The algebraic structure of skew left brace has proved to be useful as a source of set-theoretic solutions of the Yang–Baxter equation. We study in this paper the connections between left and right $\pi $-nilpotency and the structure of finite skew left braces. We also study factorisations of skew left braces and their impact on the skew left brace structure. As a consequence of our study, we define a Fitting-like ideal of a left brace. Our approach depends strongly on a description of a skew left brace in terms of a triply factorised group obtained from the action of the multiplicative group of the skew left brace on its additive group.
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.
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.
In this paper, we prove a Chern number inequality for Higgs bundles over some Kähler manifolds. As an application, we get the Bogomolov inequality for semi-stable parabolic Higgs bundles over smooth projective varieties.
For the $p$-harmonic function with strictly convex level sets, we find an auxiliary function which comes from the combination of the norm of gradient of the $p$-harmonic function and the Gaussian curvature of the level sets of $p$-harmonic function. We prove that this curvature function is concave with respect to the height of the $p$-harmonic function. This auxiliary function is an affine function of the height when the $p$-harmonic function is the $p$-Green function on ball.
If the population is rare and clustered, then simple random sampling gives a poor estimate of the population total. For such type of populations, adaptive cluster sampling is useful. But it loses control on the final sample size. Hence, the cost of sampling increases substantially. To overcome this problem, the surveyors often use auxiliary information which is easy to obtain and inexpensive. An attempt is made through the auxiliary information to control the final sample size. In this article, we have proposed two-stage negative adaptive cluster sampling design. It is a new design, which is a combination of two-stage sampling and negative adaptive cluster sampling designs. In this design, we consider an auxiliary variable which is highly negatively correlated with the variable of interest and auxiliary information is completely known. In the first stage of this design, an initial random sample is drawn by using the auxiliary information. Further, using Thompson’s (J Am Stat Assoc 85:1050–1059,
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.
In the present paper, we study the structure of cyclic DNA codes of even length over the ring ${F}_2+u{F}_2+u^2{F}_2$ where $u^3=0$. We investigate two presentations of cyclic codes of even length over ${F}_2+u{F}_2+u^2{F}_2$ satisfying the reverse constraint and the reverse-complement constraint.
In this paper, we study the expansions of Ricci flat metrics in harmonic coordinates about the infinity of ALE (Asymptotically Local Euclidean) manifolds.
This paper establishes probabilistic and statistical properties of the extension of time-invariant coefficients asymmetric $\log $ GARCH processes to periodically time-varying coefficients ($P\log $ GARCH) one. In these models, the parameters of $\log -$volatility are allowed to switch periodically between different seasons. The main motivations of this new model are able to capture the asymmetry and hence leverage effect, in addition, the volatility coefficients are not a subject to positivity constraints. So, some probabilistic properties of asymmetric $P\log $ GARCH models have been obtained, especially, sufficient conditions ensuring the existence of stationary, causal, ergodic (in periodic sense) solution and moments properties are given. Furthermore, we establish the strong consistency and the asymptotic normality of the quasi-maximum likelihood estimator (QMLE) under extremely strong assumptions. Finally, we carry out a simulation study of the performance of the QML and the $P\log $ GARCH is applied to model the crude oil prices of Algerian Saharan Blend.
In this paper, the problem of high-dimensional multivariate analysis of variance is investigated under a low-dimensional factor structure which violates some vital assumptions on covariance matrix in some existing literature. We propose a new test and derive that the asymptotic distribution of the test statistic is a weighted distribution of chi-squares of 1 degree of freedom under the null hypothesis and mild conditions. We provide numerical studies on both sizes and powers to illustrate performance of the proposed test.
Process regression models, such as Gaussian process regression model (GPR), have been widely applied to analyze kinds of functional data. This paper introduces a composite of two T-process (CT), where the first one captures the smooth global trend and the second one models local details. The CT has an advantage in the local variability compared to general T-process. Furthermore, a composite T-process regression (CTP) model is developed, based on the composite T-process. It inherits many nice properties as GPR, while it is more robust against outliers than GPR. Numerical studies including simulation and real data application show that CTP performs well in prediction.
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.
