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- Sheng Chen, Nan Li, Steven V Sam
- 2010

Let P be a polytope with rational vertices. A classical theorem of Ehrhart states that the number of lattice points in the dilations P (n) = nP is a quasi-polynomial in n. We generalize this theorem by allowing the vertices of P (n) to be arbitrary rational functions in n. In this case we prove that the number of lattice points in P (n) is a… (More)

- Bineng Zhong, Hongxun Yao, Sheng Chen, Rongrong Ji, Tat-Jun Chin, Hanzi Wang
- 2010 IEEE Computer Society Conference on Computer…
- 2010

Long-term persistent tracking in ever-changing environments is a challenging task, which often requires addressing difficult object appearance update problems. To solve them, most top-performing methods rely on online learning-based algorithms. Unfortunately, one inherent problem of online learning-based trackers is drift, a gradual adaptation of the… (More)

- Sheng Chen, Sheng Kui Ye
- Discrete Mathematics
- 2009

- Nan Li, Sheng Chen
- 2008

The paper studies some properties of the ring of integer-valued quasi-polynomials. On this ring, theory of generalized Euclidean division and generalized greatest common divisor are presented. Applications to finite simple continued fraction expansion of rational numbers and Smith normal form of integral matrices with an integer parameter are also given.

- Sheng CHEN, Nan LI
- 2008

Let A(n) be a k × s matrix and m(n) be a k dimensional vector, where all entries of A(n) and m(n) are integer-valued polynomials in n. Suppose that t(m(n)|A(n)) = #{x ∈ Z s + | A(n)x = m(n)} is finite for each n ∈ N, where Z + is the set of nonnegative integers. This paper conjectures that t(m(n)|A(n)) is an integer-valued quasi-polynomial in n for n… (More)

- Nan LI, Sheng CHEN
- 2008

Suppose that a 1 (n), a 2 (n), · · · , a s (n), m(n) are integer-valued polynomials in n with positive leading coefficients. This paper presents Popoviciu type formulas for the generalized restricted partition function p A(n) (m(n)) := #{(x 1 , · · · , x s) ∈ Z s : all x j 0, x 1 a 1 (n) + · · · + x s a s (n) = m(n)} when s = 2 or 3. In either case, the… (More)

- Hong You, Sheng Chen
- Math. Comput.
- 2003

This paper presents improved bounds for the norms of exceptional finite places of the group K 2 O F , where F is an imaginary quadratic field of class number 2 or 3. As an application we show that K 2 Z[ √ −10] = 1.

- Juncheng Li, Sheng Chen, Gözde Sarı
- 2016

By extending the definition interval of the standard cubic Catmull-Rom spline basis functions from [0,1] to [0,α], a class of cubic Catmull-Rom spline basis functions with a shape parameter α, named cubic α-Catmull-Rom spline basis functions, is constructed. Then, the corresponding cubic α-Catmull-Rom spline curves are generated based on the introduced… (More)

- Wei Song, Sheng Chen
- TheScientificWorldJournal
- 2013

Iterative equations which can be expressed by the following form f (n) (x) = H(x, f(x), f (2)(x),…, f (n-1)(x)), where n ≥ 2, are investigated. Conditions for the existence of locally expansive C (1) solutions for such equations are given.

- SHENG CHEN
- 2008

The paper studies algebraic shift equivalence of matrices over n-variable polynomial rings over a principal ideal domain D(n ≤ 2). It is proved that in the case n = 1, every non-nilpotent matrix over D[x] is algebraically strong shift equivalent to a nonsingular matrix. In the case n = 2, an example of non-nilpotent matrix over R[x, y, z] = R[x][y, z],… (More)

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