The purpose of this paper is to present the definition of [Formula: see text]-contractive mapping and to discuss the relation of [Formula: see text]-contractive mappings and [Formula: see text]-contractive mappings. Furthermore, the generalized [Formula: see text]-contraction mapping principle has been proved without the uniqueness condition. Meanwhile, the generalized [Formula: see text]-contr...

where / ( / ) is a differentiate function defined on the real number interval [a, b), and x may be a real or complex number with x*0 and x*l. Obviously, the case for x = l of (1.1) could be generally treated by means of the well-known Euler-Maclaurin summation formula. The object of this paper is to find a general summation formula for (1.1) that could be applied readily to some interesting spe...

The forward and inverse modified discrete cosine transform (MDCT) are two of the most computational intensive operations in the MPEG audio coding standard. In this paper, we used Clenshaw’s recurrence formula to transform kernels of the MDCT and IMDCT of the general length. Efficient implementations of MDCT and IMDCT are obtained. The proposed regular structures are particularly suitable for pa...

In this paper, we use quasi-variational inequalities to provide a rigorous proof of the familiar square root formula for the optimal economic order quantity (EOQ) in the classical deterministic average cost inventory model.

BACKGROUND Infant formula feeding practices are an important consideration for obesity prevention. An infant's diet is influential on their later risk of developing overweight or obesity, yet very little is known about infant formula feeding practices. It is plausible that certain modifiable practices may put children at higher risk of developing overweight or obesity, for example how much and ...

This paper presents the design of a system for the processing and recognition of online handwritten mathematical formulas. The Hidden Markov Model (HMM) based system is trained and evaluated with a writer dependent database consisting of 100 formulas for the training and an additional set of 30 formulas for the test. With the introduction of some constraints, it is possible to obtain high recog...

The matrix volume is a generalization, to rectangular matrices, of the absolute value of the determinant. In particular, the matrix volume can be used in change-of-variables formulæ, instead of the determinant (if the Jacobi matrix of the underlying transformation is rectangular). This result is applicable to integration on surfaces, illustrated here by several examples. SIAM J. Matrix Analysis...

The Malliavin-Thalmaier formula was introduced in [8] as an alternative expression for the density of a multivariate smooth random variable in Wiener space. In comparison with classical integration by parts formulae, this alternative formulation requires the application of the integration by parts formula only once to obtain an expression that can be simulated. Therefore this expression is free...