The performance of feature learning for deep convolutional neural networks (DCNNs) is increasing promptly with significant improvement in numerous applications. Recent studies on loss functions clearly describing that better normalization is helpful for improving the performance of face recognition (FR). Several methods based on different loss functions have been proposed for FR to obtain discriminative features. In this paper, we propose an additive parameter depending on multiplicative angular margin to improve the discriminative power of feature embedding that can be easily implemented. In additive parameter approach, an automatic adjustment of the seedling element as the result of angular marginal seed is offered in a particular way for the angular softmax to learn angularly discriminative features. We train the model on publically available dataset CASIA-WebFace, and our experiments on famous benchmarks YouTube Faces (YTF) and labeled face in the wild (LFW) achieve better performance than the various state-of-the-art approaches.
We introduce a four-parameter lifetime distribution called the odd log-logistic generalized Gompertz model to generalize the exponential, generalized exponential and generalized Gompertz distributions, among others. We obtain explicit expressions for the moments, moment-generating function, asymptotic distribution, quantile function, mean deviations and distribution of order statistics. The method of maximum likelihood estimation of parameters is compared by six different methods of estimations with simulation study. The applicability of the new model is illustrated by means of a real data set.
The purpose of this paper is to investigate the k-nearest neighbor classification rule for spatially dependent data. Some spatial mixing conditions are considered, and under such spatial structures, the well known k-nearest neighbor rule is suggested to classify spatial data. We established consistency and strong consistency of the classifier under mild assumptions. Our main results extend the consistency result in the i.i.d. case to the spatial case.
We study the accuracy and performance of isogeometric analysis on implicit domains when solving time-independent Schrödinger equation. We construct weighted extended PHT-spline basis functions for analysis, and the domain is presented with same basis functions in implicit form excluding the need for a parameterization step. Moreover, an adaptive refinement process is formulated and discussed with details. The constructed basis functions with cubic polynomials and only $C^{1}$ continuity are enough to produce a higher continuous field approximation while maintaining the computational cost for the matrices as low as possible. A numerical implementation for the adaptive method is performed on Schrödinger eigenvalue problem with double-well potential using 3 examples on different implicit domains. The convergence and performance results demonstrate the efficiency and accuracy of the approach.
Mesh segmentation is a fundamental and critical task in mesh processing, and it has been studied extensively in computer graphics and geometric modeling communities. However, current methods are not well suited for segmenting large meshes which are now common in many applications. This paper proposes a new spectral segmentation method specifically designed for large meshes inspired by multi-resolution representations. Building on edge collapse operators and progressive mesh representations, we first devise a feature-aware simplification algorithm that can generate a coarse mesh which keeps the same topology as the input mesh and preserves as many features of the input mesh as possible. Then, using the spectral segmentation method proposed in Tong et al. (IEEE Trans Vis Comput Graph 26(4):1807–1820, 2020), we perform partition on the coarse mesh to obtain a coarse segmentation which mimics closely the desired segmentation of the input mesh. By reversing the simplification process through vertex split operators, we present a fast algorithm which maps the coarse segmentation to the input mesh and therefore obtain an initial segmentation of the input mesh. Finally, to smooth some jaggy boundaries between adjacent parts of the initial segmentation or align with the desired boundaries, we propose an efficient method to evolve those boundaries driven by geodesic curvature flows. As demonstrated by experimental results on a variety of large meshes, our method outperforms the state-of-the-art segmentation method in terms of not only speed but also usability.
Let R be a prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, F and G, the two nonzero generalized derivations of R, I an ideal of R and $f(x_1,\ldots ,x_n)$ a multilinear polynomial over C which is not central valued on R. If
We offer a new method for proving that the maxima eigenvalue of the normalized graph Laplacian of a graph with n vertices is at least $\frac{n+1}{n-1}$ provided the graph is not complete and that equality is attained if and only if the complement graph is a single edge or a complete bipartite graph with both parts of size $\frac{n-1}{2}$. With the same method, we also prove a new lower bound to the largest eigenvalue in terms of the minimum vertex degree, provided this is at most $\frac{n-1}{2}$.
For the multiplicative background risk model, a distortion-type risk measure is used to measure the tail risk of the portfolio under a scenario probability measure with multivariate regular variation. In this paper, we investigate the tail asymptotics of the portfolio loss $\sum _{i=1}^{d}R_iS$, where the stand-alone risk vector ${\mathbf {R}}=(R_1,\ldots ,R_d)$ follows a multivariate regular variation and is independent of the background risk factor S. An explicit asymptotic formula is established for the tail distortion risk measure, and an example is given to illustrate our obtained results.
