Lateinische Epigraphik zur Zeit des dreissigjährigen Krieges: Eine Trouvaille

Discussion of the epigraphical exploits of the Danish scholar Henrik Ernst during the Thirty-Years war.

C(k)-solvability near the characteristic set for a class of planar complex vector fields of infinite type

This paper deals with semi-global C(k)-solvability of complex vector fields of the form L = partial derivative/partial derivative t + x(r) (a(x) + ib(x))partial derivative/partial derivative x, r >= 1, defined on Omega(epsilon) = (-epsilon, epsilon) x S(1), epsilon > 0, where a and b are C(infinity) real-valued functions in (-epsilon, epsilon). It is shown that the interplay between the order of vanishing of the functions a and b at x = 0 influences the C(k)-solvability at Sigma = {0} x S(1). When r = 1, it is permitted that the functions a and b of L depend on the x and t variables, that is, L = partial derivative/partial derivative t + x(a(x, t) + ib(x, t))partial derivative/partial derivative x, where (x, t) is an element of Omega(epsilon).

ALPHA-CONTRACTIONS AND ATTRACTORS FOR DISSIPATIVE SEMILINEAR HYPERBOLIC-EQUATIONS AND SYSTEMS

In this paper we discuss the existence of compact attractor for the abstract semilinear evolution equation u = Au + f (t, u); the results are applied to damped partial differential equations of hyperbolic type. Our approach is a combination of Liapunov method with the theory of alpha-contractions.

Cognitive, Mood, and Electroencephalographic Effects of Noninvasive Cortical Stimulation With Weak Electrical Currents

Objectives: The use of noninvasive cortical electrical stimulation with weak currents has significantly increased in basic and clinical human studies. Initial, preliminary studies with this technique have shown encouraging results; however, the safety and tolerability of this method of brain stimulation have not been sufficiently explored yet. The purpose of our study was to assess the effects of direct current (DC) and alternating current (AC) stimulation at different intensities in order to measure their effects on cognition, mood, and electroencephalogram. Methods: Eighty-two healthy, right-handed subjects received active and sham stimulation in a randomized order. We conducted 164 ninety-minute sessions of electrical stimulation in 4 different protocols to assess safety of (1) anodal DC of the dorsolateral prefrontal cortex (DLPFC); (2) cathodal DC of the DLPFC; (3) intermittent anodal DC of the DLPFC and; (4) AC on the zygomatic process. We used weak currents of 1 to 2 mA (for DC experiments) or 0.1 to 0.2 mA (for AC experiment). Results: We found no significant changes in electroencephalogram, cognition, mood, and pain between groups and a low prevalence of mild adverse effects (0.11% and 0.08% in the active and sham stimulation groups, respectively), mainly, sleepiness and mild headache that were equally distributed between groups. Conclusions: Here, we show no neurophysiological or behavioral signs that transcranial DC stimulation or AC stimulation with weak currents induce deleterious changes when comparing active and sham groups. This study provides therefore additional information for researchers and ethics committees, adding important results to the safety pool of studies assessing the effects of cortical stimulation using weak electrical currents. Further studies in patients with neuropsychiatric disorders are warranted.