Search results for: algebraic reasoning

Authors: Sachin Kumar

Abstract:

Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

Procedia PDF Downloads 201

Authors: Mrigakshi Das

Abstract:

The ethics of a business is currently a high profile issue owing to sensational corporate scandals that had taken place in many countries causing extensive damages to the economy and society. These corporate scandals question the morality of businessmen in general and accountants in particular. It is argued that the accountants have been the main contributors to the decline in ethical standards of a business. This researcher has reviewed the need and impact of ethics education in accounting profession. Despite of ethical interventions, the rate of accounting scandals are increasing and have left the public questioning that has the profession become really less ethical?

Keywords: accounting, ethics education and intervention in accounting, accounting education, accounting profession, moral reasoning and development, ethics education

Procedia PDF Downloads 545

Authors: Farshad Badie

Abstract:

The central focus of this article is on the fact that knowledge is constructed from an interaction between humans’ experiences and over their conceptions of constructed concepts. Logical characterisation of ‘human inductive learning over human’s constructed concepts’ within terminological systems and providing a logical background for theorising over the Human Concept Learning Problem (HCLP) in terminological systems are the main contributions of this research. This research connects with the topics ‘human learning’, ‘epistemology’, ‘cognitive modelling’, ‘knowledge representation’ and ‘ontological reasoning’.

Keywords: human concept learning, concept construction, knowledge construction, terminological systems

Procedia PDF Downloads 325

Authors: Muhammad A. Ishaq, S. U. R. Aliyu

Abstract:

This paper on an exposition of Islamic fiscal policy attempts to discuss the basic principles of Islamic fiscal policy in an Islamic economy. The paper presents a number of definitions of the subject matter, its nature and its tools of application. Government spending, taxation and public borrowings were identified as the tools of the policy. The paper identifies zakat both as a veritable source of revenue and a major instrument of economic stabilization. Furthermore, the paper presents an algebraic 2-sector and 3-sector models from the basic Keynesian model. The paper posits that in view of uniqueness of its instruments, absence of interest rate in the economy and the policy’s derive towards socioeconomic justice and redistribution, Islamic fiscal policy is capable of stabilizing Islamic economy and ushering it into the path of long term economic growth and prosperity.

Keywords: automatic built-in-stabilizers, government spending, Islamic fiscal policy, taxation, zakat

Procedia PDF Downloads 339

Authors: Nan Tang, Bin Wu, Cunfu He

Abstract:

The trapezoid rods are widely used in civil engineering as load –carrying members. Ultrasonic guided wave is one of the most popular techniques in analyzing the propagation of elastic guided wave. The goal of this paper is to investigate the propagation of elastic waves in the isotropic bar with trapezoid cross-section. Dispersion curves that describe the relationship between the frequency and velocity provide the fundamental information to describe the propagation of elastic waves through a structure. Based on the SAFE (semi-analytical finite element) a linear algebraic system of equations is obtained. By using numerical methods, dispersion curves solved for the rods with the trapezoid cross-section. These fundamental information plays an important role in applying ultrasonic guided waves to NTD for structures with trapezoid cross section.

Keywords: guided wave, dispersion, finite element method, trapezoid rod

Procedia PDF Downloads 292

Authors: Morteza Khorrami

Abstract:

The logic as an intellectual infrastructure plays an essential role in the Islamic sciences. Hence, there are a few of the verses of the Holy Quran that their interpretation is not possible due to lack of proper logic. In many verses in the Quran, argument and the respondent has requested from the audience that shows the logic rule is in the Quran. The paper which use a descriptive and analytic method, tries to show the role of logic in understanding of the Quran reasoning methods and display some of Quranic statements with mathematical symbols and point that we can help these symbols for interesting and interpretation and answering to some questions and doubts. In this paper, this problem has been mentioned that the Quran did not use two-valued logic (Aristotelian) in all cases, but the fuzzy logic can also be searched in the Quran.

