, architecture, making the design or pattern of roads, buildings, shopping mall and etc. Due to this wide range application human enjoying her life with peacefully, Graph theory creates a way for human being to connect among themselves by social network. All above applications based on graph or molecule which may be the planer, non-planer and Peterson graph or etc. Peterson graph is the most important and reasonable example of Hypo-Hamiltonian graph. In the earlier, it was found as a hypo-traceable graph (graph which has not Hamiltonian graph. Naeem et al has worked on “A Two-Connected Graph with Gallai’s Property” In his research paper he has applied the property and has found the longest path and cycle in the graph. In this research paper we will develop the 3-dimensional graph of computational molecule contains 19 vertices and will split it into three different planes (xy, xz and yz-plane), and will find the longest path, longest cycle the molecule. The designed graphs can be useful in various fields of science and technology including computational geometry, networking, theoretical computer science and circuit designing.

Optical solitons to the Perturbed Gerdjikov-Ivanov equation with quantic nonlinearity

In this article, we examine the Perturbed Gerdjikov-Ivanov equation by using the Jacobi elliptic function expansion method. This results in obtaining distinct solutions including dark, bright, singular solitons, periodic waves, singular periodic waves, and Jacobi elliptic function solutions. The 2- and 3-dimensional graphs of the reported solutions are presented. The reported results may be useful in explaining the physical features of the studied equation.

Dynamics Investigation and Solitons Formation for (2+1) -Dimensional Zoomeron Equation and Foam Drainage Equation

The prime goal of this study is to investigate novel solutions of two well-known nonlinear models namely the (2+1)-dimensional Zoomeron equation and the foam drainage equation by utilizing a powerful technique; the extended left(frac{G'}{G^{2}}right)-expansion method. Using this methodology, the hyperbolic function solutions, the trigonometric function solutions and the rational function solutions are constructed. Abundant soliton solutions are retrieved from the obtained results. The dynamical structures of the solutions are illustrated graphically through 3-dimensional graphs and the corresponding contour plots. The reported results depict the effectiveness and capability of the extended left(frac{G'}{G^{2}}right)-expansion method for handling different nonlinear partial differential equations.

Embedding Grid Graphs on Surfaces

In this paper, we analyze embeddings of grid graphs on orientable surfaces. We determine the genus of a large class of k-dimensional grid graphs and effective two-sided bounds for the genus of any 3-dimensional grid graph, both in terms of a grid graph's combinatorics. As an application, we provide a complete classification of planar and toroidal grid graphs. Our work requires a variety of combinatorial arguments to determine effective lower bounds on the genus of a grid graph, along with explicitly constructing embeddings of grid graphs on surfaces to determine effective upper bounds on their genera.

A variety of exact optical soliton solutions to the generalized (2+1)-dimensional dynamical conformable fractional Schrödinger model

In this work, our main idea is to retrieve a variety of exact optical solitons of the generalized (2+1)-dimensional nonlinear conformable fractional Schrödinger system by employing three novel integration norms. The constructed optical solitons can be divided as dark, singular, combo dark-singular, periodic, mixed periodic, and plane wave solutions. In addition, by selecting different parametric values, the physical representation of some achieved solutions is plotted in 3-dimensional, 2-dimensional, and contour graphs. Computation packages are used to verify all of the secured results by putting them back into the original model. The findings demonstrate that the examined system theoretically contains a large number of optical solitons. The constructed results rendering that the consider methods in this article are effective, concise, straightforward, efficient, and they can be used to handle some more nonlinear partial differential equations in the applied sciences. The achieved outcomes in this article may be valuable in clarifying the true meaning of numerous nonlinear advancement circumstances that develop in various domains of nonlinear sciences. Also, these fresh solutions have many applications in physics and other branches of physical sciences.

