Applied Mathematics

Journal Information
ISSN / EISSN : 2152-7385 / 2152-7393
Published by: Scientific Research Publishing, Inc. (10.4236)
Total articles ≅ 2,110
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Latest articles in this journal

Gene Whyman
Applied Mathematics, Volume 12, pp 576-586; doi:10.4236/am.2021.127041

Abstract:
The Newcomb-Benford law, which describes the uneven distribution of the frequencies of digits in data sets, is by its nature probabilistic. Therefore, the main goal of this work was to derive formulas for the permissible deviations of the above frequencies (confidence intervals). For this, a previously developed method was used, which represents an alternative to the traditional approach. The alternative formula expressing the Newcomb-Benford law is re-derived. As shown in general form, it is numerically equivalent to the original Benford formula. The obtained formulas for confidence intervals for Benford’s law are shown to be useful for checking arrays of numerical data. Consequences for numeral systems with different bases are analyzed. The alternative expression for the frequencies of digits at the second decimal place is deduced together with the corresponding deviation intervals. In general, in this approach, all the presented results are a consequence of the positionality property of digital systems such as decimal, binary, etc.
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.
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.
E. D. Wandji Tanguep, D. A. Njamen Njomen
Applied Mathematics, Volume 12, pp 322-335; doi:10.4236/am.2021.124023

Abstract:
In this article, we study the Kolmogorov-Smirnov type goodness-of-fit test for the inhomogeneous Poisson process with the unknown translation parameter as multidimensional parameter. The basic hypothesis and the alternative are composite and carry to the intensity measure of inhomogeneous Poisson process and the intensity function is regular. For this model of shift parameter, we propose test which is asymptotically partially distribution free and consistent. We show that under null hypothesis the limit distribution of this statistic does not depend on unknown parameter.
Rogelio Luck, Yucheng Liu
Applied Mathematics, Volume 12, pp 336-347; doi:10.4236/am.2021.124024

Abstract:
This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling.
Jingkun Liu, Qi Fan
Applied Mathematics, Volume 12, pp 489-499; doi:10.4236/am.2021.126034

Abstract:
The purpose of this paper is to study a semilinear Schrödinger equation with constraint in H1(RN), and prove the existence of sign changing solution. Under suitable conditions, we obtain a negative solution, a positive solution and a sign changing solution by using variational methods.
Brice M. Yambiyo, A. Manirakiza, Gaston M. N’Guérékata
Applied Mathematics, Volume 12, pp 477-488; doi:10.4236/am.2021.126033

Abstract:
In this paper, we propose a susceptible-exposed-infection-asymptomatic-hospitalized-recovered (SEIAHR) model with parameters on retrospective social distancing and masking. We estimated the model parameters from information published on the World Health Organization (WHO) website. We found that the actual reproduction number Rt varies over the period from 03 March to 07 June 2020 and moreover, effective control over contacts and the frequency of population movement would reduce the evolution of the epidemic (control c ≥ 50%). And the contact check has an influence on the base reproduction number R0.
Mohammad Shaha Alam Patwary, Soma Chowdhury Biswas
Applied Mathematics, Volume 12, pp 563-575; doi:10.4236/am.2021.127040

Abstract:
Bangladesh, a developing country, gained success towards the fifth-millennium development goals target of reducing its maternal mortality ratio by three quarters by 2015, but yet worked more on it for further reduction of maternal mortality. In this light, though Bangladesh is committed to the sustainable development goals target of reducing its maternal mortality ratio to be reduced from 170 to 105 per 100,000 live births, the scope of research on this issue is limited because the maternal morbidity data is scarce in Bangladesh. In this paper, the prospective data on maternal morbidity in rural Bangladesh (collected by BIRPERHT) have been employed to trace out the high-risk and life-threatening factors associated with pregnancy-related complications. The subject-specific generalized estimating equations (SS-GEE) model with random effect structure is used for multivariate binary data for the repeated observations. The findings indicate that the risk of suffering from pregnancy complications is higher for high economic status, lower age at marriage, not visited for medical check-ups, outside home workers, and having miscarriage or abortion. Comparing the SS-GEE model with other correlation structures and relative efficiency factors, the SS-GEE model with random effect structure is well fitted for the prospective repeated observation data.
Jan Vrbik
Applied Mathematics, Volume 12, pp 521-534; doi:10.4236/am.2021.127036

Abstract:
In most textbooks, lens aberrations are usually described in the briefest possible manner, without any attempt for their proper derivation. At the same time, monographs which do go into more detail are often inaccessible to most students and non-specialists interested in deeper understanding of this topic. This article tries to fill this gap and provide an introduction to what happens when basic formulas of Geometrical Optics are extended by third-order terms in Taylor’s expansion of sin (α). The presentation is accessible to most undergraduate students as it requires only some knowledge of basic calculus and planar geometry. The resulting five aberrations are then described in detail, including a novel derivation of the exact shape of coma. A simple Mathematica program is included to facilitate numerical exploration of the magnitude of the resulting aberrations for various optical systems.
Ning Zhao
Applied Mathematics, Volume 12, pp 556-562; doi:10.4236/am.2021.127039

Abstract:
We employ graph parameter, the rupture degree, to measure the vulnerability of k-uniform hypergraph Gk. For the k-uniform hypergraph Gk underlying a non-complete graph G = (V, E), its rupture degree r(Gk) is defined as r(Gk) = max{ω(Gk - X) - |X| - m(Gk - X): X ⊂ V(Gk), ω(Gk - X) > 1}, where X is a cut set (or destruction strategy) of Gk, ω(Gk - X) and m(Gk - X) denote the number of components and the order of a largest component in Gk - X, respectively. It is shown that this parameter can be used to measure the vulnerability of networks. In this paper, the rupture degrees of several specific classes of k-uniform hypergraph are determined.
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