Volumen 6 (2021): Heft 1 (January 2021)

Various order of implicit method has been formulated for solving initial value problems having an initial singular point. The method provides better result than those obtained by used implicit formulae developed based on Euler and Runge-Kutta methods. Romberg scheme has been used for obtaining more accurate result.

In this study, we present some new results for the time fractional mixed boundary value problems. We consider a generalization of the Heat - conduction problem in two dimensions that arises during the manufacturing of p - n junctions. Constructive examples are also provided throughout the paper. The main purpose of this article is to present mathematical results that are useful to researchers in a variety of fields.

Emerging as a new field, quantum computation has reinvented the fundamentals of Computer Science and knowledge theory in a manner consistent with quantum physics. The fact that quantum computation has superior features and new events than classical computation provides benefits in proving mathematical theories. With advances in technology, the nonlinear partial differential equations are used in almost every area, and many difficulties have been overcome by the solutions of these equations. In particular, the complex solutions of KdV and Burgers equations have been shown to be used in modeling a simple turbulence flow. In this study, Burger-like equation with complex solutions is defined in Hilbert space and solved with an example. In addition, these solutions were analyzed. Thanks to the Quantum Burgers-Like equation, the nonlinear differential equation is solved by linearizing. The pattern changes of time made the result linear. This means that the Quantum Burgers-Like equation can be used to smoothen the sonic processing.

In this manuscript, the application of the extended sinh-Gordon equation expansion method to the Davey-Stewartson equation and the (2+1)-dimensional nonlinear complex coupled Maccari system is presented. The Davey-Stewartson equation arises as a result of multiple-scale analysis of modulated nonlinear surface gravity waves propagating over a horizontal seabed and the (2+1)-dimensional nonlinear complex coupled Maccari equation describes the motion of the isolated waves, localized in a small part of space, in many fields such as hydrodynamic, plasma physics, nonlinear optics. We successfully construct some soliton, singular soliton and singular periodic wave solutions to these two nonlinear complex models. The 2D, 3D and contour graphs to some of the obtained solutions are presented.

Tomb murals are the special kind of murals that are buried underground. Due to the narrow exit of the tomb passage, the tomb murals were excavated by dividing the whole mural into blocks, which made lots of information missing between the blocks. The digital restoration technology Image inpainting uses the edge information around the missing parts to spread the information inside of the defect area and fills the information from the outside to the inside. But it is not suitable for filling the missing parts between the tomb mural blocks. Because these parts are large for exemplar-based inpainting which may make texture dislocation and for PDE which may make cartoon blur. It is a need to generate the information outwards to complete the information. The generative adversarial network uses deep learning training by the murals remains to generate the information from inside to outside, but the typical GAN doesn‘t have a good nonlinear feature. This paper provided a generating technology based on the deep convolution generative adversarial network to rebuild the missing information between the tomb mural blocks. It built the training data set of the simulation platform with Keras and designed a whole mural generation scheme based on DCGAN. In order to get better generated results to avoid the bad artifacts; it adds the nonlinear layers by choosing 13 layers convolution and 2 deconvolution layers of the generator and contained 5 layers convolution discriminator; it designed a new phased nonlinear loss function by using Pycharm pretreatment for Numpy array file data sets; finally, it completed the generate tomb mural information to obtain the good simulation effect.

With the rapid development of extensive urbanisation in the pursuit of refined quality, the management and control of architectural features in small towns have become more and more prominent, especially in the period when the planning system is nearly complete. Most small towns are still in the low efficiency or lack of the environment has become an important obstacle to the inheritance of traditional architectural style and the shaping of individual characteristics in small towns. How to provide a refined, comprehensive and efficient building style management and control system for managers, planners and subsequent architectural designers is particularly important for reversing the current disadvantages of small town style management and control. This article is problem-centred and conducts in-depth analysis from the aspects of style control ideas and style division control, trying to find a practical way of urban style control, hoping to benefit the urban development in the modernisation boom.

