Solving Procedure Research Articles

Direct Localization of Emitters Based on Sparse Bayesian Learning

In this paper, a novel perspective for the problem of direct localization of emitters is presented based on sparse Bayesian learning (SBL). The localization problem is addressed in three scenarios, where we derive the angle-of-arrival (AOA) based models for two kinds of narrowband conditions and the model jointly taking use of time-difference-of-arrival (TDOA) and AOA information. Unlike the existing $\ell _1$ -penalization based direct localization methods, we expand the localization models to the sparsity-based framework with the scheme of SBL, which makes the partly unknown dictionary based problems solvable. On the basis of the bound-optimization SBL algorithm, modifications are provided to make its solving procedures adapt to the localization models. For one thing, the learning rule of channel attenuation factors (i.e., the unknown part of the dictionaries) is added in the solving procedures. For another, we expand the original single measurement vector (SMV) based model to the multiple measurement vector (MMV) scenario. Furthermore, we modify the original procedures by updating the parameters with an alternating minimization strategy, which guarantees the convergence of the algorithms. Simulation results show the features of three SBL-based models and the performance superiority of the proposed methods.

Higher-order approximate periodic solution for the oscillator with strong nonlinearity of polynomial type

In this paper the harmonic balance method (HBM) is adopted for solving a special group of oscillators with strong nonlinear damping and elastic forces. The nonlinearity is of polynomial type. The motion is described with a strong nonlinear differential equation, whose approximate solution is assumed as a suitable sum of trigonometric functions. To find the most convenient combination of trigonometric functions as the probe function is the most important part of this investigation. Introducing the procedure of equating the terms with the same order of the trigonometric functions to zero, the problem is transformed into solving a system of nonlinear algebraic equations. Solving these equations the parameters of the solution up to high-order approximation are obtained. In the paper, the suggested solving procedure is applied for two nonlinear oscillator problems: free vibrations of a restrained uniform beam carrying an intermediate lumped mass and of a particle on a rotating parabola. The obtained approximate analytic solutions are compared with the already published results and with the numerically obtained solution. The solution up to third-order approximation is calculated. It is proved that the HBM with the suggested function gives more accurate results than the previous applied ones. Besides, the difference between the third-order approximate analytical solution and the numerical one is negligible. The method works well for different, even high, values of initial amplitudes.

On the dynamics OF NON-RIGID asteroid rotation

We have presented in this communication a new solving procedure for the dynamics of non-rigid asteroid rotation, considering the final spin state of rotation for a small celestial body (asteroid). The last condition means the ultimate absence of the applied external torques (including short-term effect from torques during collisions, long-term YORP effect, etc.).Fundamental law of angular momentum conservation has been used for the aforementioned solving procedure. The system of Euler equations for dynamics of non-rigid asteroid rotation has been explored with regard to the existence of an analytic way of presentation of the approximated solution.Despite of various perturbations (such as collisions, YORP effect) which destabilize the rotation of asteroid via deviating from the current spin state, the inelastic (mainly, tidal) dissipation reduces kinetic energy of asteroid. So, evolution of the spinning asteroid should be resulting by the rotation about maximal-inertia axis with the proper spin state corresponding to minimal energy with a fixed angular momentum.Basing on the aforesaid assumption (component K1 is supposed to be fluctuating near the given appropriate constant of the fixed angular momentum), we have obtained that 2-nd component K2 is the solution of appropriate Riccati ordinary differential equation of 1-st order, whereas component K3 should be determined via expression for K2.

Integrated Railway Rapid Transit Network Design and Line Planning problem with maximum profit

We solve the Integrated Network Design and Line Planning Problem in Railway Rapid Transit systems with the objective of maximizing the net profit over a planning horizon, in the presence of a competing transportation mode. Since the profitability of the designed network is closely related with passengers’ demand and line operation decisions, for a given demand, a transit assignment is required to compute the profit, calculating simultaneously the frequencies of lines and selecting the most convenient train units. The proposed iterative solving procedure is governed by an adaptive large neighborhood search metaheuristic which, at each iteration, calls a branch-and-cut algorithm implemented in Gurobi in order to solve the assignment and network operation problems. We provide an illustration on a real-size scenario.

