Applied Mathematics

Journal Information
ISSN / EISSN : 2152-7385 / 2152-7393
Current Publisher: Scientific Research Publishing, Inc. (10.4236)
Total articles ≅ 2,066
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Latest articles in this journal

Abd El-Moneim A. M. Teamah, Hanan H. El-Damrawy, Shaimaa M. T. Swan
Applied Mathematics, Volume 11, pp 97-118; doi:10.4236/am.2020.112010

Abstract:
Statistical analysis of lifetime data is a significant topic in social sciences, engineering, reliability, biomedical and others. We use the generalized weighted exponential distribution, as a generator to introduce a new family called generalized weighted exponential-G family, and apply this new generator to provide a new distribution called generalized weighted exponential gombertez distribution. We investigate some of its properties, moment generating function, moments, conditional moments, mean residual lifetime, mean inactivity time, strong mean inactivity time, Rényi entropy, Lorenz curves and Bonferroni. Furthermore, in this model, we estimate the parameters by using maximum likelihood method. We apply this model to a real data-set to show that the new generated distribution can produce a better fit than other classical lifetime models.
A. N. M. Rezaul Karim
Applied Mathematics, Volume 11, pp 76-83; doi:10.4236/am.2020.112008

Abstract:
The Krein-Rutman theorem is vital in partial differential equations that are non-linear and provides evidence of the presence of several significant eigenvalues useful in topological degree calculations, stability analysis, and bifurcation theory. Schr?der’s equation which has been used extensively in studies of turbulence is an equation with a single independent variable suitable for encoding self-similarity. The concept of Hilbert spaces has been an inner product space frequently used due to its convenience in countless dimensional vector analysis. This paper is aimed at proving a number of solutions through the Krein-Rutman theorem in unitary spaces especially in Hilbert spaces. It has been certainly observed that the whole Krein-Rutman theorem system has a fairly stable scope, and has strong regular features, and many non-linear elliptic operators need the most ethical principles to satisfy the comparison policy.
Fleur T. Tehrani
Applied Mathematics, Volume 11, pp 53-66; doi:10.4236/am.2020.112006

Abstract:
A new approach for solving polynomial equations is presented in this study. Two techniques for solving quartic equations are described that are based on a new method which was recently developed for solving cubic equations. Higher order polynomial equations are solved by using a new and efficient algorithmic technique. The proposed methods rely on initially identifying the vicinities of the roots and do not require the use of complicated formulas, roots of complex numbers, or application of graphs. It is proposed that under the stated conditions, the methods presented provide efficient techniques to find the roots of polynomial equations.
Kouassi Eugene, Akpata Edouard, Pokou Koffi, Eugene Kouassi, Edouard Akpata, Koffi Pokou
Applied Mathematics, Volume 11, pp 67-75; doi:10.4236/am.2020.112007

Abstract:
An important problem of actuarial risk management is the calculation of the probability of ruin. Using probability theory and the definition of the Laplace transform one obtains expressions, in the classical risk model, for survival probabilities in a finite time horizon. Then explicit solutions are found with the inversion of the double Laplace transform; using algebra, the Laplace complex inversion formula and Matlab, for the exponential claim amount distribution.
Naoto Morikawa
Applied Mathematics, Volume 11, pp 890-916; doi:10.4236/am.2020.119058

Abstract:
This paper proposes a novel category theoretic approach to describe protein’s shape, i.e., a description of their shape by a set of algebraic equations. The focus of the approach is on the relations between proteins, rather than on the proteins themselves. Knowledge of category theory is not required as mathematical notions are defined concretely. In this paper, proteins are represented as closed trajectories (i.e., loops) of flows of triangles. The relations between proteins are defined using the fusion and fission of loops of triangles, where allostery occurs naturally. The shape of a protein is then described with quantities that are measurable with unity elements called “unit loops”. That is, protein’s shape is described with the loops that are obtained by the fusion of unit loops. Measurable loops are called “integral”. In the approach, the unit loops play a role similar to the role “1” plays in the set Z of integers. In particular, the author considers two categories of loops, the “integral” loops and the “rational” loops. Rational loops are then defined using algebraic equations with “integral loop” coefficients. Because of the approach, our theory has some similarities to quantum mechanics, where only observable quantities are admitted in physical theory. The author believes that this paper not only provides a new perspective on protein engineering, but also promotes further collaboration between biology and other disciplines.
Michael Short, A. Arockia Selvakumar
Applied Mathematics, Volume 11, pp 876-889; doi:10.4236/am.2020.119057

