Mathematical Solution Research Articles

Optimal threshold padlock systems

In 1968, Liu described the problem of securing documents in a shared secret project. In an example, at least six out of eleven participating scientists need to be present to open the lock securing the secret documents. Shamir proposed a mathematical solution to this physical problem in 1979, by designing an efficient k-out-of-n secret sharing scheme based on Lagrange’s interpolation. Liu and Shamir also claimed that the minimal solution using physical locks is clearly impractical and exponential in the number of participants. In this paper we relax some implicit assumptions in their claim and propose an optimal physical solution to the problem of Liu that uses physical padlocks, but the number of padlocks is not greater than the number of participants. Then, we show that no device can do better for k-out-of-n threshold padlock systems as soon as k ⩾ 2 n , which holds true in particular for Liu’s example. More generally, we derive bounds required to implement any threshold system and prove a lower bound of O ( log ( n ) ) padlocks for any threshold larger than 2. For instance we propose an optimal scheme reaching that bound for 2-out-of-n threshold systems and requiring less than 2 log 2 ( n ) padlocks. We also discuss more complex access structures, a wrapping technique, and other sublinear realizations like an algorithm to generate 3-out-of-n systems with 2.5 n padlocks. Finally we give an algorithm building k-out-of-n threshold padlock systems with only O ( log ( n ) k − 1 ) padlocks. Apart from the physical world, our results also show that it is possible to implement secret sharing over small fields.

Enhancing Two-Phase Supply Chain Network Distribution via Three Meta-Heuristic Optimization Algorithms Subsidized by Mathematical Procedures

Supply Chain Networks Distribution (SCND) topology aims to find the best position and size for facilities to ensure optimal products flow based on the Matheuristic approach (i.e. decomposition meta-heuristics). This problem is a multi-objective function designed to reduce the transported costs and associated delivery times. The Matheuristic presents a brilliant hybridize between the meta-heuristics steps and mathematical procedures in solving large-size problems with the slightest deviation [Formula: see text]. This paper proposed an ant colony-based algorithm evolved by mathematical procedures called Mat-ACO, compared with SA “simulated annealing” and CA “Camel algorithm.” The authors deduced that the mathematical solution is limited as the instances grow, significantly if increased than 600 network hotspots. The Mat-ACO, SA, and CA results are close to counterparts obtained by LINGO, with a difference of 2.03%, 2.49%, and 3.75%, respectively, and continue to extract results from more than 1350 network hotspots. The main contribution is to find the optimum tuning parameters, which will reduce the deviation from the exact solution. This paper reveals that no feasible solution can catch the LINGO at large-size problems. At the same time, the CA is superior to SA in the large problem sizes, while Mat-ACO still presents preferred solutions in minimum time. The proposed methodology is classified as a closed-loop network strategy that targets green management.

Container Ship Planning Optimization Using Intelligent Meta-heuristic Algorithms

The timing of container ships is one of the more attractive optimization issues. Because container ships carry 80% of the volume of cargo worldwide. Hence, maritime transport and container trade are known as the backbone of global trade. Today, with the development of shipbuilding technology and increasing the frequency of maritime transport, determining the optimal route for container ships has become more and more important for shipping lines and port managers. Accordingly, the present study intends investigate the problem of optimizing the trajectory of ships using an integer linear mathematical programming model. In order to solve the proposed model, the meta-heuristic algorithms of differential evolution and gray wolf in MATLAB software are utilized. Finally, it was shown that the proposed mathematical model and solution approaches can assist ship operators and terminal managers in making sensible optimization decisions.

Analisis kemampuan literasi matematika siswa SMP Negeri 1 Juwana dalam menyelesaikan masalah matematika ditinjau dari adversity quotient