Keywords: aristotelian logic, fuzzy logic, interpretation, Holy Quran

Procedia PDF Downloads 675

Authors: M. Ndaw, G. Mendy, S. Ouya

Abstract:

Information system risk management helps to reduce or eliminate risk by implementing appropriate controls. In this paper, we propose a quantification model of controls impact on information system risks by automatizing the residual criticality estimation step of FMECA which is based on a inductive reasoning. For this, we defined three equations based on type and maturity of controls. For testing, the values obtained with the model were compared to estimated values given by interlocutors during different working sessions and the result is satisfactory. This model allows an optimal assessment of controls maturity and facilitates risk analysis of information system.

Keywords: information system, risk, control, FMECA method

Procedia PDF Downloads 355

Authors: Mariam Matiashvili

Abstract:

Argumentation is an integral part of our daily communications - formal or informal. Argumentative reasoning, techniques, and language tools are used both in personal conversations and in the business environment. Verbalization of the opinions requires the use of extraordinary syntactic-pragmatic structural quantities - arguments that add credibility to the statement. The study of argumentative structures allows us to identify the linguistic features that make the text argumentative. Knowing what elements make up an argumentative text in a particular language helps the users of that language improve their skills. Also, natural language processing (NLP) has become especially relevant recently. In this context, one of the main emphases is on the computational processing of argumentative texts, which will enable the automatic recognition and analysis of large volumes of textual data. The research deals with the linguistic analysis of the argumentative structures of Georgian political speeches - particularly the linguistic structure, characteristics, and functions of the parts of the argumentative text - claims, support, and attack statements. The research aims to describe the linguistic cues that give the sentence a judgmental/controversial character and helps to identify reasoning parts of the argumentative text. The empirical data comes from the Georgian Political Corpus, particularly TV debates. Consequently, the texts are of a dialogical nature, representing a discussion between two or more people (most often between a journalist and a politician). The research uses the following approaches to identify and analyze the argumentative structures Lexical Classification & Analysis - Identify lexical items that are relevant in argumentative texts creating process - Creating the lexicon of argumentation (presents groups of words gathered from a semantic point of view); Grammatical Analysis and Classification - means grammatical analysis of the words and phrases identified based on the arguing lexicon. Argumentation Schemas - Describe and identify the Argumentation Schemes that are most likely used in Georgian Political Speeches. As a final step, we analyzed the relations between the above mentioned components. For example, If an identified argument scheme is “Argument from Analogy”, identified lexical items semantically express analogy too, and they are most likely adverbs in Georgian. As a result, we created the lexicon with the words that play a significant role in creating Georgian argumentative structures. Linguistic analysis has shown that verbs play a crucial role in creating argumentative structures.

Keywords: georgian, argumentation schemas, argumentation structures, argumentation lexicon

Procedia PDF Downloads 70

Authors: Inayatur Rehman

Abstract:

Molodtstove developed the theory of soft sets which can be seen as an effective tool to deal with uncertainties. Since the introduction of this concept, the application of soft sets has been restricted to associative algebraic structures (groups, semi groups, associative rings, semi-rings etc.). Acceptably, though the study of soft sets, where the base set of parameters is a commutative structure, has attracted the attention of many researchers for more than one decade. But on the other hand there are many sets which are naturally endowed by two compatible binary operations forming a non-associative ring and we may dig out examples which investigate a non-associative structure in the context of soft sets. Thus it seems natural to apply the concept of soft sets to non-commutative and non-associative structures. In present paper, we make a new approach to apply Molodtsoves notion of soft sets to LA-ring (a class of non-associative ring). We extend the study of soft commutative rings from theoretical aspect.

