Mathematical Frame Research Articles

Concept lattice formalisms of Hébert’s “semic analysis” and “analysis by classification”

Abstract In this article we provide a mathematical frame to the generation of class taxonomies suggested by Hébert in his analysis of the poem <<Quelle affaire!>> (‘A Sorry Business!’) by Gilles Vigneault (b. 1928) as well as a formalization of the structure of semic isotopies in his reading of The golden ship by Émile Nelligan (1879–1941). We also examine the characteristics of inter- and intra-semic molecules at work within Réne Magritte’s painting La clef des songes. Our mathematical frame is Ganter and Wille’s extension of lattice theory called formal concept analysis, for which we explore various formalisms and constructs that allow us to reason on semic structures.

Solution Strategy and Associated Results for Fuzzy Mellin Transformation

The advancement of the Mellin transformation is that it exhibits a scale-invariant nature, and thus, it is widely used in computer science. Fuzzy Mellin transformation can provide the purposes of such problems in uncertain phenomena. The existing studies on fuzzy Mellin transformation consider the fuzzy level cut approach, which makes the fuzzy valued functions into their crisp couplets regarding lower and uppercuts. This paper reconstructs a distinct mathematical frame for the Mellin transformation in a completely fuzzy environment in the sense of a modified Hukuhara derivative. In this paper, we mean the complete fuzzy environment to describe fuzzy phenomena where the conversion of the fuzzy function to its crisp counterpart is annulled. The proposed fuzzy Mellin transformation’s superiority over existing approaches is that it can be used directly to fuzzy valued functions without converting them to their crisp counter version. The challenges to dealing with fuzzy valued mappings and inputs without its level cut representation have been tackled in this manuscript. Furthermore, numerical examples, possible applications, and further extensions of this work are hinted at in this paper.

Optimizing reverse osmosis desalination from brackish waters: Predictive approach employing response surface methodology and artificial neural network models

A mathematical model frame has been developed to optimize the performance of reverse osmosis (RO) desalination in brackish waters with medium to high salt concentrations using response surface methodology (RSM) and artificial neural network (ANN), specifically catered towards efficiently operating RO desalination systems. The RSM model aims at predicting RO performance with second-order polynomials based on 15 experimental datasets. Inputs for RSM model include feed TDS concentration, feed water flow rate, and concentration-to-desalination ratio, while the outputs consider rejection, membrane flux, performance index, and specific energy consumption. The Genetic Algorithm optimized back-propagation Neural Network was employed to update network weights and biases, leading to an optimal ANN network structure of 3–10-4. A ratio of 70 % training, 15 % validation, and 15 % test data was chosen to establish an ANN model that predicts the performance of RO desalination. The ANN model demonstrated significantly higher prediction accuracy than the RSM model, with impressive correlation coefficients of 0.9936 for the performance index and 0.9932 for SEC prediction, and low RMSE of 0.85 for rejection. To maximize the performance index and minimize specific energy consumption, a two-step optimization method was further set up by applying the RSM model to initially determine optimal process conditions followed by the ANN model to enhance the accuracy of performance forecasts. Optimal process conditions were proposed for specific feed TDS scenarios, which involved setting a feed TDS concentration limit to meet drinking water standards.

An investigation into the approach of mathematics undergraduates to a non-routine task

ABSTRACT Critical thinking and problem solving are widely recognised as valuable competencies in the twenty-first century, and indispensable skills in the workplace. In this context, we investigate the strategies employed by first-year university mathematics students when faced with a non-routine task, specifically the impossible triangle. The data collection process involved the administration of a questionnaire (70 questionnaire responses) and conducting interviews (six interviews). The study used the lens of framing to examine the interplay between the task cue and students' responses, and the Ref*AER framework to interpret the knowledge of the participants. A considerable number of students approached the task using an algorithmic mathematical frame. With reference to the Ref*AER framework, the participants' inadequate conceptions were a hindrance to the successful completion of the task. We believe that the implementation of tasks like the impossible triangle in the mathematics classroom can effectively foster students' noticing and uncover deficiencies in their knowledge.

