The Effect of Acceleration on the Separation Force in Constrained-Surface Stereolithography

Constrained-surface-based stereolithography has recently attracted much attention from both academic and industrial communities. Despite numerous experimental, numerical and theoretical efforts, the fundamental need to reduce the separation force between the newly cured part and constrained surface has not yet been completely solved. In this paper, we develop a fluid dynamics approach, proposed in our previous work, to theoretically model the separation force in 3D printing of a cylindrical part for flat and patterned windows. We demonstrate the possibility of separation force reduction with an accelerated movement of the printing platform. In particular, we investigate behaviors of transient parameter, its reduction rate, and separation force reduction with respect to elevation speed and time. The proposed approach involves deceleration and acceleration stages and allows to achieve the force reduction for the entire printing process. Finally, we provide implicit analytical solutions for time moments when switching between the stages can be done without noticeable increase of separation force and explicit expression for separation force in case of patterned window.

Mixture of Species Sampling Models

We introduce mixtures of species sampling sequences (mSSS) and discuss how these sequences are related to various types of Bayesian models. As a particular case, we recover species sampling sequences with general (not necessarily diffuse) base measures. These models include some “spike-and-slab” non-parametric priors recently introduced to provide sparsity. Furthermore, we show how mSSS arise while considering hierarchical species sampling random probabilities (e.g., the hierarchical Dirichlet process). Extending previous results, we prove that mSSS are obtained by assigning the values of an exchangeable sequence to the classes of a latent exchangeable random partition. Using this representation, we give an explicit expression of the Exchangeable Partition Probability Function of the partition generated by an mSSS. Some special cases are discussed in detail—in particular, species sampling sequences with general base measures and a mixture of species sampling sequences with Gibbs-type latent partition. Finally, we give explicit expressions of the predictive distributions of an mSSS.

On Cherednik and Nazarov-Sklyanin large N limit construction for integrable many-body systems with elliptic dependence on momenta

The infinite number of particles limit in the dual to elliptic Ruijsenaars model (coordinate trigonometric degeneration of quantum double elliptic model) is proposed using the Nazarov-Sklyanin approach. For this purpose we describe double-elliptization of the Cherednik construction. Namely, we derive explicit expression in terms of the Cherednik operators, which reduces to the generating function of Dell commuting Hamiltonians on the space of symmetric functions. Although the double elliptic Cherednik operators do not commute, they can be used for construction of the N → ∞ limit.

Экстремальная функция интерполяционных формул в пространстве W2(2,0)

One of the main problems of computational mathematics is the optimization of computational methods in functional spaces. Optimization of computational methods are well demonstrated in the problems of the theory of interpolation formulas. In this paper, we study the problem of constructing an optimal interpolation formula in a Hilbert space. Here, using the Sobolev method, the first part of the problem is solved, i.e., an explicit expression of the square of the norm of the error functional of the optimal interpolation formulas in the Hilbert space W2(2,0) is found. Одна из основных проблем вычислительной математики — оптимизация вычислительных методов в функциональных пространствах. Оптимизация вычислительных методов хорошо проявляется в задачах теории интерполяционных формул. В данной статье исследуется проблема построения оптимальной интерполяционной формулы в гильбертовом пространстве. Здесь с помощью метода Соболева решается первая часть задачи — явное выражение квадрата нормы функционала погрешности оптимальных интерполяционных формул в гильбертовом пространстве W2(2,0) .

Special Vinberg cones and the entropy of BPS extremal black holes

We consider the static, spherically symmetric and asymptotically flat BPS extremal black holes in ungauged N = 2 D = 4 supergravity theories, in which the scalar manifold of the vector multiplets is homogeneous. By a result of Shmakova on the BPS attractor equations, the entropy of this kind of black holes can be expressed only in terms of their electric and magnetic charges, provided that the inverse of a certain quadratic map (uniquely determined by the prepotential of the theory) is given. This inverse was previously known just for the cases in which the scalar manifold of the theory is a homogeneous symmetric space. In this paper we use Vinberg’s theory of homogeneous cones to determine an explicit expression for such an inverse, under the assumption that the scalar manifold is homogeneous, but not necessarily symmetric. As immediate consequence, we get a formula for the entropy of BPS black holes that holds in any model of N = 2 supergravity with homogeneous scalar manifold.