Keywords: soft sets, LA-rings, soft LA-rings, soft ideals, soft prime ideals, idealistic soft LA-rings, LA-ring homomorphism

Procedia PDF Downloads 463

Authors: Khawar Ali

Abstract:

We present the numerical study of unsteady hydromagnetic (MHD) flow and heat transfer characteristics of a viscous incompressible electrically conducting water-based hybrid metallic nanofluid (containing Cu-Au/ H₂O nanoparticles) between two orthogonally moving porous coaxial disks with suction. Different from the classical shooting methodology, we employ a combination of a direct and an iterative method (SOR with optimal relaxation parameter) for solving the sparse systems of linear algebraic equations arising from the FD discretization of the linearized self similar nonlinear ODEs. Effects of the governing parameters on the flow and heat transfer are discussed and presented through tables and graphs. The findings of the present investigation may be beneficial for the electronic industry in maintaining the electronic components under effectiveand safe operational conditions.

Keywords: heat transfer enhancement, hybrid metallic nanofluid, viscous dissipation and joule heating effect , Two dimensional flow

Procedia PDF Downloads 229

Authors: Falek Kamel

Abstract:

Free vibration analysis of beams, based on the assumptions of Bernoulli-Euler theory, has been extensively studied. Many research works have focused on the study of transverse vibrations under the application of different boundary conditions where different theories have been applied. The stiffness and mass matrices considered are those obtained by assembling those resulting from the use of the finite element method. The Jacobi method has been used to solve the eigenvalue problem. These well-known concepts have been applied to the study of beams with constant geometric and mechanical characteristics having one to two overhangs with variable lengths. Murphy studied, by an algebraic solution approach, a simply supported beam with two overhangs of arbitrary length, allowing for an experimental determination of the elastic modulus E. The advantage of our article is that it offers the possibility of extending this approach to many interesting problems formed by transversely vibrating beams with various end constraints.

Keywords: beam, finite element, transverse vibrations, end restreint, Bernoulli-Euler theory

Procedia PDF Downloads 83

Authors: Hussain Abdullah Al-Salamin, Elias Ogutu Azariah Tembe

Abstract:

Supply chain (SC) is an operational research (OR) approach and technique which acts as catalyst within central nervous system of business today. Without SC, any type of business is at doldrums, hence entropy. SC is the lifeblood of business today because it is the pivotal hub which provides imperative competitive advantage. The paper present a conceptual framework dubbed as Homomorphic Conceptual Framework for Effective Supply Chain Strategy (HCEFSC).The term homomorphic is derived from abstract algebraic mathematical term homomorphism (same shape) which also embeds the following mathematical application sets: monomorphism, isomorphism, automorphisms, and endomorphism. The HCFESC is intertwined and integrated with wide and broad sets of elements.

Keywords: homomorphism, isomorphism, monomorphisms, automorphisms, epimorphisms, endomorphism, supply chain, operational research (OR)

Procedia PDF Downloads 372

Authors: Davide Forcellini, James Marshal Kelly

Abstract:

Seismic isolation using multi-layer elastomeric isolators has been used in the United States for more than 20 years. Although isolation bearings normally have a large factor of safety against buckling due to low shear stiffness, this phenomenon has been widely studied. In particular, the linearly elastic theory adopted to study this phenomenon is relatively accurate and adequate for most design purposes. Unfortunately it cannot consider the large deformation response of a bearing when buckling occurs and the unresolved behaviour of the stability of the post-buckled state. The study conducted in this paper may be viewed as a development of the linear theory of multi-layered elastomeric bearing, simply replacing the differential equations by algebraic equations, showing how it is possible to evaluate the post-buckling behaviour and the interactions at large deformations.

Keywords: multi-layer elastomeric isolators, large deformation, compressive load, tensile load, post-buckling behaviour

Procedia PDF Downloads 435

Authors: Alexander Denzler, Marcel Wehrle, Andreas Meier

Abstract:

A knowledge base stores facts and rules about the world that applications can use for the purpose of reasoning. By applying the concept of granular computing to a knowledge base, several advantages emerge. These can be harnessed by applications to improve their capabilities and performance. In this paper, the concept behind such a construct, called a granular knowledge cube, is defined, and its intended use as an instrument that manages to cope with different data types and detect knowledge domains is elaborated. Furthermore, the underlying architecture, consisting of the three layers of the storing, representing, and structuring of knowledge, is described. Finally, benefits as well as challenges of deploying it are listed alongside application types that could profit from having such an enhanced knowledge base.