Mathematical literacy has an important role in the world of education for the assessment of AKM. SMP Negeri 1 Juwana is in an effort to prepare AKM so that information related to mathematical literacy is needed. This study aims to describe the mathematical literacy ability of class VIII F students of SMP Negeri 1 Juwana with adversity quotient climbers, campers, quitters in solving the problem of building a flat side space. The method used in this research is descriptive qualitative. The data collection used are tests and interviews. The data analysis technique was carried out in 3 stages, namely data reduction, data presentation and conclusion drawing. Test the validity of the data using source triangulation by comparing data from 2 sources. The results showed that climbers students went through the process of formulating, applying, and interpreting mathematical literacy with 6 indicators completely. Campers students go through the process of formulating, applying and interpreting mathematical literacy, butwhen applying the concept by elaborating the completion steps in finding mathematical solutions it is not optimal, the interpretation that students write is not associated with real-world problems, the explanation of the reasons given does not make sense based on context. problem. Quitter students go through the process of formulating because students do not write anything on the answer sheet when designing strategies, the application of student concepts is not appropriate and only uses 1-2 steps of completion, students do not interpret the results obtained in the context of real-world problems, explanations of the reasons given students do not make sense based on context. Factors that affect mathematical literacy skills based on AQ are generally influenced by the lack of knowledge related to mathematical literacy, not being accustomed to working on mathematical literacy-type questions.

Penalaran Matematis: Pembiasaan Soal High Order Thinking Pada Siswa Usia Sekolah Dasar

The purpose of the article is to create a mathematical reasoning modeling framework through working on high order thinking questions for elementary school students. The modeling cycle (formulating, applying, interpreting, and evaluating) is a central aspect of the conception of mathematical reasoning for students for the sake of mathematical literacy. Formulating is an individual's ability to recognize and identify opportunities to use mathematics and then provide a mathematical structure for problems presented in several contextual forms. Applying is an individual's ability to apply concepts, facts, procedures, and mathematical reasoning to solve mathematically formulated problems in order to obtain mathematical conclusions. Interpreting and evaluating (interpret and evaluate) is the individual's ability to reflect on mathematical solutions, results or conclusions and interpret them into the context of real life problems. This is a literature study, the data was collecting using literature studies on scientific journal articles and news about mathematical reasoning, high order thinking, and numeracy. The modeling cycle is recommended for teaching mathematics in elementary school through series of problem solving stages in questions with higher order thinking skill concept.

Modelling of porous core–shell adsorbent particles with various morphologies suspended in batch adsorber from analytical solutions of diffusion equations

AbstractConsidering both intra‐particle diffusion and film resistance for mass transfer, analytical solutions of transient concentration of adsorbate inside adsorbents with spherical, cylindrical, or slab‐type particles were derived for batch adsorbers by solving governing equations using the Laplace transform. Assuming Henry's or rectangular isotherm, the average concentration inside adsorbents as well as transient bulk concentration were also obtained for the particles with or without the inert core. Computations were performed to compare the results according to the shape of adsorbents by adjusting adsorbent loading, Biot number (Bi), and inert core thickness. Regardless of particle morphologies, steady‐state bulk concentration was only affected by adsorbent loading and inert core thickness, whereas the effect of Bi was confirmed from the decreasing reduction rate of adsorbate concentration with decreasing Bi. When diffusivity was dependent on time, time‐decaying diffusivity caused the increase in steady‐state concentration that was predicted by eigenfunction expansion. Experimental results using porous fibres by electrospinning were compared with the mathematical solution of a cylindrical adsorbent for the estimation of intra‐particle diffusivity. Using the solutions of the diffusion equation model, novel core–shell cylindrical adsorbents can be designed and synthesized as core–shell fibres by electrospinning with a coaxial nozzle to save the cost of the active shell layer. Such core–shell structured fibres can be adopted as adsorbents for novel batch adsorption processes and the present modelling results can be extended to other processes like fixed bed adsorbers.

Real-Time Scheduling of Autonomous Mining Trucks via Flow Allocation-Accelerated Tabu Search

Material transportation is an essential process in mining operations and accounts for a large portion of total energy consumption. With the development of automation technology, autonomous mining trucks have been deployed in open-pit mines to reduce transportation costs. Compared to manned mining trucks, autonomous trucks are more appropriate for automatic scheduling techniques due to their high informatization, high-precision perception, and sophisticated control. However, the existing truck scheduling research does not exploit autonomous trucks’ strengths to perform more delicate control, but still takes a traditional approach toward autonomous trucks. In this paper, we propose a mixed-integer programming model for joint optimization of autonomous trucks trips and speeds to minimize energy consumption. To solve the proposed scheduling model, a novel tabu search algorithm is proposed, which consists of two parts: an improved flow allocation model with matching factor is formulated in the upper part to determine the optimal truck flow, and in the lower part a tabu search procedure guided with the optimal flow is developed. Based on the mathematical model and solution technique, we also propose a real-time scheduling system of autonomous trucks for the stochastic and dynamic mining environment. A coal mine in Inner Mongolia, China, for example, we verified the effectiveness of the proposed truck scheduling model and real-time scheduling approach. We demonstrate that the proposed allocation model effectively accelerates the tabu search procedure, and for short-term decisions, the proposed solution technique satisfies the computational requirements of the real-time scheduling system.