Implicit vs explicit expression on advertising in a cross-cultural study: the mediating role of processing fluency and number of alternatives

PurposeThis study aims to examine the moderating effect of culture on the phrase expression type that affects product attitude. Moreover, to identify the mechanism by which these effects occur, the authors investigated the mediating role of processing fluency, and examined how such a mediating effect of processing fluency varies with number of alternatives.Design/methodology/approachThree experiments were conducted to verify the hypotheses presented in this study. Experiment 1 tested the effects of phrase expression type and culture on product attitude; a two-factor design (phrase expression type: explicit expression vs implicit expression) was applied, and culture was classified according to nationality. Experiment 2 tested the mediating effect of processing fluency on product attitude, using the same approach as Experiment 1. Experiment 3 tested the moderated mediating role of the number of alternatives, a between-group experimental design of 2 (phrase expression: explicit expression vs implicit expression) × 2 (number of alternatives: many vs few) was applied.FindingsExperiment 1's results demonstrate that product attitude is more favorable when implicit expressions are used for Asians, whereas it is more favorable with explicit expressions for Westerners. Experiment 2 verifies that the interaction effect between phrase expression type and culture on product attitude is mediated by processing fluency. Experiment 3's results demonstrate that the number of alternatives moderates the mediating role of processing fluency for Westerners, but has no effect on the processing fluency for Asians.Originality/valueThis study provides novel insights and expands the field of study of phrase expression types by separating the ambiguous boundaries among phrase presentation types. Furthermore, this study provides practical guidelines for establishing effective advertising strategies for companies by suggesting suitable phrase expression types based on culture.

On the Zeta-Function of Zeros of Entire Function

This article is devoted to the study of the properties of the zeta-function of zeros of entire function. We obtained an explicit expression for the kernel of the integral representation of the zetafunction in one case

Effective elastic properties of one-dimensional hexagonal quasicrystal composites

The explicit expression of Eshelby tensors for one-dimensional (1D) hexagonal quasicrystal composites is presented by using Green’s function method. The closed forms of Eshelby tensors in the special cases of spheroid, elliptic cylinder, ribbon-like, penny-shaped, and rod-shaped inclusions embedded in 1D hexagonal quasicrystal matrices are given. As an application of Eshelby tensors, the analytical expressions for the effective properties of the 1D hexagonal quasicrystal composites are derived based on the Mori-Tanaka method. The effects of the volume fraction of the inclusion on the elastic properties of the composite materials are discussed.

Explicit expression of mesophyll conductance in the traditional leaf photosynthesis-transpiration coupled model and its physiological significances

Almost all terrestrial biosphere models (TBMs) still assume infinite mesophyll conductance (gm) to estimate photosynthesis and transpiration. This assumption has caused low accuracy of TBMs to predict leaf gas exchange under certain conditions. Here, we developed a photosynthesis-transpiration coupled model that explicitly considers gm and designed an optimized parameterization solution through evaluating four different gm estimation methods in 19 C3 species at 31 experimental treatments. Temperature responses of the maximum carboxylation rate (Vcmax) and the electron transport rate (Jmax) estimated using the Bayesian retrieval algorithm and the Sharkey online calculator and gm temperature response estimated using the chlorophyll fluorescence-gas exchange method and anatomy method predicted leaf gas exchange better. The gm temperature response exhibited activation energy (delta Ha) of 63.13+-36.89 kJ mol-1 and entropy (delta S) of 654.49+-11.36 J K-1 mol-1. The gm optimal temperature (Topt_gm) explained 58% of variations in photosynthesis optimal temperature (ToptA). The gm explicit expression has equally important effects on photosynthesis and transpiration estimations. Results advanced understandings of better representation of plant photosynthesis and transpiration in TBMs.

A note on degenerate generalized Laguerre polynomials and Lah numbers

The aim of this paper is to introduce the degenerate generalized Laguerre polynomials as the degenerate version of the generalized Laguerre polynomials and to derive some properties related to those polynomials and Lah numbers, including an explicit expression, a Rodrigues type formula, and expressions for the derivatives. The novelty of the present paper is that it is the first paper on degenerate versions of orthogonal polynomials.