With the evolution of better highway services and larger traffic volume, the traditional maintenance management indicators can no longer satisfy the demands of highway traffic safety. In order to ensure timely, fast, safe, and reliable highway maintenance and repair, this paper proposes a road traffic safety maintenance evaluation method. The fuzzy maintenance evaluation method based on the gray correlation degree is used to construct the safety maintenance evaluation model. The damaged characteristics of the high-grade highway components are analysed. The parameters of the evaluation model are established using the analytic hierarchy process, and the accuracy of the model is verified through experiments. The results show that the safety service level can intuitively measure the maintenance and repair status of various transportation facilities. When the safety level is 1 (above 87 points) or 2 (above 85 points), the road maintenance and repair are in good condition and the road users have a high level of satisfaction on safety; when the safety level is 3 or 4 (80 points or less), it reflects that there are weak links in the road components, and targeted maintenance repairs are required. The results provide references for highway safety maintenance decision-making and improvement of highway traffic safety services to some extent.

New technological revolution has brought about significant changes in technological innovation activities. The platform has become an indispensable part of the innovation ecosystem of technology-intensive enterprises, which is derived from enterprise technology sharing. The main relationship of the innovation ecosystem is competition and cooperation. We use evolutionary game theory to consider the sharing behaviour of two enterprises in terms of different implicit parameters, thereby providing insight into the design of innovation ecosystem and technology innovation platform policies that promote open and shared technological innovation.

Noise logging is a method to determine the natural noise in a well. In the actual production logging process, it is a common situation that the noise data is not continuous with depth, which can be solved by the cubic spline interpolation method. This method is a piecewise interpolation method, which fits with a three-time polynomial in each segment interval, and adds up the polynomials on all intervals to get the interpolation formula. The interpolated data points are a smooth transition with good stability. In this article, the original noise data is interpolated to continuous noise data by cubic spline interpolation method, and then evaluated by noise imaging logging, which presents good results. The cubic-spline interpolation method ensures the internal connection of noise data, and also realizes the fine description and recognition of the characteristics of the output layer. This method will provide a low-cost and effective logging evaluation method for production logging, which has a wide range of applications.

Though split pole shoe can solve the problems of increased cost and decreased efficiency caused by replacing pole shoes in the test, assembling and use of split sealing devices, it fails to overcome the issue of sealing in the gap between split pole shoe's junction surface and shaft. In this paper, a split magnetic liquid sealing structure is designed, combining magnetic liquid sealing and split pole shoe's plane sealing. In our study, we have adopted three methods for split sealing and use theory and simulation to ascertain the sealing performance of the split magnetic liquid sealing structure designed by us. The results indicate that magnetic sealant bonded split pole shoes show better sealing performance as compared to those bonded by ordinary sealant, and that the structural optimisation results can meet the requirement for sealing performance. The simulation results coincide with theoretical results, which proves the correctness of this research.

With the rapid increase of information generated from all kinds of sources, temporal big data mining in business area has been paid more and more attention recently. A novel data mining algorithm for mining temporal association is proposed. Mining temporal association can not only provide better predictability for customer behaviour but also help organisations with better strategies and marketing decisions. To compare the proposed algorithm, two methods to mine temporal association are presented. One is improved based on a traditional mining algorithm, Apriori. The other is based on an Index-Tree. Moreover, the proposed method is extended to mine temporal association in multi-dimensional space. The experimental results show that the Index-Tree method outperforms the Apriori-modified method in all cases.

Artificial intelligence (AI) technology has been widely applied in various fields in recent years. Nevertheless, no systematic study has yet been conducted on the effects of AI technology on different fields. In this study, the impacts of the latest AI technology on technological innovation in different fields were analysed and quantized systematically from a patent perspective. Moreover, trends on AI technological innovation in some fields were analysed thoroughly. We conducted this study on a dataset of patents related to AI technology. Based on the patent dataset, we carried out a statistical analysis on technology fields, which we defined and classified based on international patent classification (IPC) number. Distributions of IPC in different fields were also analysed to determine the trends on AI technological innovation. The research conclusions can provide useful information to investors and enterprises, who are interested in the state of the art concerning AI technology.

