Applied Mathematics

Journal Information
ISSN / EISSN : 2152-7385 / 2152-7393
Current Publisher: Scientific Research Publishing, Inc. (10.4236)
Total articles ≅ 2,083
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Latest articles in this journal

Guoying Liu, Shuanghao Chen, Jing Xiong, Qingju Jiao
Applied Mathematics, Volume 12, pp 224-239; doi:10.4236/am.2021.123014

Abstract:
The detection of Oracle Bone Inscriptions (OBIs) is one of the most fundamental tasks in the study of Oracle Bone, which aims to locate the positions of OBIs on rubbing images. The existing methods are based on the scheme of anchor boxes, involving complex network design and a great number of anchor boxes. In order to overcome the problem, this paper proposes a simpler but more effective OBIs detector by using an anchor-free scheme, where shape-adaptive Gaussian kernels are employed to represent the spatial regions of different OBIs. More specifically, to address the problem of misdetection caused by regional overlapping between some tightly distributed OBIs, the character regions are simultaneously represented by multiscale Gaussian kernels to obtain regions with sharp edges. Besides, based on the kernel predictions of different scales, a novel post-processing pipeline is used to obtain accurate predictions of bounding boxes. Experiments show that our OBIs detector has achieved significant results on the OBIs dataset, which greatly outperforms several mainstream object detectors in both speed and efficiency. Dataset is available at http://jgw.aynu.edu.cn.
Majdi Elhiwi
Applied Mathematics, Volume 12, pp 24-31; doi:10.4236/am.2021.121003

Abstract:
The COVID-19 pandemic has become a great challenge to scientific, biological and medical research as well as to economic and social sciences. Hence, the objective of infectious disease modeling-based data analysis is to recover these dynamics of infectious disease spread and to estimate parameters that govern these dynamics. The random aspect of epidemics leads to the development of stochastic epidemiological models. We establish a stochastic combined model using numerical scheme Euler, Markov chain and Susceptible-Exposed-Infected-Recovery (SEIR) model. The combined SEIR model was used to predict how epidemics will develop and then to act accordingly. These COVID-19 data were analyzed from several countries such as Italy, Russia, USA and Iran.
Quanxiang Wang
Applied Mathematics, Volume 12, pp 241-251; doi:10.4236/am.2021.124015

Abstract:
In this paper, we propose new finite volume element schemes to numerically solve the improved Boussinesq equation with Stokes damping. The new schemes can inherit characteristic properties of the conservation of mass and the decrease of total energy from the improved Boussinesq equation with Stokes damping. Numerical experiments illustrate that the proposed schemes are second-order accuracy in space and time.
I. Lazzizzera
Applied Mathematics, Volume 12, pp 58-73; doi:10.4236/am.2021.121005

Abstract:
The SIR(D) epidemiological model is defined through a system of transcendental equations, not solvable by elementary functions. In the present paper those equations are successfully replaced by approximate ones, whose solutions are given explicitly in terms of elementary functions, originating, piece-wisely, from generalized logistic functions: they ensure exact (in the numerical sense) asymptotic values, besides to be quite practical to use, for example with fit to data algorithms; moreover they unveil a useful feature, that in fact, at least with very strict approximation, is also owned by the (numerical) solutions of the exact equations. The novelties in the work are: the way the approximate equations are obtained, using simple, analytic geometry considerations; the easy and practical formulation of the final approximate solutions; the mentioned useful feature, never disclosed before. The work’s method and result prove to be robust over a range of values of the well known non-dimensional parameter called basic reproduction ratio, that covers at least all the known epidemic cases, from influenza to measles: this is a point which doesn’t appear much discussed in analogous works.
Askar Akaev, Viktor Sadovnichiy
Applied Mathematics, Volume 12, pp 171-208; doi:10.4236/am.2021.123012