Thermal characteristics of longitudinal fin with Fourier and non-Fourier heat transfer by Fourier sine transforms

The quest for high-performance of heat transfer components on the basis of accommodating shapes, smaller weights, lower costs and little volume has significantly diverted the industries for the enhancement of heat dissipation with variable thermal properties of fins. This manuscript proposes the fractional modeling of Fourier and non-Fourier heat transfer of longitudinal fin via non-singular fractional approach. The configuration of longitudinal fin in terms of one dimension is developed for the mathematical model of parabolic and hyperbolic heat transfer equations. By considering the Fourier and non-Fourier heat transfer from longitudinal fin, the mathematical techniques of Fourier sine and Laplace transforms have been invoked. An analytic approach is tackled for handling the governing equation through special functions for the fractionalized parabolic and hyperbolic heat transfer equations in longitudinal fin. For the sake of comparative analysis of parabolic verses hyperbolic heat conduction of fin temperature, we depicted the distinct graphical illustrations; for instance, 2-dimensional graph, bar chart, contour graphs, heat graph, 3-dimensional graphs and column graphs on for the variants of different rheological impacts of longitudinal fin.

Dynamical behaviour of shallow water waves and solitary wave solutions of the Dullin-Gottwald-Holm dynamical system

In this article, we recover a variety of new families of shallow water wave and solitary wave solutions to the (1+1)-dimensional Dullin “Gottwald” Holm (DGH) system by employing new extended direct algebraic method (NEDAM). The derived results are obtained in diverse hyperbolic and periodic function forms. The attained solutions are new addition in the study of solitary wave and shallow water wave theory. In addition, 3-dimensional, 2-dimensional, and contour graphs of secured results are plotted in order to observe their dynamics with the choices of involved parameters. On the basis of achieved outcomes, we may claim that the proposed computational method is direct, dynamics, well organized, and will be useful for solving the more complicated nonlinear problems in diverse areas together with symbolic computations.

Two-wave, breather wave solutions and stability analysis to the (2 + 1)-dimensional Ito equation

The current study employs the novel Hirota bilinear scheme to investigate the nonlinear model. Thus, we acquire some two-wave and breather wave solutions to the governing equation. Breathers are pulsating localized structures that have been used to mimic extreme waves in a variety of nonlinear dispersive media with a narrow banded starting process. Several recent investigations, on the other hand, imply that breathers can survive in more complex habitats, such as random seas, despite the attributed physical restrictions. The authenticity and genuineness of all the acquired solutions agreed with the original equation. In order to shed more light on these novel solutions, we plot the 3-dimensional and contour graphs to the reported solutions with some suitable values. The governing model is also stable because of the idea of linear stability. The study’s findings may help explain the physics behind some of the challenges facing ocean engineers.

Combined effect of mineralogical and chemical parameters on swelling behaviour of expansive soils

Microlevel properties such as mineralogical and chemical compositions greatly control the macro behaviour of expansive soils. In this paper, the combined effect of mineral (i.e. montmorillonite, MMC) and chemical contents (i.e. Ca and Na in their total (T), leachable (L) and exchangeable form (CEC)) on swelling behaviour is investigated in a comprehensive way. Several 3-dimensional (3D) graphs correlating MMC and Ca/Na ratio, together, with swelling property (swelling potential, Sa, and swelling pressure, Sp) are developed. 3D plots, in general, portrayed a non-linear relationship of Sa and Sp with MMC and Ca/Na ratio, together. It is hypothesized that swelling initially is triggered by chemical parameters due to their quick and rapid ionization capability, but the overall swelling phenomenon is largely controlled by MMC. It is importantly found that expansive soils are dominant with divalent Ca++ ions up to MMC of 67% and beyond this percentage, monovalent Na+ ions are prevalent. From the interpretation of results, the maximum Sa of 18% and Sp of 93 kPa is measured at MMC of 43%, (Ca/Na)T of 10–14 and (Ca/Na)L of 2–7. It is concluded from study that total CEC + MMC for determining Sa and (Ca/Na)T + MMC for determining Sp are superior parameters to be considered. The findings of the study also excellently endorsed the results of Foster32, who stated that ionization of Na or Ca depends on the constituent mineral contents. The findings presented herein are unique, interesting and bear very practical significance, as no earlier research work reported such findings by accounting for chemical and mineralogical parameters impact, in tandem, on swelling properties.