On Flamant–Boussinesq problem with dynamical flexoelectric effect and micro-inertia effect in dielectrics subjected to dynamical wave loading

This work investigates the Flamant–Boussinesq problem for a half-space made of a homogeneous and isotropic dielectric material. The dynamical flexoelectric effect and the dynamical flexocoupling between displacement and polarization, due to mechanical and electrical states, are taken in consideration. The mechanical loading is taken as a wave of a decaying behavior in time at the surface of a half-space, while the electric potential is considered in an open circuit with no charge on the terminals. The first strain gradient theory of elasticity is used as a mathematical frame in the problem formulation. The equation of motion for the representative volume element additionally accounts for the micro-inertia effect because of the intrinsic structure of the dielectrics at the nanoscale. The governing equations and the boundary conditions for homogeneous, isotropic dielectric material are presented with reference to previous work, using a variational technique for internal energies and external forces. An analytical harmonic wave solution is obtained for the problem under consideration, involving different coupling parameters arising from the mechanical and electrical loadings. The results are analyzed and discussed. The solutions for the quantities of practical interest are represented graphically with different choices of material parameters and flexocoupling parameters. The solution is finite everywhere. The existing damping phenomenon arises, not only from the various physical parameters in the governing field equations as shown in the figures, but also through the boundary conditions.

Gradient Flows for Probabilistic Frame Potentials in the Wasserstein Space

In this paper we bring together some of the key ideas and methods of two disparate fields of mathematical research, frame theory, and optimal transport, using the methods of the second to answer questions posed in the first. In particular, we construct gradient flows in the Wasserstein space for a new potential, the tightness potential, which is a modification of the probabilistic frame potential. It is shown that the potential is suited for the application of a gradient descent scheme from optimal transport that can be used as the basis of an algorithm to evolve an existing frame toward a tight probabilistic frame.

A Corpus-based Approach to Frame ‘COVID-19 Vaccination’ in Malaysian English Newspapers

Most studies on COVID-19 have been massively dedicated on how the disease was framed in the newspaper, its psychological effects, and its message or content disinformation. Research on the COVID-19 vaccination in newspapers and its acceptance among the masses is still quite scarce. The study adopted a corpus approach that involves wordlist, keyword list, collocates, and concordance analysis to analyse how ‘COVID-19 vaccination’ was framed in a focused and specialised English Malaysian newspapers corpus. #Lanscbox 5.0 corpus tool was employed in conducting the empirical analysis. The empirical analysis revealed that ‘COVID-19 vaccination’ was positively framed in different ways in the newspaper. The analysis of collocates and concordance lines revealed that the news reports mainly used Solution-oriented Frame which highlighted the Malaysian government’s effort in combating the pandemic. The newspaper was also found to use Mathematical frame in the effort to convince the public with regards to the updates and statistics of vaccine takers. Nevertheless, the results also revealed the usage of sensational phrases that framed the COVID-19 vaccination negatively. These findings can enlighten newspaper practitioners on what should be done and avoided in framing such an issue in their writings as well as how the public will perceive it. Keywords: Corpus-based analysis, COVID-19, mass media, news article, vaccination.

Evaluation of the route selection in international freight transportation by using the CODAS technique based on interval-valued Atanassov intuitionistic sets.

The selection of a proper international freight transport route is one of the crucial tasks for decision-makers since it can affect costs, efficiency, and transportation performance. Besides, the selection of suitable and appropriate freight routes can also reduce external costs of transportation such as emissions, noise, traffic congestions, accidents, and so on. Route selection in international transportation is a complicated decision-making problem as many conflicting factors and criteria affect the assessment process. It has been observed that there is no mathematical model and methodological frame used for solving these selection problems, and decision-makers make decisions on this issue based on their own experiences and verbal judgments in the research process. Therefore, a methodological frame is required to make rational, realistic, and optimal decisions on route selection. From this perspective, the current paper proposes using the IVAIF CODAS, an extended version of the traditional CODAS techniques, and using the Atanassov interval-valued intuitionistic fuzzy sets (IVAIFS) for processing better the existing uncertainties. The proposed model is applied to solve the route selection, a real-life decision-making problem encountered in international transportation between EU countries and Turkey. According to the results of the analysis, option A6 (i.e., Route-6 (Bursa-Istanbul-Pendik-Trieste (Ro-Ro)-Austria-Frankfurt/Germany) has been determined as the best alternative. These obtained results have been approved by a comprehensive sensitivity analysis performed by using different MCDM techniques based on interval-valued intuitionistic fuzzy sets. Hence, it can be accepted that the proposed model is an applicable, robust, and powerful mathematical tool; also, it can provide very reliable, accurate, and reasonable results. As a result, the proposed model can provide a more flexible and effective decision-making environment as well as it can provide valuable advantages to the logistics and transport companies for carrying out practical, productive, and lower cost logistics operations.

