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Abstract: In this work, we aim to develop an effective fully discrete Spectral-Galerkin numerical scheme for the multi-vesicular phase-field model of lipid vesicles with adhesion potential. The essence of the scheme is to introduce several additional auxiliary variables and design some corresponding auxiliary ODEs to reformulate the system into an equivalent form so that the explicit discretization for the nonlinear terms can also achieve unconditional energy stability. Moreover, the scheme has a full decoupling structure and can avoid calculating variable-coefficient systems. The advantage of this scheme is its high efficiency and ease of implementation, that is, only by solving two independent linear biharmonic equations with constant coefficients for each phase-field variable, the scheme can achieve the second-order accuracy in time, spectral accuracy in space, and unconditional energy stability. We strictly prove that the fully discrete energy stability that the scheme holds and give a detailed step-by-step implementation process. Further, numerical experiments are carried out in 2D and 3D to verify the convergence rate, energy stability, and effectiveness of the developed algorithm. PubDate: 2022-05-10

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Abstract: This paper shows that the multiplicity of the base point locus of a projective rational surface parametrization can be expressed as the degree of the content of a univariate resultant. As a consequence, we get a new proof of the degree formula relating the degree of the surface, the degree of the parametrization, the base point multiplicity and the degree of the rational map induced by the parametrization. In addition, we extend both formulas to the case of dominant rational maps of the projective plane and describe how the base point loci of a parametrization and its reparametrizations are related. As an application of these results, we explore how the degree of a surface reparametrization is affected by the presence of base points. PubDate: 2022-05-10

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Abstract: Abstract We establish a global Torelli theorem for the complete family of Calabi-Yau threefolds arising from cyclic triple covers of \({{\mathbb {P}}}^3\) branched along six stable hyperplanes. PubDate: 2022-04-16

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Abstract: Abstract Let R be a commutative ring having nonzero identity and M be a unital R-module. Assume that \(S\subseteq R\) is a multiplicatively closed subset of R. Then, M satisfies S-Noetherian spectrum condition if for each submodule N of M, there exist \(s\in S\) and a finitely generated submodule \(F\subseteq N\) such that \(sN\subseteq \text {rad}_{M}(F)\) , where \(\text {rad}_{M}(F)\) is the prime radical of F in the sense (McCasland and Moore in Commun Algebra 19(5):1327–1341, 1991). Besides giving many properties and characterizations of S-Noetherian spectrum condition, we prove an analogous result to Cohen’s theorem for modules satisfying S-Noetherian spectrum condition. Moreover, we characterize modules having Noetherian spectrum in terms of modules satisfying the S-Noetherian spectrum condition. PubDate: 2022-03-29

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Abstract: Abstract We use reflecting Brownian motion (RBM) to prove the well-known Gauss–Bonnet–Chern theorem for a compact Riemannian manifold with boundary. The boundary integrand is obtained by carefully analyzing the asymptotic behavior of the boundary local time of RBM for small times. PubDate: 2022-03-25

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Abstract: Abstract A finite generating set of the centre of any quantum group is obtained, where the generators are given by an explicit formulae. For the slightly generalised version of the quantum group which we work with, we show that this set of generators is algebraically independent, thus the centre is isomorphic to a polynomial algebra. PubDate: 2022-03-14

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Abstract: Abstract Multiple testing has gained much attention in high-dimensional statistical theory and applications, and the problem of variable selection can be regarded as a generalization of the multiple testing. It is aiming to select the important variables among many variables. Performing variable selection in high-dimensional linear models with measurement errors is challenging. Both the influence of high-dimensional parameters and measurement errors need to be considered to avoid severely biases. We consider the problem of variable selection in error-in-variables and introduce the DCoCoLasso-FDP procedure, a new variable selection method. By constructing the consistent estimator of false discovery proportion (FDP) and false discovery rate (FDR), our method can prioritize the important variables and control FDP and FDR at a specifical level in error-in-variables models. An extensive simulation study is conducted to compare DCoCoLasso-FDP procedure with existing methods in various settings, and numerical results are provided to present the efficiency of our method. PubDate: 2022-03-01 DOI: 10.1007/s40304-020-00233-4

