Goldstone Modes in Renormalizable Supersymmetric SO(10) Model

We solve the Goldstone modes in the renormalizable SUSY SO(10) model with general couplings. The Goldstones are expressed by the Vacuum Expectation Values and the Clebsch-Gordan coefficients of relevant symmetries without explicit dependence on the parameters of the model.Comment: 27 pages. Only arXiv number for [38] adde

Goldstone Modes and Clebsch-Gordan Coefficients

We solve explicitly the Goldstone modes in spontaneously symmetry breaking models with supersymmetry. We find that, when more than one fields or representations contribute to the symmetry breaking, there exist identities among the Clebsch-Gordan coefficients which can be used as consistent checks on the calculations.Comment: 13 page

Excitons in Two-Dimensional Materials

Because of the reduced dielectric screening and enhanced Coulomb interactions, two-dimensional (2D) materials like phosphorene and transition metal dichalcogenides (TMDs) exhibit strong excitonic effects, resulting in fascinating many-particle phenomena covering both intralayer and interlayer excitons. Their intrinsic band gaps and strong excitonic emissions allow the possibility to tune the inherent optical, electrical, and optoelectronic properties of 2D materials via a variety of external stimuli, making them potential candidates for novel optoelectronic applications. In this review, we summarize exciton physics and devices in 2D semiconductors and insulators, especially in phosphorene, TMDs, and their van der Waals heterostructures (vdWHs). In the first part, we discuss the remarkably versatile excitonic landscape, including bright and dark excitons, trions, biexcitons, and interlayer excitons. In the second part, we examine common control methods to tune excitonic effects via electrical, magnetic, optical, and mechanical means. In the next stage, we provide recent advances on the optoelectronic device applications, such as electroluminescent devices, photovoltaic solar cells, and photodetectors. We conclude with a brief discussion on their potential to exploit vdWHs toward unique exciton physics and devices

The kth-order nonhomomorphicity of S-boxes

Nonhomomorphicity is a new nonlinearity criterion of a mapping or S-box used in a private key encryption algorithm. An important advantage of nonhomomorphicity over other nonlinearity criteria is that the value of nonhomomorphicity is easy to estimate by the use of a fast statistical method. Due to the Law of Large Numbers, such a statistical method is highly reliable. Major contributions of this paper are (1) to explicitly express the nonhomomorphicity by other nonlinear characteristics, (2) to identify tight upper and lower bounds on nonhomomorphicity, and (3) to find the mean of nonhomomorphicity over all the S-boxes with the same size. It is hoped that these results on nonhomomorphicity facilitate the analysis and design of S-boxes

Nonlinearity and propagation characteristics of balanced boolean functions

Three of the most important criteria for cryptographically strong Boolean functions are the balancedness, the nonlinearity and the propagation criterion. The main contribution of this paper is to reveal a number of interesting properties of balancedness and nonlinearity, and to study systematic methods for constructing Boolean functions satisfying some or all of the three criteria. We show that concatenating, splitting, modifying and multiplying (in the sense of Kronecker) sequences can yield balanced Boolean functions with a very high nonlinearity. In particular, we show that balanced Boolean functions obtained by modifying and multiplying sequences achieve a nonlinearity higher than that attainable by any previously known construction method. We also present methods for constructing balanced Boolean functions that are highly nonlinear and satisfy the strict avalanche criterion (SAC). Furthermore we present methods for constructing highly nonlinear balanced Boolean functions satisfying the propagation criterion with respect to all but one or three vectors. A technique is developed to transform the vectors where the propagation criterion is not satisfied in such a way that the functions constructed satisfy the propagation criterion of high degree while preserving the balancedness and nonlinearity of the functions. The algebraic degrees of functions constructed are also discussed, together with examples illustrating the various constructions

City-level water withdrawal in China:Accounting methodology and applications

In the context of the freshwater crisis, accounting for water withdrawal could help planners better regulate water use in different sectors to combat water scarcity. However, the water withdrawal statistics in China are patchy, and the water data across all sectors at the city level appear to be relatively insufficient. Hence, we develop a general framework to, for the first time, estimate the water withdrawal of 58 economic–social–environmental sectors in cities in China. This methodology was applied because only inconsistent water statistics collected from different data sources at the city level are available. We applied it to 18 representative Chinese cities. Different from conventional perceptions that agriculture is usually the largest water user, industrial and household water withdrawal may also occupy the largest percentages in the water-use structure of some cities. The discrepancy among annual household water use per capita in the urban areas of different cities is relatively small (as is the case for rural areas), but that between urban and rural areas is large. As a result, increased attention should be paid to controlling industrial and urban household water use in particular cities. China should specifically prepare annual water accounts at the city level and establish a timetable to tackle water scarcity, which is a basic step toward efficient and sustainable water crisis mitigation