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Non-overlapping codes are a set of codewords in $\bigcup _{n \ge 2} \mathbb {Z}_{q}^{n}$ , where $\mathbb {Z}_{q} = \{0,1, {\dots },q-1\}$ , such that the prefix of each codeword is not a suffix of any codeword in the set, including itself; and for variable-length codes, a codeword does not contain any other codeword as a subword. In this paper, we investigate a generic method to generalize binary codes to $q$ -ary ones for $q > 2$ , and analyze this generalization on the two constructions given by Levenshtein (also by Gilbert; Chee, Kiah, Purkayastha, and Wang) and Bilotta, respectively. The generalization on the former construction gives large non-expandable fixed-length non-overlapping codes whose size can be explicitly determined; the generalization on the latter construction is the first attempt to generate $q$ -ary variable-length non-overlapping codes. More importantly, this generic method allows us to utilize the generating function approach to analyze the cardinality of the underlying $q$ -ary non-overlapping codes. The generating function approach not only enables us to derive new results, e.g., recurrence relations on their cardinalities, new combinatorial interpretations for the constructions, and the superior limit of their cardinalities for some special cases, but also greatly simplifies the arguments for these results. Furthermore, we give an exact formula for the number of fixed-length words that do not contain the codewords in a variable-length non-overlapping code as subwords. This thereby solves an open problem by Bilotta and induces a recursive upper bound on the maximum size of variable-length non-overlapping codes. [ABSTRACT FROM AUTHOR]

Ti:sapphire laser has an important position in ultrashort pulse generation and wavelength tuning. The use of expensive frequency‐doubled diode‐pumped solid‐state laser as the pump source limits the promotion of its application to a certain extent. With the maturity of high‐power blue‐green laser diodes (LDs), low‐cost LD directly pumped Ti:sapphire laser becomes possible. After more than 10 years of development, the output parameters of LD pumped Ti:sapphire lasers have been greatly improved. Moreover, the lasers have been applied to optical frequency combs, multiphoton microscopy imaging, and so forth, both of which have achieved impressive results. [ABSTRACT FROM AUTHOR]

We propose a novel subcarrier and power allocation method to improve both the throughput and user fairness in orthogonal frequency division multiplexing non-orthogonal multiple access visible light communication (OFDM-NOMA VLC) systems. The proposed method considers various constraints in practical VLC systems, including bandwidth limitation, non-negative optical signal, peak power for eye safety, and quality of service. The method adopts the log utility function to improve the user fairness and is applicable to cases where the number of multiplexed users on each subcarrier is not equal to the total user number due to the decoding complexity of NOMA. The problem is generalized as a non-convex one and is solved by the genetic algorithm. Monte Carlo simulations show that at a signal to interference noise ratio of 2.5 dB, the throughput of the proposed method is 11%, 22%, and 125% higher than the conventional enhanced power allocation, the fixed power allocation, and the gain ratio power allocation algorithms, while the fairness is improved by 23%, 30%, and 49%, respectively. [ABSTRACT FROM AUTHOR]

To overcome the problems of poor plasma stability and low measurement repeatability caused by fluctuation and sputtering of liquid, a method called plasma self-confinement is proposed for liquid measurement by laser-induced breakdown spectroscopy (LIBS) in this work. With the help of shadow images, it was found that the liquid target could be returned to a calm state in a very short time, and the plasma back shock wave could be suppressed effectively. A quantitative analysis of the sodium chromate solution showed that the self-absorption could be reduced and the repeatability and sensitivity could be improved by plasma self-confinement mode LIBS when compared with liquid sheet mode LIBS. [Display omitted] • The plasma self-confinement mode for liquid analysis is proposed for the first time. • The sputtering and fluctuation of the liquid sheet are effectively suppressed, and the stability of the plasma is improved. • The self-absorption effect is reduced, and the repeatability and sensitivity for elements analysis in liquid are improved. [ABSTRACT FROM AUTHOR]