Keywords: granular computing, granular knowledge, hierarchical structuring, knowledge bases

Procedia PDF Downloads 498

Authors: Yingxu Wang, Jianhua Lu, Jun Peng, Jiawei Zhang

Abstract:

The fundamental demand in contemporary intelligent science towards Autonomous AI (AI*) is the creation of unprecedented formal means of Intelligent Mathematics (IM). It is discovered that natural intelligence is inductively created rather than exhaustively trained. Therefore, IM is a family of algebraic and denotational mathematics encompassing Inference Algebra, Real-Time Process Algebra, Concept Algebra, Semantic Algebra, Visual Frame Algebra, etc., developed in our labs. IM plays indispensable roles in training-free AI* theories and systems beyond traditional empirical data-driven technologies. A set of applications of IM-driven AI* systems will be demonstrated in contemporary intelligence science, AI*, and cognitive computers.

Keywords: intelligence mathematics, foundations of intelligent science, autonomous AI, cognitive computers, inference algebra, real-time process algebra, concept algebra, semantic algebra, applications

Procedia PDF Downloads 61

Authors: Swati Arun

Abstract:

The present paper argues that Balance of Power (BOP) needs to conjugate with certain contingencies like geography. It is evident that sea powers (‘insular’ for better clarity) are not balanced (if at all) in the same way as land powers. Its apparent that artificial insularity that the US has achieved reduces the chances of balancing (constant) and helps it maintain preponderance (variable). But how precise is this approach in assessing the dynamics between China’s rise and reaction of other powers and US. The ‘evolved’ theory can be validated by putting China and US in the equation. Systemic Relation between the nations was explained through the Balance of Power theory much before the systems theory was propounded. The BOP is the crux of functionality of ‘power relation’ dynamics which has played its role in the most astounding ways leading to situations of war and peace. Whimsical; but true that, the BOP has remained a complicated and indefinable concepts since Hans. Morganthau to Kenneth Waltz. A challenge of the BOP, however remains; “ that it has too many meanings”. In the recent times it has become evident that the myriad of expectations generated by BOP has not met the practicality of the current world politics. It is for this reason; the BoP has been replaced by Preponderance Theory (PT) to explain prevailing power situation. PT does provide an empirical reasoning for the success of this theory but fails in a abstract logical reasoning required for making a theory universal. Unipolarity clarifies the current system as one where balance of power has become redundant. It seems to reach beyond the contours of BoP, where a superpower does what it must to remain one. The centrality of this arguments pivots around - an exception, every time BOP fails to operate, preponderance of power emerges. PT does not sit well with the primary logic of a theory because it works on an exception. The evolution of such a pattern and system where BOP fails and preponderance emerges is absent. The puzzle here is- if BOP really has become redundant or it needs polishing. The international power structure changed from multipolar to bipolar to unipolar. BOP was looked at to provide inevitable logic behind such changes and answer the dilemma we see today- why US is unchecked, unbalanced? But why was Britain unchecked in 19th century and why China was unbalanced in 13th century? It is the insularity of the state that makes BOP reproduce “imbalance of power”, going a level up from off-shore balancer. This luxury of a state to maintain imbalance in the region of competition or threat is the causal relation between BOP’s and geography. America has applied imbalancing- meaning disequilibrium (in its favor) to maintain the regional balance so that over time the weaker does not get stronger and pose a competition. It could do that due to the significant parity present between the US and the rest.