A Game Theory-based Approach to Fuzzy Linear Transportation Problem

Background: Transport models have wide application areas in the real world and play an important role in reducing transportation costs, increasing service quality, etc. These models may have uncertain transportation costs and supply or demand capacities of the product. Hence, it would be effective to model the vagueness of customer demands, economic conditions, and technical or non-technical uncertainties because of uncontrollable factors. Therefore, we focus on developing a mathematical solution approach to the fuzzy transportation problems. Objective: In this paper, an integrated approach is proposed for the solution of the fuzzy linear transportation problem that has fuzzy cost coefficients in the objective function. Since transportation problem is encountered frequently in the national and international environment, it is considered that proposing a new solution method to this problem will be useful. Methods: Fuzzy cost coefficients are taken as trapezoidal fuzzy numbers due to their widespread use in the literature. Firstly, the fuzziness is removed by converting the original single objective fuzzy transportation problem into a crisp Multi-Objective Linear Programming Problem (MOLPP). After the classical payoff matrix is constructed, ratio matrices are obtained to scale the objectives. Then, an approach based on game theory is implemented to solve the MOLPP, which is handled as a zero-sum game. Results: Creating different ratio matrices in the game theory part of the approach can generate compromise solutions for the decision-makers. To demonstrate the effectiveness of the proposed approach, two numerical examples from the literature are solved. While the same solution is obtained in one of the examples, a different compromise solution set is generated, which could be presented to the decision-maker in the other example. Conclusion: In this paper, we developed a novel game theory-based approach to the fuzzy transportation problem. The proposed approach overcomes the non-linear structure due to the uncertainty in the cost coefficients. The greatest advantage of the proposed approach is that it can generate more than one optimal solution for the decision-maker.

A Simple Mathematical Solution to the Cosmological ‎Constant Problem

Assuming an energy density of the cosmological constant in Quantum Field Theory, we propose a simple mathematical ‎‎solution to the cosmological constant problem‎, i.e., the disagreement of the order of a factor 10122 between the ‎theoretical and ‎the measured value of the vacuum energy density. We try to give a non-exclusive route for our solution ‎to make physical ‎sense.‎

TCT-265 A Novel Cardiac Imaging System Design: Discovery and the Development of the Mathematical Solution for Patient-Specific Human Heart Modelling Based on Echocardiographic Waves

TCT-265 A Novel Cardiac Imaging System Design: Discovery and the Development of the Mathematical Solution for Patient-Specific Human Heart Modelling Based on Echocardiographic Waves

A Simple Mathematical Solution to the Cosmological ‎Constant Problem

Assuming an energy density of the cosmological constant in Quantum Field Theory, we propose a simple mathematical ‎‎solution to the cosmological constant problem‎, i.e., the disagreement of the order of a factor 10122 between the ‎theoretical and ‎the measured value of the vacuum energy density. We try to give a non-exclusive route for our solution ‎to make physical ‎sense.‎

The Generalized Additivity Rule for Thermal Path-Dependent Diffusion-Controlled Phase Transformation by Simultaneous Nucleation and Growth and Its Mathematical Solutions

The Generalized Additivity Rule for Thermal Path-Dependent Diffusion-Controlled Phase Transformation by Simultaneous Nucleation and Growth and Its Mathematical Solutions

A bi-objective approach based on fuzzy logic for multi-period technician routing and scheduling problems

This paper deals with a multi-period technician routing and scheduling problem. The problem carries out the tasks at various locations by being divided into teams considering differently skilled technicians. This paper provides a bi-objective mixed integer programming method to model the problem since the goals of the performed model are to optimize the travel cost while simultaneously minimizing the overtime and the waiting time. The paper introduces a fuzzy logic approach to solving the problem by offering a single Pareto solution to satisfy both objectives, rather than providing efficient solutions as in the case of classical multi-objective models. Finally, the paper presents the computational experiments and analyses to evaluate the efficiency of the suggested mathematical formulation and solution approach. The results demonstrate that the performed model accomplishes an acceptable satisfaction level.