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Abstract: Abstract One of the important issues in order to survey multivariate distribution or model dependency structure between interested variables is finding the proper copula function. Extensive studies have been done based on Akaike information criterion (AIC), copula information criterion (CIC), and pseudo-likelihood ratio and fitness test of the copula function. The previous methods of selecting copula functions when the sample size is too small are not satisfactory. Therefore, our method in this paper is based on tracking interval for the parametric copula function which is obtained using expected Kullback–Leibler risk between the two proposed non-nested parametric copula model. It can be find that optimal parametric copula between proposed copula functions in a good level of significance. Finally, efficiency and capability of our method using simulation and applied example have been shown. PubDate: 2022-03-01 DOI: 10.1007/s40304-019-00205-3

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Abstract: Abstract Based on the improvement in establishing the relations of data, this study proposes a new fuzzy time series model. In this model, the suitable number of fuzzy sets and their specific elements are determined automatically. In addition, using the percentage variations of series between consecutive periods of time, we build the fuzzy function. Incorporating all these improvements, we have a new fuzzy time series model that is better than many existing ones through the well-known data sets. The calculation of the proposed model can be performed conveniently and efficiently by a MATLAB procedure . The proposed model is also used in forecasting for an urgent problem in Vietnam. This application also shows the advantages of the proposed model and illustrates its effectiveness in practical application. PubDate: 2022-03-01 DOI: 10.1007/s40304-019-00203-5

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Abstract: Abstract In this paper, we first obtain the existence and uniqueness of solution u of elliptic equation associated with Brownian motion with singular drift. We then use the regularity of the weak solution u and the Zvonkin-type transformation to show that there is a unique weak solution to a stochastic differential equation when the drift is a measurable function. PubDate: 2022-03-01 DOI: 10.1007/s40304-020-00213-8

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Abstract: Abstract Consider n nodes \(\{X_i\}_{1 \le i \le n}\) independently and identically distributed (i.i.d.) across N cities located within the unit square S. Each city is modelled as an \(r_n \times r_n\) square, and \(\mathrm{{MSTC}}_n\) denotes the weighted length of the minimum spanning tree containing all the n nodes, where the edge length between nodes \(X_i\) and \(X_j\) is weighted by a factor that depends on the individual locations of \(X_i\) and \(X_j.\) We use approximation methods to obtain variance estimates for \(\mathrm{{MSTC}}_n\) and prove that if the cities are well connected in a certain sense, then \(\mathrm{{MSTC}}_n\) appropriately centred and scaled converges to zero in probability. Using the above proof techniques we also study \(\mathrm{{MST}}_n,\) the length of the minimum weighted spanning tree for nodes distributed throughout the unit square S with location-dependent edge weights. In this case, the variance of \(\mathrm{{MST}}_n\) grows at most as a power of the logarithm of n and we use a subsequence argument to get almost sure convergence of \(\mathrm{{MST}}_n,\) appropriately centred and scaled. PubDate: 2022-03-01 DOI: 10.1007/s40304-019-00201-7

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Abstract: Abstract The purpose of this paper is to define a new symbol class \(\Lambda \) and discuss the theory of two different pseudo-differential operators (p.d.o.) involving Fourier–Jacobi transform associated with a single symbol in \(\Lambda \) . We also derive boundedness results for p.d.o.’s in Sobolev type space. A new pseudo-differential operator is developed using the product of symbols. Finally, norm inequality for commutators between two pseudo-differential operators is obtained. PubDate: 2022-03-01 DOI: 10.1007/s40304-019-00204-4

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Abstract: Abstract In the past ten years, deep learning technology has achieved a great success in many fields, like computer vision and speech recognition. Recently, large-scale geometry data become more and more available, and the learned geometry priors have been successfully applied to 3D computer vision and computer graphics fields. Different from the regular representation of images, surface meshes have irregular structures with different vertex numbers and topologies. Therefore, the traditional convolution neural networks used for images cannot be directly used to handle surface meshes, and thus, many methods have been proposed to solve this problem. In this paper, we provide a comprehensive survey of existing geometric deep learning methods for mesh processing. We first introduce the relevant knowledge and theoretical background of geometric deep learning and some basic mesh data knowledge, including some commonly used mesh datasets. Then, we review various deep learning models for mesh data with two different types: graph-based methods and mesh structure-based methods. We also review the deep learning-based applications for mesh data. In the final, we give some potential research directions in this field. PubDate: 2022-02-14 DOI: 10.1007/s40304-021-00246-7

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Abstract: Abstract In this paper, we will first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk. In order to verify the rationality of this simulation, we propose a practical estimator associated with the LSE of the drift parameter of mixed sub-fractional Ornstein–Uhlenbeck process, and illustrate the asymptotical properties according to our method of simulation when the Hurst parameter \(H>1/2\) . PubDate: 2022-01-27 DOI: 10.1007/s40304-021-00245-8

