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2021

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Articles 151 - 180 of 352

Full-Text Articles in Applied Mathematics

An Efficient Transformer-Based Model For Vietnamese Punctuation Prediction, Hieu Tran, Cuong V. Dinh, Hong Quang Pham, Binh T. Nguyen Jul 2021

An Efficient Transformer-Based Model For Vietnamese Punctuation Prediction, Hieu Tran, Cuong V. Dinh, Hong Quang Pham, Binh T. Nguyen

Research Collection School Of Computing and Information Systems

In both formal and informal texts, missing punctuation marks make the texts confusing and challenging to read. This paper aims to conduct exhaustive experiments to investigate the benefits of the pre-trained Transformer-based models on two Vietnamese punctuation datasets. The experimental results show our models can achieve encouraging results, and adding Bi-LSTM or/and CRF layers on top of the proposed models can also boost model performance. Finally, our best model can significantly bypass state-of-the-art approaches on both the novel and news datasets for the Vietnamese language. It can gain the corresponding performance up to 21.45%21.45% and 18.27%18.27% in the overall F1-scores.

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High-Order Positivity-Preserving L2-Stable Spectral Collocation Schemes For The 3-D Compressible Navier-Stokes Equations, Johnathon Keith Upperman Jul 2021

High-Order Positivity-Preserving L2-Stable Spectral Collocation Schemes For The 3-D Compressible Navier-Stokes Equations, Johnathon Keith Upperman

Mathematics & Statistics Theses & Dissertations

High-order entropy stable schemes are a popular method used in simulations with the compressible Euler and Navier-Stokes equations. The strength of these methods is that they formally satisfy a discrete entropy inequality which can be used to guarantee L2 stability of the numerical solution. However, a fundamental assumption that is explicitly or implicitly used in all entropy stability proofs available in the literature for the compressible Euler and Navier-Stokes equations is that the thermodynamic variables (e.g., density and temperature) are strictly positive in the entire space{time domain considered. Without this assumption, any entropy stability proof for a numerical scheme …

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Finite Difference Schemes For Integral Equations With Minimal Regularity Requirements, Wesley Cameron Davis Jul 2021

Finite Difference Schemes For Integral Equations With Minimal Regularity Requirements, Wesley Cameron Davis

Mathematics & Statistics Theses & Dissertations

Volterra integral equations arise in a variety of applications in modern physics and engineering, namely in interactions that contain a memory term. Classical formulations of these problems are largely inflexible when considering non-homogeneous media, which can be problematic when considering long term interactions of real-world applications. The use of fractional derivative and integral terms naturally relax these restrictions in a natural way to consider these problems in a more general setting. One major drawback to the use of fractional derivatives and integrals in modeling is the regularity requirement for functions, where we can no longer assume that functions are as …

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Electrohydrodynamic Simulations Of Capsule Deformation Using A Dual Time-Stepping Lattice Boltzmann Scheme, Charles Leland Armstrong Jul 2021

Electrohydrodynamic Simulations Of Capsule Deformation Using A Dual Time-Stepping Lattice Boltzmann Scheme, Charles Leland Armstrong

Mathematics & Statistics Theses & Dissertations

Capsules are fluid-filled, elastic membranes that serve as a useful model for synthetic and biological membranes. One prominent application of capsules is their use in modeling the response of red blood cells to external forces. These models can be used to study the cell’s material properties and can also assist in the development of diagnostic equipment. In this work we develop a three dimensional model for numerical simulations of red blood cells under the combined influence of hydrodynamic and electrical forces. The red blood cell is modeled as a biconcave-shaped capsule suspended in an ambient fluid domain. Cell deformation occurs …

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Finding New Limit Points Of Mahler Measure By Methods Of Missing Data Restoration, Jean-Marc Sac-Epee J.M Sac-Epee, Souad El Otmani, Armand Maul, Georges Rhin Jun 2021

Finding New Limit Points Of Mahler Measure By Methods Of Missing Data Restoration, Jean-Marc Sac-Epee J.M Sac-Epee, Souad El Otmani, Armand Maul, Georges Rhin

BAU Journal - Science and Technology

It is well known that the set of Mahler measures of single variable polynomial has limit points of which a list established by D. Boyd and M. Mossinghoff has been extended through approaches based on genetic algorithms. In this paper, we wish to further extend the list of known limit points by adapting a method of missing data restoration.