Let $M$ be a noncompact complete Riemannian manifold. In this paper, we consider the following nonlinear parabolic equation on $M$
The quantile-based entropy measures possess some unique properties than their distribution function approach. The present communication deals with the study of the quantile-based Shannon entropy for record statistics. In this regard a generalized model is considered for which cumulative distribution function or probability density function does not exist and various examples are provided for illustration purpose. Further we consider the dynamic versions of the proposed entropy measure for record statistics and also give a characterization result for that. At the end, we study $F^{\alpha }$-family of distributions for the proposed entropy measure.
In this article, a novel susceptible–infected–recovered epidemic model with nonmonotonic incidence and treatment rates is proposed and analyzed mathematically. The Monod–Haldane functional response is considered for nonmonotonic behavior of both incidence rate and treatment rate. The model analysis shows that the model has two equilibria which are named as disease-free equilibrium (DFE) and endemic equilibrium (EE). The stability analysis has been performed for the local and global behavior of the DFE and EE. With the help of the basic reproduction number
In this paper, we construct a bijective mapping between a biquadratic spline space over the hierarchical T-mesh and the piecewise constant space over the corresponding crossing-vertex-relationship graph (CVR graph). We propose a novel structure, by which we offer an effective and easy operative method for constructing the basis functions of the biquadratic spline space. The mapping we construct is an isomorphism. The basis functions of the biquadratic spline space hold the properties such as linear independence, completeness and the property of partition of unity, which are the same as the properties for the basis functions of piecewise constant space over the CVR graph. To demonstrate that the new basis functions are efficient, we apply the basis functions to fit some open surfaces.
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.
We investigated the false-negative, true-negative, false-positive, and true-positive predictive values from a general group testing procedure for a heterogeneous population. We show that its false (true)-negative predictive value of a specimen is larger (smaller), and the false (true)-positive predictive value is smaller (larger) than that from individual testing procedure, where the former is in aversion. Then we propose a nested group testing procedure, and show that it can keep the sterling characteristics and also improve the false-negative predictive values for a specimen, not larger than that from individual testing. These characteristics are studied from both theoretical and numerical points of view. The nested group testing procedure is better than individual testing on both false-positive and false-negative predictive values, while retains the efficiency as a basic characteristic of a group testing procedure. Applications to Dorfman’s, Halving and Sterrett procedures are discussed. Results from extensive simulation studies and an application to malaria infection in microscopy-negative Malawian women exemplify the findings.
This paper provides necessary as well as sufficient conditions on the Hurst parameters so that the continuous time parabolic Anderson model $\frac{\partial u}{\partial t}=\frac{1}{2}\Delta +u{\dot{W}}$ on $[0, \infty )\times {{\mathbb {R}}}^d $ with $d\ge 1$ has a unique random field solution, where W(t, x) is a fractional Brownian sheet on $[0, \infty )\times {{\mathbb {R}}}^d$ and formally $\dot{W} =\frac{\partial ^{d+1}}{\partial t \partial x_1 \cdots \partial x_d} W(t, x)$. When the noise W(t, x) is white in time, our condition is both necessary and sufficient when the initial data u(0, x) is bounded between two positive constants. When the noise is fractional in time with Hurst parameter $H_0>1/2$, our sufficient condition, which improves the known results in the literature, is different from the necessary one.
In this paper, we explore sparsity and homogeneity of regression coefficients incorporating prior constraint information. The sparsity means that a small fraction of regression coefficients is nonzero, and the homogeneity means that regression coefficients are grouped and have exactly the same value in each group. A general pairwise fusion approach is proposed to deal with the sparsity and homogeneity detection when combining prior convex constraints. We develop a modified alternating direction method of multipliers algorithm to obtain the estimators and demonstrate its convergence. The efficiency of both sparsity and homogeneity detection can be improved by combining the prior information. Our proposed method is further illustrated by simulation studies and analysis of an ozone dataset.
We characterize bounded and compact positive Toeplitz operators defined on the Bergman spaces over the Siegel upper half-space.