Abstract:
Tank level control is ubiquitous in industry. The focus of this paper is on accurate liquid level control in single tank systems which can be actuated continuously and modulation of the level setpoint is also required, for example in cascade control loops or supervisory Model Predictive Control (MPC) applications. To avoid common problems encountered when using fixed gain or adaptive/gain scheduled schemes, an accurate technique based around feedback linearization and Proportional Integral (PI) control is introduced. This simple controller can maintain linear performance over the full operating range of a uniform tank. As will be demonstrated, the implementation overhead compared to a regular PI controller is negligible, making it ideal for industrial implementation. Implementation details and parameter identification for adaptive implementation are discussed. Simulations coupled with experimental results using a large-scale laboratory level control system using commercial industrial control equipment validate the approach, and illustrate its effectiveness for both level tracking and disturbance rejection.
Dev Chandra Shrestha, Saraswati Acharya, Dil Bahadur Gurung
Applied Mathematics, Volume 11, pp 753-770; doi:10.4236/am.2020.118050

Abstract:
Metabolisms play a vital role in thermoregulation in the human body. The metabolic rate varies with the activity levels and has different behaviors in nature depending on the physical activities of the person. During the activity, metabolic rate increases rapidly at the beginning and then increases slowly to become almost constant after a certain time. So, its behavior is as logistics in nature. The high metabolic rate during activity causes the increase of body core temperature up to 39˚C [1] [2]. The logistic model of metabolic rate is used to re-model Pennes’ bioheat equation for the study of temperature distribution in three layered human dermal parts during carpentering, swimming and marathon. The finite element method is used to obtain the solution of the model equation. The results demonstrate that there is a significant change in tissue temperature due to sweating and ambient temperature variations.
Marin Claudia, Domenico Leogrande, Fabio Manca
Applied Mathematics, Volume 11, pp 951-956; doi:10.4236/am.2020.1110062

Abstract:
The Dagum model is particularly suitable for the analysis of the distributions of economic quantities, such as income, assets and consumption. The purpose of this note is to derive the expression of the mean deviation from the median of the Dagum distribution to study the behavior of the scale and shape parameters in terms of absolute variability and in terms of relative variability.
Peter Y. P. Chen
Applied Mathematics, Volume 11, pp 146-156; doi:10.4236/am.2020.113013

Abstract:
We have used model scaling so that the propagation of light through space could be studied using the well-known nonlinear Schrödinger equation. We have developed a set of numerical procedures to obtain a stable propagating wave so that it could be used to find out how wavelength could increase with distance travelled. We have found that broadening of wavelength, expressed as redshift, is proportional to distance, a fact that is in agreement with many physical observations by astronomers. There are other reasons for redshifts that could be additional to the transmission redshift, resulting in the deviation from the linear relationship as often observed. Our model shows that redshift needs not be the result of an expanding space that is a long standing view held by many astrophysicists. Any theory about the universe, if bases on an expanding space as physical fact, is open to question.
Shuangte Wang, Hengguo Yu, Chuanjun Dai, Min Zhao
Applied Mathematics, Volume 11, pp 407-425; doi:10.4236/am.2020.115029

Abstract:
In this paper, we mainly considered the dynamical behavior of a predator-prey system with Holling type II functional response and Allee-like effect on predator, including stability analysis of equilibria and Hopf bifurcation. Firstly, we gave some sufficient conditions to guarantee the existence, the local and global stability of equilibria as well as non-existence of limit cycles. By using the cobweb model, some cases about the existence of interior equilibrium are also illustrated with numerical outcomes. These existence and stability conclusions of interior equilibrium are also suitable in corresponding homogeneous reaction-diffusion system subject to the Neumann boundary conditions. Secondly, we theoretically deduced that our system has saddle-node bifurcation, transcritical bifurcation and Hopf bifurcation under certain conditions. Finally, for the Hopf bifurcation, we choose d as the bifurcation parameter and presented some numerical simulations to verify feasibility and effectiveness of the theoretical derivation corresponding to the existence of yk, respectively. The Hopf bifurcations are supercritical and limit cycles generated by the critical points are stable.
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