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Universal Biological Motions For Educational Robot Theatre And Games, Rajesh Venkatachalapathy, Martin Zwick, Adam Slowik, Kai Brooks, Mikhail Mayers, Roman Minko, Tyler Hull, Bliss Brass, Marek Perkowski Jun 2021

Universal Biological Motions For Educational Robot Theatre And Games, Rajesh Venkatachalapathy, Martin Zwick, Adam Slowik, Kai Brooks, Mikhail Mayers, Roman Minko, Tyler Hull, Bliss Brass, Marek Perkowski

Complex Systems Faculty Publications and Presentations

Paper presents a concept that is new to robotics education and social robotics. It is based on theatrical games, in motions for social robots and animatronic robots. Presented here motion model is based on Drift Differential Model from biology and Fokker-Planck equations. This model is used in various areas of science to describe many types of motion. The model was successfully verified on various simulated mobile robots and a motion game of three robots called "Mouse and Cheese."

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Dpp: Deep Predictor For Price Movement From Candlestick Charts, Chih-Chieh Hung, Ying-Ju (Tessa) Chen Jun 2021

Dpp: Deep Predictor For Price Movement From Candlestick Charts, Chih-Chieh Hung, Ying-Ju (Tessa) Chen

Mathematics Faculty Publications

Forecasting the stock market prices is complicated and challenging since the price movement is affected by many factors such as releasing market news about earnings and profits, international and domestic economic situation, political events, monetary policy, major abrupt affairs, etc. In this work, a novel framework: deep predictor for price movement (DPP) using candlestick charts in the stock historical data is proposed. This framework comprises three steps: 1. decomposing a given candlestick chart into sub-charts; 2. using CNN-autoencoder to acquire the best representation of sub-charts; 3. applying RNN to predict the price movements from a collection of sub-chart representations. An …

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Grizzly Bears Mortalities And The Survival Of The Species, Courtney Swanson Jun 2021

Grizzly Bears Mortalities And The Survival Of The Species, Courtney Swanson

Senior Seminars and Capstones

In this paper we aim to understand what is happening in the grizzly bear population mortalities from the year 2010 to 2020. We are performing Classical and Regression Tree (CART) methods and Correspondence Analysis on data provided by the U.S. Geological Survey (USGS). We found certain variables in the data set to be important through CART methods. Correspondence Analysis then allowed us to compare these variables to determine their relationships and association to one another. Most of the grizzly bear deaths are human caused and mainly over land and resources such as food and habitat. This aligns with some of …

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Optimal Stopping Problems For A Family Of Continuous-Time Markov Processes, Héctor Jasso-Fuentes, Jose-Luis Menaldi, Fidel Vásquez-Rojas Jun 2021

Optimal Stopping Problems For A Family Of Continuous-Time Markov Processes, Héctor Jasso-Fuentes, Jose-Luis Menaldi, Fidel Vásquez-Rojas

Mathematics Faculty Research Publications

In this paper we study the well-know optimal stopping problem applied to a general family of continuous-time Markov process. The approach to follow is merely analytic and it is based on the characterization of stopping problems through the study of a certain variational inequality; namely one solution of this inequality will coincide with the optimal value of the stopping problem. In addition, by means of this characterization, it is possible to find the so-named continuation region, and as a byproduct obtaining the optimal stopping time. The most of the material is based on the semigroup theory, infinitesimal generators and resolvents. …

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Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria Jun 2021

Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

The article aims to study a modified Leslie-Gower predator-prey model with Allee effect II, affecting the functional response with the assumption that the extent to which the environment provides protection to both predator and prey is the same. The model has been studied analytically as well as numerically, including stability and bifurcation analysis. Compared with the predator-prey model without Allee effect, it is found that the weak Allee effect II can bring rich and complicated dynamics, such as the model undergoes to a series of bifurcations (Homoclinic, Hopf, Saddle-node and Bogdanov-Takens). The existence of Hopf bifurcation has been shown for …

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Anti-Synchronization Scheme For The Stability Analysis Of A Newly Designed Hamiltonian Chaotic System Based On Hénon-Heiles Model Using Adaptive Control Method, Ayub Khan, Anu Jain, Santosh Kaushik, Manoj Kumar, Harindri Chaudhary Jun 2021

Anti-Synchronization Scheme For The Stability Analysis Of A Newly Designed Hamiltonian Chaotic System Based On Hénon-Heiles Model Using Adaptive Control Method, Ayub Khan, Anu Jain, Santosh Kaushik, Manoj Kumar, Harindri Chaudhary

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a systematic approach to investigate the anti-synchronization among identical Hamiltonian chaotic systems has been proposed by using adaptive control method (ACM). Initially an adaptive controller and parameter update law are described to achieve asymptotical stability of state variables of given system with uncertain parameters using Lyapunov stability theory (LST). In addition, numerical simulations using MATLAB software are performed to validate the efficacy and effectiveness of the designed technique. Moreover, the proposed technique has numerous applications in encryption and secure communication.

