Recent research in machine learning witnessed a renewed interest in tensors. In particular, multilinear algebra has been leveraged to derive structured finite dimensional parametric models [1, 2]. In [3] these ideas have been generalized to reproducing kernel Hilbert spaces. The arising framework comprises existing problem formulations, such as tensor completion [4], as well as novel functional...

In this paper, a good λ estimate for the multilinear commutator associated to the fractional integral operator on the spaces of homogeneous type is obtained. Under this result, we get the(Lp(X),Lq(X)) -boundedness of the multilinear commutator. Mathematics subject classification (2010): 42B20, 42B25.

We prove local “Lp-improving” estimates for a class of multilinear Radon-like transforms satisfying a strong transversality hypothesis. As a consequence, we obtain sharp multilinear convolution estimates for measures supported on fully transversal submanifolds of euclidean space of arbitrary dimension. We also prove global estimates for the same class of Radon-like transforms under a natural ho...

Lek-Heng Lim University of Chicago 15.1 Hypermatrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-2 15.2 Tensors and Multilinear Functionals. . . . . . . . . . . . . . . . . 15-6 15.3 Tensor Rank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15-12 15.4 Border Rank . . . . . . . . . . . . . . . . . . . . . . . ....

In this paper the boundedness for a large class of multisublinear operators is established on product generalized Morrey spaces with non-doubling measures. As special cases, the corresponding results for multilinear Calderón-Zygmund operators, multilinear fractional integrals and multi-sublinear maximal operators will be obtained.

A slightly modified variant of the cubic periodic one-dimensional nonlinear Schrödinger equation is shown to be well-posed, in a relatively weak sense, in certain function spaces wider than L. Solutions are constructed as sums of infinite series of multilinear operators applied to initial data, and these multilinear operators are analyzed directly.

The study aims to determine the effect of educational attainment, length work experience on self-efficacy and also difference employees based attainment experience. To support theories study, literature was reviewed. used a descriptive correlational research design questionnaires were gather data. population all Divine Word College Laoag, Ilocos Norte, Philippines. Multilinear regression analys...

Canonical correlation analysis (CCA) is a useful technique for measuring relationship between two sets of vector data. For paired tensor data sets, we propose a multilinear CCA (MCCA) method. Unlike existing multilinear variations of CCA, MCCA extracts uncorrelated features under two architectures while maximizing paired correlations. Through a pair of tensor-to-vector projections, one architec...

We characterize the support of the free Lie algebra LZm(A) on a finite alphabet A over the ring Zm of integers mod m as the set of all words w such that m c(w), where c(w) is the greatest common divisor of the coefficients in the polynomial l∗(w), for the adjoint endomorphism l∗ of the left-normed Lie bracketing l of the free Lie ring. For words of length n this can be interpreted combinatorial...

In this study, accurate and convenient prediction models of tubular solar still performance, expressed as hourly production, were developed by utilizing machine learning. Based on experimental data, the compared, such classical artificial neural network with/without Baysian optimization, random forest traditional multilinear regression. Before applying Bayesian both predict production. But supe...