相关论文: Some Results on the Counterfeit Coins Problem II
An averaged generating function for coloured hard-dimers is being investigated by proving estimates for the latter. Furthermore, two different enumerating problems and their distributions are studied numerically.
We give a sketch for an alternative proof of a recent result by J. Tseng.
We give alternative proof of Melham's and Howard's identities on generalised Fibonacci numbers
We pose and solve a problem concerning consistent assignment of quantum probabilities to a set of bases associated with maximal projective measurements. We show that our solution is optimal. We also consider some consequences of the main…
We report in this survey some new results concerning noncommutative Chern characters: construction and the cases when they are exactly computed. The major result indicates some clear relation of these noncommutative objects and their…
In this note, we give examples that demonstrate a negative answer to the generalized numerical criterion problem for pairs.
Finite sample size corrections to the reparametrization-invariant solution of the inverse problem of probability are computed, and shown to converge uniformly to the correct distribution.
In this paper, we obtained some global approximation results for general Gamma type operators.
We study the question of whether for each n there is another integer m with lambda(m)=lambda(n), where lambda is Carmichael's function. We give a "near" proof of the fact that this is the case unconditionally, and a complete conditional…
Explicit determinations of several classes of trigonometric sums are given. These sums can be viewed as analogues or generalizations of Gauss sums. In a previous paper, two of the present authors considered primarily sine sums associated…
We determine the Sprague-Grundy value for the Common Divisor Nim$_m$ (CDN$_m$ for short) for $m \in \mathbb{Z}_{\ge 1}$, which is called COMMON DIVISOR game in [ANW, Chapter 2, Exercise 8 (p.55)].
In this paper, explicit error bounds are derived in the approximation of rank $k$ projections of certain $n$-dimensional random vectors by standard $k$-dimensional Gaussian random vectors. The bounds are given in terms of $k$, $n$, and a…
The second weight of the Generalized Reed-Muller code of order $d$ over the finite field with $q$ elements is now known for $d <q$ and $d>(n-1)(q-1)$. In this paper, we determine the second weight for the other values of $d$ which are not…
We find a nontrivial upper bound on the average value of the function M(n) which associates to every positive integer n the minimal Hamming weight of a multiple of n. Some new results about the equation M(n)=M(n') are given.
This paper is concerned with the computable error estimates for the eigenvalue problem which is solved by the general conforming finite element methods on the general meshes. Based on the computable error estimate, we can give an…
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
In this paper, we give a new bijective proof of a multiset analogue of even-odd permutations identity. This multiset version is equivalent to the original coin arrangements lemma which is a key combinatorial lemma in the Sherman's Proof of…
The problem of Hadamard quantum coin measurement in $n$ trials, with arbitrary number of repeated consecutive last states is formulated in terms of Fibonacci sequences for duplicated states, Tribonacci numbers for triplicated states and…
ApSimon considered the problem of deciding by a process of two weighings on which of a known number of mints emit either coins of a known genuine weight or emit coins of a different secondary but unknown weight. The combinatorial problem…
A new generalisation of Goldbach's conjecture (GGC) - also generalising that of Lemoine - is tested, introduced by the first author. It states that for every pair of positive integers $m_1, m_2$, every sufficiently large integer $n$…