共查询到20条相似文献,搜索用时 15 毫秒
1.
In this work, we define cumulative residual q-Fisher (CRQF) information measures for the survival function (SF) of the underlying random variables as well as for the model parameter. We also propose q-hazard rate (QHR) function via q-logarithmic function as a new extension of hazard rate function. We show that CRQF information measure can be expressed in terms of the QHR function. We define further generalized cumulative residual divergence measures between two SFs. We then examine the cumulative residual q-Fisher information for two well-known mixture models, and the corresponding results reveal some interesting connections between the cumulative residual q-Fisher information and the generalized cumulative residual divergence measures. Further, we define Jensen-cumulative residual (JCR-) measure and a parametric version of the Jensen-cumulative residual Fisher information measure and then discuss their properties and inter-connections. Finally, for illustrative purposes, we examine a real example of image processing and provide some numerical results in terms of the CRQF information measure. 相似文献
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This paper studies the properties of the derivatives of differential entropy in Costa’s entropy power inequality. For real-valued random variables, Cheng and Geng conjectured that for , , while McKean conjectured a stronger statement, whereby . Here, we study the higher dimensional analogues of these conjectures. In particular, we study the veracity of the following two statements: , where n denotes that is a random vector taking values in , and similarly, . In this paper, we prove some new multivariate cases: . Motivated by our results, we further propose a weaker version of McKean’s conjecture , which is implied by and implies . We prove some multivariate cases of this conjecture under the log-concave condition: and . A systematic procedure to prove is proposed based on symbolic computation and semidefinite programming, and all the new results mentioned above are explicitly and strictly proved using this procedure. 相似文献
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In this paper, first we introduce the full expression for the Ricci tensor of a real hypersurface M in complex two-plane Grassmannians G2(Cm+2) from the equation of Gauss. Next we prove that a Hopf hypersurface in complex two-plane Grassmannians G2(Cm+2) with commuting Ricci tensor is locally congruent to a tube of radius r over a totally geodesic G2(Cm+1). Finally it can be verified that there do not exist any Hopf Einstein hypersurfaces in G2(Cm+2). 相似文献
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In this paper we give a complete classification of pseudo-Einstein real hypersurfaces in complex two-plane Grassmannians G2(Cm+2). As an application of this result we prove that there do not exist Einstein Hopf or D⊥-invariant Einstein real hypersurfaces in G2(Cm+2). 相似文献
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In this paper, we establish new -integral and -integral identities. By employing these new identities, we establish new and - trapezoidal integral-type inequalities through strongly convex and quasi-convex functions. Finally, some examples are given to illustrate the investigated results. 相似文献
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Let , , be the noise operator acting on functions on the boolean cube . Let f be a distribution on and let . We prove tight Mrs. Gerber-type results for the second Rényi entropy of which take into account the value of the Rényi entropy of f. For a general function f on we prove tight hypercontractive inequalities for the norm of which take into account the ratio between and norms of f. 相似文献
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In this paper, we present a new method for the construction of maximally entangled states in when . A systematic way of constructing a set of maximally entangled bases (MEBs) in was established. Both cases when is divisible by d and not divisible by d are discussed. We give two examples of maximally entangled bases in , which are mutually unbiased bases. Finally, we found a new example of an unextendible maximally entangled basis (UMEB) in . 相似文献
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This paper addresses the problem of robust angle of arrival (AOA) target localization in the presence of uniformly distributed noise which is modeled as the mixture of Laplacian distribution and uniform distribution. Motivated by the distribution of noise, we develop a localization model by using the -norm with as the measurement error and the -norm as the regularization term. Then, an estimator for introducing the proximal operator into the framework of the alternating direction method of multipliers (POADMM) is derived to solve the convex optimization problem when . However, when , the corresponding optimization problem is nonconvex and nonsmoothed. To derive a convergent method for this nonconvex and nonsmooth target localization problem, we propose a smoothed POADMM estimator (SPOADMM) by introducing the smoothing strategy into the optimization model. Eventually, the proposed algorithms are compared with some state-of-the-art robust algorithms via numerical simulations, and their effectiveness in uniformly distributed noise is discussed from the perspective of root-mean-squared error (RMSE). The experimental results verify that the proposed method has more robustness against outliers and is less sensitive to the selected parameters, especially the variance of the measurement noise. 相似文献
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Anas D. Khalaf Tareq Saeed Reman Abu-Shanab Waleed Almutiry Mahmoud Abouagwa 《Entropy (Basel, Switzerland)》2022,24(5)
This study deals with drift parameters estimation problems in the sub-fractional Vasicek process given by , with , being unknown and ; here, represents a sub-fractional Brownian motion (sfBm). We introduce new estimators for and for based on discrete time observations and use techniques from Nordin–Peccati analysis. For the proposed estimators and , strong consistency and the asymptotic normality were established by employing the properties of . Moreover, we provide numerical simulations for sfBm and related Vasicek-type process with different values of the Hurst index H. 相似文献
11.