About Non-relativistic Quantum Mechanics and Electromagnetism

We describe here the coherent formulation of electromagnetism in the non-relativistic quantum-mechanical many-body theory of interacting charged particles. We use the mathematical frame of the field theory and its quantization in the spirit of the quantum electrodynamics (QED). This is necessary because a manifold of misinterpretations emerged especially regarding the magnetic field and gauge invariance. The situation was determined by the historical development of quantum mechanics, starting from the Schrödinger equation of a single particle in the presence of given electromagnetic fields, followed by the many-body theories of many charged identical particles having just Coulomb interactions. Our approach to the non-relativistic QED emphasizes the role of the gauge-invariance and of the external fields. We develop further the approximation of this theory allowing a closed description of the interacting charged particles without photons. The resulting Hamiltonian coincides with the quantized version of the Darwin Hamiltonian containing besides the Coulomb also a current-current diamagnetic interaction. We show on some examples the importance of this extension of the many-body theory.

Algorithm for the Reconstruction of Mathematical Frame Models of Bacterial Transcription Regulation

Transcription regulation plays an important role in bacterial activity. The operon concept coined by François Jacob and Jacques Monod has had a considerable effect on investigations into gene expression regulation, including modeling. However, most such studies have considered the regulation models devised manually for one or several operons. For that reason, the objective of the present study was automated genome model reconstruction for different bacteria. The suggested algorithm accounted for all possible interactions of transcription factors and their binding sites in an operon’s promoter region. Transcription factor enumeration was performed using the deep-first search technique. The obtained models are of interest for those involved in the research of transcription factor regulatory effects on bacterial gene expression in microbiology and biotechnology.

A mathematical framework of ANFIS tuned UPQC controlled RES based isolated microgrid system

This paper presented a nascent mathematical modeling of ANFIS tuned Unified Power Quality Conditioner (UPQC) controlled hybrid microgrid incoprating an Induction generator (IG) for a wind energy- system and an alternator for conventional generation. The mathematical frame of the hybrid microgrid system is presented using power equalities. A powerful Flexible AC Transmission system (FACTS) controller UPQC, generally used with conventional sources is considered to control the voltage and reactive power flow in the presented microgrid framework. Further Adaptive Neuro-Fuzzy Inference System (ANFIS) technique has been used to optimize the FACTS controller UPQC in MATLAB software.

Crossing Bar Lines: The Politics and Practices of Black Musical Space

Crossing Bar Lines: The Politics and Practices of Black Musical Space

An improved proximal method with quasi-distance for nonconvex multiobjective optimization problem

Abstract Multiobjective optimization is the optimization with several conflicting objective functions. However, it is generally tough to find an optimal solution that satisfies all objectives from a mathematical frame of reference. The main objective of this article is to present an improved proximal method involving quasi-distance for constrained multiobjective optimization problems under the locally Lipschitz condition of the cost function. An instigation to study the proximal method with quasi distances is due to its widespread applications of the quasi distances in computer theory. To study the convergence result, Fritz John’s necessary optimality condition for weak Pareto solution is used. The suitable conditions to guarantee that the cluster points of the generated sequences are Pareto–Clarke critical points are provided.

A model of octopus epidermis pattern mimicry mechanisms using inverse operation of the Turing reaction model.

Many cephalopods such as octopi and squid can purposefully and rapidly change their skin color. Furthermore, it is widely known that some octopi have the ability to rapidly change the color and unevenness of their skin to mimic their surroundings. However, there has been little research published on the mechanisms by which an octopus recognizes its surrounding landscape and changes its skin pattern. We are unaware of any hypothetical model that explains this mimicry mechanism to date. In this study, the mechanism of octopus skin pattern change was assumed to be based on the Turing pattern model. Here, pattern formation using the Turing model was realized using an equivalent filter calculation model and a cellular automaton instead of directly solving the differential equations. It was shown that this model can create various patterns using two feature parameters. Furthermore, for visual recognition where two features are extracted from the Turing pattern image, a method that requires minimal calculation using the characteristics of the cellular Turing pattern model is proposed. These two calculations can be expressed in the same mathematical frame based on the cellular automaton model using a convolution filter. As a result, a model that is capable of extracting features from patterns and reconstructing those patterns rapidly can be created. This represents a basic model of the mimicry mechanism of octopi. Further, this study demonstrates the potential for creating a model with minimal learning calculation for application to machine learning.