Creativity is one of the core characteristics of talent; for this reason, the creativity development of applied undergraduates should be one of the basic components of their education. This article gives an overview of the meaning of the creativity of applied undergraduates and makes a literature knowledge-mining and expert investigation on the factors affecting the creativity development. We obtained more than 100 influencing factors, filtered out the duplicative factors, and formed the remaining factors into a questionnaire. A survey was conducted among 1460 teachers and students of some applied undergraduates in Heilongjiang Province. By using principal component analysis (PCA) to analyse the questionnaire, the key factors that affect the creativity development of applied undergraduates are obtained, and the key factors are systematically analysed. According to the results of the analysis, the specific ways and methods of the creativity development of applied undergraduates are put forward.

Based on the case of a highway reconstruction and extension project in Guangdong Province, a decision-making system for the treatment of the old pavement diseases of semi-rigid base asphalt pavement's reconstruction and extension has been established. The load-carrying capacity of the old pavement structure has been obtained by the Benkleman beam deflectometer; the damage condition of the road surface has been determined by investigation of road surface diseases; the restorability of the pavement diseases has been evaluated by investigation of the pavement maintenance history; the interior damage condition of the pavement has been detected by the three-dimensional ground-penetrating radar; furthermore, the decision-making system of the old pavement damage treatment scheme has been constructed and the treatment scheme of old pavement diseases has been put forward by using the four-hierarchy indexes of ‘the load-carrying capacity + the condition of road surface + the maintenance history + the interior damage condition of the pavement’; and the treatment effect of pavement diseases has been verified by bearing capacity test. The results show that the variation level of the deflection representative value of the old pavement has been reduced by about 8.2% ∼ 25.1% by adopting different diseases treatment schemes in different sections; 44.2% by adopting the deep grouting of the roadbed scheme, and 61.6% effectively by using the plan of milling all the asphalt layers and the upper base, and then relaying the C20 plain concrete to the top of the upper base and relaying asphalt mixture. The decision-making system for the treatment of the old pavement diseases of the semi-rigid base asphalt pavement's reconstruction and extension can effectively guide the treatment of old pavement disease, notably improve the load-carrying capacity of old pavement structure and the balance of the load-bearing capacity in different sections of the pavement structure.

Moving pieces to become black alternation with white (MPBBAW)is a game in which black and white pieces are continuously arranged by moving. This article traces the problem of MPBBAW and points out the possibility and necessity of computer calculation and commercial application of the problem. Using the non- recursive algorithm based on dimensionality reduction, this article deals with the problem of n-order MPBBAW. The special-order problem is solved and resubstituted. Thus, the computer processing and rule exploration of n-order and n-order MPBBAW are realised. As an auxiliary card, C++ is used to provide 20 black and 20 white pieces as an example. This article lays a foundation for the computer calculation and commercial application of MPBBAW.

It is impossible to study the relationship between water damage and voidage of asphalt pavement because the voidage of pavement core sample cannot be determined accurately. Based on the industrial computed tomography (CT) scanning technology for core samples of real void fraction measurement, dynamic water flushing apparatus to water damage damage of core samples, the CT scan void fraction and destruction after the relationship between splitting strength and CPN rutting depth of core samples, respectively, set up different lanes of void fraction and cleavage strength and the fitting formula of rut depth.

To accurately understand the insulation status of primary heating pipe network in the Chengyin District of Daqing City, its present insulation status has been tested through the enthalpy drop method. The field test results, with the data processing, are compared and analyzed, which reveals that there are weak links in the insulation structure of the primary heating pipe network in the Chengyin area. Before the insulation structure is optimized according to the field conditions, which provides a basis and reference for testing the insulation status of the heating pipe network, and has a guiding significance for evaluating and optimizing the insulation structure of pipe network.

The author presents the design and development of vibration performance detection and analysis system for commercial vehicles based on the theory of mechanical vibration performance testing and analysis theory, vibration signal acquisition and time domain analysis theory and Fourier transform principle.. The system performs the functions of data acquisition, signal analysis, spectrogram display, data storage, control output and time domain and frequency domain. Further, this system is used to test the vibration of commercial vehicles on the road to verify the integrity and reliability of the system function. The results of the experiments show that all functions of the system achieved the system design goals, and moreover, it shows that the system has strong practicability and high economy.