Keywords: balance of power, china, preponderance of power, US

Procedia PDF Downloads 278

Authors: Dipo Dunsin, Mohamed C. Ghanem, Karim Ouazzane

Abstract:

Digital investigators often have a hard time spotting evidence in digital information. It has become hard to determine which source of proof relates to a specific investigation. A growing concern is that the various processes, technology, and specific procedures used in the digital investigation are not keeping up with criminal developments. Therefore, criminals are taking advantage of these weaknesses to commit further crimes. In digital forensics investigations, artificial intelligence is invaluable in identifying crime. It has been observed that an algorithm based on artificial intelligence (AI) is highly effective in detecting risks, preventing criminal activity, and forecasting illegal activity. Providing objective data and conducting an assessment is the goal of digital forensics and digital investigation, which will assist in developing a plausible theory that can be presented as evidence in court. Researchers and other authorities have used the available data as evidence in court to convict a person. This research paper aims at developing a multiagent framework for digital investigations using specific intelligent software agents (ISA). The agents communicate to address particular tasks jointly and keep the same objectives in mind during each task. The rules and knowledge contained within each agent are dependent on the investigation type. A criminal investigation is classified quickly and efficiently using the case-based reasoning (CBR) technique. The MADIK is implemented using the Java Agent Development Framework and implemented using Eclipse, Postgres repository, and a rule engine for agent reasoning. The proposed framework was tested using the Lone Wolf image files and datasets. Experiments were conducted using various sets of ISA and VMs. There was a significant reduction in the time taken for the Hash Set Agent to execute. As a result of loading the agents, 5 percent of the time was lost, as the File Path Agent prescribed deleting 1,510, while the Timeline Agent found multiple executable files. In comparison, the integrity check carried out on the Lone Wolf image file using a digital forensic tool kit took approximately 48 minutes (2,880 ms), whereas the MADIK framework accomplished this in 16 minutes (960 ms). The framework is integrated with Python, allowing for further integration of other digital forensic tools, such as AccessData Forensic Toolkit (FTK), Wireshark, Volatility, and Scapy.

Keywords: artificial intelligence, computer science, criminal investigation, digital forensics

Procedia PDF Downloads 212

Authors: R. J. Chang

Abstract:

A cyclostationary Gaussian linearization method is formulated for investigating the time average response of nonlinear system under sinusoidal signal and white noise excitation. The quantitative measure of cyclostationary mean, variance, spectrum of mean amplitude, and mean power spectral density of noise is analyzed. The qualitative response behavior of stochastic jump and bifurcation are investigated. The validity of the present approach in predicting the quantitative and qualitative statistical responses is supported by utilizing Monte Carlo simulations. The present analysis without imposing restrictive analytical conditions can be directly derived by solving non-linear algebraic equations. The analytical solution gives reliable quantitative and qualitative prediction of mean and noise response for the Duffing system subjected to both sinusoidal signal and white noise excitation.

Keywords: cyclostationary, duffing system, Gaussian linearization, sinusoidal, white noise

Procedia PDF Downloads 489

Authors: Adriano Valdes-Gomez, Francisco Javier Sevilla

Abstract:

We devise a numerical algorithm to simulate the diffusion of a Brownian particle restricted to the surface of a three-dimensional sphere when the particle is under the effects of an external potential that is coupled linearly. It is obtained using elementary geometry, yet, it converges, in the weak sense, to the solutions to the Smoluchowski equation. Rotations on the sphere, which are the analogs of linear displacements in euclidean spaces, are calculated using algebraic operations and then by a proper scaling, which makes the algorithm efficient and quite simple, especially to what may be the short-time propagator approach. Our findings prove that the global effects of curvature are taken into account in both dynamic and stationary processes, and it is not restricted to work in configuration space, neither restricted to the overdamped limit. We have generalized it successfully to simulate the Kramers or the Ornstein-Uhlenbeck process, where it is necessary to work directly in phase space, and it may be adapted to other two dimensional surfaces with non-constant curvature.