Effective Automatic Radar Bias Estimation Scheme Using Targets of Opportunity

In multi-radar air surveillance scenario bias in individual radar measurements is an important prerequisite for effective fusion of radar data. Conventional bias computation approaches depend on GPS fitted air sorties for computation of bias in radar measurements. The method proposed in this paper computes radar bias automatically using GPS data available from Automatic Dependent Surveillance Broadcast (ADS-B) measurements from targets of opportunity. The proposed method computes the bias in radar measurements without the need of costly dedicated calibration sorties or multiple radars and thereby reducing the cost and manual effort. This paper provides details about the mathematical frame works of recursive weighted least square based bias estimation algorithm and the associated data conversion formats in different coordinate systems. The proposed method preprocess the correlated radar and AD-B measurements and selects measurement pairs from linear segments for time alignment. This paper provides a detailed scheme of automatic bias estimation process with different parameters involved in controlling the accuracy and periodicity of the bias to be computed. The scheme developed in this paper also includes a bias validation module and a unique averaging method to ensure accuracy and smooth variations across the measurement batches considered for computation. The simulation results obtained in this paper suggest the utility of the proposed approach for practical bias computation applications in a cost effective way. The method developed in this paper is based on insight obtained from analysis of recorded data from field deployed radars.

Tundish Process Performance Parameters and Their Direct Estimation from a New, Plant Measurement-Based Formalism

A mathematical frame work has been developed to quantitatively investigate inclusion floatation and generation phenomena in a tundish during continuous casting of LCAK (low carbon aluminum killed) steel. Embodying industrial scale measurements of dissolved and total aluminum in VD (vacuum degasser), tundish and bloom in a materials balance frame work, two key dimensionless parameters, viz., inclusion generation (GI) and floatation (FI) indices, have been formulated. To demonstrate their adequacy, as a test case, a 13 metric ton bloom casting tundish has been considered and plant scale data from nearly fifty heats applied. The analysis reveals barely satisfactory inclusion floatation coupled with significant generation, indicating essentially sub-optimal tundish process performance.

On the well posedness of static boundary value problem within the linear dilatational strain gradient elasticity

In this paper, it is proven an existence and uniqueness theorem for weak solutions of the equilibrium problem for linear isotropic dilatational strain gradient elasticity. Considered elastic bodies have as deformation energy the classical one due to Lamé but augmented with an additive term that depends on the norm of the gradient of dilatation: only one extra second gradient elastic coefficient is introduced. The studied class of solids is therefore related to Korteweg or Cahn–Hilliard fluids. The postulated energy naturally induces the space in which the aforementioned well-posedness result can be formulated. In this energy space, the introduced norm does involve the linear combination of some specific higher-order derivatives only: it is, in fact, a particular example of anisotropic Sobolev space. It is also proven that aforementioned weak solutions belongs to the space H^1(div,V), i.e. the space of H^1 functions whose divergence belongs to H^1. The proposed mathematical frame is essential to conceptually base, on solid grounds, the numerical integration schemes required to investigate the properties of dilatational strain gradient elastic bodies. Their energy, as studied in the present paper, has manifold interests. Mathematically speaking, its singularity causes interesting mathematical difficulties whose overcoming leads to an increased understanding of the theory of second gradient continua. On the other hand, from the mechanical point of view, it gives an example of energy for a second gradient continuum which can sustain externally applied surface forces and double forces but cannot sustain externally applied surface couples. In this way, it is proven that couple stress continua, introduced by Toupin, represent only a particular case of the more general class of second gradient continua. Moreover, it is easily checked that for dilatational strain gradient continua, balance of force and balance of torques (or couples) are not enough to characterise equilibrium: to this aim, externally applied surface double forces must also be specified. As a consequence, the postulation scheme based on variational principles seems more suitable to study second gradient continua. It has to be remarked finally that dilatational strain gradient seems suitable to model the experimentally observed behaviour of some material used in 3D printing process.