Development and Application of Programming Education Model Based on Visual Thinking Strategy for Pre-service Teachers

In the software-oriented society, the importance of computational thinking for problem solving is increasing day by day. In particular, programming is a good way to improve this kind of computational thinking, and beginners are having difficulties in creating and programming procedures for problem solving. In this study, we developed a Thinking-Revise-Encoding-Evaluating (TREE) model based on a visual thinking strategy for pre-service teachers and applied a 15-week curriculum. The results of the study showed that pre-service teachers' SW education perception, block programming ability, computational thinking, and satisfaction were significant.

Keterampilan Pemecahan Masalah MatematisPada Peserta Didik Kelas V Sekolah Dasar

The purpose of this research is to analyzing mathematical problem solving skills in fifth grade elementary school students. The research is descriptive research, using a qualitative approach. The technique of collecting data uses tests. The research subjects were fifth grade students of SD Negeri Danukusuman in the 2018/2019 academic year. The data analysis technique used is descriptive and content analysis. The results of research indicate that mathematical problem solving skills in the solid figure of fifth grade elementary school students were still low. In the indicators of problem comprehension skills, the percentage of skilled students is 62.5%. On the indicator of skills for problem solving, the percentage of skilled students is 21.88%. On the skill indicator carrying out the problem solving procedure, the percentage of skilled students is 0.09%. On the skill indicator, checking and drawing conclusions, the percentage of skilled students is 0.06%. The results of this research were preliminary studies for developing innovative learning models to improve problem solving skills. Keywords: problem solving skills, mathematics learning, solid figure, students, elementary school

A Conforming Augmented Finite Element Method for Modeling Arbitrary Cracking in Solids

Abstract This paper presents a conforming augmented finite element method (C-AFEM) that can account for arbitrary cracking in solids with similar accuracy of other conforming methods, but with a significantly improved numerical efficiency of about ten times. We show that the numerical gains are mainly due to our proposed new solving procedure, which involves solving a local problem for crack propagation and a global problem for structural equilibrium, through a tightly coupled two-step process. Through several numerical benchmarking examples, we further demonstrate that the C-AFEM is more accurate and mesh insensitive when compared with the original A-FEM, and both C-AFEM and A-FEM are much more robust and efficient than other parallel methods including the extended finite element method (XFEM)/generalized finite element (GFEM) and the conforming embedded discontinuity method.

Implementation of Genetic Algorithms for Optimization of Transportation Problem

Transportation problem is a model which is commonly used in data structure solving a problem (human problem solving due to the computational method) because all the humans are related to transportation in any type of manner. Normally, traditional mathematical procedures used for solving the problem which is quite lengthy, after the computational solving procedures it comes to the bit easier to solve it except traditional lengthy methods. The Genetic Algorithm (GA) is most powerful tool for solving transportation problem. It refines the better optimal solution, for enhancing the optimization of transportation problem, using genetic algorithms lots of the work already has been done. This paper discusses the impact of genetic algorithms on two different types of systems environments i.e., Single-Processor Environment Systems and Multi-Processor Environment Systems, for solving the transportation problem and found the best optimal solution time of both systems.
 
 Index Terms— Transportation Problem, Genetics Algorithm (GA), Single-Processor Systems, Multi-Processor Systems, Optimization.

Implementation of Genetic Algorithms for Optimization of Transportation Problem

Transportation problem is a model which is commonly used in data structure solving a problem (human problem solving due to the computational method) because all the humans are related to transportation in any type of manner. Normally, traditional mathematical procedures used for solving the problem which is quite lengthy, after the computational solving procedures it comes to the bit easier to solve it except traditional lengthy methods. The Genetic Algorithm (GA) is most powerful tool for solving transportation problem. It refines the better optimal solution, for enhancing the optimization of transportation problem, using genetic algorithms lots of the work already has been done. This paper discusses the impact of genetic algorithms on two different types of systems environments i.e., Single-Processor Environment Systems and Multi-Processor Environment Systems, for solving the transportation problem and found the best optimal solution time of both systems.
 