Keywords: diffusion on the sphere, Fokker-Planck equation on the sphere, non equilibrium processes on the sphere, numerical methods for diffusion on the sphere

Procedia PDF Downloads 181

Authors: Alibakhsh Kasaeian, Mohammad Sameti, Zahra Noori, Mona Rastgoo Bahambari

Abstract:

Nowadays, the parabolic trough solar collector technology has become the most promising large-scale technology among various solar thermal generations. In this paper, a detailed numerical heat transfer model for a parabolic trough collector with nanofluid is presented based on the finite difference approach for which a MATLAB code was developed. The model was used to simulate the performance of a parabolic trough solar collector’s linear receiver, called a heat collector element (HCE). In this model, the heat collector element of the receiver was discretized into several segments in axial directions and energy balances were used for each control volume. All the heat transfer correlations, the thermodynamic equations and the optical properties were considered in details and the set of algebraic equations were solved simultaneously using iterative numerical solutions. The modeling assumptions and limitations are also discussed, along with recommendations for model improvement.

Keywords: heat transfer, nanofluid, numerical analysis, trough

Procedia PDF Downloads 371

Authors: R. Mellah, R. Toumi

Abstract:

This paper presents a new adaptive neuro-fuzzy controller equipped with compensatory fuzzy control (CNFI) in order to not only adjusts membership functions but also to optimize the adaptive reasoning by using a compensatory learning algorithm. The proposed control structure includes both CNFI controllers for which one is used to control in force the master robot and the second one for controlling in position the slave robot. The experimental results obtained, show a fairly high accuracy in terms of position and force tracking under free space motion and hard contact motion, what highlights the effectiveness of the proposed controllers.

Keywords: compensatory fuzzy, neuro-fuzzy, control adaptive, teleoperation

Procedia PDF Downloads 324

Authors: Han Hyuk Cho, Hanik Jo

Abstract:

In recent years, coding education has been globally emphasized, and the Free Semester System and coding education were introduced to the public schools from the beginning of 2016 and 2018 respectively in Korea. With the introduction of the Free Semester System and the rising demand of Computational Thinking (CT) capacity, this paper aims to design ‘Coding Environment’ and Minecraft-like Turtlecraft in which learners can design and construct mathematical objects through mathematical symbolic expressions. Students can transfer the constructed mathematical objects to the Turtlecraft environment (open-source codingmath website), and also can print them out through 3D printers. Furthermore, we design learnable mathematics and coding curriculum by representing the figurate numbers and patterns in terms of executable expression in the coding context and connecting them to algebraic symbols, which will allow students to experience mathematical patterns and symbolic coding expressions.

Keywords: coding education, computational thinking, mathematics education, TurtleMAL and Turtlecraft

Procedia PDF Downloads 206

Authors: Harendra Singh, Rajesh Pandey

Abstract:

The paper presents a numerical method based on operational matrix of integration and Ryleigh method for the solution of a class of non-linear fractional variational problems (NLFVPs). Chebyshev first kind polynomials are used for the construction of operational matrix. Using operational matrix and Ryleigh method the NLFVP is converted into a system of non-linear algebraic equations, and solving these equations we obtained approximate solution for NLFVPs. Convergence analysis of the proposed method is provided. Numerical experiment is done to show the applicability of the proposed numerical method. The obtained numerical results are compared with exact solution and solution obtained from Chebyshev third kind. Further the results are shown graphically for different fractional order involved in the problems.

Keywords: non-linear fractional variational problems, Rayleigh-Ritz method, convergence analysis, error analysis

Procedia PDF Downloads 298

Authors: Ashwani Kumar

Abstract:

Use of NIR light for imaging the biological tissue and to quantify its optical properties is a good choice over other invasive methods. Optical tomography involves two steps. One is the forward problem and the other is the reconstruction problem. The forward problem consists of finding the measurements of transmitted light through the tissue from source to detector, given the spatial distribution of absorption and scattering properties. The second step is the reconstruction problem. In X-ray tomography, there is standard method for reconstruction called filtered back projection method or the algebraic reconstruction methods. But this method cannot be applied as such, in optical tomography due to highly scattering nature of biological tissue. A hybrid algorithm for reconstruction has been implemented in this work which takes into account the highly scattered path taken by photons while back projecting the forward data obtained during Monte Carlo simulation. The reconstructed image suffers from blurring due to point spread function.