DMatrix: Toward fast and accurate queries in graph stream

The graph stream has recently arisen in many interactive scenarios. Characterizing with large volume and high dynamic, graph streams are known to be difficult for high-speed summary and analysis, especially provided with limited resource availability. Existing solutions mainly use sketch-based methods to estimate the weight of items (e.g., Count-Min Sketch) and preserve the underlying graph structure information (e.g., TCM). Unfortunately, these solutions neither support complex graph-based queries nor achieve efficient real-time queries. In view of these limitations, we design DMatrix, a novel 3-dimensional graph sketch to facilitate fast and accurate queries in graph stream. Both structural query and weight-based estimation are supported with DMatrix. Through the integration of representative key reservation and majority voting, DMatrix can effectively narrow the error bounds of queries with real-time response efficiency. Both theoretical analysis and experimental results confirm that our solution is superior in accuracy and efficiency comparing with the state-of-the-art.

The influence of the differential conformable operators through modern exact solutions of the double Schrödinger-Boussinesq system

This paper discusses the influence of newly differential conformable operators (DCOs) on the behavior of the nonlinear evolutionary systems through their exact solutions. For this objective, we consider the double Schrödinger-Boussinesq system under the impact of the DCOs, which is an important model for explaining the interactive features of the short and moderately long waves in plasma and laser mediums. Modern and general exact solutions are extracted via the Kudryashov method and the advantages of the DCOs. These solutions are nonlinear wave solutions, which are expressed in solitary and periodic forms To better accommodate the impact of the DCOs on the behavior of the presented solutions, some physical demonstrations under appropriate values for the physical factors are given with 3-dimensional (3D), contour, and 2-dimensional (2D) illustrative graphs. Based on the recent literature, disclosing the influence of the DOCs on the nonlinear behavior of the double Schrödinger-Boussinesq system is a modern contribution and generalizes plentiful past outcomes.

Graphic Representation of a Dimensional Expansion of Triangular Fuzzy Number

We calculate Zadeh’s max-min composition operators for two 3-dimensional triangular fuzzy numbers. We prove that if the 3-dimensional result is limited to 2 dimensions, it is the same as the 2-dimensional result, which is shown as a graph. Since a 3-dimensional graph cannot be drawn, the value of the membership function is expressed with color density. We cut a 3-dimensional triangular fuzzy number by a perpendicular plane passing a vertex, and consider the cut plane as a domain. The value of the membership function for each point on the cut plane is also expressed with color density. The graph expressing the value of the membership function, defined in the plane as a 3-dimensional graph using the z -axis value instead of expressing with color density, is consistent with the results in the 2-dimensional case.

PROGRAM MATLAB UNTUK MEDIA ALAT PENGANALISA PERCOBAAN FISIKA BAGI MAHASISWA STMIK BINA PATRIA

The Matlab application program is often used as a data processing tool as well as tables, 2 or 3 dimensional graphs.
 Practicum activities for Physics subjects in general, the results of physics experiments are written directly into the experimental report. In practicum activities, the campus tries to make or design a Matlab application program for practicum activities. The results are processed using a computer application program, before being recorded in the report.
 The Matlab application program is often used as a tool for processing data and tables, 2 and 3-dimensional graphs.
 Students are given experimental data on Physics about this Matlab program, then analyzed and presented in graphical form and others.
 The result was that after being given additional lessons in the Matlab program, students processed the results of the physics experiment, and found out if there were experimental data that needed to be improved. Equipped with a tutor textbook.
 
 
 Keywords: Matlab, Physics Experiment, 2D 3D graphics.