Robust Estimation in Continuous–Discrete Cubature Kalman Filters for Bearings-Only Tracking

The model of bearings-only tracking is generally described by discrete–discrete filtering systems. Discrete robust methods are also frequently used to address measurement uncertainty problems in bearings-only tracking. The recently popular continuous–discrete filtering system considers the state model of the target to be continuous in time, and is more suitable for bearings-only tracking because of its higher mathematical solution accuracy. However, the sufficient evaluation of robust methods in continuous–discrete systems is not available. In addition, in the different continuous–discrete measurement environments, the choice of a robust algorithm also needs to be discussed. To fill this gap, this paper firstly establishes the continuous–discrete target tracking model, and then evaluates the performance of proposed robust square-root continuous–discrete cubature Kalman filter algorithms in the measurement of uncertainty problems. From the simulation results, the robust square-root continuous–discrete maximum correntropy cubature Kalman filter algorithm and the variational Bayesian square-root continuous–discrete cubature Kalman filter algorithm have better environmental adaptability, which provides a promising means for solving continuous–discrete robust problems.

Integration Method for Response History Analysis of Single-Degree-of-Freedom Systems with Negative Stiffness

The present article deals with the mathematical investigation of a negative-stiffness ideal system that can be used in seismic isolation of civil engineering structures. Negative-stiffness systems can be used in the seismic isolation of structures, because in the case of a strong earthquake, they do not easily allow vibrations to develop. These negative-stiffness systems can be significantly more efficient than the usual seismic isolation systems, as they drastically reduce the vibrational amplitudes of structures, as well as eliminate the inertial seismic structure loadings. The mathematical investigation of a negative-stiffness ideal system provides documented answers about the effect of negative-stiffness systems in the seismic behavior of structures. First, the differential equation of motion of a single-degree-of-freedom oscillator (SDoF) is formulated, without classical damping, but with negative stiffness. Furthermore, the mathematical solution of the equation of motion is given, where it is proven that this solution does not describe a structure vibration. Furthermore, the seismic structure motion follows an exponential increase when the seismic ground excitation is purely sinusoidal. Finally, to calculate the real response of the negative-stiffness system, a suitable modification of the Newmark iterative numerical method is proposed.

Uni-CARE: Universal Interface via Cloud Archive Repository Express

Uni-CARE—Universal interface has emerged from Cloud Archive Repository Express that utilizes algorithmic machine learning as a “fastlane” without explicitly coding required to bridge the gap between DATA and wiseCIO. Uni-CARE incorporates DATA of digital archiving & trans-analytics with wiseCIO of web-based intelligent service into a triad for content management and delivery (CMD) that orchestrates Anything as a Service (XaaS) by using mathematical and computational solutions to cloud-based distributed problems. This article presents automated universal interface design through cloud archival repository express in CARE for “DNA-like” ingredients with trivial information eliminated through deep learning. Conceptually, Uni-CARE innovates with algorithmic machine learning and introduces express tokens for information interchange (eTokin) to promote seamless intercommunications among the CMD triad and semantic enrichment of digital archiving via online analytics for XaaS. Specifically, Uni-CARE collaborative with DATA and wiseCIO empowers ordinary users to be UNIQ professionals: such as ubiquitous manager on content management and delivery, novel designer on universal interface and user-centric experience, intelligent expert for business intelligence, and quinary liaison with Anything orchestrated as a Service. The novel designer enabled by Uni-CARE automates layouts of control items, containers and/or folders for hierarchical “in-&-out” interactivity, and multi-aspects through bulletins and/or tabs for contextual “self-paced” spontaneity with individual entities (as bodies) extendable/shrinkable. Furthermore, the CMD triad collaborative with DATA and wiseCIO as a whole harnesses rapid prototyping for human-computer interfacing and propels cohesive assembly from Anything orchestrated as a Service. More importantly, Uni-CARE enables instant typing online publishing over DATA in eTokin, efficient presentation to end-users with diligent intelligence delivered for business, education, and entertainment (iBEE) on wiseCIO through highly robotic process automation.

