Hyers–Ulam–Rassias stability of Cauchy equation in the space of Schwartz distributions

We reformulate and prove the Hyers–Ulam–Rassias stability of Cauchy equation in the space of Schwartz tempered distributions and Fourier hyperfunctions.     

A lower bound for the convexity number of some graphs

Given a connected graphG, we say that a setC ?V(G) is convex inG if, for every pair of verticesx, y ∈ C, the vertex set of everyx-y geodesic inG is contained inC. The convexity number ofG is the cardinality of a maximal proper convex set inG. In this paper, we show that every pairk, n of integers with 2 ≤k ≤ n?1 is realizable as the convexity number and order, respectively, of some connected triangle-free graph, and give a lower bound for the convexity number ofk-regular graphs of ordern withn>k+1.     

A Multisensor Deconvolution Problem

Meisters and Peterson gave an equivalent condition under which the multisensor deconvolution problem has a solution when there are two convolvers, each the characteristic function of an interval. In this article we find additional conditions under which the deconvolution problem for multiple characteristic functions is solvable. We extend the result to the space of Gevrey distributions and prove that every linear operator S, fromthe space of Gevrey functions with compact support onto itself, which commutes with translations can be represented as convolution with a unique Gevrey distribution T of compact support. Finally, we find explicit formula for deconvolvers when the convolvers satisfy weaker conditions than the equivalence conditions using nonperiodic sampling method.     

An expedient synthesis of an isofervenulin analogue

An efficient approach has been developed for the synthesis of an isofervenulin analogue 1 employing a one‐pot condensation‐substitution reaction of a chlorocarboethoxytriazine (electrophile) with a urea (nucleophile). The resulting cyclization reaction resulted in the synthesis of a pyrimido‐heterocycle in good yield in either acidic or basic media. The former was assisted by utilizing trimethylsilyl chloride.     

Determination of carbamazepine by chemiluminescence detection using chemically prepared tris(2,2'-bipyridine)ruthenium(III) as oxidant.

A new chemiluminescence method for the determination of carbamazepine (CBZ) has been developed. The method is based on the chemiluminescence produced in the reaction of tris(2,2'-bipyridine)ruthenium(III) and CBZ in an acidic medium. The chemiluminescence intensity was enhanced by organic solvents in the reaction system. Under the optimum experimental conditions, the calibration curve was linear over the range 4.0 x 10(-3)-8.6 x 10(-7) mol/L for CBZ. The detection limit (S/N = 3) was 2.5 x 10(-7) mol/L and the relative standard deviation of six replicate measurements was 2.6% for 4.0 x 10(-4) mol/L of CBZ. The possible reaction mechanism were also discussed. The chemiluminescence method was successfully applied to assay the CBZ contents in pharmaceutical tablets.     

Laplacians and the Cheeger Inequality for Directed Graphs

We consider Laplacians for directed graphs and examine their eigenvalues. We introduce a notion of a circulation in a directed graph and its connection with the Rayleigh quotient. We then define a Cheeger constant and establish the Cheeger inequality for directed graphs. These relations can be used to deal with various problems that often arise in the study of non-reversible Markov chains including bounding the rate of convergence and deriving comparison theorems.Received September 8, 2004     

A systematic design method to obtain broadband characteristics for singly-fed electromagnetically coupled patch antennas for circular polarization

We present a systematic, empirical design technique to obtain optimum broadband impedance, axial-ratio (AR) and gain bandwidths for a singly-fed electromagnetically coupled patch antenna for circular polarization. Our investigation has also revealed tradeoffs amongst obtainable AR, impedance bandwidth and AR bandwidth. Using two design examples at different frequency bands and for different senses of circular polarization, we have demonstrated the effectiveness of the proposed knowledge-based tuning method. We have obtained at C-band measured values of impedance bandwidth (VSWR/spl les/2) equal to 43%, 3-dB AR bandwidth of 8%, AR of less than 0.3 dB and a mean gain level of 7 dB. For the Ku-band element, a 40% impedance bandwidth and a 17.3% of 3-dB AR bandwidth have been obtained with a peak gain of 7.2 dBic.     

Proton-exchanged LiNbO/sub 3/ optical waveguides using stearic acid

Proton-exchanged optical waveguides have been fabricated in z-cut LiNbO/sub 3/ using a new proton source: stearic acid. These waveguides were characterized optically and were found to exhibit a step index profile with Delta n=0.118 measured at 0.633 mu m. The propagation losses were typically around 1.5 dB/cm, and the diffusion constant and the activation energy for the proton-exchange process were measured to be 5*10/sup 6/ mu m/sup 2//h and 69 kJ/mol, respectively.<>     

Spectral characteristics of vertical-cavity surface-emitting lasers with external optical feedback

The measurement of the effects of external optical feedback on the spectra of VCSELs (vertical-cavity surface-emitting lasers) is reported. It is surprising that VCSELs have a sensitivity to optical feedback comparable to that of conventional edge-emitting lasers such as DFBs despite their significantly different structures. This is because the extremely short cavity length of VCSELs negates the effects of their highly reflective output mirrors. As in edge-emitting lasers, VCSELs exhibit well-defined regimes of feedback effects in their spectra. Since optical isolators cannot be easily applied to VCSELs due to their array structure, these lasers may be most useful in applications which are not sensitive to the spectral qualities of the light source.<>