Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 13

Search results for: derivations

13 Inner Derivations of Low-Dimensional Diassociative Algebras

Authors: M. A. Fiidow, Ahmad M. Alenezi

Abstract:

In this work, we study the inner derivations of diassociative algebras in dimension two and three, an algorithmic approach is adopted for the computation of inner derivation, using some results from the derivation of finite dimensional diassociative algebras. Some basic properties of inner derivation of finite dimensional diassociative algebras are also provided.

Keywords: diassociative algebras, inner derivations, derivations, left and right operator

Procedia PDF Downloads 202
12 On Lie-Central Derivations and Almost Inner Lie-Derivations of Leibniz Algebras

Authors: Natalia Pacheco Rego

Abstract:

The Liezation functor is a map from the category of Leibniz algebras to the category of Lie algebras, which assigns a Leibniz algebra to the Lie algebra given by the quotient of the Leibniz algebra by the ideal spanned by the square elements of the Leibniz algebra. This functor is left adjoint to the inclusion functor that considers a Lie algebra as a Leibniz algebra. This environment fits in the framework of central extensions and commutators in semi-abelian categories with respect to a Birkhoff subcategory, where classical or absolute notions are relative to the abelianization functor. Classical properties of Leibniz algebras (properties relative to the abelianization functor) were adapted to the relative setting (with respect to the Liezation functor); in general, absolute properties have the corresponding relative ones, but not all absolute properties immediately hold in the relative case, so new requirements are needed. Following this line of research, it was conducted an analysis of central derivations of Leibniz algebras relative to the Liezation functor, called as Lie-derivations, and a characterization of Lie-stem Leibniz algebras by their Lie-central derivations was obtained. In this paper, we present an overview of these results, and we analyze some new properties concerning Lie-central derivations and almost inner Lie-derivations. Namely, a Leibniz algebra is a vector space equipped with a bilinear bracket operation satisfying the Leibniz identity. We define the Lie-bracket by [x, y]lie = [x, y] + [y, x] , for all x, y . The Lie-center of a Leibniz algebra is the two-sided ideal of elements that annihilate all the elements in the Leibniz algebra through the Lie-bracket. A Lie-derivation is a linear map which acts as a derivative with respect to the Lie-bracket. Obviously, usual derivations are Lie-derivations, but the converse is not true in general. A Lie-derivation is called a Lie-central derivation if its image is contained in the Lie-center. A Lie-derivation is called an almost inner Lie-derivation if the image of an element x is contained in the Lie-commutator of x and the Leibniz algebra. The main results we present in this talk refer to the conditions under which Lie-central derivation and almost inner Lie-derivations coincide.

Keywords: almost inner Lie-derivation, Lie-center, Lie-central derivation, Lie-derivation

Procedia PDF Downloads 69
11 Derivation of BCK\BCI-Algebras

Authors: Tumadhir Fahim M Alsulami

Abstract:

The concept of this paper builds on connecting between two important notions, fuzzy ideals of BCK-algebras and derivation of BCI-algebras. The result we got is a new concept called derivation fuzzy ideals of BCI-algebras. Followed by various results and important theorems on different types of ideals. In chapter 1: We presented the basic and fundamental concepts of BCK\ BCI- algebras as follows: BCK/BCI-algebras, BCK sub-algebras, bounded BCK-algebras, positive implicative BCK-algebras, commutative BCK-algebras, implicative BCK- algebras. Moreover, we discussed ideals of BCK-algebras, positive implicative ideals, implicative ideals and commutative ideals. In the last section of chapter 1 we proposed the notion of derivation of BCI-algebras, regular derivation of BCI-algebras and basic definitions and properties. In chapter 2: It includes 3 sections as follows: Section 1 contains elementary concepts of fuzzy sets and fuzzy set operations. Section 2 shows O. G. Xi idea, where he applies fuzzy sets concept to BCK-algebras and we studied fuzzy sub-algebras as well. Section 3 contains fuzzy ideals of BCK-algebras basic definitions, closed fuzzy ideals, fuzzy commutative ideals, fuzzy positive implicative ideals, fuzzy implicative ideals, fuzzy H-ideals and fuzzy p-ideals. Moreover, we investigated their concepts in diverse theorems and propositions. In chapter 3: The main concept of our thesis on derivation fuzzy ideals of BCI- algebras is introduced. Chapter 3 splits into 4 sections. We start with General definitions and important theorems on derivation fuzzy ideal theory in section 1. Section 2 and 3 contain derivations fuzzy p-ideals and derivations fuzzy H-ideals of BCI- algebras, several important theorems and propositions were introduced. The last section studied derivations fuzzy implicative ideals of BCI-algebras and it includes new theorems and results. Furthermore, we presented a new theorem that associate derivations fuzzy implicative ideals, derivations fuzzy positive implicative ideals and derivations fuzzy commutative ideals. These concepts and the new results were obtained and introduced in chapter 3 were submitted in two separated articles and accepted for publication.

Keywords: BCK, BCI, algebras, derivation

Procedia PDF Downloads 33
10 Some Properties in Jordan Ideal on 3-Prime Near-Rings

Authors: Abdelkarim Boua, Abdelhakim Chillali

Abstract:

The study of non-associative structures in algebraic structures has become a separate entity; for, in the case of groups, their corresponding non-associative structure i.e. loops is dealt with separately. Similarly there is vast amount of research on the nonassociative structures of semigroups i.e. groupoids and that of rings i.e. nonassociative rings. However it is unfortunate that we do not have a parallel notions or study of non-associative near-rings. In this work we shall attempt to generalize a few known results and study the commutativity of Jordan ideal in 3-prime near-rings satisfying certain identities involving the Jordan ideal. We study the derivations satisfying certain differential identities on Jordan ideals of 3-prime near-rings. Moreover, we provide examples to show that hypothesis of our results are necessary. We give some new results and examples concerning the existence of Jordan ideal and derivations in near-rings. These near-rings can be used to build a new codes.

Keywords: 3-prime near-rings, near-rings, Jordan ideal, derivations

Procedia PDF Downloads 213
9 Gravitational Frequency Shifts for Photons and Particles

Authors: Jing-Gang Xie

Abstract:

The research, in this case, considers the integration of the Quantum Field Theory and the General Relativity Theory. As two successful models in explaining behaviors of particles, they are incompatible since they work at different masses and scales of energy, with the evidence that regards the description of black holes and universe formation. It is so considering previous efforts in merging the two theories, including the likes of the String Theory, Quantum Gravity models, and others. In a bid to prove an actionable experiment, the paper’s approach starts with the derivations of the existing theories at present. It goes on to test the derivations by applying the same initial assumptions, coupled with several deviations. The resulting equations get similar results to those of classical Newton model, quantum mechanics, and general relativity as long as conditions are normal. However, outcomes are different when conditions are extreme, specifically with no breakdowns even for less than Schwarzschild radius, or at Planck length cases. Even so, it proves the possibilities of integrating the two theories.

Keywords: general relativity theory, particles, photons, Quantum Gravity Model, gravitational frequency shift

Procedia PDF Downloads 288
8 Wave Transmitting Boundary in Dynamic Analysis for an Elastoplastic Medium Using the Material Point Method

Authors: Chinh Phuong Do

Abstract:

Dynamic analysis of slope under seismic condition requires the elimination of spurious reflection at the bounded domain. This paper studies the performances of wave transmitting boundaries, including the standard viscous boundary and the viscoelastic boundary to the material point method (MPM) framework. First, analytical derivations of these non-reflecting conditions particularly to the implicit MPM are presented. Then, a number of benchmark and geotechnical examples will be shown. Overall, the results agree well with analytical solutions, indicating the ability to accurately simulate the radiation at the bounded domain.

