Global Whitney‘s Lemma and its Application in Plasticity Theory

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A Fixed Point Theorem and its Application to Best Approximation

The object of this paper is twofold. First, a fixed point theorem of G.L. Cain, Jr. and M. Z. Nashed [1] is generalized. Second, the theorem (Theoreml) is utilized to obtain theorems on best approximation which extend and unify the results of Meinardus [2], Singh [ 3—4 ], and Sahney Singh-Whitfield [5].     

Learning with coefficient-based regularization and ℓ1 −penalty

The least-square regression problem is considered by coefficient-based regularization schemes with ?¹??penalty. The learning algorithm is analyzed with samples drawn from unbounded sampling processes. The purpose of this paper is to present an elaborate concentration estimate for the algorithms by means of a novel stepping stone technique. The learning rates derived from our analysis can be achieved in a more general setting. Our refined analysis will lead to satisfactory learning rates even for non-smooth kernels.     

Primal and dual alternating direction algorithms for ℓ 1-ℓ 1-norm minimization problems in compressive sensing

In this paper, we propose, analyze and test primal and dual versions of the alternating direction algorithm for the sparse signal reconstruction from its major noise contained observation data. The algorithm minimizes a convex non-smooth function consisting of the sum of ? ₁-norm regularization term and ? ₁-norm data fidelity term. We minimize the corresponding augmented Lagrangian function alternatively from either primal or dual forms. Both of the resulting subproblems admit explicit solutions either by using a one-dimensional shrinkage or by an efficient Euclidean projection. The algorithm is easily implementable and it requires only two matrix-vector multiplications per-iteration. The global convergence of the proposed algorithm is established under some technical conditions. The extensions to the non-negative signal recovery problem and the weighted regularization minimization problem are also discussed and tested. Numerical results illustrate that the proposed algorithm performs better than the state-of-the-art algorithm YALL1.     

A Discrete-Time Clark–Ocone Formula and its Application to an Error Analysis

In this paper, we will establish a discrete-time version of Clark(–Ocone–Haussmann) formula, which can be seen as an asymptotic expansion in a weak sense. The formula is applied to the estimation of the error caused by the martingale representation. Throughout, we use another distribution theory with respect to Gaussian rather than Lebesgue measure, which can be seen as a discrete Malliavin calculus.     

A Rapidly Convergence Algorithm for Linear Search and its Application

The essence of the linear search is one-dimension nonlinear minimization problem, which is an important part of the multi-nonlinear optimization, it will be spend the most of operation count for solving optimization problem. To improve the efficiency, we set about from quadratic interpolation, combine the advantage of the quadratic convergence rate of Newton's method and adopt the idea of Anderson-Bjorck extrapolation, then we present a rapidly convergence algorithm and give its corresponding convergence conclusions. Finally we did the numerical experiments with the some well-known test functions for optimization and the application test of the ANN learning examples. The experiment results showed the validity of the algorithm.     

Estimation of the location parameter of the ℓ1-norm symmetric matrix variate distributions

An identity of integrals for the ℓ₁-norm symmetric matrix variate distributions with unknown common location parameter and unknown and possibly unequal scale parameters of the columns is established. An unbiased estimator for the location parameter is obtained and is shown to dominate the maximum likelihood estimator under the squared error loss. Under certain conditions this unbiased estimator is the uniformly minimum variance unbiased estimator.     

Norming subspaces isomorphic to ℓ 1

Norming subspaces are studied widely in the duality theory of Banach spaces. These subspaces are applied to the Borel and Baire classifications of the inverse operators. The main result of this article asserts that the dual of a Banach space X contains a norming subspace isomorphic to l₁ provided that the following two conditions are satisfied: (1) X^* contains a subspace isomorphic to l₁; and (2) X^* contains a separable norming subspace.     

The Mindlin-Medick Plate Theory and Its Application Under Flexoelectricity and Temperature Effects北大核心CSCD

Based on the Hamiltonian variational principle, the 2D field equations and boundary conditions for flexoelectricity were derived, and the corresponding governing equations were obtained through substitution of the constitutive relation and geometric equations into the field equation. The in⁃plane tensile deformation, thick⁃ ness⁃stretch deformation, symmetric thickness⁃shear deformation, and their coupled flexoelectric polarization of flexoelectric nanoplates caused by inhomogeneous temperature changes, were studied. The displacement fields and electric potential fields were solved with the double Fourier series method. The results demonstrate that, all fields are sensitive to the temperature load, which raises the prospect of controlling the mechanical and electrical behaviors of flexoelectric nanoplates by means of the temperature field. The effects of the thermal field and mechanical field on the displacement field were compared and examined. The work extends the Mind⁃ lin⁃Medick plate structure analysis theory in view of the flexoelectric and temperature effects, and provides a reference for the structural design of micro⁃ and nano⁃scale devices. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

A Generalization of the Siegel–Walfisz Theorem and its Application

We investigate the distribution of integers with a fixed number of prime factors in arithmetic progressions, and obtain a generalization of the Siegel–Walfisz theorem under the extended Riemann hypothesis. As an application, we consider a problem of P. Erd?s, A. M. Odlyzko and A. Sárközy about the representation of residue classes modulo q by products of two integers with a fixed number of prime factors. We show some conditional results.     

Spaces with Dual Order-Isomorphic to ℓ1

We establish that an ordered Banach space is order-isomorphic to c₀ if and only if it is a -Dedekind complete vector lattice and its norm dual is order-isomorphic to ₁.     

On an Interpolatory Inequality of Erdős and Turán and its Application

The paper generalizes an old inequality of Erds and Turán on adjacent fundamental Lagrange interpolatory polynomials. We mention an application, too.     

B-vex Fuzzy Mappings and Its Application to Fuzzy Optimization Problems

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Homotopy Theory of A∞ Ring Spectra and Applications to MU-Modules

We give a definition of a derivation of an A ring spectrum and relate this notion to topological Hochschild cohomology. Strict multiplicative structure is introduced into Postnikov towers and generalized Adams towers of A -ring spectra. An obstruction theory for lifting multiplicative maps is constructed. The developed techniques are then applied to show that a broad class of complex-oriented spectra admit structures of MU-algebras where MU is the complex cobordism spectrum. Various computations of topological derivations and topological Hochschild cohomology are made.     

Numerical Evaluation of Dynamic Behavior of Ornstein–Uhlenbeck Processes Modified by Various Boundaries and its Application to Pricing Barrier Options

In financial engineering, one often encounters barrier options in which an action promised in the contract is taken if the underlying asset value becomes too high or too low. In order to compute the corresponding prices, it is necessary to capture the dynamic behavior of the associated stochastic process modified by boundaries. To the best knowledge of the authors, there is no algorithmic approach available to compute such prices repeatedly in a systematic manner. The purpose of this paper is to develop computational algorithms to capture the dynamic behavior of Ornstein-Uhlenbeck processes modified by various boundaries based on the Ehrenfest approximation approach established in Sumita et al. (J Oper Res Soc Jpn 49:256–278, 2006). As an application, we evaluate the prices of up-and-out call options maturing at time τ _M with strike price K _S written on a discount bond maturing at time T, demonstrating the usefulness, speed and accuracy of the proposed computational algorithms.