Keywords: NIR light, tissue, blurring, Monte Carlo simulation

Procedia PDF Downloads 493

Authors: Berhane Tewelday Weldhiwot

Abstract:

This research investigates the pivotal role of modular forms in modern cryptographic systems, particularly focusing on their applications in secure communications and data integrity. Modular forms, which are complex analytic functions with rich arithmetic properties, have gained prominence due to their connections to number theory and algebraic geometry. This study begins by outlining the fundamental concepts of modular forms and their historical development, followed by a detailed examination of their applications in cryptographic protocols such as elliptic curve cryptography and zero-knowledge proofs. By employing techniques from analytic number theory, the research delves into how modular forms can enhance the efficiency and security of cryptographic algorithms. The findings suggest that leveraging modular forms not only improves computational performance but also fortifies security measures against emerging threats in digital communication. This work aims to contribute to the ongoing discourse on integrating advanced mathematical theories into practical applications, ultimately fostering innovation in cryptographic methodologies.

Keywords: modular forms, cryptography, elliptic curves, applications, mathematical theory

Procedia PDF Downloads 16

Authors: J. Juan Peña, J. Morales, J. García-Ravelo, J. García-Martínez

Abstract:

It is known that by introducing alternative forms of exponential and logarithmic functions, the Tsallis entropy Sᵩ is itself a generalization of Shannon entropy S. In this work, from a deformation through a scaling function applied to the differential operator, it is possible to generate a q-deformed calculus as well as a q-deformed arithmetic, which not only allows generalizing the exponential and logarithmic functions but also any other standard function. The updated q-deformed differential operator leads to an updated integral operator under which the functions are integrated together with a weight function. For each differentiable function, it is possible to identify its q-deformed partner, which is useful to generalize other algebraic relations proper of the original functions. As an application of this proposal, in this work, a generalization of exponential and logarithmic functions is studied in such a way that their relationship with the thermodynamic functions, particularly the entropy, allows us to have a q-deformed expression of these. As a result, from a particular scaling function applied to the differential operator, a q-deformed arithmetic is obtained, leading to the generalization of the Tsallis entropy.

Keywords: q-calculus, q-deformed arithmetic, entropy, exponential functions, thermodynamic functions

Procedia PDF Downloads 78

Authors: Shubham Jaiswal

Abstract:

During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: nonlinear porous media equation, shifted Jacobi polynomials, operational matrix, spectral collocation method

Procedia PDF Downloads 439

Authors: R. Tariq, R. Lee

Abstract:

Background: Additional demands placed on senior clinical teams with ongoing COVID-19 management has accelerated the need to harness the wider healthcare professional resources and upskill them to take on greater clinical responsibility safely. The UK NHS Long Term Plan (2019)¹ emphasises the importance of expanding Advanced Practitioners’ (APs) roles to take on more clinical diagnostic responsibilities to cope with increased demand. In acute settings, APs are often the first point of care for patients and require training to take on initial triage responsibilities efficiently and safely. Critically, their roles include determining which onward services the patients may require, and assessing whether they can be treated at home, avoiding unnecessary admissions to the hospital. Dem Dx is a Clinical Reasoning Platform (CRP) that claims to help frontline healthcare professionals independently assess and triage patients. It guides the clinician from presenting complaints through associated symptoms to a running list of differential diagnoses, media, national and institutional guidelines. The objective of this study was to compare the clinical referral rates and guidelines adherence registered by the HMR Urgent Community Care Team (UCCT)² and Dem Dx recommendations using retrospective cases. Methodology: 192 cases seen by the UCCT were anonymised and reassessed using Dem Dx clinical pathways. We compared the UCCT’s performance with Dem Dx regarding the appropriateness of onward referrals. We also compared the clinical assessment regarding adherence to NICE guidelines recorded on the clinical notes and the presence of suitable guidance in each case. The cases were audited by two medical doctors. Results: Dem Dx demonstrated appropriate referrals in 85% of cases, compared to 47% in the UCCT team (p<0.001). Of particular note, Dem Dx demonstrated an almost 65% (p<0.001) improvement in the efficacy and appropriateness of referrals in a highly experienced clinical team. The effectiveness of Dem Dx is in part attributable to the relevant NICE and local guidelines found within the platform's pathways and was found to be suitable in 86% of cases. Conclusion: This study highlights the potential of clinical decision support, as Dem Dx, to improve the quality of onward clinical referrals delivered by a multidisciplinary team in primary care. It demonstrated that it could support healthcare professionals in making appropriate referrals, especially those that may be overlooked by providing suitable clinical guidelines directly embedded into cases and clear referral pathways. Further evaluation in the clinical setting has been planned to confirm those assumptions in a prospective study.

Keywords: advanced practitioner, clinical reasoning, clinical decision-making, management, multidisciplinary team, referrals, triage

Procedia PDF Downloads 149

Authors: Stephen O. Amaraihu

Abstract:

This research investigated the effect of Computer Based Instruction on Students’ interest, achievement, and retention in Algebra in Abia State College of Education (Technical), Arochukwu. Three research questions and two hypotheses guided the study. Two instruments, Maths Achievement Test (MAT) and Maths Interest Inventory were employed, to test a population of three hundred and sixteen (316) NCE 1 students in algebra. It is expected that this research will lead to the improvement of students’ performance and enhance their interest and retention of basic algebraic concept. It was found that the majority of students in the college are not proficient in the use of ICT as a result of a lack of trained personnel. It was concluded that the state government was not ready to implement the usage of mathematics in Abia State College of Education. The paper recommends, amongst others, the employment of mathematics Lectures with competent skills in ICT and the training of lecturers of mathematics.

Keywords: achievement, computer based instruction, interest, retention

Procedia PDF Downloads 209

Authors: Lavinia Ciungu

Abstract:

In the last decades, developing algebras related to the logical foundations of quantum mechanics became a central topic of research. Generally known as quantum structures, these algebras serve as models for the formalism of quantum mechanics. In this work, we introduce the notion of quantum-Wajsberg algebras by redefining the quantum-MV algebras starting from involutive BE algebras. We give a characterization of quantum-Wajsberg algebras, investigate their properties, and show that, in general, quantum-Wajsberg algebras are not (commutative) quantum-B algebras. We also define the ∨-commutative quantum-Wajsberg algebras and study their properties. Furthermore, we prove that any Wajsberg algebra (bounded ∨-commutative BCK algebra) is a quantum-Wajsberg algebra, and we give a condition for a quantum-Wajsberg algebra to be a Wajsberg algebra. We prove that Wajsberg algebras are both quantum-Wajsberg algebras and commutative quantum-B algebras. We establish the connection between quantum-Wajsberg algebras and quantum-MV algebras, proving that the quantum-Wajsberg algebras are term equivalent to quantum-MV algebras. We show that, in general, the quantum-Wajsberg algebras are not commutative quantum-B algebras and if a quantum-Wajsberg algebra is self-distributive, then the corresponding quantum-MV algebra is an MV algebra. Our study could be a starting point for the development of other implicative counterparts of certain existing algebraic quantum structures.

Keywords: quantum-Wajsberg algebra, quantum-MV algebra, MV algebra, Wajsberg algebra, BE algebra, quantum-B algebra

Procedia PDF Downloads 15