Mathematical Algorithms

This paper presents a new algorithm for efficient prime number generation based on the Goldbach Conjecture and its relation to arithmetic symmetry. The algorithm uses the assumption, derived from the conjecture, that around every number there exists at least one symmetric pair of prime numbers, which significantly reduces the number of candidates for testing. Even without a full proof of the conjecture, its partial validity (e.g., 90% or 50%) is sufficient for a simplified and accelerated generation process. We demonstrate the effectiveness of the method by generating 10 prime numbers with 200 digits in less than half an hour using a fast search procedure.

The use of mathematical algorithms in industrial operations us very relevant because can determine the principal steps of the flow production and to detect very fast and easy, some possible errors of workers of the manufacturing areas and of industrial equipment, machinery of systems utilized in the industrial process used to the manufactured products process. This investigation was made in an electronic industry installed in the Tijuana city, which is considered an industrial city and located in the northwest of the Mexican Republic. This scientific study was very important because with the mathematical algorithms, was supporting to increase the productivity and quality yielding of the electronics industry where was made this investigation. The scientific study was made in 2022, where was utilized some statistical methods using the Cronbach coefficient and making an interview to the managers of this electronic industry evaluated. The education technology method used in this investi...

A new version of fractional minimal cost flow problem with fuzzy arc costs is focused in this study. The fuzzy arc costs are applied as in most of the real-world applications, the parameters have high degree of uncertainty. The goal of this problem is to determine the minimum fuzzy fractional cost of sending and passing a specified flow value into and from a network. A decomposition-based solution methodology is introduced to tackle this problem. The methodology applies Zadeh's extension principle to decompose the problem to two upper bound and lower bound problems. These problems are capable of being solved for different a-cut values to construct the fuzzy fractional minimal cost flow value as the objective function value. The efficiency of the proposed solution methodology is studied over some well-known examples of fractional minimal cost flow problem. The obtained results show the superiority of the proposed approach comparing to the methods of the literature.

In this paper, a transportation problem with an objective function as the sum of a linear and fractional function is considered. The linear function represents the total transportation cost incurred when the goods are shipped from various sources to the destinations and the fractional function gives the ratio of sales tax to the total public expenditure. Our objective is to determine the transportation schedule which minimizes the sum of total transportation cost and ratio of total sales tax paid to the total public expenditure. Sometimes, situations arise where either reserve stocks have to be kept at the supply points, for emergencies or there may be extra demand in the markets. In such situations, the total flow needs to be controlled or enhanced. In this paper, a special class of transportation problems is studied where in the total transportation flow is restricted to a known specified level. A related transportation problem is formulated and it is shown that to each basic feasible solution which is called corner feasible solution to related transportation problem, there is a corresponding feasible solution to this restricted flow problem. The optimal solution to restricted flow problem may be obtained from the optimal solution to related transportation problem. An algorithm is presented to solve a capacitated linear plus linear fractional transportation problem with restricted flow. The algorithm is supported by a real life example of a manufacturing company.

The use of mathematical algorithms in industrial operations us very relevant because can determine the principal steps of the flow production and to detect very fast and easy, some possible errors of workers of the manufacturing areas and of industrial equipment, machinery of systems utilized in the industrial process used to the manufactured products process. This investigation was made in an electronic industry installed in the Tijuana city, which is considered an industrial city and located in the northwest of the Mexican Republic. This scientific study was very important because with the mathematical algorithms, was supporting to increase the productivity and quality yielding of the electronics industry where was made this investigation. The scientific study was made in 2022, where was utilized some statistical methods using the Cronbach coefficient and making an interview to the managers of this electronic industry evaluated. The education technology method used in this investigation was very relevant to improve the productivity and quality indices, because students of a university that participated were important homework’s in the industry evaluated

Utilization of phasor measurement units (PMUs) in the monitoring, protection and control of power systems has become increasingly important in recent years. The aim of the optimal PMU placement (OPP) problem is to provide the minimal PMU installations to ensure full observability of the power system. Several methods, based on mathematical and heuristic algorithms, have been suggested for the OPP problem. This paper presents a thorough description of the state of the art of the optimization methods applied to the OPP problem, analyzing and classifying current and future research trends in this field.

This paper discusses a paradox in a capacitated transportation problem where the objective function is the sum of two fractional functions consisting of variable costs only. A paradoxical situation arises in a transportation problem when value of the objective function falls below the optimal value and this lower value is attainable by shipping larger quantities of goods over the same routes that were previously designated as optimal. Firstly, optimality condition at which a feasible solution of fractional plus fractional capacitated transportation problem will be an optimal solution is established. Then a sufficient condition for the existence of paradox is found. If paradox exists, then the procedure for finding the best paradoxical pair is proposed which ultimately gives a paradoxical range of flows. Moreover, a method is proposed to find the paradoxical solution for a specified flow . Developed algorithm is applied on the real data taken from the account keeping books of the fir...