 Index Terms— Transportation Problem, Genetics Algorithm (GA), Single-Processor Systems, Multi-Processor Systems, Optimization.

Application of a variable neighborhood search algorithm to a fleet size and mix vehicle routing problem with electric modular vehicles

The emergence of new promising technologies used in electric transportation offers opportunities to achieve sustainable urban freight deliveries. In particular fleets of electric vehicles are seen as an efficient ecologic and economic transportation alternative for operating last-mile goods distribution in cities. This paper deals with the use of electric modules which can be added or removed from a freight vehicle to help gain capacity or respect delays when delivering customers. Since the electric vehicles have a limited battery capacity, they have to stop and recharge them at dedicated stations during the delivery tours. However, with the modular feature, this problem of disturbing the whole distribution process for recharging the batteries can be reduced and sometimes overlooked. This paper objective is to design and find the optimal routing strategy for a fleet of electric modular vehicles operating the last-mile delivery, with the minimal cost including the acquisition, the travel and the recharging ones. The research problem arising from the structure of the fleet can be associated with both a truck and trailer problem and a fleet size and mix vehicle routing problem with time windows using electric vehicles. This problem is presented in the first part of the article with the proposed solving procedure. More precisely, for big instances of the problem which is NP-Hard, a Variable Neighborhood Search (VNS) is designed and adapted. Experimental studies carried out on some benchmark instances show that the VNS performs impressively well in comparison with the best solving approaches of the literature.

On-Load Field Prediction of Surface-Mounted PM Machines Considering Nonlinearity Based on Hybrid Field Model

Analytical models show weakness in dealing with saturation in surface-mounted permanent-magnet machines. A hybrid field model (HFM) integrating complex permeance method (CPM) and lumped parameter magnetic circuit model (LPMCM) is proposed in this paper for predicting the on-load magnetic field considering nonlinearity effect of stator lamination. In the proposed model, the CPM calculates the field in the air gap and magnet regions, while LPMCM calculates the magnetic potential distribution inside the iron reflecting nonlinearity effect. The equivalent current sheet is obtained to replace such distribution on the stator bore. Moreover, local magnetic saturation of tooth tip is also transformed into equivalent current on the tooth surface. A solving procedure is proposed to calculate the equivalent current and guarantee the convergence. Compared with CPM, the proposed model considering the saturation effect significantly improves the prediction accuracy of the on-load performance. The HFM predictions are compared with finite element and experimental results. The excellent agreement validates its effectiveness.

Shrinkage of Real Power Loss by Enriched Brain Storm Optimization Algorithm

<p class="Author">This paper proposes Enriched Brain Storm Optimization (EBSO) algorithm is used for soving reactive power problem. Human being are the most intellectual creature in this world. Unsurprisingly, optimization algorithm stimulated by human being inspired problem solving procedure should be advanced than the optimization algorithms enthused by collective deeds of ants, bee, etc. In this paper, we commence a new Enriched brain storm optimization algorithm, which was enthused by the human brainstorming course of action. In the projected Enriched Brain Storm Optimization (EBSO) algorithm, the vibrant clustering strategy is used to perk up the k-means clustering process. The most important view of the vibrant clustering strategy is that; regularly execute the k-means clustering after a definite number of generations, so that the swapping of information wrap all ideas in the clusters to accomplish suitable searching capability. This new approach leads to wonderful results with little computational efforts. In order to evaluate the efficiency of the proposed Enriched Brain Storm Optimization (EBSO) algorithm, has been tested standard IEEE 118 & practical 191 bus test systems and compared to other standard reported algorithms. Simulation results show that Enriched Brain Storm Optimization (EBSO) algorithm is superior to other algorithms in reducing the real power loss.</p>

