Subjects: Mathematics >> Computational Mathematics. submitted time 2023-12-25
Abstract: This paper introduces a new kind of multigrid approach for semilinear elliptic problems, which is based on the symmetric interior penalty discontinuous Galerkin (SIPDG) method. We first give an optimal error estimate of the SIPDG method for the problem. Then, we design a type of multigrid method, which is called the multilevel correction method, and derive a-priori error estimates. The primary idea of this method is to take the solution of the semilinear problem and utilize it to establish a sequence of solutions for associated linear boundary value problem on discontinuous finite element spaces and a newly defined low dimensional augmented subspace. Lastly, numerical experiments are offered to confirm the suggested method's precision and effectiveness.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Algebra and Number Theory submitted time 2023-12-11
Abstract: Let be a k-algebra defined over a field k. This paper consider the two questions: If the tensor M⊗N on A is zero, under what situation is either M = 0 or N = 0? If the element, say m⊗n , in M⊗N is zero, under what situation is either m=0 or n = 0?
Subjects: Mathematics >> Control and Optimization. submitted time 2023-12-04
Abstract: In this paper, we mainly dicuss the analytic conditions of copositivity of a class of 4th order 3-dimensional symmetric tensors. For a 4th order 3-dimensional symmetric tensor with its entries $1$ or $-1$, an analytic necessary and sufficient condition is given for its strict copositivity with the help of the properties of strictly semi-positive tensors. And by means of usual maxi-min theory, a necessary and sufficient condition is established for copositivity of such a tensor also. Applying these conclusions to a general 4th order 3-dimensional symmetric tensor, the analytic conditions are successfully obtained for verifying the (strict) copositivity, and these conditions can be very easily parsed and validated.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Algebra and Number Theory Subjects: Mathematics >> Discrete Mathematics and Combinatorics submitted time 2023-12-04
Abstract: Let $A_n$ be the Nakayama algebra of type $A$ with quadratic Jacobson radical to be zero and $X_n$ be the Nakayama algebra of type $A$ with quadratic Jacobson radical to be zero. In this paper, we consider the k-tensor $A_n otimes X_n$ and the classification of the indecomposable modules over $A_n otimes X_n$. Moreover, we provide a counting formula to compute the number of isoclasses of indecomposable $A_n otimes X_n$ -modules.
Peer Review Status:Awaiting Review
Subjects: Physics >> Nuclear Physics Subjects: Mathematics >> Computational Mathematics. submitted time 2023-09-29
Abstract: Machine learning-based modeling of reactor physics problems has attracted increasing interest in recent years.
Despite some progress in one-dimensional problems, there is still a paucity of benchmark studies that are easy
to solve using traditional numerical methods albeit still challenging using neural networks for a wide range
of practical problems. We present two networks, namely the Generalized Inverse Power Method Neural Net#2;
work (GIPMNN) and Physics-Constrained GIPMNN (PC-GIPIMNN) to solve K-eigenvalue problems in neu#2;
tron diffusion theory. GIPMNN follows the main idea of the inverse power method and determines the lowest
eigenvalue using an iterative method. The PC-GIPMNN additionally enforces conservative interface condi#2;
tions for the neutron flux. Meanwhile, Deep Ritz Method (DRM) directly solves the smallest eigenvalue by
minimizing the eigenvalue in Rayleigh quotient form. A comprehensive study was conducted using GIPMNN,
PC-GIPMNN, and DRM to solve problems of complex spatial geometry with variant material domains from
the field of nuclear reactor physics. The methods were compared with the standard finite element method. The
applicability and accuracy of the methods are reported and indicate that PC-GIPMNN outperforms GIPMNN
and DRM.
Subjects: Mathematics >> Algebra and Number Theory submitted time 2023-08-07
Abstract: It is showed that for gentle algebra, the simple module and projective module can be characterized by matrix model, and a matrix representation of projective resolution of simple module is provided. Thus the global dimension of a gentle algebra can be characterized by a
special submatrix sequence induced by its matrix model. Furthermore, by showing that above special submatrix sequences correspond to maximal non-trivial forbidden paths on the quiver of gentle algebra, the global dimension of gentle algebra equals the length of the maximal nontrivial forbidden path is obtained.