Effective Diffusivity From Analytical Solution for Banks of Cylinders

Abstract Benchmarks are provided for the evaluation of the effective coefficient for species diffusion, or electrical/thermal conduction, in structured porous media. The cases considered corresponding to doubly periodic rows of circular cylinders, for which a power series solution has been previously obtained, from complex variable theory. Both inline and staggered geometries are considered for three common configurations: inline-square, rotated-square, and equilateral geometries. From these mathematical solutions, values for the effective conduction/diffusion coefficient are readily constructed. The results are presented in terms of correlations for the ratio of effective-to-bulk conductivity/diffusivity or microstructural parameter, as a function of porosity. It is shown that near identical results with the present analytical analysis are obtained using calculations based on a finite-volume method and also with a previous mathematical analysis for the case of inline-square geometry. The present analytical solutions are also compared with two well-known correlations for random porous media, based on effective medium and percolation theory. It is shown that agreement with the analytical solution is not in general particularly good and depends on the choice of fitting parameters. The present results may be used as canonical data for comparative studies with numerical procedures to enumerate microstructural parameters for arbitrary-shaped occlusions in random geometries.

Graph Burning: Mathematical Formulations and Optimal Solutions

The graph burning problem is an NP-hard combinatorial optimization problem that helps quantify how vulnerable a graph is to contagion. This paper introduces three mathematical formulations of the problem: an integer linear program (ILP) and two constraint satisfaction problems (CSP1 and CSP2). Thanks to off-the-shelf optimization software, these formulations can be solved optimally over arbitrary graphs; this is relevant because the only algorithms designed to date for this problem are approximation algorithms and heuristics, which do not guarantee to find optimal solutions. We empirically compared the proposed formulations using random graphs and off-the-shelf optimization software. The results show that CSP1 and CSP2 tend to reach optimal solutions in less time than the ILP. Therefore, we executed them over some benchmark graphs of order at most 5908. The previously best-known solutions for some of these graphs were improved. We draw some empirical observations from the experimental results. For instance, we find the tendency: the larger the graph’s optimal solution, the more difficult it is to find it. Finally, the resulting set of optimal solutions might be helpful as a benchmark dataset for the performance evaluation of non-exact algorithms.

Analytical solution of unsteady heat conduction in multilayer internal combustion engine walls

An analytical solution of the unsteady heat conduction problem in multilayer walls was developed and applied to study thermal barrier coatings for reciprocating internal combustion engines. The mathematical solution was derived using the matrix method and complex analysis/residue-calculus Laplace transform inversion techniques. The one-dimensional domain includes a time-varying heat flux on the combustion chamber surface, and a time-varying temperature on the backside coolant surface. These boundary conditions are simulated as the superposition of two adjacent triangular, unit-magnitude pulses, which gives a piece-wise linear representation of the applied flux or temperature history. The temperature at any location of interest is found as the convolution of the transfer function, which results from the inversion, with the discrete-time heat flux or backside temperature history. The transfer functions describe the exact response and only depend on multilayer architecture, therefore, they can be computed a priori. The triangular pulse method provides a more than two order of magnitude reduction in computation time compared to a finite difference solution at the same level of accuracy. A 104-fold speed increase relative to a finite difference solution was realized when using the Overlap-add convolution technique for a full drive cycle simulation, i.e., a long time record. The surface response or transfer function acts like a finite impulse response and can be viewed in the frequency domain to reveal complementary information about coating performance.

Wave Propagation in Smart Sandwich Plates with Functionally Graded Nanocomposite Porous Core and Piezoelectric Layers in Multi-Physics Environment

This research provides a mathematical model and solution for investigating wave propagation in graphene platelets (GPLs)-reinforced functionally graded (FG) metal foam plates integrated with piezoelectric actuator and sensor layers resting on an orthotropic visco-Pasternak medium in magneto-electro-thermo environment. The FG porous nanocomposite core and the actuator piezoelectric layer are exposed to steady magnetic and electric fields, respectively. The electric potential between two piezoelectric layers is governed by a proportional-derivative controller. The Halpin–Tsai micromechanics model and the Kelvin–Voigt model are adopted to express the effective elastic modulus of the FG porous nanocomposite core and material viscoelasticity of the core and piezoelectric layers, respectively. The governing equations of smart FG porous nanocomposite plates under thermal environment are derived grounded on the refined third-order shear deformation theory. Upon the validated theoretical model, the wave velocities and frequencies in plates are obtained by solving governing equations analytically. Finally, the effects of material viscoelasticity, porosity distribution and coefficient, GPL distribution and weight fraction, the plate and GPL geometries and external environment on wave propagation characteristics are demonstrated comprehensively. This work provides guidance on tunable control of wave propagation in smart sandwich plates affected by complex external environments.