A unified procedure for free transverse vibration of rectangular and annular sectorial plates

A unified solution procedure applicable for analyzing the free transverse vibration of both rectangular and annular sectorial plates is presented in this study. For the annular sectorial plate, the basic theory is simplified by a variable transformation in the radial direction. The analogies of coordinate system, geometry and potential energy between the two different shapes are drawn and then unified in one framework by introducing the shape parameter. A generalized solving procedure for the two shapes becomes feasible under the unified framework. The solution adopts the spectro-geometric form that has the advantage of describing the geometry of structure by mathematical or design parameters. The assumed displacement field and its derivatives are continuous and smooth in the entire domain, thereby accelerating the convergence. In this study, the admissible functions are formulated in simple trigonometric forms of the mass and stiffness matrices for both rectangular and annular sectorial plates can be obtained, thereby making the method computationally effective, especially for analyzing annular sectorial plates. The generality, accuracy and efficiency of the unified approach for both shapes are fully demonstrated and verified through benchmark examples involving classical and elastic boundary conditions.

The Effect of Divorce on Parents on The Ethics of Class 3 XIIA Students at State Vocational High School 2 Ponorogo

This study aims to determine the impact of divorce perents on Akhlak of students in SMKN 2 Ponorogo. The problems at SMKN 2 Ponorogo based on the results of the preliminary research showed that the students whose parents divorced at Ponorogo State Vocational High School was very much, of the total 1,075 students, about 90 students whose parents were divorced and about 130 students who were broken home or his parents separated but not yet officially divorced. Based on the subject matter studied, the impact of divorce on the Akhlak students in SMKN 2 Ponorogo, the researchers used qualitative research, because the qualitative descriptive method was the problem solving procedure investigated by describing the state of the subject of research based on facts in the field. Data collection includes semi-structured interviews, observation and documentation. As for analyzing the data, researchers used 3 techniques, namely data reduction, data display, and conclusion drawing. The results of this study reveal that there are 2 kinds effects of parental divorce on students' morals or behaviors in school, the first is the positive influence that students vent the divorce problem of both parents to study harder so that they get good grades and become one of the outstanding students and the second negative influences are students becoming more reserved, lonely and arrogant. The solution for the child who is divorced is to maintain communication with both parents, show achievements to their parents, and maintain the full attention of both parents. This research also reveals that one of the causes divorce is economic problems and infidelity.

Customer's order acceptance and scheduling to maximise total profit

In this paper, in order to maximise total profit, the order acceptance and scheduling problem was generalised by considering some customers with their own orders who do not agree with partial rejection/acceptance of them. Therefore, it was assumed that accepting or rejecting one customer is equal to accepting or rejecting all his orders. In addition, the considered penalty function for scheduling the orders was total weighted lateness. A mathematical programming model, an upper bound, a branch and bound, and an efficient heuristic algorithm were proposed for this problem. It was shown that before starting the problem solving procedure, it is possible to certainly reject or accept some customers. The proposed branch and bound algorithm solved 93% of 810 randomly designed problem instances in a reasonable time. Besides, the heuristic algorithm solved the problem instances with the size of 2,000 customers at most with 0.1% deviation from a lower bound.

Customer's order acceptance and scheduling to maximise total profit

In this paper, in order to maximise total profit, the order acceptance and scheduling problem was generalised by considering some customers with their own orders who do not agree with partial rejection/acceptance of them. Therefore, it was assumed that accepting or rejecting one customer is equal to accepting or rejecting all his orders. In addition, the considered penalty function for scheduling the orders was total weighted lateness. A mathematical programming model, an upper bound, a branch and bound, and an efficient heuristic algorithm were proposed for this problem. It was shown that before starting the problem solving procedure, it is possible to certainly reject or accept some customers. The proposed branch and bound algorithm solved 93% of 810 randomly designed problem instances in a reasonable time. Besides, the heuristic algorithm solved the problem instances with the size of 2,000 customers at most with 0.1% deviation from a lower bound.