Subjects: Mathematics >> Applied Mathematics Subjects: Physics >> Interdisciplinary Physics and Related Areas of Science and Technology submitted time 2023-07-04
Abstract:
Based on the Golomb's pseudorandomness assumptions on idea pseudorandom sequences and FIPS 140-2 pseudorandomness test, this paper first presents a new approach for improving the pseudorandomness of pseudorandom sequences. Second, using a generalized synchronization theorem, and three chaotic maps constructs one 8-dimensional chaotic generalized synchronization system (8DCGSS). Then using the 8DCGSS designs a chaotic
pseudorandom number generator (CPRNG). The keyspace of the CPRNG is larger than 2^{1117}. Third, using FIPS 140-2 pseudorandomness test criterions and generalized FIPS 140-2 pseudorandomness test criterions measures, respectively, the pseudorandomness of the keystreams with length 20 000, 100 000 and 1 000 000 generated via the CPRNG, an Matlab PRNG, an RC4 algorithm, and an m-sequence with period 2^{20} - 1, and the corresponding improved keystreams by our approach. The results show that the presented approach can increase significantly the pseudorandomness of the keystreams generated by the four PRNGs. The key streams generated by the m-sequence do not have sound pseudorandomness when the lengths of the key streams are less than 100 000.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Statistics and Probability Subjects: Psychology >> Statistics in Psychology submitted time 2023-07-02
Abstract: Taking the goodness of fit test (Chi test) as an example, this paper attempts to calculate the Bayesian factor BF10 of n-fold Bernoulli test by the Excel software (using JASP software as the evidence). The results showed that in the range of 0.15-0.55 (the rate of samples which are all "true"), the calculated results of Excel were more accurate, and the differences between the two (Excel and JASP) were not statistically significant (P>0.3).
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematics (General) Subjects: Mathematics >> Logic submitted time 2023-06-20
Abstract: The aim of this paper is to study well-connected residuated lattices and residually finite residuated lattices. So far, well-connected residuated lattices not only a main tool for studying RLsi but also a subdirect irreducible representation object
of residuated lattices. In this paper we both investigate the above two aspects by using some different methods. Finally, we introduce the residually finite residuated lattices and characterize them from algebraic, logical and topological perspectives,
respectively.
Peer Review Status:Awaiting Review
Subjects: Geosciences >> Geography Subjects: Mathematics >> Control and Optimization. submitted time 2023-05-13
Abstract: Location problems have been widely applied to service planning of public health, compulsory education, emergency management, and delivery logistics. However, the mainstream location models are usually to optimize the efficiency objectives such as travel cost, facility cost and the number of customs to be served, rather than the equality objectives. A few location models aim to optimize one of the equality measures, such as the variance of distances, the deviation of distances, the Gini coefficient between the travel distances, and the variance of spatial accessibility indexes. However, the facility locations, capacities and their service areas can be easily distorted by most equality-oriented objective functions. In this paper, a spatially envy objective function for service equality is proposed to overcome the shortcomings of commonly used equality functions. The envy value of customers at a location is determined by their travel distance that beyond a predefined distance. The envy function can be added to mainstream location models in a weighted manner. As a result, the capacitated p-median problem (CPMP) is enhanced as CPMP-envy. The original and improved models were tested on three large instances. Case experiments show that the equality measures, such as maximum travel distance, variance of distances, coefficient of variation, and Gini coefficient between travel distances, can be substantially improved by minimizing the weighted sum of spatial envy and travel cost. It is argued that the envy indicator has theoretical and practical potentials in facility planning towards spatial equality of public service.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematics (General) Subjects: Hydraulic Engineering >> Basic Disciplines of Hydraulic Engineering submitted time 2023-04-28