Keywords: dynamic analysis, implicit, MPM, non-reflecting boundary

Procedia PDF Downloads 122
7 Evaluation of DNA Paternity Testing Accuracy of Child Trafficking Cases

Authors: Wing Kam Fung, Kexin Yu

Abstract:

Child trafficking has been a serious problem in modern China. The Chinese government has established a national anti-trafficking DNA database to help reunite missing children with their families. The database collects DNA information from missing children's parents, trafficked and homeless children, then conducts paternity tests to find matched pairs. This paper considers the matching accuracy in such cases by looking into the exclusion probability in paternity testing. First, the situation of child trafficking in China is introduced. Next, derivations of the exclusion probability for both one-parent and two-parents cases are given, followed by extension to allow for 1 or 2 mutations. The accuracy of paternity testing of child trafficking cases is then assessed using the exclusion probabilities and available data. Finally, the number of loci that should be used to ensure a correct match is investigated.

Keywords: child trafficking, DNA database, exclusion probability, paternity testing

Procedia PDF Downloads 388
6 The Creative Unfolding of “Reduced Descriptive Structures” in Musical Cognition: Technical and Theoretical Insights Based on the OpenMusic and PWGL Long-Term Feedback

Authors: Jacopo Baboni Schilingi

Abstract:

We here describe the theoretical and philosophical understanding of a long term use and development of algorithmic computer-based tools applied to music composition. The findings of our research lead us to interrogate some specific processes and systems of communication engaged in the discovery of specific cultural artworks: artistic creation in the sono-musical domain. Our hypothesis is that the patterns of auditory learning cannot be only understood in terms of social transmission but would gain to be questioned in the way they rely on various ranges of acoustic stimuli modes of consciousness and how the different types of memories engaged in the percept-action expressive systems of our cultural communities also relies on these shadowy conscious entities we named “Reduced Descriptive Structures”.

Keywords: algorithmic sonic computation, corrected and self-correcting learning patterns in acoustic perception, morphological derivations in sensorial patterns, social unconscious modes of communication

Procedia PDF Downloads 100
5 Hybrid Equity Warrants Pricing Formulation under Stochastic Dynamics

Authors: Teh Raihana Nazirah Roslan, Siti Zulaiha Ibrahim, Sharmila Karim

Abstract:

A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study.

Keywords: Cox-Ingersoll-Ross model, equity warrants, Heston model, hybrid models, stochastic

Procedia PDF Downloads 45
4 Vibration Absorption Strategy for Multi-Frequency Excitation

Authors: Der Chyan Lin

Abstract:

Since the early introduction by Ormondroyd and Den Hartog, vibration absorber (VA) has become one of the most commonly used vibration mitigation strategies. The strategy is most effective for a primary plant subjected to a single frequency excitation. For continuous systems, notable advances in vibration absorption in the multi-frequency system were made. However, the efficacy of the VA strategy for systems under multi-frequency excitation is not well understood. For example, for an N degrees-of-freedom (DOF) primary-absorber system, there are N 'peak' frequencies of large amplitude vibration per every new excitation frequency. In general, the usable range for vibration absorption can be greatly reduced as a result. Frequency modulated harmonic excitation is a commonly seen multi-frequency excitation example: f(t) = cos(ϖ(t)t) where ϖ(t)=ω(1+α sin⁡(δt)). It is known that f(t) has a series expansion given by the Bessel function of the first kind, which implies an infinity of forcing frequencies in the frequency modulated harmonic excitation. For an SDOF system of natural frequency ωₙ subjected to f(t), it can be shown that amplitude peaks emerge at ω₍ₚ,ₖ₎=(ωₙ ± 2kδ)/(α ∓ 1),k∈Z; i.e., there is an infinity of resonant frequencies ω₍ₚ,ₖ₎, k∈Z, making the use of VA strategy ineffective. In this work, we propose an absorber frequency placement strategy for SDOF vibration systems subjected to frequency-modulated excitation. An SDOF linear mass-spring system coupled to lateral absorber systems is used to demonstrate the ideas. Although the mechanical components are linear, the governing equations for the coupled system are nonlinear. We show using N identical absorbers, for N ≫ 1, that (a) there is a cluster of N+1 natural frequencies around every natural absorber frequency, and (b) the absorber frequencies can be moved away from the plant's resonance frequency (ω₀) as N increases. Moreover, we also show the bandwidth of the VA performance increases with N. The derivations of the clustering and bandwidth widening effect will be given, and the superiority of the proposed strategy will be demonstrated via numerical experiments.