Motivated by the needs of vortex methods, we describe three different exact or approximate solutions to the Poisson equation on the surface of a sphere when the forcing is a Gaussian of the three-dimensional distance, ∇2ψ=exp(-2?2(1-cos(θ))-CGauss(?). (More precisely, the forcing is a Gaussian minus the “Gauss constraint constant”, CGauss; this subtraction is necessary because ψ is bounded, for any type of forcing, only if the integral of the forcing over the sphere is zero [Y. Kimura, H. Okamoto, Vortex on a sphere, J. Phys. Soc. Jpn. 56 (1987) 4203–4206; D.G. Dritschel, Contour dynamics/surgery on the sphere, J. Comput. Phys. 79 (1988) 477–483]. The Legendre polynomial series is simple and yields the exact value of the Gauss constraint constant, but converges slowly for large ?. The analytic solution involves nothing more exotic than the exponential integral, but all four terms are singular at one or the other pole, cancelling in pairs so that ψ is everywhere nice. The method of matched asymptotic expansions yields simpler, uniformly valid approximations as series of inverse even powers of ? that converge very rapidly for the large values of ? (?>40) appropriate for geophysical vortex computations. The series converges to a nonzero O(exp(-4?2)) error everywhere except at the south pole where it diverges linearly with order instead of the usual factorial order. 相似文献
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In this paper we give topological and affine classification of complete noncompact flat 4-manifolds. In particular, we show that the number of diffeomorphism classes of them is equal to 44. The affine classification uses the results of [M. Sadowski, Affinely equivalent complete flat manifolds, Cent. Eur. J. Math. 2 (2) (2004) 332–338]. The affine and the topological equivalence classes are the same for flat manifolds not homotopy equivalent to S1,T2 or the Klein bottle. 相似文献
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Blaum–Roth Codes are binary maximum distance separable (MDS) array codes over the binary quotient ring , where , and p is a prime number. Two existing all-erasure decoding methods for Blaum–Roth codes are the syndrome-based decoding method and the interpolation-based decoding method. In this paper, we propose a modified syndrome-based decoding method and a modified interpolation-based decoding method that have lower decoding complexity than the syndrome-based decoding method and the interpolation-based decoding method, respectively. Moreover, we present a fast decoding method for Blaum–Roth codes based on the LU decomposition of the Vandermonde matrix that has a lower decoding complexity than the two modified decoding methods for most of the parameters. 相似文献
16.
This article estimates several integral inequalities involving -convexity via the quantum calculus, through which Important integral inequalities including Simpson-like, midpoint-like, averaged midpoint-trapezoid-like and trapezoid-like are extended. We generalized some quantum integral inequalities for q-differentiable -convexity. Our results could serve as the refinement and the unification of some classical results existing in the literature by taking the limit . 相似文献
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We consider a complete nonnegative biminimal submanifold M (that is, a complete biminimal submanifold with λ≥0) in a Euclidean space EN. Assume that the immersion is proper , that is, the preimage of every compact set in EN is also compact in M. Then, we prove that M is minimal. From this result, we give an affirmative partial answer to Chen’s conjecture. For the case of λ<0, we construct examples of biminimal submanifolds and curves. 相似文献
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We investigate complete spacelike hypersurfaces in Lorentz–Minkowski space with two distinct principal curvatures and constant mth mean curvature. By using Otsuki’s idea, we obtain the global classification result. As their applications, we obtain some characterizations for hyperbolic cylinders. We prove that the only complete spacelike hypersurfaces in Lorentz–Minkowski (n+1)-spaces (n≥3) of nonzero constant mth mean curvature (m≤n−1) with two distinct principal curvatures λ and μ satisfying inf(λ−μ)2>0 are the hyperbolic cylinders. We also obtain a global characterization for hyperbolic cylinder Hn−1(c)×R in terms of square length of the second fundamental form. 相似文献
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Philosophers frequently define knowledge as justified, true belief. We built a mathematical framework that makes it possible to define learning (increasing number of true beliefs) and knowledge of an agent in precise ways, by phrasing belief in terms of epistemic probabilities, defined from Bayes’ rule. The degree of true belief is quantified by means of active information : a comparison between the degree of belief of the agent and a completely ignorant person. Learning has occurred when either the agent’s strength of belief in a true proposition has increased in comparison with the ignorant person (), or the strength of belief in a false proposition has decreased (). Knowledge additionally requires that learning occurs for the right reason, and in this context we introduce a framework of parallel worlds that correspond to parameters of a statistical model. This makes it possible to interpret learning as a hypothesis test for such a model, whereas knowledge acquisition additionally requires estimation of a true world parameter. Our framework of learning and knowledge acquisition is a hybrid between frequentism and Bayesianism. It can be generalized to a sequential setting, where information and data are updated over time. The theory is illustrated using examples of coin tossing, historical and future events, replication of studies, and causal inference. It can also be used to pinpoint shortcomings of machine learning, where typically learning rather than knowledge acquisition is in focus. 相似文献
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In this paper, we present hybridizable discontinuous Galerkin methods for the numerical solution of steady and time-dependent nonlinear convection–diffusion equations. The methods are devised by expressing the approximate scalar variable and corresponding flux in terms of an approximate trace of the scalar variable and then explicitly enforcing the jump condition of the numerical fluxes across the element boundary. Applying the Newton–Raphson procedure and the hybridization technique, we obtain a global equation system solely in terms of the approximate trace of the scalar variable at every Newton iteration. The high number of globally coupled degrees of freedom in the discontinuous Galerkin approximation is therefore significantly reduced. We then extend the method to time-dependent problems by approximating the time derivative by means of backward difference formulae. When the time-marching method is (p+1)th order accurate and when polynomials of degree p?0 are used to represent the scalar variable, each component of the flux and the approximate trace, we observe that the approximations for the scalar variable and the flux converge with the optimal order of p+1 in the L2-norm. Finally, we apply element-by-element postprocessing schemes to obtain new approximations of the flux and the scalar variable. The new approximate flux, which has a continuous interelement normal component, is shown to converge with order p+1 in the L2-norm. The new approximate scalar variable is shown to converge with order p+2 in the L2-norm. The postprocessing is performed at the element level and is thus much less expensive than the solution procedure. For the time-dependent case, the postprocessing does not need to be applied at each time step but only at the times for which an enhanced solution is required. Extensive numerical results are provided to demonstrate the performance of the present method. 相似文献