In the process of rapid urbanization, gentrification and commercialization have inevitably appeared in the historical districts of Jiangnan. Although they optimize the space environment of the historic district and promote the development of economy and tourism, they have resulted in disadvantages such as insufficient vitality of the space group, rigid space interface, lack of space quality and lack of regional culture. Mathematical calculation can be used to analyse the data of 15 historical blocks, determine the key points of the protection of historical blocks in Jiangnan area and then put forward reasonable construction strategies. This paper starts from the four elements of space group, space structure, space quality and space vitality, identifies the key points and key point of the historical block protection in Jiangnan area, and then puts forward the reasonable place building strategy.

With the relevant requirements of energy-saving and green buildings put forward by our country, carrying out the building energy consumption analysis is the premise and foundation of implementing energy-saving improvement of the existing buildings. Nowadays, modern office buildings, whose energy consumption structure and proportion are relatively stable, are widely used. The energy review work of an existing office building in severe cold region is carried out. Investigation and statistics on the general situation of buildings, the general situation of energy consumption and water system consumption and the total energy consumption are implemented. Based on the audit, the energy consumption situation and characteristics in a certain year are analysed. According to the characteristics of energy-using structure, the energy-saving potential of buildings is analysed, and the reasonable energy-saving opinions and suggestions are proposed to provide theoretical support for the energy-saving management of office buildings in severe cold areas.

Attribute reduction is a key issue in the research of rough sets. Aiming at the shortcoming of attribute reduction algorithm based on discernibility matrix, an attribute reduction method based on sample extraction and priority is presented. Firstly, equivalence classes are divided using quick sort for computing compressed decision table. Secondly, important samples are extracted from compressed decision table using iterative self-organizing data analysis technique algorithm(ISODATA). Finally, attribute reduction of sample decision table is conducted based on the concept of priority. Experimental results show that the attribute reduction method based on sample extraction and priority can significantly reduce the overall execution time and improve the reduction efficiency.

Precise motion control is a challenging and important goal in the application of mobile robots. The mechanical structure of a novel mobile robot is presented. Using the support vector machine learning control method in statistical theory, the human control strategy is represented by the parametric model without knowledge of the actual robot mathematical model. Moreover, using the learning controller, the position motion control experiments of the robot are carried out. The results of the experiments show that this learning control method is feasible and valid for the precise position control of the mobile robot, and the maxim error is less than 32 cm in a 10 m linear movement.

With the passage of time, the ‘born after 2000’ student group has stepped into the university campus and gradually become the main force of the college student cadre team. It has brought many new challenges while playing a huge role. The ‘born after 2000’ student group has distinctive group characteristics under the brand of the times, such as strong self-consciousness, rich material conditions and diverse network behaviour. The management of the college student cadre team needs to make new changes based on the characteristics of the ‘born after 2000’ student group. Therefore, from the perspective of competence, this paper combines the characteristics of the ‘born after 2000’ student group with the competence training and carries out countermeasures research on the competence cultivation of ‘born after 2000’ college student cadres from the four aspects of selection and appointment, education and training, supervision and assessment, reward and incentive, to solve the practical problems in the cultivation of college student cadres under the new situation, and provides some reference for the future-related theoretical research and educational practice.

Effective inspection of pipelines is of significant importance in the industry. In order to reduce human labour, risk and expenses in this area, robots can be applied. The pipe robot should perform not only the linear motion in the axial direction but also the rotary motion in the circumferential direction while working. Meanwhile, in order to achieve reasonable performance and efficiency, these robots should have high enough normal linear motion velocity. They should be able to cross a pipe in one direction to another pipe in a different direction to achieve the over-obstacle function. In this study, a double-joint wheeled robot model is established to fulfil the actions of fast walking, rotation around the pipe and over-obstacle on spatial pipes. Based on the expected position on the pipe for the robot constructed by the proposed model, the precise starting position and control synthesis of the axial and circumferential velocities are initially determined. In order to study the velocity synthesis more accurately, the pipe is unfolded along the axial direction to transform the spatial motion into a plane motion. A novel spatial distribution form of driving wheels is proposed. In addition, based on the initial position of the straight, T-shaped, L-shaped, two-axis ‘+’-shaped and spatial three-axis ‘+’-shaped pipes, the posture adjustment of the robot prior, during and after the over-obstacle is investigated. Furthermore, the corresponding planning algorithms are established.