Keywords: Bessel function, bandwidth, frequency modulated excitation, vibration absorber

Procedia PDF Downloads 69
3 Evaluation of Solid-Gas Separation Efficiency in Natural Gas Cyclones

Authors: W. I. Mazyan, A. Ahmadi, M. Hoorfar

Abstract:

Objectives/Scope: This paper proposes a mathematical model for calculating the solid-gas separation efficiency in cyclones. This model provides better agreement with experimental results compared to existing mathematical models. Methods: The separation ratio efficiency, ϵsp, is evaluated by calculating the outlet to inlet count ratio. Similar to mathematical derivations in the literature, the inlet and outlet particle count were evaluated based on Eulerian approach. The model also includes the external forces acting on the particle (i.e., centrifugal and drag forces). In addition, the proposed model evaluates the exact length that the particle travels inside the cyclone for the evaluation of number of turns inside the cyclone. The separation efficiency model derivation using Stoke’s law considers the effect of the inlet tangential velocity on the separation performance. In cyclones, the inlet velocity is a very important factor in determining the performance of the cyclone separation. Therefore, the proposed model provides accurate estimation of actual cyclone separation efficiency. Results/Observations/Conclusion: The separation ratio efficiency, ϵsp, is studied to evaluate the performance of the cyclone for particles ranging from 1 microns to 10 microns. The proposed model is compared with the results in the literature. It is shown that the proposed mathematical model indicates an error of 7% between its efficiency and the efficiency obtained from the experimental results for 1 micron particles. At the same time, the proposed model gives the user the flexibility to analyze the separation efficiency at different inlet velocities. Additive Information: The proposed model determines the separation efficiency accurately and could also be used to optimize the separation efficiency of cyclones at low cost through trial and error testing, through dimensional changes to enhance separation and through increasing the particle centrifugal forces. Ultimately, the proposed model provides a powerful tool to optimize and enhance existing cyclones at low cost.

Keywords: cyclone efficiency, solid-gas separation, mathematical model, models error comparison

Procedia PDF Downloads 267
2 Hypersonic Propulsion Requirements for Sustained Hypersonic Flight for Air Transportation

Authors: James Rate, Apostolos Pesiridis

Abstract:

In this paper, the propulsion requirements required to achieve sustained hypersonic flight for commercial air transportation are evaluated. In addition, a design methodology is developed and used to determine the propulsive capabilities of both ramjet and scramjet engines. Twelve configurations are proposed for hypersonic flight using varying combinations of turbojet, turbofan, ramjet and scramjet engines. The optimal configuration was determined based on how well each of the configurations met the projected requirements for hypersonic commercial transport. The configurations were separated into four sub-configurations each comprising of three unique derivations. The first sub-configuration comprised four afterburning turbojets and either one or two ramjets idealised for Mach 5 cruise. The number of ramjets required was dependent on the thrust required to accelerate the vehicle from a speed where the turbojets cut out to Mach 5 cruise. The second comprised four afterburning turbojets and either one or two scramjets, similar to the first configuration. The third used four turbojets, one scramjet and one ramjet to aid acceleration from Mach 3 to Mach 5. The fourth configuration was the same as the third, but instead of turbojets, it implemented turbofan engines for the preliminary acceleration of the vehicle. From calculations which determined the fuel consumption at incremental Mach numbers this paper found that the ideal solution would require four turbojet engines and two Scramjet engines. The ideal mission profile was determined as being an 8000km sortie based on an averaging of popular long haul flights with strong business ties, which included Los Angeles to Tokyo, London to New York and Dubai to Beijing. This paper deemed that these routes would benefit from hypersonic transport links based on the previously mentioned factors. This paper has found that this configuration would be sufficient for the 8000km flight to be completed in approximately two and a half hours and would consume less fuel than Concord in doing so. However, this propulsion configuration still result in a greater fuel cost than a conventional passenger. In this regard, this investigation contributes towards the specification of the engine requirements throughout a mission profile for a hypersonic passenger vehicle. A number of assumptions have had to be made for this theoretical approach but the authors believe that this investigation lays the groundwork for appropriate framing of the propulsion requirements for sustained hypersonic flight for commercial air transportation. Despite this, it does serve as a crucial step in the development of the propulsion systems required for hypersonic commercial air transportation. This paper provides a methodology and a focus for the development of the propulsion systems that would be required for sustained hypersonic flight for commercial air transportation.

Keywords: hypersonic, ramjet, propulsion, Scramjet, Turbojet, turbofan

Procedia PDF Downloads 227
1 Using AI Based Software as an Assessment Aid for University Engineering Assignments

Authors: Waleed Al-Nuaimy, Luke Anastassiou, Manjinder Kainth

Abstract:

As the process of teaching has evolved with the advent of new technologies over the ages, so has the process of learning. Educators have perpetually found themselves on the lookout for new technology-enhanced methods of teaching in order to increase learning efficiency and decrease ever expanding workloads. Shortly after the invention of the internet, web-based learning started to pick up in the late 1990s and educators quickly found that the process of providing learning material and marking assignments could change thanks to the connectivity offered by the internet. With the creation of early web-based virtual learning environments (VLEs) such as SPIDER and Blackboard, it soon became apparent that VLEs resulted in higher reported computer self-efficacy among students, but at the cost of students being less satisfied with the learning process . It may be argued that the impersonal nature of VLEs, and their limited functionality may have been the leading factors contributing to this reported dissatisfaction. To this day, often faced with the prospects of assigning colossal engineering cohorts their homework and assessments, educators may frequently choose optimally curated assessment formats, such as multiple-choice quizzes and numerical answer input boxes, so that automated grading software embedded in the VLEs can save time and mark student submissions instantaneously. A crucial skill that is meant to be learnt during most science and engineering undergraduate degrees is gaining the confidence in using, solving and deriving mathematical equations. Equations underpin a significant portion of the topics taught in many STEM subjects, and it is in homework assignments and assessments that this understanding is tested. It is not hard to see that this can become challenging if the majority of assignment formats students are engaging with are multiple-choice questions, and educators end up with a reduced perspective of their students’ ability to manipulate equations. Artificial intelligence (AI) has in recent times been shown to be an important consideration for many technologies. In our paper, we explore the use of new AI based software designed to work in conjunction with current VLEs. Using our experience with the software, we discuss its potential to solve a selection of problems ranging from impersonality to the reduction of educator workloads by speeding up the marking process. We examine the software’s potential to increase learning efficiency through its features which claim to allow more customized and higher-quality feedback. We investigate the usability of features allowing students to input equation derivations in a range of different forms, and discuss relevant observations associated with these input methods. Furthermore, we make ethical considerations and discuss potential drawbacks to the software, including the extent to which optical character recognition (OCR) could play a part in the perpetuation of errors and create disagreements between student intent and their submitted assignment answers. It is the intention of the authors that this study will be useful as an example of the implementation of AI in a practical assessment scenario insofar as serving as a springboard for further considerations and studies that utilise AI in the setting and marking of science and engineering assignments.

Keywords: engineering education, assessment, artificial intelligence, optical character recognition (OCR)

Procedia PDF Downloads 35