Abstract: In this paper, we mainly provide a proper maintenance plan for the Kariba Dam in Africa which falls into disrepair and is facing to collapse. Firstly, we make a threshold analysis of the three options about their costs which include people’s moving, old dam’s removing, new dams’ building, later repairing, ecological destruction and their incomes which include generation energy, avoiding of flood disasters’ loss, providing employment, tourism resources and ecological protection. Then we get the specific relationship between benefits and years with some collected data. Both of the results show that the third option is the best choice from the economic view. And the result is completely as same as the conclusion we get after studying deeply on Option 3. Secondly, we regard water management capabilities as the safety coefficient of dams. We select 30 seed points along the riverbank for preparing the establishment of dams. With flow-between-riverway model, Manning equations, large Cauchy distribute function we get the scores of the seed points. We give an advice that the number of dams should be more and the positions of dams should be well-distributed. Then, we build an assessment model by analytic hierarchy process. We select three factors among all the factors, safety, economy and population. After testing the consistency, we get the weights of each factor: 0.6442, 0.2705, 0.0852. Then we value the factors and get an optimal scheme during the assessment with 0-1 integer programming: the number of dams is 17 and the longitude and latitude of them are shown in Table 17. The sensitivity of the result is tested as well. We also provide some strategies for the managers of ZRA to use. We suggest that they should use the dams normally in general. With the Dam-break model, we find 13 points among 17 points which are shown in Table 20. The dams at the 13 points need to be closed when there is a flood and it is just the opposite when the drought happens. For the extreme water flow, we assume an ideal water flow at first. The extreme water flow has to be adjusted to satisfy the ideal one. As for the restrictions in extreme conditions, the biggest impact happens at the 8th point among the 17 points. If the duration of maximum flow is t0, the drainage time t to make the water flow return to the normal level equals to 4.95t0.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematics (General) submitted time 2023-04-27
Abstract: This paper demonstrates the invariant distribution of a stochastic dynamical system. We give the invariant distribution and numerical examples. We also present a further discussion on the computation details.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Computational Mathematics. submitted time 2023-04-20
Abstract: We present the Parareal-CG algorithm for time-dependent differential equations in this work. The algorithm is a parallel in time iteration algorithm utilizes Chebyshev-Gauss spectral collocation method for fine propagator F and backward Euler method for coarse propagator G. As far as we know, this is the first time that the spectral method used as the F propagator of the parareal algorithm. By constructing the stable function of the Chebyshev-Gauss spectral collocation method for the symmetric positive definite (SPD) problem, we find out that the Parareal-CG algorithm and the Parareal-TR algorithm, whose F propagator is chosen to be a trapezoidal ruler, converge similarly, i.e., the Parareal-CG algorithm converge as fast as Parareal-Euler algorithm with sufficient Chebyhsev-Gauss points in every coarse grid. Numerical examples including ordinary differential equations and time-dependent partial differential equations are given to illustrate the high efficiency and accuracy of the proposed algorithm.
Peer Review Status:Awaiting Review
Subjects: Medicine, Pharmacy >> Preclinical Medicine Subjects: Mathematics >> Statistics and Probability submitted time 2023-04-19
Abstract: Objective To investigate the current status of data transformation in Meta analysis of single proportions. Methods A literature search in PubMed was performed to retrieve researches of Meta analysis of single proportions published in 2017, and 481 records were returned. Results In 123 researches with full texts, only 33 (26.8%) described data transformation for proportions. Among which, double arcsine transformation was used 20 times, logit transformation 8, squared arcsine transformation 3, log transformation 1 and raw proportion 1. There was no relation between pooled portions and data transformation method (P=0.217). Conclusion Data transformation is important in Meta analysis of single proportions, however, it is yet to determined which transformation method is best. So, data transformation should be clarified in published papers.
Peer Review Status:Awaiting Review
Subjects: Medicine, Pharmacy >> Preclinical Medicine Subjects: Mathematics >> Statistics and Probability submitted time 2023-04-19
Abstract: Objective To compare different data transformations in Meta analysis for single proportions. Methods Two simulation data were constructed for Meta analysis under fixed effect model and random effect model, different adding values when event number was zero, and five different data transformation methods (raw proportion, log transformation, logit transformation, arcsine transformation and double arcsine transformation). Mean of pooled portion, bias, proportion bias, mean squared error, proportion mean squared error, proportion mean squared error and 95% confidence coverage were calculated. Results For Meta analysis of single proportions based on binomial distribution, generally, arcsine transformation performed best. When event number was zero, different values added to it did not improve the result much. Bias of pooled proportion was rather big when the population proportion is below 0.05. Conclusion Arcsine data transformation performed best during the simulation study for Meta analysis of single proportions. Caution should be used when dealing with population proportion less than 0.05.
