Iris F. Zhang

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We observe that the classical Faulhaber’s theorem on sums of odd powers also holds for an arbitrary arithmetic progression, namely, the odd power sums of any arithmetic progression a+b, a+2b, . . . , a+nb is a polynomial in na+ n(n + 1)b/2. While this assertion can be deduced from the original Fauhalber’s theorem, we give an alternative formula in terms of(More)
The fluorescence quantum yield (Phi(f)), fluorescence lifetime (tau(f)), intersystem crossing quantum yield (Phi(isc)) and redox potentials of seven halogenated fluoresceins in their dianion forms were measured and compared in methanol to get a deep insight into the effect of halogeno atoms on their photophysics. It is found that the heavy atom effect alone(More)
We introduce the notion of arithmetic progression blocks or m-AP-blocks of Zn, which can be represented as sequences of the form (x, x+m,x+2m, . . . , x+ (i−1)m) (mod n). Then we consider the problem of partitioning Zn into m-APblocks. We show that subject to a technical condition, the number of partitions of Zn into m-AP-blocks of a given type is(More)
In the past decade, the complexity of video games have increased dramatically and so have the complexity of software systems behind them [7]. The difficulty in designing and testing games invariably leads to bugs that manifest themselves across funny video reels on graphical glitches and millions of submitted support tickets [8] [12]. This paper presents an(More)
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