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Maximum Difference Extreme Difference Method For Finding The Initial Basic Feasible Solution Of Transportation Problems, Ridwan Raheem Lekan, Lord Clifford Kavi, Nancy Ann Neudauer Jun 2021

Maximum Difference Extreme Difference Method For Finding The Initial Basic Feasible Solution Of Transportation Problems, Ridwan Raheem Lekan, Lord Clifford Kavi, Nancy Ann Neudauer

Applications and Applied Mathematics: An International Journal (AAM)

A Transportation Problem can be modeled using Linear Programming to determine the best transportation schedule that will minimize the transportation cost. Solving a transportation problem requires finding the Initial Basic Feasible Solution (IBFS) before obtaining the optimal solution. We propose a new method for finding the IBFS called the Maximum Difference Extreme Difference Method (MDEDM) which yields an optimal or close to the optimal solution. We also investigate the computational time complexity of MDEDM, and show that it is O(mn).

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A High Order Finite Difference Method To Solve The Steady State Navier-Stokes Equations, Nihal J. Siriwardana, Saroj P. Pradhan Jun 2021

A High Order Finite Difference Method To Solve The Steady State Navier-Stokes Equations, Nihal J. Siriwardana, Saroj P. Pradhan

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we develop a fourth order finite difference method to solve the system of steady state Navier-Stokes equations and apply it to the benchmark problem known as the square cavity flow problem. The numerical results of 𝑢-velocity components and 𝑣-velocity components obtained at the center of the cavity are compared with the results obtained by the method developed by Greenspan and Casulli to solve the time dependent system of Navier-Stokes equations. The method described in this article is easy to implement and it has been shown to be more efficient and stable than the method by Greenspan and …

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Casson Fluid Flow Past On Vertical Cylinder In The Presence Of Chemical Reaction And Magnetic Field, Gaurav Kumar, S.M.K. Rizvi Jun 2021

Casson Fluid Flow Past On Vertical Cylinder In The Presence Of Chemical Reaction And Magnetic Field, Gaurav Kumar, S.M.K. Rizvi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we have examined the behavior of unsteady flow of a viscous, incompressible and electrically conducting Casson fluid past an impulsively started vertical cylinder with variable temperature and mass diffusion in the presence of transversely applied uniform magnetic field and chemical reaction. The temperature and concentration level near the surface increase linearly with time. The governing equations of non-dimensional form of flow model have been solved numerically by using Crank-Nicolson implicit finite difference method. The velocity profile is discussed with the help of graphs drawn for different parameters like Casson fluid parameter, Prandtl number, chemical reaction parameter and …

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Variation Iteration Method For Solving Ethanol And Acetaldehyde Concentrations In A Fixed Bed Laboratory Reactor, K. M. Dharmalingam, M. Veeramuni, Hadi Rezazadeh, Cemil Tunç Jun 2021

Variation Iteration Method For Solving Ethanol And Acetaldehyde Concentrations In A Fixed Bed Laboratory Reactor, K. M. Dharmalingam, M. Veeramuni, Hadi Rezazadeh, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we investigate the effects of nonlinear behaviour of the dimensionless concentrations of the ethanol and acetaldehyde in a fixed bed laboratory reactor. The work is based on solving the nonlinear differential equation of concentration of the ethanol and acetaldehyde by means of the He’s variational iteration method (VIM). Also, the numerical simulation (4th order Runge – Kutta method) is reported using Matlab software. The analytical solutions are compared with numerical results in order to achieve conclusions based on not only for accuracy and efficiency of the solutions, but also the simplicity of the taken procedures which would …

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A Novel Color Image Encryption Scheme Based On Arnold’S Cat Map And 16-Byte S-Box, Tariq Shah, Ayesha Qureshi, Muhammad Usman Jun 2021

A Novel Color Image Encryption Scheme Based On Arnold’S Cat Map And 16-Byte S-Box, Tariq Shah, Ayesha Qureshi, Muhammad Usman

Applications and Applied Mathematics: An International Journal (AAM)