Abstract:
The aim of this study was to develop an adequate mathematical model for long-term forecasting of technological progress and economic growth in the digital age (2020-2050). In addition, the task was to develop a model for forecast calculations of labor productivity in the symbiosis of “man + intelligent machine”, where an intelligent machine (IM) is understood as a computer or robot equipped with elements of artificial intelligence (AI), as well as in the digital economy as a whole. In the course of the study, it was shown that in order to implement its goals the Schumpeter-Kondratiev innovation and cycle theory on forming long waves (LW) of economic development influenced by a powerful cluster of economic technologies engendered by industrial revolutions is most appropriate for a long-term forecasting of technological progress and economic growth. The Solow neoclassical model of economic growth, synchronized with LW, gives the opportunity to forecast economic dynamics of technologically advanced countries with a greater precision up to 30 years, the time which correlates with the continuation of LW. In the information and digital age, the key role among the main factors of growth (capital, labour and technological progress) is played by the latter. The authors have developed an information model which allows for forecasting technological progress basing on growth rates of endogenous technological information in economics. The main regimes of producing technological information, corresponding to the eras of information and digital economies, are given in the article, as well as the Lagrangians that engender them. The model is verified on the example of the 5th information LW for the US economy (1982-2018) and it has had highly accurate approximation for both technological progress and economic growth. A number of new results were obtained using the developed information models for forecasting technological progress. The forecasting trajectory of economic growth of developed countries (on the example of the USA) on the upward stage of the 6th LW (2018-2042), engendered by the digital technologies of the 4th Industrial Revolution is given. It is also demonstrated that the symbiosis of human and intelligent machine (IM) is the driving force in the digital economy, where man plays the leading role organizing effective and efficient mutual work. Authors suggest a mathematical model for calculating labour productivity in the digital economy, where the symbiosis of “human + IM” is widely used. The calculations carried out with the help of the model show: 1) the symbiosis of “human + IM” from the very beginning lets to realize the possibilities of increasing work performance in the economy with the help of digital technologies; 2) the largest labour productivity is achieved in the symbiosis of “human + IM”, where man labour prevails, and the lowest labour productivity is seen where the largest part of the work is performed by IM; 3) developed countries may achieve labour productivity of 3% per year by the mid-2020s, which has all the chances to stay up to the 2040s.
Qingning Wang
Applied Mathematics, Volume 12, pp 262-268; doi:10.4236/am.2021.124017

Abstract:
The spectral radius of a graph is the maximum eigenvalues of its adjacency matrix. In this paper, using the property of quotient graph, the sharp upper bounds for the spectral radii of some adhesive graphs are determined.
Ni Hua
Applied Mathematics, Volume 12, pp 32-57; doi:10.4236/am.2021.121004

Abstract:
This paper deals with a class of n-degree polynomial differential equations. By the fixed point theorem and mathematical analysis techniques, the existence of one (n is an odd number) or two (n is an even number) periodic solutions of the equation is obtained. These conclusions have certain application value for judging the existence of periodic solutions of polynomial differential equations with only one higher-order term.
W. E. Ahmed
Applied Mathematics, Volume 12, pp 75-84; doi:10.4236/am.2021.122006

Abstract:
As it is known, Binomial expansion, De Moivre’s formula, and Euler’s formula are suitable methods for computing the powers of a complex number, but to compute the powers of an octonion number in easy way, we need to derive suitable formulas from these methods. In this paper, we present a novel way to compute the powers of an octonion number using formulas derived from the binomial expansion.
Donald A. Drew
Applied Mathematics, Volume 12, pp 1-17; doi:10.4236/am.2021.121001

Abstract:
Addiction is a societal issue with many negative effects. Substances that cause addictive reactions are easily ingested and interact with some part of the neural pathway. This paper describes a mathematical model for the systemic level of a substance subject to degradation (via metabolism) and reversible binding to psychoactive sites. The model allows the determination of bound substance levels during the processing of a dose, and how the maximum level depends on system parameters. The model also allows the study of a particular periodic repetitive dosing described by a rapid ingestion if a dose is at constant intervals.
Chunyang Ma
Applied Mathematics, Volume 12, pp 18-23; doi:10.4236/am.2021.121002

Abstract:
From ancient times to the present, mathematicians have put forward many series expressions of the circular constant. Because of the importance of the circular constant to mathematical physics, the research on circular constant has never stopped. In this paper, the general function expression of the circular constant was given by studying the transient heat conduction equation. From the physical aspect of the derivation process of the circular constant expression, we can conclude that there is an infinite number of different series exist that can be used to express π.
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