In the following we discuss a well-known binomial identity. Many proofs by different methods are known for this identity. Here we present another proof, which uses linear ordinary differential equations of the first order. Several proofs of the well-known identity n ∑ k=0 ( n + k n ) 2 = 2 (1) [4, (1.79)] appear in the literature. In [3, Equation (5.20)], it is proved using partial sums of bino...

We show an explicit formula, with a quite easy deduction, for the exponential matrix $e^{tA}$ of real and finite square $A$ (and complex ones also). The elementary method developed avoids Jordan canonical form, eigenvectors, resolution any linear system, inversion, polynomial interpolation, integration, functional analysis, generalized Fibonacci sequences. basic tools are Cayley-Hamilton theore...

The present study provides clear-cut experimental evidence for solvent-induced configuration mixing and complete triplet state inversion at room temperature in a Pt(ii) charge transfer complex bearing a combination of energetically proximate charge transfer and intraligand triplet excited states.

A numerical method to deconvolve complex body waves into a multiple shock sequence is developed. With the assumption that all the constituent events of a multiple shock have identical fault geometry and depth, the far-field source time function is obtained as a superposiUon of ramp functions. The height and the onset time of the ramp functions are determined by matching the synthetic waveforms ...

Bipartitional relations were introduced by Foata and Zeilberger in their characterization of relations which give rise to equidistribution of the associated inversion statistic and major index. We consider the natural partial order on bipartitional relations given by inclusion. We show that, with respect to this partial order, the bipartitional relations on a set of size [Formula: see text] for...

The asymmetric unit of the title complex, [Cu(2)(C(8)H(4)NO(6))(2)Cl(2)(C(10)H(8)N(2))(2)]·2H(2)O, contains two half binuclear complex molecules and two solvent water molecules; the complete complex molecule is generated by the application of a centre of inversion in each case. Each independent Cu(II) cation is penta-coordinated within a distorted square-pyramidal environment defined by a two μ...

Progress on the POFFIS high frequency flow imaging method is described. Both theoretical and experimental advances have occurred during the current year. Some success was achieved at imaging an off-axis trailer hitch flaw. However, the issue of variable speed was not completely resolved and research on this issue will continue.

Simplified solutions to determine binary elements by astrometry were obtained in terms of elementary functions (Asada et al. 2004), and therefore require neither iterative nor numerical methods. In the framework of the simplified solution, this paper discusses the remaining two parameters of the time of periastron passage and the longitude of ascending node in order to complete the solution. We...