The presented work sets out to subsidize to the general body of knowledge in the field of cryptography application by evolving color image encryption and decryption scheme based on the amalgamation of pixel shuffling and efficient substitution. Arnold’s cat map is applied to snap off the correlation in pixels of image and the shuffled image is encrypted by 16-byte S-box substitution. Computer simulations with a standard test image and the outcome is presented to scrutinize the competence of the projected system. Several image-quality measures and security analyses have been made out for the encrypted image to estimate the statistical and …

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Significance Of Coriolis Force On Eyring-Powell Flow Over A Rotating Non-Uniform Surface, Abayomi S. Oke, Winifred N. Mutuku Jun 2021

Significance Of Coriolis Force On Eyring-Powell Flow Over A Rotating Non-Uniform Surface, Abayomi S. Oke, Winifred N. Mutuku

Applications and Applied Mathematics: An International Journal (AAM)

Coriolis force plays significant roles in natural phenomena such as atmospheric dynamics, weather patterns, etc. Meanwhile, to circumvent the unreliability of Newtonian law for flows involving varying speed, Eyring-Powell fluid equations are used in computational fluid dynamics. This paper unravels the significance of Coriolis force on Eyring-Powell fluid over the rotating upper horizontal surface of a paraboloid of revolution. Relevant body forces are included in the Navier-Stokes equations to model the flow of non-Newtonian Eyring-Powell fluid under the influence of Coriolis force. Using similarity transformation, the governing equations are nondimensionalized, thereby transforming the nonlinear partial differential equations to a system …

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Thermal-Diffusion And Diffusion-Thermo Effects On Heat And Mass Transfer In Chemically Reacting Mhd Casson Nanofluid With Viscous Dissipation, Timothy L. Oyekunle, Mojeed T. Akolade, Samson A. Agunbiade Jun 2021

Thermal-Diffusion And Diffusion-Thermo Effects On Heat And Mass Transfer In Chemically Reacting Mhd Casson Nanofluid With Viscous Dissipation, Timothy L. Oyekunle, Mojeed T. Akolade, Samson A. Agunbiade

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we examined the combined effects of dissipation and chemical reaction in Casson nanofluid motion through a vertical porous plate subjected to the magnetic field effect placed perpendicular to the flow channel. The physical problem is modeled using partial differential equations (PDEs). These sets of PDEs, with suitable similarity transformations, are simplified into ordinary differential equations (ODEs). Collocation technique with legendary basis function is utilized in solving the transformed equations. The numerical analysis on velocity, concentration, and temperature are plotted and tabled for different flow parameters. Our findings show that by raising the Casson parameter close to infinity, …

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Hall Current And Radiation Effects On Unsteady Natural Convection Mhd Flow With Inclined Magnetic Field, U. S. Rajput, Naval K. Gupta Jun 2021

Hall Current And Radiation Effects On Unsteady Natural Convection Mhd Flow With Inclined Magnetic Field, U. S. Rajput, Naval K. Gupta

Applications and Applied Mathematics: An International Journal (AAM)

In the present paper, Hall current and radiation effects on unsteady natural convection MHD flow with inclined magnetic field is studied. The viscous, incompressible and an electrically conducting fluid is considered. This model contains equations of motion, equation of energy and diffusion equation. The system of partial differential equations is transformed to dimensionless equations by using dimensionless variables. Exact solution of governing equations is obtained by Laplace Transform Technique. For analysing the solution of the model, desirable sets of the values of the parameters have been considered. The obtained results of velocity, concentration and temperature have been analysed with the …

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Covid-19 Modeling With Caution In Relaxing Control Measures And Possibilities Of Several Peaks In Cameroon, S. Y. Tchoumi, Y. T. Kouakep, D. J. Fotsa Mbogne, J. C. Kamgang, V. C. Kamla, D. Bekolle Jun 2021

Covid-19 Modeling With Caution In Relaxing Control Measures And Possibilities Of Several Peaks In Cameroon, S. Y. Tchoumi, Y. T. Kouakep, D. J. Fotsa Mbogne, J. C. Kamgang, V. C. Kamla, D. Bekolle

Applications and Applied Mathematics: An International Journal (AAM)

We construct a new model for the comprehension of the Covid-19 dynamics in Cameroon. We present the basic reproduction number and perform some numerical analysis on the possible outcomes of the epidemic. The major results are the possibilities to have several peaks before the end of the first outbreak for an uniform strategy, and the danger to have a severe peak after the adoption of a careless strategy of barrier anti-Covid-19 measures that follow a good containment period.

