澄清对相对论性原理和协变性的误解

近来有些文章断言,在一个惯性参考系里能量守恒的物理系统,在别的参考系看来能量也一定守恒.实际上这些作者混淆了物理方程式的协变性和相对性原理.本文将澄清这一误解.     

Viscosity solutions to a parabolic inhomogeneous equation associated with infinity Laplacian

We obtain the existence and uniqueness results of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate and singular parabolic inhomogeneous equation of the form ut- ΔN∞u = f,where ΔN∞denotes the so-called normalized infinity Laplacian given by ΔN∞u =1|Du|2 D2 uD u, Du.     

Multiple rogue wave and solitary solutions for the generalized BK equation via Hirota bilinear and SIVP schemes arising in fluid mechanics

The multiple lump solutions method is employed for the purpose of obtaining multiple soliton solutions for the generalized Bogoyavlensky-Konopelchenko(BK) equation. The solutions obtained contain first-order, second-order, and third-order wave solutions. At the critical point,the second-order derivative and Hessian matrix for only one point is investigated, and the lump solution has one maximum value. He's semi-inverse variational principle(SIVP) is also used for the generalized BK equation. Three major cases are studied, based on two different ansatzes using the SIVP. The physical phenomena of the multiple soliton solutions thus obtained are then analyzed and demonstrated in the figures below, using a selection of suitable parameter values.This method should prove extremely useful for further studies of attractive physical phenomena in the fields of heat transfer, fluid dynamics, etc.     

Investigation of Heisenberg algebra for a modified anti-de Sitter and modified antiSnyder models

In this paper,we consider a possible modification of the de Sitter and anti-de Sitter space for the extended uncertainty principle.For the modified anti-de Sitter model we discuss the representation and wave functions of the momentum operator for a one-dimensional box problem.Also,we consider modified Snyder and anti-Snyder models for the generalized uncertainty principle.Then,we assume the Hamiltonian with different potential and solve the Heisenberg algebra for the modified(anti)-de Sitter and(anti)-Snyder models in both position and in the momentum space.     

Sharper uncertainty principles associated with Lp-norm

Motivated by the well-established phase derivative embedded technique, this study devotes to sharper uncertainty principles related to the L^p-norm type of uncertainty product, giving rise to two kinds of uncertainty inequalities that improve the classical result through providing tighter lower bounds. The conditions that truly reach these better estimates are obtained. Examples and simulations are carried out to verify the correctness of the derived results, and finally, possible applications in time-frequency analysis are also given.     

Deposition pattern of drying droplets

The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research. When the droplet includes nonvolatile solutes, the evaporation of the solvent induces rich deposition patterns of solutes on the substrate. Understanding the formation mechanism of these patterns has important ramifications for technical applications,ranging from coating to inkjet printing to disease detection. This topical review addresses the development of physical understanding of tailoring the specific ring-like deposition patterns of drying droplets. We start with a brief introduction of the experimental techniques that are developed to control these patterns of sessile droplets. We then summarize the development of the corresponding theory. Particular attention herein is focused on advances and issues related to applying the Onsager variational principle (OVP) theory to the study of the deposition patterns of drying droplets. The main obstacle to conventional theory is the requirement of complex numerical solutions, but fortunately there has been recent groundbreaking progress due to the OVP theory. The advantage of the OVP theory is that it can be used as an approximation tool to reduce the high-order conventional hydrodynamic equations to first-order evolution equations,facilitating the analysis of soft matter dynamic problems. As such, OVP theory is now well poised to become a theory of choice for predicting deposition patterns of drying droplets.     

Mind the correct basis set: A case study for predicting gas phase acidities of small compounds using calculations from first principles

Some of the most popular computational methods have been utilized to determine a dependency of the acidity trend of the first‐row hydrides on a choice of basis set. For about three decades, methyl anion ( ) was known as the strongest base but after Tian et al. were able to produce the gas phase lithium monoxide anion (LiO–) they discovered it was a stronger base than (Tian et al., Proc Natl Acad Soc USA 2008, 105, 7647). Furthermore, the authors confirmed their experimental results using high‐level ab initio methods, namely W1 and W2C composite methods, as well as complete active space‐averaged quadratic coupled cluster and Brueckner Doubles with triple excitation contribution (BD(T)) within the aug‐cc‐pVQZ basis set. These methods are highly demanding in terms of the computational effort as well as a level of expertise needed from the user to correctly conduct such calculations. We have shown that the proper acidity trend, that is, , can be obtained with less expensive, ”black‐box” type methods if only the basis set is properly chosen. Our results prove that the diffuse augmented basis sets are absolutely necessary for appropriate predictions of acidities. Our calculations show that the correct order of is achieved by augmenting relatively small cc‐pVXZ (X = D,T) basis sets. A similar effect is observed for the family of Pople's basis sets. Our estimate for with CCSD(T)/aug‐cc‐pVTZ was 423.8 kcal/mol, which agrees very well with the experimental value 425.7 ± 6.1 kcal/mol. An important finding is that the proper acidity trend may be reversed if the basis sets are not correctly selected. © 2014 Wiley Periodicals, Inc.     

紫色石蕊溶液配制方法的探究

石蕊溶液在碱性溶液中变色不明显,这个问题虽小,但它一直困扰着我们的实验教学活动。利用手机软件颜色识别器、数字传感器等几种软硬件技术手段,对石蕊试剂的选择、配制方法的优化、溶液pH的调节等方面进行探究,试图配制出在酸碱性溶液中显色明显的石蕊溶液。