Additive slacks-based measure: Computational strategy and extension to network DEA

The current paper visits a set of data envelopment analysis (DEA) models that identify inefficiency by optimizing input and output slacks. These slacks are aggregated either in an additive or ratio form. Only the ratio slacks-based DEA models can be solved as a linear program and generate a DEA score between zero and unity. The additive slacks-based model can be equivalent to the Russell graph measure and converted into a second order cone programming (SOCP) problem whose solving procedure has become a mature technology. As such, the additive slacks-based model can also yield a DEA score between zero and unity. This study shows that the additive slacks-based model can be applied to modelling network DEA where the internal structures of decision making units (DMUs) are of interest. The additive slacks-based network DEA can be solved using SOCP technique and adapted to the preference of the decision maker by choosing the weights for aggregating individual components in the network structures. It is shown that the additive slacks-based approach can yield divisional efficiencies of Pareto optimal equivalences to be selected by the decision maker when compared to the existing ratio slacks-based measure. An example and solving codes are provided in the current study.

On a new type of solving procedure for Euler–Poisson equations (rigid body rotation over the fixed point)

In this paper, we proceed to develop a new approach which was formulated first in Ershkov (Acta Mech 228(7):2719–2723, 2017) for solving Poisson equations: a new type of the solving procedure for Euler–Poisson equations (rigid body rotation over the fixed point) is suggested in the current research. Meanwhile, the Euler–Poisson system of equations has been successfully explored for the existence of analytical solutions. As the main result, a new ansatz is suggested for solving Euler–Poisson equations: the Euler–Poisson equations are reduced to a system of three nonlinear ordinary differential equations of first order in regard to three functions $$\Omega _{i}$$ ( $$i = 1, 2, 3$$ ); the proper elegant approximate solution has been obtained as a set of quasi-periodic cycles via re-inversing the proper elliptical integral. So the system of Euler–Poisson equations is proved to have analytical solutions (in quadratures) only in classical simplifying cases: (1) Lagrange’s case, or (2) Kovalevskaya’s case or (3) Euler’s case or other well-known but particular cases.

A Conflict-Driven Solving Procedure for Poly-Power Constraints

This paper studies the satisfiability problem of poly-power constraints (conjunctions of poly-power equations and inequalities), in which poly-powers are univariate nonlinear functions that extend integer exponents of polynomials to real algebraic exponents. To solve the poly-power constraint, we present a sound and complete procedure that incorporates conflict-driven learning with the exclusion algorithm for isolating positive roots of poly-powers. Furthermore, we introduce a kind of optimal interval-splitting, based on the Stern–Brocot tree and on binary rational numbers respectively, so that the operands occurring in the execution are chosen to be as simple as possible. The solving procedure, thereby, turns out to be promisingly efficient on randomly generated examples.

On a new type of solving procedure for Laplace tidal equation

In this paper, we present a new approach for solving Laplace tidal equations (LTE) which was formulated first in [S.V.Ershkov, A Riccati-type solution of Euler-Poisson equations of rigid body rotation over the fixed point, Acta Mechanica, 228(7), 2719 (2017)] for solving Poisson equations: a new type of the solving procedure for Euler-Poisson equations (rigid body rotation over the fixed point) is implemented here for solving momentum equation of LTE, Laplace tidal equations. Meanwhile, the system of Laplace tidal equations (including continuity equation) has been successfully explored with respect to the existence of analytical way for presentation of the solution. As the main result, the new ansatz is suggested here for solving LTE: solving momentum equation is reduced to solving system of 3 nonlinear ordinary differential equations of 1-st order in regard to 3 components of the flow velocity (depending on time t), along with the continuity equation which determines the spatial part of solution. Nevertheless, the proper elegant partial solution has been obtained due to invariant dependence between temporary components of the solution. In addition to this, it is proved here that the system of Laplace tidal equations has not the analytical presentation of solution (in quadratures) in case of nonzero fluid pressure in the Ocean, as well as nonzero total gravitational potential and the centrifugal potential (due to planetary rotation).