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Modelling Classroom Space Allocation At University Of Rwanda-A Linear Programming Approach, Kambombo Mtonga, Evariste Twahirwa, Santhi Kumaran, Kayalvizhi Jayavel Jun 2021

Modelling Classroom Space Allocation At University Of Rwanda-A Linear Programming Approach, Kambombo Mtonga, Evariste Twahirwa, Santhi Kumaran, Kayalvizhi Jayavel

Applications and Applied Mathematics: An International Journal (AAM)

Education and training play a key role as the human capital function. This is especially true for tertiary education. However, infrastructure and equipment limitations are some factors that limits levels of students' enrollment in universities. This is moreso the case in developing countries where much of the infrastructure developments are donor-funded. For institutional managers and administrators, the allocating of the limited available classroom space is a constant problem that needs sophisticated approaches to deal with. Linear Optimization technique has shown promise in dealing with this problem. This research seeks to assess the Rwandan education system and highlight strides made to …

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Bessel-Maitland Function Of Several Variables And Its Properties Related To Integral Transforms And Fractional Calculus, Ankita Chandola, Rupakshi M. Pandey, Ritu Agarwal Jun 2021

Bessel-Maitland Function Of Several Variables And Its Properties Related To Integral Transforms And Fractional Calculus, Ankita Chandola, Rupakshi M. Pandey, Ritu Agarwal

Applications and Applied Mathematics: An International Journal (AAM)

In the recent years, various generalizations of Bessel function were introduced and its various properties were investigated by many authors. Bessel-Maitland function is one of the generalizations of Bessel function. The objective of this paper is to establish a new generalization of Bessel-Maitland function using the extension of beta function involving Appell series and Lauricella functions. Some of its properties including recurrence relation, integral representation and differentiation formula are investigated. Moreover, some properties of Riemann-Liouville fractional operator associated with the new generalization of Bessel-Maitland function are also discussed.

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Approximate 2-Dimensional Pexider Quadratic Functional Equations In Fuzzy Normed Spaces And Topological Vector Space, Mohammad A. Abolfathi, Ali Ebadian Jun 2021

Approximate 2-Dimensional Pexider Quadratic Functional Equations In Fuzzy Normed Spaces And Topological Vector Space, Mohammad A. Abolfathi, Ali Ebadian

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we prove the Hyers-Ulam stability of the 2-dimensional Pexider quadratic functional equation in fuzzy normed spaces. Moreover, we prove the Hyers-Ulam stability of this functional equation, where f, g are functions defined on an abelian group with values in a topological vector space.

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Outcomes Of Aspheric Primaries In Robe’S Circular Restricted Three-Body Problem, Bhavneet Kaur, Shipra Chauhan, Dinesh Kumar Jun 2021

Outcomes Of Aspheric Primaries In Robe’S Circular Restricted Three-Body Problem, Bhavneet Kaur, Shipra Chauhan, Dinesh Kumar

Applications and Applied Mathematics: An International Journal (AAM)

We consider the Robe’s restricted three-body problem in which the bigger primary is assumed to be a hydrostatic equilibrium figure as an oblate spheroid filled with a homogeneous incompressible fluid, around which a circular motion is described by the second primary, that is a finite straight segment. The aim of this note is to investigate the effect of oblateness and length parameters on the motion of an infinitesimal body that lies inside the bigger primary. The locations of the equilibrium points are approximated by the series expansions and it is found that two collinear equilibrium points lying on the line …

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Global Stability Of Generalized Within-Host Chikungunya Virus Dynamics Models, Taofeek O. Alade, Afeez Abidemi, Cemil Tunç, Shafeek A. Ghaleb Jun 2021

Global Stability Of Generalized Within-Host Chikungunya Virus Dynamics Models, Taofeek O. Alade, Afeez Abidemi, Cemil Tunç, Shafeek A. Ghaleb

Applications and Applied Mathematics: An International Journal (AAM)

This paper proposes two models of a general nonlinear within-host Chikungunya virus (CHIKV) dynamics. The production, incidence, proliferation and removal rates of all compartments are modeled by general nonlinear functions that satisfy a set of reasonable conditions. The second model takes into consideration two forms of infected host cells: (i) latently infected cells which do not produce the CHIKV, (ii) actively infected cells which generate the CHIKV particles. We show that all the solutions of the models are nonnegative and bounded. The global stability of the steady states of the models is proven by applying Lyapunov method and LaSalle’s invariance …

