Aliasing Error of Sampling Series in Wavelet Subspaces

Alising error arises whenever a sampling formula, valid for a prescribed space, is applied to a function in a bigger space. In this work, we estimate the aliasing error of classic and average sampling expansions in wavelet subspaces of a multiresolution analysis.     

Molecular dynamics study on the effects of stamp shape, adhesive energy, and temperature on the nanoimprint lithography process

Molecular dynamics simulations of nanoimprint lithography (NIL) were performed to investigate the effects of three critical process parameters in NIL: stamp shape, adhesive energy between the stamp and polymer film, and imprint temperature. The proposed simulation model of the NIL process consists of an amorphous SiO₂ stamp with a line pattern, an amorphous poly(methylmethacrylate) film, and a Si substrate under the periodic boundary condition in the horizontal direction to simulate a real NIL process imprinting periodical line patterns. The behavior of polymer deformation and the effects of adhesion on pattern transfer were investigated by observing the deformation process, calculating the imprint and separation forces, and analyzing the density and stress distribution inside the polymer film. In addition, their dependency on the process parameters is also discussed with reference to the changes in pattern shape, adhesive energy between the stamp and polymer atoms, and imprint temperature of the polymer film. During the imprint process, the rectangular pattern shows inferior cavity filling and higher stress concentration compared to trapezoidal and triangular patterns because it requires much larger flow and deformation of the polymer film. Low imprint temperature also produces high stress concentration and large imprint force due to the lower fluidity of polymer film. In the separation process, the rectangular pattern generates the largest separation force and causes the most serious defects of the transferred pattern and even the polymer film, while the triangular pattern shows the most satisfactory pattern transfer. In addition, the adhesive energy between the stamp and the polymer film also strongly influences the adhesion between the stamp and the polymer film. Low adhesive energy reduces the separation force of the stamp and transferred pattern defects, and therefore enhances the quality of pattern transfer.     

Valuation ideals and primary <Emphasis Type="Italic">w</Emphasis>-ideals

Let D be an integral domain, V (D) (resp., t-V (D)) be the set of all valuation (resp., t-valuation) ideals of D, and w-P(D) be the set of primary w-ideals of D. Let D[X] be the polynomial ring over D, c(f) be the ideal of D generated by the coefficients of f ∈ D[X], and N _v = {f ∈ D[X] | c(f) _v = D}. In this paper, we study integral domains D in which w-P(D) ? t-V (D), t-V (D) ? w-P(D), or t-V (D) = w-P(D). We also study the relationship between t-V (D) and \(V\left( {D{{\left[ X \right]}_{{N_v}}}} \right)\), and characterize when t-V (A + XB[X]) ? w-P(A + XB[X]) holds for a proper extension A ? B of integral domains.     

Electrical conductivity of the system Y2O3CeO2

The electrical conductivity of the system Y₂O₃CeO₂ was measured in the temperature range 500–1100°C and P_o2 range 10^–7?10^?1 atm. Possible defect models were suggested on the basis of conductivity data, which were investigated as a function of temperature and of P_o2. The observed activation energies were 0.40 eV and 1.79 eV in the low- and high-temperature regions, respectively. The observed conductivity dependences on P_o2 were in the temperature range 500–750°C and at temperatures from 750–1100°C. It is suggested that the system Y₂O₃CeO₂ shows a mixed ionic plus hole conduction due to an O^″_i defect and an electronic hole conduction due to a V^'''_Y defect in the low- and high-temperature regions, respectively.     

Progressive formation of fine and coarse ripples on SiC surface by repeated irradiation of femtosecond laser pulses

In this work, we report the progressive formation of first nanoparticles, next fine ripples, and eventually coarse ripples during the irradiation of single-crystal 6H-SiC surfaces with increasing number of femtosecond laser pulses (λ = 515 nm, τ = 250 fs, repetition rate = 100 kHz). At laser fluences greater than the single-pulse ablation threshold, nanoparticles were produced on the surface by the first few pulses over which fine ripple patterns overlapped at increased pulse numbers. As the pulse number was further increased over ten, the surface was gradually transformed into a coarse ripple–covered one. At laser fluence below the threshold, however, only fine ripples were formed nonuniformly.     

Machine learning identification of symmetrized base states of Rydberg atoms

Studying the complex quantum dynamics of interacting many-body systems is one of the most challenging areas in modern physics. Here, we use machine learning (ML) models to identify the symmetrized base states of interacting Rydberg atoms of various atom numbers (up to six) and geometric configurations. To obtain the data set for training the ML classifiers, we generate Rydberg excitation probability profiles that simulate experimental data by utilizing Lindblad equations that incorporate laser intensities and phase noise. Then, we classify the data sets using support vector machines (SVMs) and random forest classifiers (RFCs). With these ML models, we achieve high accuracy of up to 100% for data sets containing only a few hundred samples, especially for the closed atom configurations such as the pentagonal (five atoms) and hexagonal (six atoms) systems. The results demonstrate that computationally cost-effective ML models can be used in the identification of Rydberg atom configurations.     

Terwilliger algebras of wreath products by quasi-thin schemes

The structure of Terwilliger algebras of wreath products by thin schemes or one-class schemes was studied in [A. Hanaki, K. Kim, Y. Maekawa, Terwilliger algebras of direct and wreath products of association schemes, J. Algebra 343 (2011) 195–200]. In this paper, we will consider the structure of Terwilliger algebras of wreath products by quasi-thin schemes. This gives a generalization of their result.     

m=±1 and m=±2 mode helicon wave excitation

The characteristics of plasma produced by plane polarized m=±1 and m=±2 mode helicon waves were investigated for the first time. Plane polarized m=±1 and m=±2 mode helicon waves were mainly excited using a Nagoya type III antenna and a quadrupole antenna, respectively. Two-dimensional cross-field measurements of ArII optical emission induced by hot electrons were made to investigate the RF power deposition. The components of the wave magnetic field measured with a magnetic probe were compared with the field profiles computed for the m=±1 and m=±2 modes. Two and four high intensity plasma columns were observed for the m=±1 and m=±2modes, respectively. These columns were located at the regions between the antenna legs. The radial profiles of the wave magnetic field were in good agreement with computations     

Global estimates of fundamental solutions for higher-order Schr?dinger equations

In this paper we first establish global pointwise time-space estimates of the fundamental solution for Schr?dinger equations, where the symbol of the spatial operator is a real non-degenerate elliptic polynomial. Then we use such estimates to establish related L ^p ?CL ^q estimates on the Schr?dinger solution. These estimates extend known results from the literature and are sharp. This result was lately already generalized to a degenerate case (cf. [4]).     

Sputter-deposited ZnO thin films consisting of nano-networks for binder-free dye-sensitized solar cells

ZnO nano-network structures with high porosity were prepared for use in the photoelectrodes of binder-free dye-sensitized solar cells (DSSCs) by DC sputtering and subsequent thermal oxidation. Zn thin films prepared at 100 °C showed nano-network structures with high porosity, while those prepared at 25 °C did not. This was partially attributed to the high mobility of sputter-deposited particles that arrived at the surface of the substrate and partially to a supersaturation mechanism. The prepared nano-network Zn was successfully transformed to ZnO without a morphological change via subsequent annealing in air. The power conversion efficiency of DSSCs based on the ZnO nano-network structures exhibited 10 times higher efficiency than those based on ZnO film prepared at 25 °C because of its large surface area for adsorption of dye molecules. The thickness of the ZnO nano-network structures increased linearly at 10 μm h^?1 as a function of sputter time. As the film thickness increased, the power conversion efficiency of DSSCs increased from 1.09% to 1.82%.