With ever increasing complexity and intelligence of the modern cities, protecting key public facilities and important targets from any damage is a major challenge for the security sector. In all types of anti-terrorism prediction models, the prediction of attack behaviour is indispensable. Therefore, the attack behaviour model plays an important role in the anti-terrorism security system. This paper builds the attacker’s behaviour model, and carries out the prediction about the possible attack behaviour by the attacker model based on random strategy. According to the attack strategies, analysis and construction of the attack tree and attack graph are carried out based on the state-based stochastic model. The paper describes the security system in detail taking use of the state-based stochastic model method, so as to clarify the state distribution and the transfer relationship between the states of various security resources after threatened by attacks. At the same time, this paper applies the state-based stochastic model to establish the attacker model through the impact of attack on the security system.

The energy consumption of office buildings is analysed, and the influential factors to be considered in architectural design that affect the light and heat environment of office buildings are summarised. The original building model was established by Ecotect, and variable methods were adopted to simulate the influence of different influencing factors on the light and thermal environment, and to quantitatively evaluate the importance of different factors on energy consumption of buildings. This analysis provides an important basis for optimised energy saving design, and finally puts forward the optimal design strategy for energy saving, so as to build harmonious light and heat architectural environment.

Stock price forecasting is an eye-catching research topic. In previous works, many researchers used a single method or combination of methods to make predictions. However, accurately predicting stock prices is very difficult. To improve the predicting precision, in this study, an innovative prediction approach was proposed by recurrent substitution of forecast error into the historical neural network model through three steps. According to the historical data, the initial predicted value of the next day is obtained through the neural network. Then, the prediction error of the next day is obtained through the neural network according to the historical prediction error. Finally, the initial predicted value and the prediction error are added to obtain the final predicted value of the next day. We use recurrent neural network prediction methods, such as Long Short-Term Memory Network Model and Gated Recurrent Unit, which are popular in the recent neural network study. In the simulations, the past stock prices of China from June 2010 to August 2017 are used as training data, and those from September 2017 to April 2018 are used as test data. The experimental findings demonstrate that the proposed method with forecast error gives a more accurate prediction result for the stock’s high price on the next day, which indicates that the performance of the proposed one is superior to that of the traditional models without forecast error.

The dynamic characteristics and liquid sloshing of a circular tank are analysed using ADINA software through seismic response analyses. The maximum sloshing wave height for the circular tank under unidirectional horizontal seismic action is developed. The calculation method involves three parameters such as tank radius, seismic coefficient and dynamic coefficient. The dynamic coefficient of liquid sloshing is determined corresponding to the long-period seismic design β spectrum with a 5% damping ratio using basic sloshing period. The established method can guide the seismic design of liquid-containing structures. The established method of calculating sloshing wave height is compared with those in the American code.

In recent years, rural e-commerce has been actively improving, but the contradiction between talent demand and supply has become increasingly prominent. This article combines the four dimensions of personal characteristics, professional attitude, family background and external environment to conduct empirical research on willingness to engage in rural e-commerce among e-commerce major students. The results show that the willingness to engage in rural e-commerce is generally low, which influences internship experience, academic planning, salary expectations, career perception, family attitudes, school guidance and public opinion.

This paper takes the deep ore body of Yunnan Phosphate Group Co. Ltd, the largest open-pit chemical mining enterprise in China, as the research background, and systematically introduces the technical problems recognised by many Chinese researchers in the past eight years on the open-pit to underground mining of gently inclined thin to medium-thick ore bodies with a soft interlayer. It shows that the mining of open-pit transferred to underground is a complex engineering system, and the underground stope surrounding rock and overlying strata present a nonlinear failure process. Through mining process innovation, mining method innovation and improvement, research was undertaken on new processes and technologies for phosphorus mining under complex conditions. The relevant research results not only have important economic value and academic significance for Yunnan Phosphate Group Co. Ltd. but also have important guidance and impetus to the exploitation of a large number of similar phosphate resources in China.