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Abstract: Abstract This article deals with some new chain imputation methods by using two auxiliary variables under missing completely at random (MCAR) approach. The proposed generalized classes of chain imputation methods are tested from the viewpoint of optimality in terms of MSE. The proposed imputation methods can be considered as an efficient extension to the work of Singh and Horn (Metrika 51:267–276, 2000), Singh and Deo (Stat Pap 44:555–579, 2003), Singh (Stat A J Theor Appl Stat 43(5):499–511, 2009), Kadilar and Cingi (Commun Stat Theory Methods 37:2226–2236, 2008) and Diana and Perri (Commun Stat Theory Methods 39:3245–3251, 2010). The performance of the proposed chain imputation methods is investigated relative to the conventional chain-type imputation methods. The theoretical results are derived and comparative study is conducted and the results are found to be quite encouraging providing the improvement over the discussed work. PubDate: 2022-01-21 DOI: 10.1007/s40304-021-00251-w

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Abstract: Abstract In this article, we carry out stochastic comparisons on the maximum order statistics arising from two batches of multiple-outlier gamma random variables with different shape and scale parameters. It is proved that, under certain conditions, the majorization order between the vectors of shape parameters together with the weak majorization order [p-larger order] between the vectors of scale parameters implies the likelihood ratio order [hazard rate order] between the largest order statistics. The results established here strengthen and generalize some known ones in the literature. PubDate: 2022-01-12 DOI: 10.1007/s40304-021-00247-6

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Abstract: Abstract In this paper, it is shown that for a minimal system (X, G), if H is a normal subgroup of G with finite index n, then X can be decomposed into n components of closed sets such that each component is minimal under H-action. Meanwhile, we prove that for a residual set of points in a minimal system with finitely many commuting homeomorphisms, the set of return times to any non-empty open set contains arbitrarily long geometric progressions in multidimension, extending a previous result by Glasscock, Koutsogiannis and Richter. PubDate: 2021-12-01 DOI: 10.1007/s40304-020-00230-7

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Abstract: Abstract In this paper, we study in frequency domain some probabilistic and statistical properties of continuous-time version of the well-known bilinear processes driven by a standard Brownian motion. This class of processes which encompasses many commonly used processes in the literature was defined as a nonlinear stochastic differential equation which has raised considerable interest in the last few years. So, the \({\mathbb {L}}_{2}\) -structure of the process is studied and its covariance function is given. These structures will lead to study the strong consistency and asymptotic normality of the Whittle estimates of the unknown parameters involved in the process. Finite sample properties are also considered through Monte Carlo experiments. In end, the model is then used to model the exchanges rate of the Algerian Dinar against the US dollar. PubDate: 2021-12-01 DOI: 10.1007/s40304-019-00196-1

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Abstract: Abstract This paper investigates and discusses the use of information divergence, through the widely used Kullback–Leibler (KL) divergence, under the multivariate (generalized) \(\gamma \) -order normal distribution ( \(\gamma \) -GND). The behavior of the KL divergence, as far as its symmetricity is concerned, is studied by calculating the divergence of \(\gamma \) -GND over the Student’s multivariate t-distribution and vice versa. Certain special cases are also given and discussed. Furthermore, three symmetrized forms of the KL divergence, i.e., the Jeffreys distance, the geometric-KL as well as the harmonic-KL distances, are computed between two members of the \(\gamma \) -GND family, while the corresponding differences between those information distances are also discussed. PubDate: 2021-12-01 DOI: 10.1007/s40304-019-00200-8

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Abstract: Abstract Let \(\sigma =\{\sigma _i i\in I\}\) be some partition of all primes \({\mathbb {P}}\) and G a finite group. A subgroup H of G is said to be \(\sigma \) -subnormal in G if there exists a subgroup chain \(H=H_0\le H_1\le \cdots \le H_n=G\) such that either \(H_{i-1}\) is normal in \(H_i\) or \(H_i/(H_{i-1})_{H_i}\) is a finite \(\sigma _j\) -group for some \(j \in I\) for \(i = 1, \ldots , n\) . We call a finite group G a \(T_{\sigma }\) -group if every \(\sigma \) -subnormal subgroup is normal in G. In this paper, we analyse the structure of the \(T_{\sigma }\) -groups and give some characterisations of the \(T_{\sigma }\) -groups. PubDate: 2021-09-12 DOI: 10.1007/s40304-021-00240-z