The Additive Input-Doubling Method Based on the SVR with Nonlinear Kernels: Small Data Approach

The problem of effective intellectual analysis in the case of handling short datasets is topical in various application areas. Such problems arise in medicine, economics, materials science, science, etc. This paper deals with a new additive input-doubling method designed by the authors for processing short and very short datasets. The main steps of the method should include the procedure of data augmentation within the existing dataset both in rows and columns (without training), the use of nonlinear SVR to implement the training procedure, and the formation of the result based on the author’s procedure. The authors show that the developed data augmentation procedure corresponds to the principles of axial symmetry. The training and application procedures of the method developed are described in detail, and two algorithmic implementations are presented. The optimal parameters of the method operation were selected experimentally. The efficiency of its work during the processing of short datasets for solving the prediction task was established experimentally by comparison with other methods of this class. The highest prediction accuracy based on both proposed algorithmic implementations of a method among all of the investigated ones was defined. The main areas of application of the developed method are described, and its shortcomings and prospects of further research are given.

Algebraicity of special L-values attached to Siegel–Jacobi modular forms

In this work we obtain algebraicity results on special L-values attached to Siegel–Jacobi modular forms. Our method relies on a generalization of the doubling method to the Jacobi group obtained in our previous work, and on introducing a notion of near holomorphy for Siegel–Jacobi modular forms. Some of our results involve also holomorphic projection, which we obtain by using Siegel–Jacobi Poincaré series of exponential type.

ANALYTIC PROPERTIES OF EISENSTEIN SERIES AND STANDARD -FUNCTIONS

We prove a functional equation for a vector valued real analytic Eisenstein series transforming with the Weil representation of $\operatorname{Sp}(n,\mathbb{Z})$ on $\mathbb{C}[(L^{\prime }/L)^{n}]$ . By relating such an Eisenstein series with a real analytic Jacobi Eisenstein series of degree $n$ , a functional equation for such an Eisenstein series is proved. Employing a doubling method for Jacobi forms of higher degree established by Arakawa, we transfer the aforementioned functional equation to a zeta function defined by the eigenvalues of a Jacobi eigenform. Finally, we obtain the analytic continuation and a functional equation of the standard $L$ -function attached to a Jacobi eigenform, which was already proved by Murase, however in a different way.

Light propagation within N95 Filtered Face Respirators: A simulation study for UVC decontamination

This study presents numerical simulations of UVC light propagation through seven different filtered face respirators (FFR) to determine their suitability for UV germicidal inactivation (UVGI). UV propagation was modelled using the FullMonte program for two external light illuminations. The optical properties of the dominant three layers were determined using the inverse adding doubling method. The resulting fluence rate volume histograms and the lowest fluence rate recorded in the modelled volume, sometimes in the nW cm-2, provide feedback on a respirator’s suitability for UVGI and the required exposure time for a given light source. While UVGI can present an economical approach to extend an FFR’s useable lifetime, it requires careful optimization of the illumination setup and selection of appropriate respirators.Abstract Figure

-ADIC -FUNCTIONS FOR UNITARY GROUPS

This paper completes the construction of $p$ -adic $L$ -functions for unitary groups. More precisely, in Harris, Li and Skinner [‘ $p$ -adic $L$ -functions for unitary Shimura varieties. I. Construction of the Eisenstein measure’, Doc. Math.Extra Vol. (2006), 393–464 (electronic)], three of the authors proposed an approach to constructing such $p$ -adic $L$ -functions (Part I). Building on more recent results, including the first named author’s construction of Eisenstein measures and $p$ -adic differential operators [Eischen, ‘A $p$ -adic Eisenstein measure for unitary groups’, J. Reine Angew. Math.699 (2015), 111–142; ‘ $p$ -adic differential operators on automorphic forms on unitary groups’, Ann. Inst. Fourier (Grenoble)62(1) (2012), 177–243], Part II of the present paper provides the calculations of local $\unicode[STIX]{x1D701}$ -integrals occurring in the Euler product (including at $p$ ). Part III of the present paper develops the formalism needed to pair Eisenstein measures with Hida families in the setting of the doubling method.