In the current literature, a new Smarandache-type arithmetic function, involving binomial coefficients, has been proposed by Sandor. The new function, denoted by SS(n), is named the Sandor-Smarandache function. It has been found that, like many Smarandache-type functions, SS(n) is not multiplicative. Sandor found SS(n) when n (≥3) is an odd integer. Since then, the determination of SS(n) for even n remains a challenging problem. It has been shown that the function has a simple form even when n is even and not divisible by 3. This paper finds SS(n) in some particular cases of n, and finds an upper bound of SS(n) for some special forms of n. Some equations involving the Sandor-Smarandache function and pseudo-Smarandache function have been studied. A list of values of SS(n) for n = 1(1)480, calculated on a computer, is appended at the end of the paper.
Machine Translation Systems are part of Natural Language Processing (NLP) that makes communication possible among people using their own native language through computer and smart media devices. This paper describes recent progress in language dictionaries and machine translation commonly used for communications and social interaction among people or Internet users worldwide who speak different languages. Problems of accuracy and quality related to computer translation systems encountered in web & Apps-based translation are described and discussed. Possible programming solutions to the problems are also put forward to create software tools that are able to analyze and synthesize language intelligently based on semantic representation of sentences and phrases. Challenges and problems on Apps-based machine translation on smart devices towards AI, NLP, smart learning and understanding still remain until now, and need to be addressed and solved through collaboration between computational linguists and computer scientists.
The objective of this paper is to investigate palindromes in three Smarandache-type arithmetic functions,namely, the Smarandache function S(n), the pseudo Smarandache function Z(n), and the Sandor-Smarandache function SS(n).
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