Eco-activism in social networks and consumption practices of megalopolises’ residents

Introduction. The increasing role of ecology in citizens’ daily occurrence is becoming a factor in changing consumer behavior. More and more people are interested in the eco-agenda, added to thematic communities in social networks, and guided by the self-restraint principles. Materials and Methods. Mixed data collection paradigm applied during the study. It includes analysis of both primary and secondary information. Primary information was collected using three methods: content analysis, online survey (quantitative strategy), and semi-formal interview (qualitative strategy). We applied both mathematical data processing and frame analysis of statements, as well as analysis of materials in the public domain. Residents of Russian megalopolises have become key objects; for collecting primary information – Ekaterinburg, for secondary information – Moscow and St. Petersburg, residents of Russia. Research results and discussion. Social networks with specific forms of user interaction have a mobilizing ability. Signing petitions, and mass cleaning of the surrounding area is not a rare phenomenon. The study analyzes the frames of active, moderate, and passive users of social networks. There is a difference in the level of inclusion of environmental practices in daily consumption for each of them. High mobility from passive users’ group to the moderate group was revealed. This is reflected in consumer practices such as refusing to buy, from plastic bags to personal cars. Conclusions. The study demonstrated the correlation between changing consumer values and their interest in focusing on green practices.

Reinforcement learning for optimal scheduling of Glioblastoma treatment with Temozolomide

Background: Glioblastoma multiforme (GBM) is the most frequent primary brain tumor in adults and Temozolomide (TMZ) is an effective chemotherapeutic agent for its treatment. In Silico models of GBM growth provide an appropriate foundation for analysis and comparison of different regimens. We propose a mathematical frame for patient specific design of optimal chemotherapy regimens for GBM patients. Methods: The proposed frame includes online interaction of a virtual GBM with an optimizing agent. Spatiotemporal dynamics of GBM growth and its response to TMZ are simulated with a three dimensional hybrid cellular automaton. Q learning is tailored to the virtual GBM for treatment optimization aimed at minimizing tumor size at the end of treatment course. Q learning consists of a learning agent that interacts with the virtual GBM. System state is affected by the agent decisions and the obtained rewards guide Q learning to the optimal schedule. Results: Computational results confirm that the optimal chemotherapy schedule depends on some patient specific parameters including body weight, tumor size and its position in the brain. Furthermore, the algorithm is used for scheduling 2100 mg of TMZ on a virtual GBM and the obtained schedule is to administer150 mg of TMZ every other day. The obtained schedule is compared to the standard 7/14 regimen and the results show that it is superior to the 7/14 regimen in minimizing tumor size. Conclusion: The proposed frame is an appropriate decision support system for patient specific design of TMZ administration regimens on GBM patients. Also, since the obtained optimal schedule outperforms the standard 7/14 regimen, it is worthy of further clinical testing.

Practical Verifiable Computation by Using a Hardware-Based Correct Execution Environment

The verifiable computation paradigm has been studied extensively as a means to verifying the result of outsourced computation. In said scheme, the verifier requests computation from the prover and verifies the result by checking the output and proof received from the prover. Although they have great potential for various critical applications, verifiable computations have not been widely used in practice, because of their significant performance overhead. Existing cryptography-based approaches incur significant overhead, because a cryptography-based mathematical frame needs to be constructed, which prevents deviation from the correct computation. The proposed approach is to reduce the overhead by trusting the computing hardware platform where the computation is outsourced. If one trusts the hardware to do the computation, the hardware can take the place of the cryptographic computing frame, thereby guaranteeing correct computation. The key challenge of this approach is to define what exactly the hardware should guarantee for verifiable computation. For this, we introduce the concept of Correct Execution Environment (CEE), which guarantees instruction correctness and state preservation. We prove that these two requirements are satisfactory conditions for a correct output. By employing a CEE, the verifiable computation scheme can be simplified, and its overhead can be reduced drastically. The presented experimental results demonstrate that the execution time is approximately 1.7 million times faster and the verification time over 50 times faster than a state-of-the-art cryptographic approach.