Pervious concrete is a concrete mixture prepared from cement, aggregates, water, little or no fines, and in some cases admixtures. The hydrological property of pervious concrete is the primary reason for its reappearance in construction. Much research has been conducted on plain concrete, but little attention has been paid to porous concrete, particularly to the analytical prediction modeling of its permeability. In this paper, two important aspects of pervious concrete due to permeability and compressive strength are investigated using artificial neural networks (ANN) based on laboratory data. The proposed network is intended to represent a reliable functional relationship between the input independent variables accounting for the variability of permeability and compressive strength of a porous concrete. Results of the Back Propagation model indicate that the general fit and replication of the data regarding the data points are quite fine. The R-square goodness of fit of predicted ...

BACKGROUND This study aimed to evaluate and compare the prediction accuracy of two data mining techniques, including decision tree and neural network models in labeling diagnosis to gastrointestinal prescriptions in Iran. METHODS This study was conducted in three phases: data preparation, training phase, and testing phase. A sample from a database consisting of 23 million pharmacy insurance claim records, from 2004 to 2011 was used, in which a total of 330 prescriptions were assessed and used to train and test the models simultaneously. In the training phase, the selected prescriptions were assessed by both a physician and a pharmacist separately and assigned a diagnosis. To test the performance of each model, a k-fold stratified cross validation was conducted in addition to measuring their sensitivity and specificity. RESULT Generally, two methods had very similar accuracies. Considering the weighted average of true positive rate (sensitivity) and true negative rate (specificity), ...

The data of real world applications generally cannot be expressed strictly. An efficient way of handling this situation is expressing the data as intervals. Thus, this paper focus on the Indefinite Quadratic Interval Transportation Problem (IQITP) in which all the parameters i.e. cost and risk coefficients of the objective function, supply and demand quantities are expressed as intervals. A Taylor series approach is presented for the solution of IQITP by means of the expression of intervals with its left and right limits. Also a numerical example is executed to illustrate the procedure

In the present paper, anon linear transportation problem with specified flow is studied. I fin addition to the flow constraint, the minimum requirement of each destination is also specified then the situation arises of distributing at minimum cost a certain commodity produced in a country, after keeping reserve stocks, to various states with minimum requirement of each state specified. Are lated transportation problem is formed in which the flow constraint is replaced by two extra destinations, one for supplementing the total flow up to the specified level, and the other for identifying the supply points preferred to keeper serves. Optimal basic feasible solution of the related transportation problem so formulate dis shown to give an optimal solution of the given problem. A numerical example is included in support of theory. Keywords: optimum time cost trade off, capacityated transportation problem, non l i n e a r transportation problem, specified flow.

The present paper presents an algorithm to find optimum time-cost trade off pairs in a fixed charge linear capacitated transportation problem with enhanced flow. Sometimes, situations arise where either reserve stocks have to be kept at supply points say, for emergencies, or there may be extra demand in the markets. In such situations, the total flow needs to be controlled or enhanced. Moreover, sometimes a fixed charge (like set up cost for machines, landing fees at an airport, cost of renting a vehicle) is also associated with every origin that gives rise to fixed charge problem. In this paper a special class of transportation problem is studied, where the total transportation flow is enhanced to a specified level. A numerical example is given to illustrate the developed algorithm.

The present paper presents an algorithm to solve a linear plus linear fractional transportation problem with enhanced flow. Sometimes, situations arise where either reserve stocks have to be kept at supply points say, for emergencies, or there may be extra demand in the markets. In such situations, the total flow needs to be controlled or enhanced. In this paper ,a special class of transportation problem is studied where total transportation flow is enhanced to a known specified level.A related transportation problem is formulated and it is established that a special type of feasible solution called corner feasible solution of related transportation problembear one to one correspondence with the feasible solutionof the givenenhanced flow problem. The optimal solution to enhanced flow problem may be obtained from the optimal solution to related transportation problem. An algorithm is presented to solve a capacitated linear plus linear fractional transportation problem with enhanced flow. A real life example of a company is included in support of the theory.

In this paper the authors are concerned with the problem of empirical model building when models from the class of Feedforward Neural Networks are considered. In this case, empirical model building consists of the following four tasks: network's structure selection, ...

Initial Vs. boundary value problems  An example of an Initial value problem is given by the second order ODE    with initial conditions y(0) = 0 and y′(0) = 1  The difference between Initial and Boundary value problem is that rather than initial conditions being imposed at the same point in the independent variable (in this case, t), boundary conditions are imposed at different values of the Independent variable.

The fixed charge (fixed cost) may present the cost of renting a vehicle, landing fees in an airport, setup cost for machines in a manufacturing environment, etc. In this paper, we discuss fixed charge capacitated in a non-linear transportation problem. Thereby, we establish local optimum condition of this problem. Next we establish an algorithm for solving this transportation problem. Also, we illustrate a numerical example to support this algorithm.

In this paper, a capacitated fixed charge bi-criterion indefinite quadratic transportation problem, giving the same priority to cost as well as time is studied. An algorithm to find the efficient cost-time trade off pairs in a capacitated fixed charge bicriterion indefinite quadratic transportation problem is developed. The algorithm is based on the concept of solving the indefinite quadratic fixed charge transportation problem and reading the corresponding time from the time matrix. It is illustrated with the help of a numerical example.