Peer Review Status:Awaiting Review
Subjects: Medicine, Pharmacy >> Preclinical Medicine Subjects: Mathematics >> Statistics and Probability submitted time 2023-04-19
Abstract: The common method of sample size calculation for single proportion comparison (performance goal) is normal asymptotic approach, sometimes with corresponding data transformation such as squared arcsine, while exact probability usually needs commercial statistics software or programming. We use the free software R to calculate the sample size for single proportion via exact probability, and considering of the non-monotone increasing relationship between power and sample size with exact probability, we provide intuitive figure demonstration besides giving direct calculation results. We hope this will facilitate study design with performance goal.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Geometry and Topology submitted time 2023-02-22
Abstract: In this paper, we give a complete classifification of harmonic and biharmon#2;
ic Riemannian submersions π : (R^3 , g_Sol) → (N^2 , h) from Sol space into a
surface by proving that there is neither harmonic nor biharmonic Riemann#2;
ian submersion π : (R^3 , g_Sol) → (N^2 , h) from Sol space no matter what
the base space (N2 , h) is. We also prove that a Riemannian submersion
π : (R^3 , g_Sol) → (N^2 , h) from Sol space exists only when the base space is
a hyperbolic space form.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Geometry and Topology submitted time 2023-02-22
Abstract:
In this paper, we study biharmonic isometric immersions of a surface into and biharmonic Riemannian submersions from 3-dimensional Berger spheres. We obtain a classifification of proper biharmonic isometric immersions of a surface with constant mean curvature into Berger 3-spheres. We also give a complete classifification of proper biharmonic Hopf tori in Berger 3-sphere.
For Riemannian submersions, we prove that a Riemannian submersion from Berger 3-spheres into a surface is biharmonic if and only if it is harmonic.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Mathematics (General) Subjects: Information Science and Systems Science >> Information Security Technology submitted time 2023-02-18
Abstract: Constructing linear codes with few weights is an important research topic in coding and cryptography theory. The weight hierarchy of code also has basic theoretical significance in coding theory, and plays an important role in secret communications. In this paper, a class of 3-weight and a class of 4-weight binary linear codes are constructed, and their weight distributions and weight hierarchies are determined by exponential sum theory.
Peer Review Status:Awaiting Review
Subjects: Mathematics >> Computational Mathematics. submitted time 2023-02-15 Cooperative journals: 《桂林电子科技大学学报》
Abstract: The aim of this paper is to estimate the risk of Zika and dengue fever (DEN)infection that imports from Asia and
causes local outbreaks. Based on the oversea epidemic data and the floating population between 2015 and 2017, an input
model was built to estimate the number of imported cases, and the local epidemic transmission probability and basic regeneration
number were calculated via the branching process under different temperatures and herd immunity levels. The imported
cases of Zika in China mainly came from Singapore, Thailand and Vietnam, with the predicted number of cases as 7.0
(95% CI:6.5-7.5), 2.0 (95% CI:1.8-2.2) and 1.0 (95% CI:0.9-1.1). The imported DEN cases were mainly from Thailand,
Malaysia, Singapore, Vietnam, Philippines, Indonesia, India and Korea, the predicted number of cases as 700.0
(95%CI:679.8-720.2), 654.1 (95%CI:641.8-666.2), 376.3 (95% CI:368.2-384.1), 277.1 (95% CI:268.6-285.3),
241.20 (95% CI:233.6-248.8), 67.03 (95% CI:59.6-74.5), 9.1 (95% CI:6.7-11.3) and 3.0 (95% CI:1.9-4.1). The
optimum temperature for Zika and DEN transmission is around 28.9 ℃, in which the risk probability of local transmission is
24.4% and 99.9%, respectively. When the human herd immunity level is 0, 0.2 and 0.6, the basic reproduction numbers
of Zika and DEN are 8.1, 6.7, 3.2 and 3.2, 2.7, 1.3, respectively. The imported cases mainly come from South Asia.
South-central and south-eastern China are top-risk areas for local transmission, especially in June-August. The infection in
Singapore is more likely to cause Zika outbreak in China, while the infection in Thailand, Vietnam, Malaysia and Singapore
are the biggest cause of local transmission of DEN in China.