Nica’s <Emphasis Type="Italic">q</Emphasis>-Convolution is Not Positivity Preserving

It is shown that the q-convolution of Nica is not positivity preserving unless q=0 or q=1, i.e. the q-convolution of two probability measures with finite moments of all orders is not necessarily a probability measure.Supported by Grant-in-Aid for JSPS Fellows     

Monolithic carrier-envelope phase-stabilization scheme

A new scheme for stabilizing the carrier-envelope (CE) phase of a few-cycle laser pulse train is demonstrated. Self-phase modulation and difference-frequency generation in a single periodically poled lithium niobate crystal that transmits the main laser beam allows CE phase locking directly in the usable output. The monolithic scheme obviates the need for splitting off a fraction of the laser output for CE phase control, coupling into microstructured fiber, and separation and recombination of spectral components. As a consequence, the output yields 6-fs, 800-nm pulses with an unprecedented degree of short- and long-term reproducibility of the electric field waveform.     

Intranasal irradiation with the xenon chloride ultraviolet B laser improves allergic rhinitis

We earlier reported that the 308 nm xenon chloride (XeCl) ultraviolet B (UVB) laser is highly effective for the treatment of inflammatory skin diseases. Since UVB irradiation has been shown to exert both local and systemic immunosuppression, we investigated the clinical efficacy of UVB irradiation in allergic rhinitis. In an open study, groups of patients with severe allergic rhinitis received intranasal irradiation with a 308 nm XeCl UVB excimer laser for two weeks. In the low-dose group (n=10), treatment was given twice weekly, starting with 0.25x the individual minimal erythema dose (MED), whereas patients in the medium-dose group (n=8) were treated four times weekly, starting with 0.4x MED. In each group, the dosage was gradually increased. Evaluation was based on the symptom scores. The effect of the XeCl laser on the skin prick test reaction was also studied. In the low-dose group, seven patients completed the study, and there was no improvement in the nasal symptoms. In the medium-dose group, the XeCl UVB irradiation significantly inhibited the rhinorrhoea, the sneezing, the nasal obstruction and the total nasal score (p<0.05). The XeCl UVB excimer laser also inhibited the allergen-induced skin prick test in a dose-dependent manner. These results suggest that the XeCl UVB excimer laser might serve as a new therapeutic tool in the treatment of allergic rhinitis.     

Weak type inequalities for the Walsh and bounded Ciesielski systems

We investigate both the Walsh system and the bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system can be obtained from the Haar system. We show that the maximal operator of the Fejér means of the Walsh-- and Ciesielski--Fourier series is bounded from the Hardy space H _1/2 to the space weak L_1/2if m -1, |k| m+1. As a consequence, we obtain a new proof for the fact that the Fejér means of the Walsh-- or Ciesielski--Fourier series of a function f L ₁ converge to f a.e.     

Θ-summability of Fourier series

A general summability method of orthogonal series is given with the help of an integrable function Θ. Under some conditions on Θ we show that if the maximal Fejér operator is bounded from a Banach space X to Y, then the maximal Θ-operator is also bounded. As special cases the trigonometric Fourier, Walsh, Walsh--Kaczmarz, Vilenkin and Ciesielski--Fourier series and the Fourier transforms are considered. It is proved that the maximal operator of the Θ-means of these Fourier series is bounded from H _p to L _p (1/2<p≤; ∞) and is of weak type (1,1). In the endpoint case p=1/2 a weak type inequality is derived. As a consequence we obtain that the Θ-means of a function f∈L ₁ converge a.e. to f. Some special cases of the Θ-summation are considered, such as the Weierstrass, Picar, Bessel, Riesz, de la Vallée-Poussin, Rogosinski and Riemann summations. Similar results are verified for several-dimensional Fourier series and Hardy spaces.     

The maximal Fejér operator on real Hardy spaces

We prove that the maximal Fej'er operator is not bounded on the real Hardy spaces H ¹, which may be considered over and . We also draw corollaries for the corresponding Hardy spaces over ² and ². This revised version was published online in August 2006 with corrections to the Cover Date.     

Unwinding of DNA polymerases by the antitumor drug,cis-diamminedichloroplatinum(II)

The helix-turn-helix motifs of the DNA binding domains of human polymerase-alpha and polymerase-kappa are dramatically perturbed upon binding to cisplatin with concomitant release of zinc.     

(C,α) Summability of Walsh—Fourier Series

The one-dimensional dyadic martingale Hardy spaces H _p are introduced and it is proved that the maximal operator of the (C,) means of a Walsh—Fourier series is bounded from H _p to L _p (1/( + 1) < p < ) and is of weak type (L ₁,L ₁). As a consequence, we obtain the summability result due to Fine; more exactly, the (C,) means of the Walsh—Fourier series of a function f L ₁ converge a.e. to the function in question. Moreover, we prove that the (C,) means are uniformly bounded on H _p whenever 1/( + 1) < p < . We define the two-dimensional dyadic hybrid Hardy space H ₁ and verify that the maximal operator of the (C,,) means of a two-dimensional function is of weak type H ₁ ,L ₁). Consequence, the Walsh—Fourier series of every function f H ₁ is (C,,) summable to the function f.     

Extension of a theorem of Fejér to double Fourier-Stieltjes series

A theorem of Fejér states that if a periodic function F is of bounded variation on the closed interval [0, 2π], then the nth partial sum of its formally differentiated Fourier series divided by n converges to π^-1[F(x+0)-F(x-0)] at each point x. The generalization of this theorem for Fourier-Stieltjes series of (nonperiodic) functions of bounded variation is also well known. The aim of the present article is to extend these results to the (m, n)th rectangular partial sum of double Fourier or Fourier-Stieltjes series of a function F(x, y) of bounded variation over the closed square [0, 2π]×[0, 2π] in the sense of Hardy and Krause. As corollaries, we also obtain the following results:

Cellular automata for the spreading of technologies in socio-economic systems

We introduce an agent-based model for the spreading of technological developments in socio-economic systems where the technology is mainly used for the collaboration/interaction of agents. Agents use products of different technologies to collaborate with each other which induce costs proportional to the difference of technological levels. Additional costs arise when technologies of different providers are used. Agents can adopt technologies and providers of their interacting partners in order to reduce their costs leading to microscopic rearrangements of the system. Analytical calculations and computer simulations revealed that starting from a random configuration of different technological levels a complex time evolution emerges where the spreading of advanced technologies and the overall technological progress of the system are determined by the amount of advantages more advanced technologies provide, and by the structure of the social environment of agents. We show that agents tend to form clusters of identical technological level with a power law size distribution. When technological progress arises, the spreading of technologies in the system can be described by extreme order statistics.