By feat of Maple 17 and a subsidiary ordinary differential equation, a new extension algebraic method is chosen to construct the travelling wave solutions to the proximate equation set involving an arbitrary parameter for long waves over shallow-water. Multiple triangle periodic solutions and new Jacobi elliptic function solutions are obtained. This procedure is applicable to other nonlinear partial differential equations as well.

In this study, we give basic definitions and notions about Sheffer stroke operation and Sheffer stroke basic algebra. After presenting Sheffer stroke basic algebra on a given interval, named interval Sheffer stroke basic algebra, we give some features of an interval Sheffer stroke basic algebra. Then we investigate solutions to the set-theoretical Yang-Baxter equation in this algebraic structure by using its features.

In this paper, we investigate some new characterizations in the algebraic nature of neutrosophic submodule defined over a classical module using single valued neutrosophic set. We additionally characterized the neutrosophic point and determined the algebraic properties of neutrosophic point using the operations defined on neutrosophic submodule. Finley we examined a neutrosophic set as a generator of a neutrosophic submodule and derived some related concepts.

We provide sufficient conditions for the existence of periodic solutions for the differential systems x′=y,   y′=z,   z′=−y−εF(t,x,y,z),   andx′=y, y′=−x−εG(t,x,y,z,u), z′=u, u′=−z−εH(t,x,y,z,u), \matrix{{x' = y,\;\;\;y' = z,\;\;\;z' = - y - \varepsilon F(t,x,y,z),\;\;\;{\rm{and}}} \cr {x' = y,\quad y' = - x - \varepsilon G(t,x,y,z,u),\quad z' = u,\quad u' = - z - \varepsilon H(t,x,y,z,u),} \hfill \cr } where F, G and H are 2π–periodic functions in the variable t and ɛ is a small parameter. These differential systems appear frequently in many problems coming from the sciences and the engineering.

In this work, we consider a (2+1) dimensional nonlinear Schrödinger system which appears in the theory of nonlinear optics and describe transmission of the optical pulses in optical fibers. We attain certain special type traveling wave solutions of the under investigated model by help of finite series expansion and auxiliary differential equations. In this manner, we exploit exp(−ϕ(ε)) and modified Kudryashov approaches as solution procedures. Moreover, we make tanh ansatz because of the being even order of the reduced ordinary differential equation. The obtained solutions are in the form of dark soliton, combined soliton, symmetrical Lucas sine, Lucas cosine functions, and periodic wave solutions. We present also some graphical simulations of the solutions corresponding to values of parameters which leads to a better understanding the phenomena.

In this study, we introduce the relationship between the Tutte polynomials and dichromatic polynomials of (2,n)-torus knots. For this aim, firstly we obtain the signed graph of a (2,n)-torus knot, marked with {+} signs, via the regular diagram of its. Whereupon, we compute the Tutte polynomial for this graph and find a generalization through these calculations. Finally we obtain dichromatic polynomial lying under the unmarked states of the signed graph of the (2,n)-torus knots by the generalization.

In this paper, the problem of two equal collinear cracks is analytically studied for two-dimensional (2D) arbitrarily polarized magneto-electro-elastic materials. The electric and magnetic poling directions make arbitrary angles with the crack line. The Stroh's formalism and complex variable methodology is utilized to reduce the problem into non-homogeneous Riemann Hilbert problem. This numerical problem is then comprehended with the Riemann Hilbert way to obtain the intensity factors for stress, electric displacement and magnetic induction. A numerical contextual analysis is displayed for the BaTiO₃ – CoFe₂O₄ composite. The numerical examination demonstrates that the change in electric/magnetic poling directions influences the intensity factors.

Using projection (submersion) of the cotangent bundle T*M over a manifold M, we define a semi-tensor (pull-back) bundle tM of type (p,q). The aim of this study is to investigate complete lift of vector fields in a special class of semi-tensor bundle tM of the type (p,q). We also have a new example for good square in this work.

In this paper, we have studied the equations of motion for the problem, which are regularised in the neighbourhood of one of the finite masses and the existence of periodic orbits in a three-dimensional coordinate system when μ = 0. Finally, it establishes the canonical set (l, L, g, G, h, H) and forms the basic general perturbation theory for the problem.