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Two Temperature Dual-Phase-Lag Fractional Thermal Investigation Of Heat Flow Inside A Uniform Rod, Vinayak Kulkarni, Gaurav Mittal Jun 2021

Two Temperature Dual-Phase-Lag Fractional Thermal Investigation Of Heat Flow Inside A Uniform Rod, Vinayak Kulkarni, Gaurav Mittal

Applications and Applied Mathematics: An International Journal (AAM)

A non-classical, coupled, fractionally ordered, dual-phase-lag (DPL) heat conduction model has been presented in the framework of the two-temperature theory in the bounded Cartesian domain. Due to the application of two-temperature theory, the governing heat conduction equation is well-posed and satisfying the required stability criterion prescribed for a DPL model. The mathematical formulation has been applied to a uniform rod of finite length with traction free ends considered in a perfectly thermoelastic homogeneous isotropic medium. The initial end of the rod has been exposed to the convective heat flux and energy dissipated by convection into the surrounding medium through the …

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Numerical Solution Of Fuzzy Fractional Differential Equation By Haar Wavelet, Sakineh Khakrangin, Tofigh Allahviranloo, Nasser Mikaeilvand, Saeid Abbasbandy Jun 2021

Numerical Solution Of Fuzzy Fractional Differential Equation By Haar Wavelet, Sakineh Khakrangin, Tofigh Allahviranloo, Nasser Mikaeilvand, Saeid Abbasbandy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we deal with a wavelet operational method based on Haar wavelet to solve the fuzzy fractional differential equation in the Caputo derivative sense. To this end, we derive the Haar wavelet operational matrix of the fractional order integration. The given approach provides an efficient method to find the solution and its upper bond error. To complete the discussion, the convergence theorem is subsequently expressed in detail. So far, no paper has used the Harr wavelet method using generalized difference and fuzzy derivatives, and this is the first time we have done so. Finally, the presented examples reflect …

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Numerical Technique For Solving Fractional-Order Of Ivgtt Glucose-Insulin Interaction, M. A. Abdelkawy Jun 2021

Numerical Technique For Solving Fractional-Order Of Ivgtt Glucose-Insulin Interaction, M. A. Abdelkawy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we use a numerical technique to solve fractional nonlinear differential equations systems that arise in Bergman’s minimal model that describe blood glucose and insulin metabolism, after intravenous tolerance testing. Shifted Jacobi -Gauss-Radau collocation (SJ-GR-C) method is developed for approximating the proposed model. The principal target in our technique is to transform the proposed model to a system of algebraic equations. Finally, numerical simulation is introduced to illustrate the analytical results.

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Axisymmetric Thermoelastic Response In A Semi-Elliptic Plate With Kassir’S Nonhomogeneity In The Thickness Direction, Sonal Bhoyar, Vinod Varghese, Lalsingh Khalsa Jun 2021

Axisymmetric Thermoelastic Response In A Semi-Elliptic Plate With Kassir’S Nonhomogeneity In The Thickness Direction, Sonal Bhoyar, Vinod Varghese, Lalsingh Khalsa

Applications and Applied Mathematics: An International Journal (AAM)

The main objective is to investigate the transient thermoelastic reaction in a nonhomogeneous semi-elliptical elastic plate heated sectionally on the upper side of the semi-elliptic region. It has been assumed that the thermal conductivity, calorific capacity, elastic modulus and thermal coefficient of expansion were varying through thickness of the nonhomogeneous material according to Kassir’s nonhomogeneity relationship. The transient heat conduction differential equation is solved using an integral transformation technique in terms of Mathieu functions. In these formulations, modified total strain energy is obtained by incorporating the resulting moment and force within the energy term, thus reducing the step of the …

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Chudnovsky's Conjecture And The Stable Harbourne-Huneke Containment, Sankhaneel Bisui, Eloísa Grifo, Huy Tài Hà, Thái Thành Nguyên Jun 2021

Chudnovsky's Conjecture And The Stable Harbourne-Huneke Containment, Sankhaneel Bisui, Eloísa Grifo, Huy Tài Hà, Thái Thành Nguyên

Department of Mathematics: Faculty Publications

We investigate containment statements between symbolic and ordinary powers and bounds on the Waldschmidt constant of defining ideals of points in projective spaces. We establish the stable Harbourne conjecture for the defining ideal of a general set of points. We also prove Chudnovsky’s Conjecture and the stable version of the Harbourne–Huneke containment conjectures for a general set of sufficiently many points.

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