The F-index is the whole of 3D squares of vertex degrees in a chart G. It as of late turned into the subject of a few investigates because of its extraordinary capability of uses. The point of this paper is to register the F-record of triangular prickly plant chain, square desert flora chains, 6-sided cactus restraints and polyomino restraints. In addition, we decided the extremal chains in the desert plant chains and polyomino fastens as for the F-index.

A large family of explicit exact solutions to both Korteweg- de Vries and modified Korteweg- de Vries equations are determined by the implementation of the new extended direct algebraic method. The procedure starts by reducing both equations to related ODEs by compatible travelling wave transforms. The balance between the highest degree nonlinear and highest order derivative terms gives the degree of the finite series. Substitution of the assumed solution and some algebra results in a system of equations are found. The relation between the parameters is determined by solving this system. The solutions of travelling wave forms determined by the application of the approach are represented in explicit functions of some generalized trigonometric and hyperbolic functions and exponential function. Some more solutions with different characteristics are also found.

In this paper, we give an explicit form of the scalar curvaure for the limiting case of the eigenvalue of the hypersurface Dirac operator which arises in the positive mass theorem for black holes. Then, we show that the hypersurface is an Einstein.

In this paper, we define boundary of neutrosophic soft set, neutrosophic soft dense set, neutrosophic soft basis and neutrosophic soft subspace topology on neutrosophic soft topological spaces. Furthermore, some important theorems are proved and interesting examples are given.

We analyze some properties of diagonal lift of tensor fields of type (1,1) in semi-cotangent bundles with the help of adapted frames.

In the present note, we have given a new integral identity via Conformable fractional integrals and some further properties. We have proved some integral inequalities for different kinds of convexity via Conformable fractional integrals. We have also showed that special cases of our findings gave some new inequalities involving Riemann-Liouville fractional integrals.

As a cryptosystem, Nth Truncated Polynomial Ring (NTRU) is established on the fast and easy calculation. Improving the security is aimed by enlarging a ring where the processes execute and enhancing the number of a private key and a public key. In this study, NTRU takes over the Galois rings and is analysed by adding a new private key.

Chaotic dynamics of various continuous and discrete-time mathematical models are used frequently in many practical applications. Many of these applications demand the chaotic behavior of the model to be robust. Therefore, it has been always a challenge to find mathematical models which exhibit robust chaotic dynamics. In the existing literature there exist a very few studies of robust chaos generators based on simple 1-D mathematical models. In this paper, we have proposed an infinite family consisting of simple one-dimensional piecewise smooth maps which can be effectively used to generate robust chaotic signals over a wide range of the parameter values.

This article offers an analysis of entropy generated in mixed convection due to a vertical stretching cylinder placed in heat-generating fluid-saturated porous medium. The governing system of partial differential equations is subjected to a similarity transformation that results in boundary value problem (BVP) comprising ordinary differentials. The BVP solved numerically by Runge-Kutta integration scheme supplemented with shooting method provides momentum and thermal regimes which are readily exploited to enumerate entropy. The entropy distribution is traced and analysed for various parameters’ values.

A modified analytical solution of the quadratic non-linear oscillator has been obtained based on an extended iteration method. In this study, truncated Fourier terms have been used in each step of iterations. The frequencies obtained by this technique show good agreement with the exact frequency. The percentage of error between the exact frequency and our third approximate frequency is as low as 0.001%. There is no algebraic complexity in our calculation, which is why this technique is very easy. The results have been compared with the exact and other existing results, which are both convergent and consistent.

Fractional analysis has evolved considerably over the last decades and has become popular in many technical and scientific fields. Many integral operators which ables us to integrate from fractional orders has been generated. Each of them provides different properties such as semigroup property, singularity problems etc. In this paper, firstly, we obtained a new kernel, then some new integral inequalities which are valid for integrals of fractional orders by using Riemann-Liouville fractional integral. To do this, we used some well-known inequalities such as Hölder's inequality or power mean inequality. Our results generalize some inequalities exist in the literature.